thewordsmiths/stem_mcqa · Datasets at Hugging Face

subject stringclasses 1 value	question stringlengths 3 1.14k	options listlengths 5 5	solution stringlengths 18 3.7k	answer stringclasses 5 values
mathematics	If a town of 35,000 people is growing at a rate of approx. 1% per year, the population of the town in 5 years will be closest to?	[ "a.36000", "b.37000", "c.38000", "d.39000", "e.40000" ]	1% is quite small and hence the answer is A) The answer is: A	A
mathematics	In the xy-coordinate system, what is the slope of the line that goes through the point (1, 1) and is equidistant from the two points P = (3, 7) and Q = (9, 11)?	[ "0.5", "0.625", "0.75", "0.875", "1.0" ]	First, get the middle coordinate between (3,7) and (9,11)... x = 3 + (9-3)/2 = 6 y = 7 + (11-7)/2 = 9 Second, get the slope of (9,6) and (1,1). m = 6-1 / 9-1 = 5/8 = 0.625 Answer: B The answer is: B	B
mathematics	During a recent track meet, Peter ran x meters of the 100 meter dash in 6 seconds; running at the same rate, how many seconds will it take Peter to run z meters of the 200 meter dash?	[ "6z/x", "6zx", "6x/z", "6/xz", "xz/6" ]	Speed of Peter = x/6 meters per second Time needed to run z meters = DISTANCE/SPEED = z / (x/6) = 6z/x Option A The values 100m and 200m have no role to play here and are just given to confuse you. The answer is: A	A
mathematics	Find the area of a parallelogram with base 24 cm and height 16 cm?	[ "776", "384", "666", "288", "211" ]	Area of a parallelogram = base * height = 24 * 16 = 384 cm2 Answer: B The answer is: B	B
mathematics	A man spends Rs. 1500 per month on an average for the first three months, Rs 1550 for next four months and Rs. 1800 per month for the last five months and saves Rs . 5200 a year. What is his average monthly income?	[ "2075", "2100", "2200", "2300", "2400" ]	Explanation: Total expenditure for the first 3 months = 3 Ã— 1500 = 4500 Total expenditure for 4 months = 4 Ã— 1550 = 6200 Total expenditure for 5 months = 5 Ã— 1800 = 9000 Total expenditure and saving (which is income for one year) = 4500 + 6200 + 9000 + 5200 = Rs. 24900 So, Average monthly income = 24900/12 = Rs. 2075 Answer A The answer is: A	A
mathematics	If a and b are positive even integers, and the least common multiple of a and b is expressed as a*b/r, which of the following statements could be false?	[ "n is a factor of both a and b", "(ab)/n < ab", "ab is multiple of 2.", "(ab)/n is a multiple of 2.", "r is a multiple of 4." ]	If we divide bynand get a multiple ofaand of b, then r must be a common factor. Answer A must be true. Ifaandbare even integers, dividing by a factor (also an integer) results in something smaller than the productab. Answer B must be true. If eitheraorbis even, thenabmust be even. Answer C must be true. If both are even, the smallest either number can be is 2. Thus, the smallest common factor must be 2. Answer D must be true. Ifbis 6 andais 2,nwould be 6, which is not 4. E can be false. The answer is: E	E
mathematics	A and B can do a piece of work in 3 days, B and C in 4 days, C and A in 6 days. How long will C take to do it?	[ "33", "28", "24", "97", "16" ]	Explanation: 2c = Â¼ + 1/6 â€“ 1/3 = 1/12 c = 1/24 => 24 days Answer:C The answer is: C	C
mathematics	If a number is chosen at random from the set {1, 2, 3, ...., 100}, then the probability that the chosen number is a perfect cube is	[ "1/25", "1/27", "1/28", "1/22", "1/24" ]	We have 1, 8, 27 and 64 as perfect cubes from 1 to 100. Thus, the probability of picking a perfect cube is 4/100 = 1/25. Answer:A The answer is: A	A
mathematics	The height of the wall is 6 times its width and length of the wall is 7 times its height .if the volume of the wall be 6804 cu.m.its width is	[ "3m", "5m", "6m", "7m", "8m" ]	Explanation: Let width = x Then, height=6x and length=42x 42x Ã— 6x Ã— x = 6804 x = 3 Answer: A The answer is: A	A
mathematics	A cube of edge 5cm is immersed completely in a rectangular vessel containing water. If the dimensions of the base of vessel are 10cm * 5cm , find the rise in water level?	[ "2.5cm", "3.6cm", "5cm", "6.43cm", "7.56cm" ]	Increase in volume = volume of the cube = 555 cm^3 Rise in water level = volume / area = 555/10*5 = 2.5cm Answer is A The answer is: A	A
mathematics	In given series 1, 2, 6, 15, 31, 56, 91 only one number is incorrect. Find out that wrong number	[ "91", "92", "90", "60", "61" ]	1, 1 + 12 = 2, 2 + 22 = 6, 6 + 32 = 15, 15 + 42 = 31, 31 + 52 = 56, 56 + 62 = 92 Last number of given series must be 92 not 91. ANSWER:A The answer is: A	A
mathematics	A total of 40 men and 25 women were at a party, and the average (arithmetic mean) age of all of the adults at the party was exactly 35 years. If the average age of the men was exactly 38 years, which of the following was closest to the average age, in years, of the women?	[ "31", "30.2", "32", "32.5", "33" ]	Let Aw = average age of women Average = (Number of men X average age of men + Number of women X average age of women)/total number of people 35 * 65 = 40 * 38 + 25 * Aw =>2275 = 1520 + 25 Aw => 25 Aw = 755 =>Aw = 30.2 Answer B The answer is: B	B
mathematics	For an upcoming charity event, a male vocalist has agreed to sing 5 out of 7 “old songs” and 3 out of 6 “new songs.” How many ways can the singer make his selection?	[ "25", "50", "140", "480", "600" ]	=7C56C3 =76/365/3 =722*5 =140 Ans = C The answer is: C	C
mathematics	Ten years ago, P was half of Q's age. If the ratio of their present ages is3:4, what will be the total of their present ages?	[ "45", "40", "35", "30", "25" ]	Let present age of P and Q be 3x and 4x respectively. Ten years ago, P was half of Q's age ⇒(3x−10)=1(4x−10)/2 ⇒6x−20=4x−10 ⇒2x=10 ⇒x=5 Total of their present ages 3x+4x=7x=7*5=35 ANSWER:C The answer is: C	C
mathematics	A can do a work in 12days. When he had worked for 3days, B joinedhim. If they complete the work in 3more days, in how manydays can Balone finish the work?	[ "3 days", "4 days", "6 days", "7 days", "9 days" ]	sax Work done by Afar 3 days : i J .. Remzming war — 1 .Work done by (A + B) for 1 day : . Work done by a for 1 day 6 days C The answer is: C	C
mathematics	In traveling from a dormitory to a certain city, a student went 1/3 of the way by foot, 3/5 of the way by bus, and the remaining 2 kilometers by car. What is the distance, in kilometers, from the dormitory to the city?	[ "30", "45", "60", "90", "120" ]	Whole trip = distance by foot + distance by bus + distance by car x = 1/3x + 3/5x + 2 x - 1/3x - 3/5x = 2 x = 30km Option: A The answer is: A	A
mathematics	In a box, there are 8 red, 5 blue and 6 green balls. One ball is picked up randomly. What is the probability that it is neither blue nor green?	[ "2/3", "8/21", "3/7", "9/22", "8/19" ]	Explanation: Total number of balls = (8 + 5 + 6) = 19 Let E = event that the ball drawn is neither blue nor green =e vent that the ball drawn is red. Therefore, n(E) = 8. P(E) = 8/19. Answer: Option E The answer is: E	E
mathematics	Ramesh and Neelesh start walking to meet one another from places 25 kms apart. If Ramesh walks at the rate of 2 kms an hour and Neelesh at 3 kms an hour, how many hours will it be before they meet?	[ "2 hr", "3 hr", "4 hr", "5 hr", "6 hr" ]	velocity of ramesh =2km/h velocity of neelesh =3km/h both start moving from both the end of 25km let at time t they meet let ramesh walks x km than neelesh have walk =25-x km 2=x/t.......(a) 3=25-x/t.....(b) on solving t=5 hr. ANSWER:D The answer is: D	D
mathematics	Water consists of hydrogen and oxygen, and the approximate ratio, by mass, of hydrogen to oxygen is 2:16. Approximately how many grams of oxygen are there in 153 grams of water?	[ "16", "72", "112", "136", "142" ]	Since the ratio, by mass, of hydrogen to oxygen is 2:16, then oxygen is 16/(2+16)=8/9 of mass of water. Therefore there are 153*8/9=136 grams of oxygen in 153 grams of water. Answer: D. The answer is: D	D
mathematics	A certain telescope increases the visual range at a particular location from 90 kilometers to 150 kilometers. By what percent is the visual range increased by using the telescope ?	[ "30%", "33 1/2%", "40%", "60%", "66 2/3%" ]	Original visual range = 90 km New visual range = 150 km Percent increase in the visual range by using the telescope = (150-90)/90 * 100% = 2/3 * 100% = 66.67 % Answer E The answer is: E	E
mathematics	The ratio of the present ages of P and Q is 3:4. 5 years ago, the ratio of their ages was 5:7. Find the their present ages?	[ "30, 40", "30, 50", "60, 40", "10, 30", "50, 40" ]	Answer: Option A Their present ages be 3X and 4X. 5 years age, the ratio of their ages was 5:7, then (3X - 5):(4X - 5) = 5:7 X = 35 - 25 => X = 10. Their present ages are: 30, 40. The answer is: A	A
mathematics	A fruit-salad mixture consists of apples, peaches, and grapes in the ratio 6:5:2, respectively, by weight. If 78 pounds of the mixture is prepared, the mixture includes how many more pounds of apples than grapes?	[ "24", "12", "9", "6", "4" ]	We can first set up our ratio using variable multipliers. We are given that a fruit-salad mixture consists of apples, peaches, and grapes, in the ratio of 6:5:2, respectively, by weight. Thus, we can say: apples : peaches : grapes = 6x : 5x : 2x We are given that 39 pounds of the mixture is prepared so we can set up the following question and determine a value for x: 6x + 5x + 2x = 78 13x = 78 x = 6 Now we can determine the number of pounds of apples and of grapes. pounds of grapes = (2)(6) = 12 pounds of apples = (6)(6) = 36 Thus we know that there are 36 -12 = 24 more pounds of apples than grapes. Answer is A. The answer is: A	A
mathematics	A jogger running at 9 km/hr along side a railway track is 200 m ahead of the engine of a 120 m long train running at 45 km/hr in the same direction. In how much time will the train pass the jogger?	[ "88", "27", "32", "80", "12" ]	Speed of train relative to jogger = 45 - 9 = 36 km/hr. = 36 * 5/18 = 10 m/sec. Distance to be covered = 200 + 120 = 320 m. Time taken = 320/10 = 32 sec. Answer: C The answer is: C	C
mathematics	Goldenrod and No Hope are in a horse race with 8 contestants. How many different arrangements of finishes are there if No Hope always finishes before Goldenrod and if all of the horses finish the race?	[ "40320", "20160", "12000", "2400", "2100" ]	All 8 horses can finish the race in 8! way (assuming no tie). If no tie is possible between No Hope and Goldenrod, then in half of these cases No Hope will be before Goldenrod and in half of these cases after (not necessarily right before or right after). How else? So, there are 8!/2=20160 different arrangements of finishes where No Hope always finishes before Goldenrod. Answer: B. The answer is: B	B
mathematics	Paul's income is 40% less than Rex's income, Quentin's income is 20% less than Paul's income, and Sam's income is 40% less than Paul's income. If Rex gave 40% of his income to Sam and 60% of his income to Quentin, Quentin's new income would be what fraction of Sam's new income?	[ "11/12", "13/17", "13/19", "12/19", "27/19" ]	MAKE R = 10 P = 0.6R = 6 Q = 0.8P = 4.8 S= 0.6P = 3.6 FOR THAT WE GET S = 7.6 AND Q 10.8 SO 10.8/7.6 = 2.7/ 1.9 Ans:E The answer is: E	E
mathematics	In Arun’s opinion, his weight is greater than 65 kg but less than 72 kg. His brother doest not agree with Arun and he thinks that Arun’s weight is greater than 60 kg but less than 70 kg. His mother’s view is that his weight cannot be greater than 68 kg. If all are them are correct in their estimation, what is the average of different probable weights of Arun?	[ "66 kg", "67 kg", "68 kg", "69 kg", "None of these" ]	Explanation: Let Arun’s weight by X kg. According to Arun, 65 < X < 72 According to Arun’s brother, 60 < X < 70. According to Arun’s mother, X <= 68 The values satisfying all the above conditions are 66, 67 and 68. Required average = [66+67+68/3]=[201/3]=67kg Answer B The answer is: B	B
mathematics	Calculate how long it will take a swimmer to swim a distance of 10km against the current of a river which flows at 3km/hr, given that he can swim in still water at 5km/h	[ "3", "4", "5", "6", "7" ]	swim in still water at = 5 speed of river= 3 US = 5 - 3= 2 Distance = 10 T = 10/2 = 5 Answer: C The answer is: C	C
mathematics	An investor purchased 100 shares of stock X at 6 1/8 dollars per share and sold them all a year later at 12 dollars per share. If the investor paid a 2 percent brokerage fee on both the total purchase price and the total selling price, which of the following is closest to the investor's percent gain on this investment?	[ "192%", "94%", "280%", "300%", "380%" ]	If the purchase price was 6$ per share then the investor would have made a profit of 100%. Since the purchase price is slightly more than 6$ the profit would be slightly less than 100%. Also a 2% brokerage is negligible and it brings down the profit percentage only by a small value. Approximation is very useful to solve these kind of problems as the answer choices are far apart. Answer:B The answer is: B	B
mathematics	A searchlight on top of the watchtower makes 2 revolutions per minute. What is the probability that a man appearing near the tower will stay in the dark for at least 6 seconds?	[ "5/6", "4/5", "3/4", "2/3", "1/2" ]	The searchlight completes one revolution every 30 seconds. The probability that the man's area will be lit up is 6/30=1/5. The probability that he will stay in the dark is 1-1/5=4/5 The answer is B. The answer is: B	B
mathematics	Tough and Tricky questions: Exponents. If a and b are positive integers and x = 5^a and y = 4^b, which of the following is a possible units digit of xy?	[ "1", "4", "5", "7", "0" ]	Only Units digit of X and Y contribute to the Units digit of XY. Finding all values ofXfor positive values ofa When, a=1; X=5 a=2; X=25 a=3; X=125........ Units digit repeat in a cycle of 5...... Similarly, Finding all values ofYfor positive values ofb When, b=1; Y=4 b=2; Y= 16 b=3; Y= 64....... Units digit repeat in cycle of 4,6,4.... So, possible value of Units digit of XY can be found by considering all possibilities of Units digit of X and Y When X=5 and Y=4: Units digit of XY = 20 When X=5 and Y=6: Units digit of XY = 30 Only one possibility for Units digit of XY i.e. 0. therefore answer is E The answer is: E	E
mathematics	Four years ago,the father’s age was three times the age of his son.The total of the ages of the father and the son after four years,will be 64 years.What is the father’s age at present ?	[ "32 years", "36 years", "44 years", "None of these", "49 years" ]	Solution Let the ages of father and son 4 years ago be 3x and x years respectively. Then,[(3x + 4) + 4] + [(x + 4)+ 4]= 64 ⇔ 4x = 48 ⇔ x =12. ∴ Father's present age = 3x = 36 years. Answer D The answer is: D	D
mathematics	The sum of ages of 5 children born 3 years different each is 60 yrs. What is the age of the Elder child?	[ "17", "19", "16", "18", "21" ]	Let the ages of children be x, (x + 3), (x + 6), (x + 9) and (x + 12) years. Then, x + (x + 3) + (x + 6) + (x + 9) + (x + 12) = 60 5x = 30 x = 6. x+12= 6+12= 18 D The answer is: D	D
mathematics	A computer can perform c calculations in s seconds. How many minutes will it take the computer to perform A calculations?	[ "60as/c", "as/c", "as/60c", "60c/as", "a/60cs" ]	As 'thick' as this question might look, it's actually a fairly straight-forward Rate question and can be solved by TESTing VALUES. We're told that a computer can perform a calculations in S seconds. Let's TEST.... a = 2 S = 3 2 calculations every 3 seconds = 40 calculations every 1 minute We're asked how many MINUTES it will take to perform K calculations. Since we already know that the computer can perform 40 calculations in 1 minute, let's TEST... K = 80 So we're looking for an answer that = 2 when C = 2, S = 3 and K = 80 Answer A: 60KS/a = 60(80)(3)/2 = 7200 This is NOT a match Answer B: KS/a = (80)(3)/2 = 120 This is NOT a match Answer C: KS/60a = (80)(3)/(60)(2) = 2 This IS a match Answer D: 60a/KS = 60(2)/(80)(3) = 1/2 This is NOT a match Answer E: K/60aS = 80/(60)(2)(3) = a fraction. This is NOT a match C The answer is: C	C
mathematics	A car dealer sold x used cars and y new cars during May. If the number of used cars sold was 10 greater than the number of new cars sold. Which of the following expresses this relationship ?	[ "x > 10y", "x > y + 10", "x > y – 10", "x = y + 10", "x = y – 10" ]	Given: x used cars and y new cars Number of used cars (x) sold was 10 greater than the number of new cars (y) sold So, x is 10 greater than y To show their relative sizes let's write x LARGER than y to get: x and y Our goal is to create an EQUATION. So, how do we make these two values EQUAL? Well, we need to make the smaller value (y) bigger. 10 bigger to be exact. So, we get x = y + 10 Answer: D The answer is: D	D
mathematics	What will be the cost of building a fence around a square plot with area equal to 36 sq ft, if the price per foot of building the fence is Rs. 58?	[ "3944", "2287", "2977", "2668", "1392" ]	Let the side of the square plot be a ft. a2 = 36=> a = 6 Length of the fence = Perimeter of the plot = 4a = 24 ft. Cost of building the fence = 24 * 58 = Rs. 1392. Answer:E The answer is: E	E
mathematics	A batsman makes a score of 100 runs in the 17th inning and thus increases his averages by 5. What is his average after 17th inning?	[ "39", "35", "20", "40.5", "41.5" ]	let the average after 16th inning =x then total run after 16th inning=16x then total run after 17th inning=16x+100 then average run after 17th inning=(16x+100)/17 (16x+100)/17=x+5 = > 16x+100 = 17x+85 => x =15 x=15; average after 17th inning =15+5=20 ANSWER:C The answer is: C	C
mathematics	Sam, Suresh and Sanket run a race of 1400 meters. Sam runs twice as fast as Suresh while Suresh runs thrice as fast as Sanket. If Sanket finishes the race by clocking 15 minutes, how far was Suresh from the finish line when Sam must have finished the race?	[ "2887", "278", "987", "700", "278" ]	Explanation: When Sanket finishes the race in 15 minutes, Suresh & Sam would finish the same race in 5 minutes and 2.5 minutes respectively. Thus, when Sam reaches the ”finish” mark, Suresh must be “half-way” through i.e. 700 meters behind the “finish” line when “Sam” must have finished the race. ANSWER:D The answer is: D	D
mathematics	If a particular player is always chosen, in how many ways can a cricket-be chosen out of 15 players?	[ "1100", "1134", "1240", "1340", "1365" ]	A particular player is always chosen, it means that 10 players are selected out of the remaining 14 players. =. Required number of ways = 14C10 = 14C4 = 14!/4!x19! = 1365 E The answer is: E	E
mathematics	Smith can do a work in 15 days while Johnson can do it in 25 days. How long will they take if both work together?	[ "3 4/9 days", "8 4/9 days", "9 3/8 days", "6 3/8 days", "7 3/8 days" ]	Explanation: 1/15 + 1/25 = 8/75 75/8 = 9 3/8 days Answer: C The answer is: C	C
mathematics	A man walking at a rate of 10km/hr crosses a bridge in 3 minutes. The length of the bridge is?	[ "500", "650", "250", "111", "236" ]	Speed = 105/18 = 50/18 m/sec Distance covered in 5 minutes = 50/18 5 *60 = 500 m Answer is A The answer is: A	A
mathematics	At Atira's party there were five times as many females as males. There were three times as many adults as children. Which of the following could NOT be the number of people at the party?	[ "384", "258", "216", "120", "72" ]	we have to work on the info and understand what that info takes us to... 1) there were five times as many females as males At Atira's party.. this means F=5M.. so total number=6M.. 2) There were three times as many adults as children.. A=3C... or total = 4C.. so the total is 4C or 6M.. since C and M have to be positive integers, we can say for sure that Total is a multiple of 4 and 6.. or Total is multiple of LCM of 4,6.. LCM of 4,6= 12.. lets see which number is not multiple of 12.. A. 384...1232 B. 258... no C. 216....1218 D. 120....1210 E. 72......126.. so B is our answer.. The answer is: B	B
mathematics	In a group of 15 people, 8 read English, 7 read French while 3 of them read none of these two. How many of them read French and English both?	[ "2", "3", "4", "7", "5" ]	In the following Venn diagram, F and E represent people who read French and English respectively. Now, [F+({F ∩ E}) + E] = 15-3 (or) F+E+(F ∩ E) = 12 ......(1) Also, F+(F ∩ E) = 7; E+(F ∩ E) = 8. By adding, F+E+2(F ∩ E) = 15 ---------- (2) By subtracting (1) from (2), we get (F ∩ E) = 3. ∴ 3 of them read both French and English. Answer:B The answer is: B	B
mathematics	Two employees X and Y are paid a total of Rs. 550 per week by their employer. If X is paid 120 percent of the sum paid to Y, how much is Y paid per week?	[ "Rs. 150", "Rs. 300", "Rs. 250", "Rs. 200", "Rs. 220" ]	Explanation: Let the amount paid to X per week =x and the amount paid to Y per week =y 12y/10+y=550 22y/10=550 y=5500/22=500/2=250 ANSWER IS C The answer is: C	C
mathematics	The jogging track in a sports complex is 1000 meters in circumference. Deepak and his wife start from the same point and walk in opposite directions at 20 km/hr and 14 km/hr respectively. They will meet for the first time in?	[ "50min", "40min", "34min", "25min", "20min" ]	Clearly, the two will meet when they are 1000 m apart To be 20+14 = 34 km apart, they take 1 hour To be 1000 m apart, they take 34 * 1000/1000 = 34 min. Answer is C The answer is: C	C
mathematics	In the Biotechnology class of 2000, there were E graduates. 32 of the graduates found a job, 45 continued on to their second degree and 13 did both. If only 9 people didn't do both, What is E equal to?	[ "69.", "71.", "73.", "75.", "76." ]	Total = 32 +45 -13 +9 = 73 .... My first post on the forum... I hope I am correct C is correct choice. The answer is: C	C
mathematics	If x = \|x\| , then which one of the following statements could be true? I. x = 0 II. x < 0 III. x > 0	[ "None", "I only", "III only", "I and II and III", "II and III" ]	Answer copied from NOVA guide Statement I could be true because ± 0 = −(+0) = −(0) = 0 . Statement II could be true because the right side of the equation is always negative [ ± x = (a positive number) = a negative number]. Now, if one side of an equation is always negative, then the other side must always be negative, otherwise the opposite sides of the equation would not be equal. Since Statement III is the opposite of Statement II, it must be false. But let’s show this explicitly: Suppose x were positive. Then x = x, and the equation x = ± x becomes x = x. Dividing both sides of this equation by x yields 1 = 1. This is contradiction. Hence, x cannot be positive. The answer is (D). The answer is: D	D
mathematics	If line L passes through point (m, n) and (– m, – n), where m and n are not 0, which of the following must be true? I. The slope of L is positive II. L exactly passes through origin III. The slope of L is negative	[ "III only", "II only", "I only", "I and II only", "II and III only" ]	Let (m,n) = (2,3) (-m,-n) = (-2,-3) Slope = (3+3)/(2+2) = 6/4 = 3/2 So III may not be true Let (m,n) = (2,-3) then (-m,-n) = (-2,3) So slope = (3 +3)/(-2-2) = -3/2 so I may not be true So such a line would be -> (y - 3) = 3/2(x - 2) => 2y - 6 = 3x - 6 => 2y - 3x = 0, hence no x or y intercept, so it passes through origin. II is true. Answer - B The answer is: B	B
mathematics	The Sum of first N consecutive odd integers is N^2. What is the sum of all odd integers between 11 and 41 inclusive.	[ "351", "364", "416", "424", "450" ]	We're dealing with a sequence of CONSECUTIVE ODD INTEGERS: 11 to 41, inclusive. We're asked for the SUM of this group. 1) Start with the sum of the smallest and the biggest: 11 + 41 =52 2) Now look at the 'next smallest' and the 'next biggest': 13 + 39 = 52 Now we have proof that there is no middle term. We have 8 bunches of 52. 8(52) = 416 C The answer is: C	C
mathematics	The ratio of money with Ram and Gopal is 7 : 17 and that with Gopal and Krishan is 7: 17. If Ram has Rs. 686, Krishan has ?	[ "s. 2890", "s. 4046", "s. 1190", "s. 1620", "s. 2680" ]	Ram : Gopal = 7 : 17 = 49 : 119 Gopal : Krishan = 7 : 17 = 119 : 289 Ram : Gopal : Krishan = 49 : 119 : 289 Ram : Krishan = 49 : 289 Thus, 49 : 289 = 686 : N &there N = 289 x 686 / 49 = Rs. 4046 Answer :B The answer is: B	B
mathematics	Paul sells encyclopedias door-to-door. He earns $170 on every paycheck, regardless of how many sets he sells. In addition, he earns commission as follows: Commission Sales 10% $0.00 - $10,000.00 5% $10,000.01 ---> He does not earndouble commission.That is, if his sales are $12,000, he earns 10% on the first $10,000 and 5% on the remaining $2,000. His largest paycheck of the year was $1,320. What were his sales for that pay period?	[ "13,000", "14,800", "16,400", "15,800", "19,600" ]	His pay check was $1320. Out of this, $170 was his fixed salary so the total commission he earned was $1320 - $170 = $1150 He earns 10% on the sales of first $10,000 which gives a commission of $1000. He earns 5% on every subsequent dollar. Since he earns another $150, he must have had sales of another 150*(100/5) = 3000 So his total sales must have been $10,000 + $3000 = $13,000 A The answer is: A	A
mathematics	Five years ago the average of the ages of A and B was 40 years and now the average of the ages of B and C is 44 years. What will be the age of the B ten years hence?	[ "22", "88", "26", "96", "51" ]	Let the present ages of A, B and C be a, b and c respectively. Given, [(a - 5) + (b - 5)] / 2 = 40 => a + b = 90 --- (1) (b + c)/2 = 44 => b + c = 88 --- (2) From (1) and (2), we cannot find b. Answer: B The answer is: B	B
mathematics	In a function they are distributing noble prize. In how many ways can 3 prizes be distributed among 4 boys when No boy gets more than one prize?	[ "12", "14", "17", "24", "27" ]	Sol. In this case, repetitions are not allowed. So, the first prize can be given in 4 ways. The second in 3 ways and the third in 2 ways. But fundamental principle, (4 x 3 x 2) ways = 24 ways 4: Or 4p = — 4:- 4X3X2X1- 24 ways D The answer is: D	D
mathematics	Roy was suffering from severe headaches. He went to see his doctor and the doctor gave him five tablets asking him to take one tablet every 15 minutes. How much time will it take Roy to consume all the five tablets?	[ "60 minutes", "65 minutes", "50 minutes", "45 minutes", "55 minutes" ]	A 60 minutes Roy will be able to consume all the five tablets in an hour. Tablet 1 will be taken in 0 min. Tablet 2 will be taken in 15 min. Tablet 3 will be taken in 30 min. Tablet 4 will be taken in 45 min. Tablet 5 will be taken in 60 min. The answer is: A	A
mathematics	How many 3 digit positive integers R exist that when divided by 7 leave a remainder of 5?	[ "128", "142", "143", "141", "129" ]	Minimum three digit number is 100 and maximum three digit number is 999. The first three digit number that leaves remainder 5 when divided by 7 is 103. 14 * 7 = 98 +5 = 103 The second three digit number that leaves remainder 5 when divided by 7 is 110. 15 * 7 = 105 +5 =110 The third three digit number that leaves remainder 5 when divided by 7 is 117 and so on The last three digit number that leaves remainder 5 when divided by 7 is 999 142 * 7 = 994 + 5 = 999 Therefore, we identify the sequence 103,110,117.....999 use the formula of last term Last term = first term + (n - 1) * common difference you will get the answer 129 that is definitely E. The answer is: E	E
mathematics	If four coins are tossed, the probability of getting heads only?	[ "4/16", "2", "1/16", "2/16", "3/16" ]	Since four coins are tossed, sample space = 16 Getting heads=1 p(E) = 1/16 ANSWER:C The answer is: C	C
mathematics	A train passes a platform in 25 seconds. The same train passes a man standing on the platform in 20 seconds. If the speed of the train is 54 km/hr, The length of the platform is	[ "75", "25", "26", "23", "22" ]	Speed of the train = 54 km/hr = (54×10)/36 m/s = 15 m/s Length of the train = speed × time taken to cross the man = 15×20 = 300 m Let the length of the platform = L Time taken to cross the platform = (300+L)/15 => (300+L)/15 = 20 => 300+L = 15×25 = 375 => L = 375-300 = 75 meter Answer is A. The answer is: A	A
mathematics	Train P crosses a pole in 30 seconds and train Q crosses the same pole in one minute and 15 seconds. The length of train P is three-fourths the length of train Q. What is the ratio of the speed of train P to that of train Q?	[ "5:8", "5:6", "5:1", "5:3", "5:2" ]	Given that train P crosses a pole in 30 seconds and train Q crosses the same pole in one minute and 15 seconds. Let the length of train P be LP and that of train Q be LQ given that LP = 3/4 LQ As the train P and Q crosses the pole in 30 seconds and 75 seconds respectively, => Speed of train P = VP = LP/30 Speed of train Q = VQ = LQ/75 LP = 3/4 LQ => VP = 3/4 LQ/(30) = LQ/40 Ratio of their speeds = VP : VQ = LQ/40 : LQ/75 => 1/40 : 1/75 = 1 5:8 Answer:A The answer is: A	A
mathematics	A, B, and C working alone can finish constructing a house in 6, 9, and 12 hours respectively. A starts alone and works for 1 hour. He is then joined by B and they work together for 1 hour. Finally C joins them and they all work together to finish the work. If they start working at 9 am, at what time will they finish?	[ "11:38 am", "11:49 am", "12:11 pm", "12:32 pm", "12:43 pm" ]	A completes 1/6 of the job each hour. B completes 1/9 of the work each hour. C completes 1/12 of the work each hour. A completes 1/6 of the work in the first hour. Working together, A and B complete another 5/18 for a total of 8/18. Working together, A, B, and C can complete 13/36 of the work each hour. To complete 20/36, the time required is (20/36) / (13/36) = 20/13 hours. The work will be completed at 12:00 plus 7*60/13 minutes which is about 12:32 pm. The answer is D. The answer is: D	D
mathematics	Point X is located on line segment AB and point Y is located on line segment CD. If AB = CD and AX < CY, then	[ "XB < YD", "XB < YD", "AX > XB", "AX < CD", "AX > AB" ]	A------X--B C--Y------D AX < CD. Answer: D. The answer is: D	D
mathematics	A man bets on no. 16 on a roulette wheel 14 times and losses each time. On the 15th span he does a quick calculation and finds out that the no. 12 had appeared twice in the 14 spans and is therefore, unable to decide whether to bet on 16 or 12 in the 15th span. Which will give him the best chance and what are the odds of winning on the bet that he takes?	[ "Either 37 ;30:1", "Either ;35:1", "Either 15;15:12", "Either 21;35:1", "Either 17;35:12" ]	Each of the span is an independent event and the outcome of the 15th span will not depend on the outcome of the earlier spans. Either ;35:1 B) The answer is: B	B
mathematics	Two friends decide to get together; so they start riding bikes towards each other. They plan to meet halfway. Each is riding at 6 MPH. They live 36 miles apart. One of them has a pet carrier pigeon and it starts flying the instant the friends start traveling. The pigeon flies back and forth at 40 MPH between the 2 friends until the friends meet. How many miles does the pigeon travel?	[ "54", "110", "120", "16", "180" ]	C 120 It takes 3 hours for the friends to meet; so the pigeon flies for 3 hours at 40 MPH = 120 miles The answer is: C	C
mathematics	504 can be expressed as a product of primes as .	[ "2 × 2 × 3 × 3 × 7 × 7", "2 × 3 × 3 × 3 × 7 × 7", "2 × 3 × 3 × 3 × 3 × 7", "2 × 2 × 2 × 3 × 3 × 7", "NONE OF THE ABOVE" ]	It is clear that 504 = 2 × 2 × 2 × 3 × 3 × 7 Answer: Option D The answer is: D	D
mathematics	If z2 + 4y2 = 4zy, then z : y is :	[ "2 : 1", "1 : 2", "1 : 1", "1 : 4", "1 : 5" ]	as the coefficient of z is 1 and coefficient of y is 4 ANSWER:D The answer is: D	D
mathematics	A cistern has a leak which would empty the cistern in 20 minutes. A tap is turned on which admits 4 liters a minute into the cistern, and it is emptied in 24 minutes. How many liters does the cistern hold?	[ "480", "992", "772", "662", "188" ]	1/x - 1/20 = -1/24 x = 120 120 * 4 = 480 Answer:A The answer is: A	A
mathematics	The LCM of two numbers is 2310 and HCF is 61. If one of the numbers is 210. Then what is the other number ?	[ "715", "671", "330", "582", "465" ]	First number * Second Number = LCM * HCF Other number = 2310 * 61 / 210 = 11*61 = 671 ANSWER :B The answer is: B	B
mathematics	The average of five consecutive odd numbers A, B, C, D and E is 13. What percent of B is C ?	[ "98.2", "102.8", "108.2", "118.2", "122.8" ]	Explanation : In such a case the middle number (C) is the average ∴ C = 13 and B = 11 Required percentage = 13/11 x 100 = 118.2 Answer : Option D The answer is: D	D
mathematics	A car takes 6 hours to cover a distance of 540 Km. how much should the speed in Kmph be maintained to cover the same direction in 3/2th of the previous time?	[ "40 Kmph", "52 Kmph", "60 Kmph", "76 Kmph", "80 Kmph" ]	Time = 6 Distance = 540 3/2 of 6 hours = 6 * 3/2 = 9 Hours Required speed = 540/9 = 60 Kmph C) The answer is: C	C
mathematics	The daily high temperatures were recorded at an Antarctic weather station. If a temperature of -38.2 degrees Celsius is 2 units of standard deviation below the mean temperature, and a temperature of -22.6 degrees Celsius is 4 units of standard deviation above the mean, which of the following temperatures is 1 unit of standard deviation below the mean?	[ "-35.6 degrees Celsius", "-33.0 degrees Celsius", "-30.4 degrees Celsius", "-27.8 degrees Celsius", "-25.2 degrees Celsius" ]	Let us suppose mean = M and SD = d. So, we are given M - 2d = -38.2 and M + 4d = -22.6 solving both the equations, we will get M = -33 an d = 2.6 So, we need to find out M - d = -33 - 2.6 = -35.6. Hence, A The answer is: A	A
mathematics	An art gallery owner is hanging paintings for a new show. Of the five paintings she has to choose from, she can only hang three on the main wall of the gallery. Assuming that she hangs as many as possible on that wall, in how many ways can she arrange the paintings?	[ "18", "30", "64", "20", "216" ]	Arrangement means permutations questions.. 5P3 = 5!/3! = 20 . ANS option D is correct answer.. The answer is: D	D
mathematics	Two pipes A and B can fill a cistern in 20 and 30 minutes respectively, and a third pipe C can empty it in 40 minutes. How long will it take to fill the cistern if all the three are opened at the same time?	[ "17 1/9", "17 1/3", "17 1/7", "17 1/9", "17 1/1" ]	1/20 + 1/30 - 1/40 = 7/120 120/7 = 17 1/7 Answer: C The answer is: C	C
mathematics	A salt manufacturing company produced a total of 5000 tonnes of salt in January of a particular year. Starting from February its production increased by 200 tonnes every month over the previous months until the end of the year. Find its average monthly production for that year?	[ "2989", "2765", "6110", "2989", "9772" ]	Total production of salt by the company in that year = 5000 + 5200 + 5400 + .... + 7200 = 73400. Average monthly production of salt for that year = 73400/12 = 6116. Answer:C The answer is: C	C
mathematics	Insert the missing number 6, 7, 9, 13, 21, ...	[ "25", "29", "37", "32", "30" ]	Difference between two numbers in the series is multiplied by 2 to get the next number 6,7 ...Difference is 1 7,9 Difference is 2 9,13 difference is 4 13,21 Difference is 8 21, 37 Difference is 16 ANSWER:C The answer is: C	C
mathematics	If x represents the sum of the interior angles of a triangle and y represents the sum of the interior angles of a regular pentagon, then the difference between x and y is equal to the sum of the interior angles of what geometric shape?	[ "Circle", "Square", "Rhombus", "Trapezoid", "Pentagon" ]	Sum of angles of triangle = 180(3-2) = 180 => using formula sum of interior angles of polygon = 180(n-2) where n is the number of sides in a polygon Sum of angles in Pentagon = 180*(5-2) =540 Difference =540 - 180= 360 => Cirlcle hence (A). The answer is: A	A
mathematics	On dividing a number by 56, we get 29 as remainder. On dividing the same number by 8, what will be the remainder ?	[ "4", "5", "6", "8", "9" ]	Explanation: Formula: (DivisorQuotient) + Remainder = Dividend. Soln: (56Q)+29 = D -------(1) D%8 = R -------------(2) From equation(2), ((56*Q)+29)%8 = R. => Assume Q = 1. => (56+29)%8 = R. => 85%8 = R => 5 = R. Answer B The answer is: B	B
mathematics	The average age of 20 men in the class is 16.6 years. Five new men join and the new average becomes 15.56 years. What was the average age of five new men?	[ "15.5", "15.4", "15.25", "15.3", "11.4" ]	Total age of 20 men = 16.6 x 20 = 332 Now, total age of 25 men = 389. Total age of five men added later = 389 - 332 = 57. Hence, the total average of five men = 57/5 = 11.4 ANSWER:E The answer is: E	E
mathematics	Lion, rat stay in jungle happily. Lion lies on: Mon, Tue, Wed. Rat lies on: Wed, Thurs , Sat. If lion says: I didn't lie yesterday. Rat says: I didn’t lie yesterday. So what day is today?	[ "Tuesday", "wednesday", "Thursday", "Friday", "Sunday" ]	Tuesday -- lion ll tell lie on tuesday lion is saying lie that he didn't lie sday [ again a lie... bcozzz lion ll say lie on monday also] Tuesday -- Rat ll not say lie on tuesday ANSWER:A The answer is: A	A
mathematics	Ram and Shakil run a race of 2000m. First Ram gives Shakil a start of 200m and beats him by 1 minute.Next Ram gives shakil a start of 6 min and is beaten by 1000 meters . Find the time in minutes in which Ram and Shakil can run the race seperately.	[ "12.18", "10.18", "10.12", "8.1", "8.2" ]	LET r be velocity of ram and s be the velocity of Shakil then (2000/r)=(1800/s)-60......(1) second case distance Shakil travel in 6 min=360s again equating time for both 1000/r=(2000-360s)/s.......(2) solving (1) &(2) we get s=20/6 putting value in first we get time =480sec=8min ANSWER:D The answer is: D	D
mathematics	If f(a)=4a-6, what is the value of (f(5a)-f(a))/2 ?	[ "12a-6", "10a+5", "5a/6", "4a-6", "20a+6" ]	f(a)=4a-6 f(5a) = 20a-6 (f(5a)-f(a))/2 = (20a-6+4a-6)/2 = 12a-6 Answer is The answer is: A	A
mathematics	In expressing a length 810472 km as nearly as possible with three significant digits, find the percentage error.	[ "0.034", "0.024", "0.352", "0.063", "0.026" ]	Error = (81.5 – 81.472)km = 0.028. Required percentage = [(0.028/81.472)*100]% = 0.034%. Answer A. The answer is: A	A
mathematics	In an apartment building that has 490 units, 4 out of every 7 units are currently rented, including 1/6 of the one-bedroom units. If, of the rented apartments, there is a 6:1 ratio of two-bedroom units to one-bedroom units, and the building only consists of two-bedroom and one-bedroom units, how many two-bedroom units are not rented?	[ "50", "70", "100", "105", "10" ]	Rented = 4/7490 = 280. Rented two-bedroom = 6/7280 = 240; Rented one-bedroom = 1/7280 = 40 (or 280-240=40). Rented one-bedroom units are 1/5 of all one-bedroom: 1/6{All one bedroom} = 40 --> {All one-bedroom} = 240. {All two-bedroom} = 490 - 240 = 250. Two-bedroom not rented = 250 - 240 = 10 Answer: E The answer is: E	E
mathematics	What is the sum of the greatest common factor and the lowest common multiple of 36 and 56?	[ "592", "520", "508", "560", "584" ]	Prime factorization of the given numbers 36= 2^2 * 3^2 56= 2^3 *7 Greatest common factor = 4 Lowest common multiple = 504 Sum = 4+ 504 = 508 Answer C The answer is: C	C
mathematics	When the integer k is divided by 7, the remainder is 1. Which of the following expressions below when divided by 7, will have a remainder of 5? I. 4k + 1 II. 6k + 6 III. 8k + 2	[ "I only", "II only", "III only", "I and II only", "I, II and III" ]	k = 7j + 1 4k + 1 = 28j + 4 + 1 = 28j + 5 6k + 6 = 42j + 6 + 6 = 42j + 7 + 5 8k + 2 = 56j + 8 + 2 = 56j + 7 + 3 The answer is D. The answer is: D	D
mathematics	The average salary of a person for the months of January, February, March and April is Rs.8000 and that for the months February, March, April and May is Rs.8500. If his salary for the month of May is Rs.6500, find his salary for the month of January?	[ "2177", "2876", "4500", "2981", "2711" ]	Sum of the salaries of the person for the months of January, February, March and April = 4 * 8000 = 32000 ----(1) Sum of the salaries of the person for the months of February, March, April and May = 4 * 8500 = 34000 ----(2) (2)-(1) i.e. May - Jan = 2000 Salary of May is Rs.6500 Salary of January = Rs.4500.Answer: C The answer is: C	C
mathematics	The cost of 2 benchs and 3 tables is Rs.1300. The cost of 3 benchs and 2 tables is Rs.1200. The cost of each table is more than that of each bench by?	[ "900", "200", "100", "400", "600" ]	C 100 2C + 3T = 1300 --- (1) 3C + 3T = 1200 --- (2) Subtracting 2nd from 1st, we get -C + T = 100 => T - C = 100 The answer is: C	C
mathematics	A person can row at 9 kmph and still water. He takes 3 1/2 hours to row from A to B and back. What is the distance between A and B if the speed of the stream is 1 kmph?	[ "16 km", "87 km", "89 km", "67 km", "20 km" ]	Let the distance between A and B be x km. Total time = x/(9 + 1) + x/(9 - 1) = 3.5 => x/10 + x/8 = 7/2 => (4x + 5x)/40 = 7/2 => x = 16 km. Answer:A The answer is: A	A
mathematics	A soccer team played 160 games and won 65 percent of them. How many games did it win?	[ "84", "94", "104", "114", "124" ]	65% of 160 =x 0.65*160 = x 104=x answer :C The answer is: C	C
mathematics	. In a certain city, 60 percent of the registered voters are Democrats and the rest are Republicans. In a mayoral race, if 70 percent of the registered voters who are Democrats and 20 percent of the registered voters who are Republicans are expected to vote for Candidate A, what percent of the registered voters are expected to vote for Candidate A ?	[ "50%", "53%", "54%", "55%", "57%" ]	Registered voters = 100 D = 60 R = 40 70% of D ( 60) = 42 20% of R ( 40 ) = 8 Total voter% of registered voters = 50 / 100 50% Ans A The answer is: A	A
mathematics	Birbal is a witty trader who trade of a mystical fruit grown far in north. He travels from one place to another with three sacks which can hold 30 fruits each. None of the sack can hold more than 30 fruits. On his way, he has to pass through thirty check points and at each check point, he has to give one fruit for each sack to the authorities. How many mystical fruits remain after he goes through all the thirty check points?	[ "23", "24", "25", "26", "27" ]	Solution: 25 Fruits Remember we told you that Birbal is a witty trader. So his sole motive is to get rid of the sacks as fast as he can. For the first sack: He must be able to fill fruits from one sack to other two sacks. Assume that he is able to do that after M check points. Now to find M, (Space in first sack) M + (Space in second sack) M = (Remaining fruits in Third Sack) 30 – M M = 10 Thus after 10 checkpoints, Birbal will be left with only 2 sacks containing 30 fruits each. Now he must get rid of the second sack. For that, he must fill the fruits from second sack to the first sack. Assume that he manages to do that after N checkpoints. (Space in First Sack) N = (Remaining fruits in second sack) 30 – N N = 15 Thus after he has crossed 25 checkpoints, he will be left be one sack with 30 fruits in it. He has to pass five more checkpoints where he will have to give five fruits and he will be left with twenty five fruits once he has crossed all thirty check points. Answer C The answer is: C	C
mathematics	For integers x and y, if 91x = 8y, which of the following must be true? I. y > x II. y/7 is an integer III. The cube root of x is an integer	[ "I only", "II only", "III only", "I and II", "II and III" ]	Given 91x=8y It can be equal when x = 8 or -8 and y = 91 or -91 So Statement (I) y < x if we take x = -8 and y =-91 but y > x if we take x = 8 and y = -91, so (I) is not true always Statement (2) in any case 91/7 or -91/7 is an integer that is 13 or -13. So it is true Statement (3) cube root of 8 or -8 is 2 and -2 respectively. So it is true always. answer is E The answer is: E	E
mathematics	How many positive integers arethere from 0 to 1000 that leave a remainder of 3 on division by 7 & a remainder of 2 on division by 4?	[ "30", "36", "38", "42", "46" ]	Number should be of the form 7n + 3 and 4m + 2. The LCM of 7 and 4 is 28. So, let us see what are the possible remainders when we divide this number by 28. A number of the form 7n + 3 can be written as 28K + 3 or 28k + 10 or 28 + 17 or 28k + 24. A number of the form 4m + 2 can be written as 28l + 2, 28l + 6, 28l + 10, 28l + 14, 28l + 18, 28l + 22, 28l + 26. For a detailed discussion on how we get to this, look at this post. Within these, the only common term is 28K + 10. The numbers in this sequence are 10, 38, 66.....990. We still need to figure out how many numbers are there in this sequence. We are going in steps of 28, so let us see if we can write these numbers in terms of 28p + r. 10 = 28 * 0 + 10 38 = 28 * 1 + 10 66 = 28 * 2 + 10 94 = 28 * 3 + 10 ........................... 990 = 28 * 35 + 10 There are 36 numbers in this sequence. Correct Answer: 36 B The answer is: B	B
mathematics	Two varieties of wheat - A and B costing Rs. 9 per kg and Rs. 15 per kg were mixed in the ratio 3 : 7. If 5 kg of the mixture is sold at 25% profit, find the profit made?	[ "Rs. 16.58", "Rs. 16.51", "Rs. 16.59", "Rs. 16.50", "Rs. 16.52" ]	Explanation: Let the quantities of A and B mixed be 3x kg and 7x kg. Cost of 3x kg of A = 9(3x) = Rs. 27x Cost of 7x kg of B = 15(7x) = Rs. 105x Cost of 10x kg of the mixture = 27x + 105x = Rs. 132x Cost of 5 kg of the mixture = 132x/10x (5) = Rs. 66 Profit made in selling 5 kg of the mixture = 25/100 (cost of 5 kg of the mixture) = 25/100 * 66 = Rs. 16.50 Answer:D The answer is: D	D
mathematics	The least number which should be added to 2497 so that the sum is exactly divisible by 5, 6, 4 and 3 is:	[ "21", "23", "26", "29", "30" ]	L.C.M. of 5, 6, 4 and 3 = 60. On dividing 2497 by 60, the remainder is 37. Number to be added = (60 - 37) = 23. answer :B The answer is: B	B
mathematics	A tank has 5 inlet pipes. Three pipes are narrow and two are wide. Each of the three narrow pipes works at 1/2 the rate of each of the wide pipes. All the pipes working together will take what fraction R of time taken by the two wide pipes working together to fill the tank?	[ "1/2", "2/3", "3/4", "3/7", "4/7" ]	I always plug in for these questions.. I find them easier Let 2 large pipes each work fill 10lts/hr small ones = 1/2*10 = 5 total 5 = 10+10+5+5+5 = 35 lts/hrs now assume the total capacity = 140 lts ( LCM of 20,35) Qn :All the pipes working together will take what fraction of time taken by the two wide pipes working together to fill the tank all working together will take 140/35 = 4 hrs two large pipes working will take 140/20 = 7 hrs hence ratio R= 4/7 = E The answer is: E	E
mathematics	On rainy mornings, Mo drinks exactly N cups of hot chocolate (assume that N is an integer). On mornings that are not rainy, Mo drinks exactly 2 cups of tea. Last week Mo drank a total of 16 cups of tea and hot chocolate together. If during that week Mo drank 4 more tea cups than hot chocolate cups, then how many rainy days were there last week?	[ "6", "3", "4", "5", "2" ]	T= the number of cups of tea C= the number of cups of hot chocolate T+C = 16 T-C=4 -> T= 10. C=6. Mo drinks 5 cups of tea a day then number of days that are not rainy = 10/2 = 5 So number of rainy days = 7-5 = 2 E is the answer. The answer is: E	E
mathematics	An empty pool being filled with water at a constant rate takes 7 hours to fill to 3/5 of its capacity. How much more time will it take to finish filling the pool?	[ "5 hr 30 min", "5 hr 20 min", "4 hr 40 min", "3 hr 12 min", "2 hr 40 min" ]	(3/5) of a pool/ 7 hours = 3/35 (the rate) (3 pools/35 hours) = (2/5* pool)/ x hours Cross multiply 3x = (2/5) 35 x = 4 2/3 2/3 of an hour = 40 minutes C The answer is: C	C
mathematics	If K is the sum of reciprocals of the consecutive integers from 33 to 38, inclusive, then K is closest in value to which of the following?	[ "1/12", "1/10", "1/8", "1/7", "1/4" ]	1/33 , 1/34 , 1/35 , 1/36 , 1/37 , 1/38 Hypothetically , assume all 6 Numbers to be 1/33 Hence sum of it would result in = 6/33 ( almost equals 1/6 , or slightly more than 1/6 - ) If all 6 nos were to be 1/38 ... Sum of which would result in 6/38 = 3/19 . Hence answer should lie between 1/6 and 1/7 (3/21) D i.e 1/7 The answer is: D	D
mathematics	Robert is travelling on his cycle and has calculated to reach point A at 2 P.M. if he travels at 10 kmph, he will reach there at 12 noon if he travels at 15 kmph. At what speed must he travel to reach A at 1 P.M.?	[ "9 km/hour", "10 km/hour", "11 km/hour", "12 km/hour", "None of these" ]	Explanation: We need to calculate the distance, then we can calculate the Ɵme and finally our answer. Lets solve this, Let the distance travelled by x km Time = Distance/Speed x10−x15=2[because, 2 pm - 12 noon = 2 hours]3x−2x=60x=60.Time=DistanceSpeedTime@10km/hr=6010=6hours So 2 P.M. - 6 = 8 A.M Robert starts at 8 A.M. He have to reach at 1 P.M. i.e, in 5 hours So, Speed = 60/5 = 12 km/hr Answer: D The answer is: D	D
mathematics	What are the number of ways to select 3 men and 2 women such that one man and one woman are always selected?	[ "12", "10", "30", "99", "123" ]	The number of ways to select three men and two women such that one man and one woman are always selected = Number of ways selecting two men and one woman from men and five women = ⁴C₂ * ⁵C₁ = (4 * 3)/(2 * 1) * 5 = 30 ways. Answer:C The answer is: C	C
mathematics	If you divide a number into 3 equal groups and then divide each group in half, you end up with 13. What number did you start with?	[ "76", "77", "78", "79", "None of these" ]	Solution: Suppose the start number is x Division into 3 equal groups is: x/3, and then in half is (x/3)/2 = 13 x/6 = 13 x = 13 * 6 = 78 Answer C The answer is: C	C
mathematics	A boy has six trousers and 13 shirts. In how many different ways can he select a trouser and a shirt?	[ "238 ways", "87 ways", "66 ways", "78 ways", "121 ways" ]	Explanation: The boy can select one trouser in six ways. The boy can select one shirt in 13 ways. The number of ways in which he can select one trouser and one shirt is 6 * 13 = 78 ways. Answer: D The answer is: D	D

mathematics

If a town of 35,000 people is growing at a rate of approx. 1% per year, the population of the town in 5 years will be closest to?

[ "a.36000", "b.37000", "c.38000", "d.39000", "e.40000" ]

1% is quite small and hence the answer is A) The answer is: A

A

mathematics

In the xy-coordinate system, what is the slope of the line that goes through the point (1, 1) and is equidistant from the two points P = (3, 7) and Q = (9, 11)?

[ "0.5", "0.625", "0.75", "0.875", "1.0" ]

First, get the middle coordinate between (3,7) and (9,11)... x = 3 + (9-3)/2 = 6 y = 7 + (11-7)/2 = 9 Second, get the slope of (9,6) and (1,1). m = 6-1 / 9-1 = 5/8 = 0.625 Answer: B The answer is: B

B

mathematics

During a recent track meet, Peter ran x meters of the 100 meter dash in 6 seconds; running at the same rate, how many seconds will it take Peter to run z meters of the 200 meter dash?

[ "6z/x", "6zx", "6x/z", "6/xz", "xz/6" ]

Speed of Peter = x/6 meters per second Time needed to run z meters = DISTANCE/SPEED = z / (x/6) = 6z/x Option A The values 100m and 200m have no role to play here and are just given to confuse you. The answer is: A

A

mathematics

Find the area of a parallelogram with base 24 cm and height 16 cm?

[ "776", "384", "666", "288", "211" ]

Area of a parallelogram = base * height = 24 * 16 = 384 cm2 Answer: B The answer is: B

B

mathematics

A man spends Rs. 1500 per month on an average for the first three months, Rs 1550 for next four months and Rs. 1800 per month for the last five months and saves Rs . 5200 a year. What is his average monthly income?

[ "2075", "2100", "2200", "2300", "2400" ]

Explanation: Total expenditure for the first 3 months = 3 Ã— 1500 = 4500 Total expenditure for 4 months = 4 Ã— 1550 = 6200 Total expenditure for 5 months = 5 Ã— 1800 = 9000 Total expenditure and saving (which is income for one year) = 4500 + 6200 + 9000 + 5200 = Rs. 24900 So, Average monthly income = 24900/12 = Rs. 2075 Answer A The answer is: A

A

mathematics

If a and b are positive even integers, and the least common multiple of a and b is expressed as a*b/r, which of the following statements could be false?

[ "n is a factor of both a and b", "(a*b)/n < ab", "ab is multiple of 2.", "(a*b)/n is a multiple of 2.", "r is a multiple of 4." ]

If we divide bynand get a multiple ofaand of b, then r must be a common factor. Answer A must be true. Ifaandbare even integers, dividing by a factor (also an integer) results in something smaller than the productab. Answer B must be true. If eitheraorbis even, thenabmust be even. Answer C must be true. If both are even, the smallest either number can be is 2. Thus, the smallest common factor must be 2. Answer D must be true. Ifbis 6 andais 2,nwould be 6, which is not 4. E can be false. The answer is: E

E

mathematics

A and B can do a piece of work in 3 days, B and C in 4 days, C and A in 6 days. How long will C take to do it?

[ "33", "28", "24", "97", "16" ]

Explanation: 2c = Â¼ + 1/6 â€“ 1/3 = 1/12 c = 1/24 => 24 days Answer:C The answer is: C

C

mathematics

If a number is chosen at random from the set {1, 2, 3, ...., 100}, then the probability that the chosen number is a perfect cube is

[ "1/25", "1/27", "1/28", "1/22", "1/24" ]

We have 1, 8, 27 and 64 as perfect cubes from 1 to 100. Thus, the probability of picking a perfect cube is 4/100 = 1/25. Answer:A The answer is: A

A

mathematics

The height of the wall is 6 times its width and length of the wall is 7 times its height .if the volume of the wall be 6804 cu.m.its width is

[ "3m", "5m", "6m", "7m", "8m" ]

Explanation: Let width = x Then, height=6x and length=42x 42x Ã— 6x Ã— x = 6804 x = 3 Answer: A The answer is: A

A

mathematics

A cube of edge 5cm is immersed completely in a rectangular vessel containing water. If the dimensions of the base of vessel are 10cm * 5cm , find the rise in water level?

[ "2.5cm", "3.6cm", "5cm", "6.43cm", "7.56cm" ]

Increase in volume = volume of the cube = 5*5*5 cm^3 Rise in water level = volume / area = 5*5*5/10*5 = 2.5cm Answer is A The answer is: A

A

mathematics

In given series 1, 2, 6, 15, 31, 56, 91 only one number is incorrect. Find out that wrong number

[ "91", "92", "90", "60", "61" ]

1, 1 + 12 = 2, 2 + 22 = 6, 6 + 32 = 15, 15 + 42 = 31, 31 + 52 = 56, 56 + 62 = 92 Last number of given series must be 92 not 91. ANSWER:A The answer is: A

A

mathematics

A total of 40 men and 25 women were at a party, and the average (arithmetic mean) age of all of the adults at the party was exactly 35 years. If the average age of the men was exactly 38 years, which of the following was closest to the average age, in years, of the women?

[ "31", "30.2", "32", "32.5", "33" ]

Let Aw = average age of women Average = (Number of men X average age of men + Number of women X average age of women)/total number of people 35 * 65 = 40 * 38 + 25 * Aw =>2275 = 1520 + 25 Aw => 25 Aw = 755 =>Aw = 30.2 Answer B The answer is: B

B

mathematics

For an upcoming charity event, a male vocalist has agreed to sing 5 out of 7 “old songs” and 3 out of 6 “new songs.” How many ways can the singer make his selection?

[ "25", "50", "140", "480", "600" ]

=7C5*6C3 =7*6/3*6*5/3 =7*2*2*5 =140 Ans = C The answer is: C

C

mathematics

Ten years ago, P was half of Q's age. If the ratio of their present ages is3:4, what will be the total of their present ages?

[ "45", "40", "35", "30", "25" ]

Let present age of P and Q be 3x and 4x respectively. Ten years ago, P was half of Q's age ⇒(3x−10)=1(4x−10)/2 ⇒6x−20=4x−10 ⇒2x=10 ⇒x=5 Total of their present ages 3x+4x=7x=7*5=35 ANSWER:C The answer is: C

C

mathematics

A can do a work in 12days. When he had worked for 3days, B joinedhim. If they complete the work in 3more days, in how manydays can Balone finish the work?

[ "3 days", "4 days", "6 days", "7 days", "9 days" ]

sax Work done by Afar 3 days : i J .. Remzming war — 1 .Work done by (A + B) for 1 day : . Work done by a for 1 day 6 days C The answer is: C

C

mathematics

In traveling from a dormitory to a certain city, a student went 1/3 of the way by foot, 3/5 of the way by bus, and the remaining 2 kilometers by car. What is the distance, in kilometers, from the dormitory to the city?

[ "30", "45", "60", "90", "120" ]

Whole trip = distance by foot + distance by bus + distance by car x = 1/3x + 3/5x + 2 x - 1/3x - 3/5x = 2 x = 30km Option: A The answer is: A

A

mathematics

In a box, there are 8 red, 5 blue and 6 green balls. One ball is picked up randomly. What is the probability that it is neither blue nor green?

[ "2/3", "8/21", "3/7", "9/22", "8/19" ]

Explanation: Total number of balls = (8 + 5 + 6) = 19 Let E = event that the ball drawn is neither blue nor green =e vent that the ball drawn is red. Therefore, n(E) = 8. P(E) = 8/19. Answer: Option E The answer is: E

E

mathematics

Ramesh and Neelesh start walking to meet one another from places 25 kms apart. If Ramesh walks at the rate of 2 kms an hour and Neelesh at 3 kms an hour, how many hours will it be before they meet?

[ "2 hr", "3 hr", "4 hr", "5 hr", "6 hr" ]

velocity of ramesh =2km/h velocity of neelesh =3km/h both start moving from both the end of 25km let at time t they meet let ramesh walks x km than neelesh have walk =25-x km 2=x/t.......(a) 3=25-x/t.....(b) on solving t=5 hr. ANSWER:D The answer is: D

D

mathematics

Water consists of hydrogen and oxygen, and the approximate ratio, by mass, of hydrogen to oxygen is 2:16. Approximately how many grams of oxygen are there in 153 grams of water?

[ "16", "72", "112", "136", "142" ]

Since the ratio, by mass, of hydrogen to oxygen is 2:16, then oxygen is 16/(2+16)=8/9 of mass of water. Therefore there are 153*8/9=136 grams of oxygen in 153 grams of water. Answer: D. The answer is: D

D

mathematics

A certain telescope increases the visual range at a particular location from 90 kilometers to 150 kilometers. By what percent is the visual range increased by using the telescope ?

[ "30%", "33 1/2%", "40%", "60%", "66 2/3%" ]

Original visual range = 90 km New visual range = 150 km Percent increase in the visual range by using the telescope = (150-90)/90 * 100% = 2/3 * 100% = 66.67 % Answer E The answer is: E

E

mathematics

The ratio of the present ages of P and Q is 3:4. 5 years ago, the ratio of their ages was 5:7. Find the their present ages?

[ "30, 40", "30, 50", "60, 40", "10, 30", "50, 40" ]

Answer: Option A Their present ages be 3X and 4X. 5 years age, the ratio of their ages was 5:7, then (3X - 5):(4X - 5) = 5:7 X = 35 - 25 => X = 10. Their present ages are: 30, 40. The answer is: A

A

mathematics

A fruit-salad mixture consists of apples, peaches, and grapes in the ratio 6:5:2, respectively, by weight. If 78 pounds of the mixture is prepared, the mixture includes how many more pounds of apples than grapes?

[ "24", "12", "9", "6", "4" ]

We can first set up our ratio using variable multipliers. We are given that a fruit-salad mixture consists of apples, peaches, and grapes, in the ratio of 6:5:2, respectively, by weight. Thus, we can say: apples : peaches : grapes = 6x : 5x : 2x We are given that 39 pounds of the mixture is prepared so we can set up the following question and determine a value for x: 6x + 5x + 2x = 78 13x = 78 x = 6 Now we can determine the number of pounds of apples and of grapes. pounds of grapes = (2)(6) = 12 pounds of apples = (6)(6) = 36 Thus we know that there are 36 -12 = 24 more pounds of apples than grapes. Answer is A. The answer is: A

A

mathematics

A jogger running at 9 km/hr along side a railway track is 200 m ahead of the engine of a 120 m long train running at 45 km/hr in the same direction. In how much time will the train pass the jogger?

[ "88", "27", "32", "80", "12" ]

Speed of train relative to jogger = 45 - 9 = 36 km/hr. = 36 * 5/18 = 10 m/sec. Distance to be covered = 200 + 120 = 320 m. Time taken = 320/10 = 32 sec. Answer: C The answer is: C

C

mathematics

Goldenrod and No Hope are in a horse race with 8 contestants. How many different arrangements of finishes are there if No Hope always finishes before Goldenrod and if all of the horses finish the race?

[ "40320", "20160", "12000", "2400", "2100" ]

All 8 horses can finish the race in 8! way (assuming no tie). If no tie is possible between No Hope and Goldenrod, then in half of these cases No Hope will be before Goldenrod and in half of these cases after (not necessarily right before or right after). How else? So, there are 8!/2=20160 different arrangements of finishes where No Hope always finishes before Goldenrod. Answer: B. The answer is: B

B

mathematics

Paul's income is 40% less than Rex's income, Quentin's income is 20% less than Paul's income, and Sam's income is 40% less than Paul's income. If Rex gave 40% of his income to Sam and 60% of his income to Quentin, Quentin's new income would be what fraction of Sam's new income?

[ "11/12", "13/17", "13/19", "12/19", "27/19" ]

MAKE R = 10 P = 0.6R = 6 Q = 0.8P = 4.8 S= 0.6P = 3.6 FOR THAT WE GET S = 7.6 AND Q 10.8 SO 10.8/7.6 = 2.7/ 1.9 Ans:E The answer is: E

E

mathematics

In Arun’s opinion, his weight is greater than 65 kg but less than 72 kg. His brother doest not agree with Arun and he thinks that Arun’s weight is greater than 60 kg but less than 70 kg. His mother’s view is that his weight cannot be greater than 68 kg. If all are them are correct in their estimation, what is the average of different probable weights of Arun?

[ "66 kg", "67 kg", "68 kg", "69 kg", "None of these" ]

Explanation: Let Arun’s weight by X kg. According to Arun, 65 < X < 72 According to Arun’s brother, 60 < X < 70. According to Arun’s mother, X <= 68 The values satisfying all the above conditions are 66, 67 and 68. Required average = [66+67+68/3]=[201/3]=67kg Answer B The answer is: B

B

mathematics

Calculate how long it will take a swimmer to swim a distance of 10km against the current of a river which flows at 3km/hr, given that he can swim in still water at 5km/h

[ "3", "4", "5", "6", "7" ]

swim in still water at = 5 speed of river= 3 US = 5 - 3= 2 Distance = 10 T = 10/2 = 5 Answer: C The answer is: C

C

mathematics

An investor purchased 100 shares of stock X at 6 1/8 dollars per share and sold them all a year later at 12 dollars per share. If the investor paid a 2 percent brokerage fee on both the total purchase price and the total selling price, which of the following is closest to the investor's percent gain on this investment?

[ "192%", "94%", "280%", "300%", "380%" ]

If the purchase price was 6$ per share then the investor would have made a profit of 100%. Since the purchase price is slightly more than 6$ the profit would be slightly less than 100%. Also a 2% brokerage is negligible and it brings down the profit percentage only by a small value. Approximation is very useful to solve these kind of problems as the answer choices are far apart. Answer:B The answer is: B

B

mathematics

A searchlight on top of the watchtower makes 2 revolutions per minute. What is the probability that a man appearing near the tower will stay in the dark for at least 6 seconds?

[ "5/6", "4/5", "3/4", "2/3", "1/2" ]

The searchlight completes one revolution every 30 seconds. The probability that the man's area will be lit up is 6/30=1/5. The probability that he will stay in the dark is 1-1/5=4/5 The answer is B. The answer is: B

B

mathematics

Tough and Tricky questions: Exponents. If a and b are positive integers and x = 5^a and y = 4^b, which of the following is a possible units digit of xy?

[ "1", "4", "5", "7", "0" ]

Only Units digit of X and Y contribute to the Units digit of XY. Finding all values ofXfor positive values ofa When, a=1; X=5 a=2; X=25 a=3; X=125........ Units digit repeat in a cycle of 5...... Similarly, Finding all values ofYfor positive values ofb When, b=1; Y=4 b=2; Y= 16 b=3; Y= 64....... Units digit repeat in cycle of 4,6,4.... So, possible value of Units digit of XY can be found by considering all possibilities of Units digit of X and Y When X=5 and Y=4: Units digit of XY = 20 When X=5 and Y=6: Units digit of XY = 30 Only one possibility for Units digit of XY i.e. 0. therefore answer is E The answer is: E

E

mathematics

Four years ago,the father’s age was three times the age of his son.The total of the ages of the father and the son after four years,will be 64 years.What is the father’s age at present ?

[ "32 years", "36 years", "44 years", "None of these", "49 years" ]

Solution Let the ages of father and son 4 years ago be 3x and x years respectively. Then,[(3x + 4) + 4] + [(x + 4)+ 4]= 64 ⇔ 4x = 48 ⇔ x =12. ∴ Father's present age = 3x = 36 years. Answer D The answer is: D

D

mathematics

The sum of ages of 5 children born 3 years different each is 60 yrs. What is the age of the Elder child?

[ "17", "19", "16", "18", "21" ]

Let the ages of children be x, (x + 3), (x + 6), (x + 9) and (x + 12) years. Then, x + (x + 3) + (x + 6) + (x + 9) + (x + 12) = 60 5x = 30 x = 6. x+12= 6+12= 18 D The answer is: D

D

mathematics

A computer can perform c calculations in s seconds. How many minutes will it take the computer to perform A calculations?

[ "60as/c", "as/c", "as/60c", "60c/as", "a/60cs" ]

As 'thick' as this question might look, it's actually a fairly straight-forward Rate question and can be solved by TESTing VALUES. We're told that a computer can perform a calculations in S seconds. Let's TEST.... a = 2 S = 3 2 calculations every 3 seconds = 40 calculations every 1 minute We're asked how many MINUTES it will take to perform K calculations. Since we already know that the computer can perform 40 calculations in 1 minute, let's TEST... K = 80 So we're looking for an answer that = 2 when C = 2, S = 3 and K = 80 Answer A: 60KS/a = 60(80)(3)/2 = 7200 This is NOT a match Answer B: KS/a = (80)(3)/2 = 120 This is NOT a match Answer C: KS/60a = (80)(3)/(60)(2) = 2 This IS a match Answer D: 60a/KS = 60(2)/(80)(3) = 1/2 This is NOT a match Answer E: K/60aS = 80/(60)(2)(3) = a fraction. This is NOT a match C The answer is: C

C

mathematics

A car dealer sold x used cars and y new cars during May. If the number of used cars sold was 10 greater than the number of new cars sold. Which of the following expresses this relationship ?

[ "x > 10y", "x > y + 10", "x > y – 10", "x = y + 10", "x = y – 10" ]

Given: x used cars and y new cars Number of used cars (x) sold was 10 greater than the number of new cars (y) sold So, x is 10 greater than y To show their relative sizes let's write x LARGER than y to get: x and y Our goal is to create an EQUATION. So, how do we make these two values EQUAL? Well, we need to make the smaller value (y) bigger. 10 bigger to be exact. So, we get x = y + 10 Answer: D The answer is: D

D

mathematics

What will be the cost of building a fence around a square plot with area equal to 36 sq ft, if the price per foot of building the fence is Rs. 58?

[ "3944", "2287", "2977", "2668", "1392" ]

Let the side of the square plot be a ft. a2 = 36=> a = 6 Length of the fence = Perimeter of the plot = 4a = 24 ft. Cost of building the fence = 24 * 58 = Rs. 1392. Answer:E The answer is: E

E

mathematics

A batsman makes a score of 100 runs in the 17th inning and thus increases his averages by 5. What is his average after 17th inning?

[ "39", "35", "20", "40.5", "41.5" ]

let the average after 16th inning =x then total run after 16th inning=16x then total run after 17th inning=16x+100 then average run after 17th inning=(16x+100)/17 (16x+100)/17=x+5 = > 16x+100 = 17x+85 => x =15 x=15; average after 17th inning =15+5=20 ANSWER:C The answer is: C

C

mathematics

Sam, Suresh and Sanket run a race of 1400 meters. Sam runs twice as fast as Suresh while Suresh runs thrice as fast as Sanket. If Sanket finishes the race by clocking 15 minutes, how far was Suresh from the finish line when Sam must have finished the race?

[ "2887", "278", "987", "700", "278" ]

Explanation: When Sanket finishes the race in 15 minutes, Suresh & Sam would finish the same race in 5 minutes and 2.5 minutes respectively. Thus, when Sam reaches the ”finish” mark, Suresh must be “half-way” through i.e. 700 meters behind the “finish” line when “Sam” must have finished the race. ANSWER:D The answer is: D

D

mathematics

If a particular player is always chosen, in how many ways can a cricket-be chosen out of 15 players?

[ "1100", "1134", "1240", "1340", "1365" ]

A particular player is always chosen, it means that 10 players are selected out of the remaining 14 players. =. Required number of ways = 14C10 = 14C4 = 14!/4!x19! = 1365 E The answer is: E

E

mathematics

Smith can do a work in 15 days while Johnson can do it in 25 days. How long will they take if both work together?

[ "3 4/9 days", "8 4/9 days", "9 3/8 days", "6 3/8 days", "7 3/8 days" ]

Explanation: 1/15 + 1/25 = 8/75 75/8 = 9 3/8 days Answer: C The answer is: C

C

mathematics

A man walking at a rate of 10km/hr crosses a bridge in 3 minutes. The length of the bridge is?

[ "500", "650", "250", "111", "236" ]

Speed = 10*5/18 = 50/18 m/sec Distance covered in 5 minutes = 50/18 * 5 *60 = 500 m Answer is A The answer is: A

A

mathematics

At Atira's party there were five times as many females as males. There were three times as many adults as children. Which of the following could NOT be the number of people at the party?

[ "384", "258", "216", "120", "72" ]

we have to work on the info and understand what that info takes us to... 1) there were five times as many females as males At Atira's party.. this means F=5M.. so total number=6M.. 2) There were three times as many adults as children.. A=3C... or total = 4C.. so the total is 4C or 6M.. since C and M have to be positive integers, we can say for sure that Total is a multiple of 4 and 6.. or Total is multiple of LCM of 4,6.. LCM of 4,6= 12.. lets see which number is not multiple of 12.. A. 384...12*32 B. 258... no C. 216....12*18 D. 120....12*10 E. 72......12*6.. so B is our answer.. The answer is: B

B

mathematics

In a group of 15 people, 8 read English, 7 read French while 3 of them read none of these two. How many of them read French and English both?

[ "2", "3", "4", "7", "5" ]

In the following Venn diagram, F and E represent people who read French and English respectively. Now, [F+({F ∩ E}) + E] = 15-3 (or) F+E+(F ∩ E) = 12 ......(1) Also, F+(F ∩ E) = 7; E+(F ∩ E) = 8. By adding, F+E+2(F ∩ E) = 15 ---------- (2) By subtracting (1) from (2), we get (F ∩ E) = 3. ∴ 3 of them read both French and English. Answer:B The answer is: B

B

mathematics

Two employees X and Y are paid a total of Rs. 550 per week by their employer. If X is paid 120 percent of the sum paid to Y, how much is Y paid per week?

[ "Rs. 150", "Rs. 300", "Rs. 250", "Rs. 200", "Rs. 220" ]

Explanation: Let the amount paid to X per week =x and the amount paid to Y per week =y 12y/10+y=550 22y/10=550 y=5500/22=500/2=250 ANSWER IS C The answer is: C

C

mathematics

The jogging track in a sports complex is 1000 meters in circumference. Deepak and his wife start from the same point and walk in opposite directions at 20 km/hr and 14 km/hr respectively. They will meet for the first time in?

[ "50min", "40min", "34min", "25min", "20min" ]

Clearly, the two will meet when they are 1000 m apart To be 20+14 = 34 km apart, they take 1 hour To be 1000 m apart, they take 34 * 1000/1000 = 34 min. Answer is C The answer is: C

C

mathematics

In the Biotechnology class of 2000, there were E graduates. 32 of the graduates found a job, 45 continued on to their second degree and 13 did both. If only 9 people didn't do both, What is E equal to?

[ "69.", "71.", "73.", "75.", "76." ]

Total = 32 +45 -13 +9 = 73 .... My first post on the forum... I hope I am correct C is correct choice. The answer is: C

C

mathematics

If x = |x| , then which one of the following statements could be true? I. x = 0 II. x < 0 III. x > 0

[ "None", "I only", "III only", "I and II and III", "II and III" ]

Answer copied from NOVA guide Statement I could be true because ± 0 = −(+0) = −(0) = 0 . Statement II could be true because the right side of the equation is always negative [ ± x = (a positive number) = a negative number]. Now, if one side of an equation is always negative, then the other side must always be negative, otherwise the opposite sides of the equation would not be equal. Since Statement III is the opposite of Statement II, it must be false. But let’s show this explicitly: Suppose x were positive. Then x = x, and the equation x = ± x becomes x = x. Dividing both sides of this equation by x yields 1 = 1. This is contradiction. Hence, x cannot be positive. The answer is (D). The answer is: D

D

mathematics

If line L passes through point (m, n) and (– m, – n), where m and n are not 0, which of the following must be true? I. The slope of L is positive II. L exactly passes through origin III. The slope of L is negative

[ "III only", "II only", "I only", "I and II only", "II and III only" ]

Let (m,n) = (2,3) (-m,-n) = (-2,-3) Slope = (3+3)/(2+2) = 6/4 = 3/2 So III may not be true Let (m,n) = (2,-3) then (-m,-n) = (-2,3) So slope = (3 +3)/(-2-2) = -3/2 so I may not be true So such a line would be -> (y - 3) = 3/2(x - 2) => 2y - 6 = 3x - 6 => 2y - 3x = 0, hence no x or y intercept, so it passes through origin. II is true. Answer - B The answer is: B

B

mathematics

The Sum of first N consecutive odd integers is N^2. What is the sum of all odd integers between 11 and 41 inclusive.

[ "351", "364", "416", "424", "450" ]

We're dealing with a sequence of CONSECUTIVE ODD INTEGERS: 11 to 41, inclusive. We're asked for the SUM of this group. 1) Start with the sum of the smallest and the biggest: 11 + 41 =52 2) Now look at the 'next smallest' and the 'next biggest': 13 + 39 = 52 Now we have proof that there is no middle term. We have 8 bunches of 52. 8(52) = 416 C The answer is: C

C

mathematics

The ratio of money with Ram and Gopal is 7 : 17 and that with Gopal and Krishan is 7: 17. If Ram has Rs. 686, Krishan has ?

[ "s. 2890", "s. 4046", "s. 1190", "s. 1620", "s. 2680" ]

Ram : Gopal = 7 : 17 = 49 : 119 Gopal : Krishan = 7 : 17 = 119 : 289 Ram : Gopal : Krishan = 49 : 119 : 289 Ram : Krishan = 49 : 289 Thus, 49 : 289 = 686 : N &there N = 289 x 686 / 49 = Rs. 4046 Answer :B The answer is: B

B

mathematics

Paul sells encyclopedias door-to-door. He earns $170 on every paycheck, regardless of how many sets he sells. In addition, he earns commission as follows: Commission Sales 10% $0.00 - $10,000.00 5% $10,000.01 ---> He does not earndouble commission.That is, if his sales are $12,000, he earns 10% on the first $10,000 and 5% on the remaining $2,000. His largest paycheck of the year was $1,320. What were his sales for that pay period?

[ "13,000", "14,800", "16,400", "15,800", "19,600" ]

His pay check was $1320. Out of this, $170 was his fixed salary so the total commission he earned was $1320 - $170 = $1150 He earns 10% on the sales of first $10,000 which gives a commission of $1000. He earns 5% on every subsequent dollar. Since he earns another $150, he must have had sales of another 150*(100/5) = 3000 So his total sales must have been $10,000 + $3000 = $13,000 A The answer is: A

A

mathematics

Five years ago the average of the ages of A and B was 40 years and now the average of the ages of B and C is 44 years. What will be the age of the B ten years hence?

[ "22", "88", "26", "96", "51" ]

Let the present ages of A, B and C be a, b and c respectively. Given, [(a - 5) + (b - 5)] / 2 = 40 => a + b = 90 --- (1) (b + c)/2 = 44 => b + c = 88 --- (2) From (1) and (2), we cannot find b. Answer: B The answer is: B

B

mathematics

In a function they are distributing noble prize. In how many ways can 3 prizes be distributed among 4 boys when No boy gets more than one prize?

[ "12", "14", "17", "24", "27" ]

Sol. In this case, repetitions are not allowed. So, the first prize can be given in 4 ways. The second in 3 ways and the third in 2 ways. But fundamental principle, (4 x 3 x 2) ways = 24 ways 4: Or 4p = — 4:- 4X3X2X1- 24 ways D The answer is: D

D

mathematics

Roy was suffering from severe headaches. He went to see his doctor and the doctor gave him five tablets asking him to take one tablet every 15 minutes. How much time will it take Roy to consume all the five tablets?

[ "60 minutes", "65 minutes", "50 minutes", "45 minutes", "55 minutes" ]

A 60 minutes Roy will be able to consume all the five tablets in an hour. Tablet 1 will be taken in 0 min. Tablet 2 will be taken in 15 min. Tablet 3 will be taken in 30 min. Tablet 4 will be taken in 45 min. Tablet 5 will be taken in 60 min. The answer is: A

A

mathematics

How many 3 digit positive integers R exist that when divided by 7 leave a remainder of 5?

[ "128", "142", "143", "141", "129" ]

Minimum three digit number is 100 and maximum three digit number is 999. The first three digit number that leaves remainder 5 when divided by 7 is 103. 14 * 7 = 98 +5 = 103 The second three digit number that leaves remainder 5 when divided by 7 is 110. 15 * 7 = 105 +5 =110 The third three digit number that leaves remainder 5 when divided by 7 is 117 and so on The last three digit number that leaves remainder 5 when divided by 7 is 999 142 * 7 = 994 + 5 = 999 Therefore, we identify the sequence 103,110,117.....999 use the formula of last term Last term = first term + (n - 1) * common difference you will get the answer 129 that is definitely E. The answer is: E

E

mathematics

If four coins are tossed, the probability of getting heads only?

[ "4/16", "2", "1/16", "2/16", "3/16" ]

Since four coins are tossed, sample space = 16 Getting heads=1 p(E) = 1/16 ANSWER:C The answer is: C

C

mathematics

A train passes a platform in 25 seconds. The same train passes a man standing on the platform in 20 seconds. If the speed of the train is 54 km/hr, The length of the platform is

[ "75", "25", "26", "23", "22" ]

Speed of the train = 54 km/hr = (54×10)/36 m/s = 15 m/s Length of the train = speed × time taken to cross the man = 15×20 = 300 m Let the length of the platform = L Time taken to cross the platform = (300+L)/15 => (300+L)/15 = 20 => 300+L = 15×25 = 375 => L = 375-300 = 75 meter Answer is A. The answer is: A

A

mathematics

Train P crosses a pole in 30 seconds and train Q crosses the same pole in one minute and 15 seconds. The length of train P is three-fourths the length of train Q. What is the ratio of the speed of train P to that of train Q?

[ "5:8", "5:6", "5:1", "5:3", "5:2" ]

Given that train P crosses a pole in 30 seconds and train Q crosses the same pole in one minute and 15 seconds. Let the length of train P be LP and that of train Q be LQ given that LP = 3/4 LQ As the train P and Q crosses the pole in 30 seconds and 75 seconds respectively, => Speed of train P = VP = LP/30 Speed of train Q = VQ = LQ/75 LP = 3/4 LQ => VP = 3/4 LQ/(30) = LQ/40 Ratio of their speeds = VP : VQ = LQ/40 : LQ/75 => 1/40 : 1/75 = 1 5:8 Answer:A The answer is: A

A

mathematics

A, B, and C working alone can finish constructing a house in 6, 9, and 12 hours respectively. A starts alone and works for 1 hour. He is then joined by B and they work together for 1 hour. Finally C joins them and they all work together to finish the work. If they start working at 9 am, at what time will they finish?

[ "11:38 am", "11:49 am", "12:11 pm", "12:32 pm", "12:43 pm" ]

A completes 1/6 of the job each hour. B completes 1/9 of the work each hour. C completes 1/12 of the work each hour. A completes 1/6 of the work in the first hour. Working together, A and B complete another 5/18 for a total of 8/18. Working together, A, B, and C can complete 13/36 of the work each hour. To complete 20/36, the time required is (20/36) / (13/36) = 20/13 hours. The work will be completed at 12:00 plus 7*60/13 minutes which is about 12:32 pm. The answer is D. The answer is: D

D

mathematics

Point X is located on line segment AB and point Y is located on line segment CD. If AB = CD and AX < CY, then

[ "XB < YD", "XB < YD", "AX > XB", "AX < CD", "AX > AB" ]

A------X--B C--Y------D AX < CD. Answer: D. The answer is: D

D

mathematics

A man bets on no. 16 on a roulette wheel 14 times and losses each time. On the 15th span he does a quick calculation and finds out that the no. 12 had appeared twice in the 14 spans and is therefore, unable to decide whether to bet on 16 or 12 in the 15th span. Which will give him the best chance and what are the odds of winning on the bet that he takes?

[ "Either 37 ;30:1", "Either ;35:1", "Either 15;15:12", "Either 21;35:1", "Either 17;35:12" ]

Each of the span is an independent event and the outcome of the 15th span will not depend on the outcome of the earlier spans. Either ;35:1 B) The answer is: B

B

mathematics

Two friends decide to get together; so they start riding bikes towards each other. They plan to meet halfway. Each is riding at 6 MPH. They live 36 miles apart. One of them has a pet carrier pigeon and it starts flying the instant the friends start traveling. The pigeon flies back and forth at 40 MPH between the 2 friends until the friends meet. How many miles does the pigeon travel?

[ "54", "110", "120", "16", "180" ]

C 120 It takes 3 hours for the friends to meet; so the pigeon flies for 3 hours at 40 MPH = 120 miles The answer is: C

C

mathematics

504 can be expressed as a product of primes as .

[ "2 × 2 × 3 × 3 × 7 × 7", "2 × 3 × 3 × 3 × 7 × 7", "2 × 3 × 3 × 3 × 3 × 7", "2 × 2 × 2 × 3 × 3 × 7", "NONE OF THE ABOVE" ]

It is clear that 504 = 2 × 2 × 2 × 3 × 3 × 7 Answer: Option D The answer is: D

D

mathematics

If z2 + 4y2 = 4zy, then z : y is :

[ "2 : 1", "1 : 2", "1 : 1", "1 : 4", "1 : 5" ]

as the coefficient of z is 1 and coefficient of y is 4 ANSWER:D The answer is: D

D

mathematics

A cistern has a leak which would empty the cistern in 20 minutes. A tap is turned on which admits 4 liters a minute into the cistern, and it is emptied in 24 minutes. How many liters does the cistern hold?

[ "480", "992", "772", "662", "188" ]

1/x - 1/20 = -1/24 x = 120 120 * 4 = 480 Answer:A The answer is: A

A

mathematics

The LCM of two numbers is 2310 and HCF is 61. If one of the numbers is 210. Then what is the other number ?

[ "715", "671", "330", "582", "465" ]

First number * Second Number = LCM * HCF Other number = 2310 * 61 / 210 = 11*61 = 671 ANSWER :B The answer is: B

B

mathematics

The average of five consecutive odd numbers A, B, C, D and E is 13. What percent of B is C ?

[ "98.2", "102.8", "108.2", "118.2", "122.8" ]

Explanation : In such a case the middle number (C) is the average ∴ C = 13 and B = 11 Required percentage = 13/11 x 100 = 118.2 Answer : Option D The answer is: D

D

mathematics

A car takes 6 hours to cover a distance of 540 Km. how much should the speed in Kmph be maintained to cover the same direction in 3/2th of the previous time?

[ "40 Kmph", "52 Kmph", "60 Kmph", "76 Kmph", "80 Kmph" ]

Time = 6 Distance = 540 3/2 of 6 hours = 6 * 3/2 = 9 Hours Required speed = 540/9 = 60 Kmph C) The answer is: C

C

mathematics

The daily high temperatures were recorded at an Antarctic weather station. If a temperature of -38.2 degrees Celsius is 2 units of standard deviation below the mean temperature, and a temperature of -22.6 degrees Celsius is 4 units of standard deviation above the mean, which of the following temperatures is 1 unit of standard deviation below the mean?

[ "-35.6 degrees Celsius", "-33.0 degrees Celsius", "-30.4 degrees Celsius", "-27.8 degrees Celsius", "-25.2 degrees Celsius" ]

Let us suppose mean = M and SD = d. So, we are given M - 2d = -38.2 and M + 4d = -22.6 solving both the equations, we will get M = -33 an d = 2.6 So, we need to find out M - d = -33 - 2.6 = -35.6. Hence, A The answer is: A

A

mathematics

An art gallery owner is hanging paintings for a new show. Of the five paintings she has to choose from, she can only hang three on the main wall of the gallery. Assuming that she hangs as many as possible on that wall, in how many ways can she arrange the paintings?

[ "18", "30", "64", "20", "216" ]

Arrangement means permutations questions.. 5P3 = 5!/3! = 20 . ANS option D is correct answer.. The answer is: D

D

mathematics

Two pipes A and B can fill a cistern in 20 and 30 minutes respectively, and a third pipe C can empty it in 40 minutes. How long will it take to fill the cistern if all the three are opened at the same time?

[ "17 1/9", "17 1/3", "17 1/7", "17 1/9", "17 1/1" ]

1/20 + 1/30 - 1/40 = 7/120 120/7 = 17 1/7 Answer: C The answer is: C

C

mathematics

A salt manufacturing company produced a total of 5000 tonnes of salt in January of a particular year. Starting from February its production increased by 200 tonnes every month over the previous months until the end of the year. Find its average monthly production for that year?

[ "2989", "2765", "6110", "2989", "9772" ]

Total production of salt by the company in that year = 5000 + 5200 + 5400 + .... + 7200 = 73400. Average monthly production of salt for that year = 73400/12 = 6116. Answer:C The answer is: C

C

mathematics

Insert the missing number 6, 7, 9, 13, 21, ...

[ "25", "29", "37", "32", "30" ]

Difference between two numbers in the series is multiplied by 2 to get the next number 6,7 ...Difference is 1 7,9 Difference is 2 9,13 difference is 4 13,21 Difference is 8 21, 37 Difference is 16 ANSWER:C The answer is: C

C

mathematics

If x represents the sum of the interior angles of a triangle and y represents the sum of the interior angles of a regular pentagon, then the difference between x and y is equal to the sum of the interior angles of what geometric shape?

[ "Circle", "Square", "Rhombus", "Trapezoid", "Pentagon" ]

Sum of angles of triangle = 180*(3-2) = 180 => using formula sum of interior angles of polygon = 180*(n-2) where n is the number of sides in a polygon Sum of angles in Pentagon = 180*(5-2) =540 Difference =540 - 180= 360 => Cirlcle hence (A). The answer is: A

A

mathematics

On dividing a number by 56, we get 29 as remainder. On dividing the same number by 8, what will be the remainder ?

[ "4", "5", "6", "8", "9" ]

Explanation: Formula: (Divisor*Quotient) + Remainder = Dividend. Soln: (56*Q)+29 = D -------(1) D%8 = R -------------(2) From equation(2), ((56*Q)+29)%8 = R. => Assume Q = 1. => (56+29)%8 = R. => 85%8 = R => 5 = R. Answer B The answer is: B

B

mathematics

The average age of 20 men in the class is 16.6 years. Five new men join and the new average becomes 15.56 years. What was the average age of five new men?

[ "15.5", "15.4", "15.25", "15.3", "11.4" ]

Total age of 20 men = 16.6 x 20 = 332 Now, total age of 25 men = 389. Total age of five men added later = 389 - 332 = 57. Hence, the total average of five men = 57/5 = 11.4 ANSWER:E The answer is: E

E

mathematics

Lion, rat stay in jungle happily. Lion lies on: Mon, Tue, Wed. Rat lies on: Wed, Thurs , Sat. If lion says: I didn't lie yesterday. Rat says: I didn’t lie yesterday. So what day is today?

[ "Tuesday", "wednesday", "Thursday", "Friday", "Sunday" ]

Tuesday -- lion ll tell lie on tuesday lion is saying lie that he didn't lie sday [ again a lie... bcozzz lion ll say lie on monday also] Tuesday -- Rat ll not say lie on tuesday ANSWER:A The answer is: A

A

mathematics

Ram and Shakil run a race of 2000m. First Ram gives Shakil a start of 200m and beats him by 1 minute.Next Ram gives shakil a start of 6 min and is beaten by 1000 meters . Find the time in minutes in which Ram and Shakil can run the race seperately.

[ "12.18", "10.18", "10.12", "8.1", "8.2" ]

LET r be velocity of ram and s be the velocity of Shakil then (2000/r)=(1800/s)-60......(1) second case distance Shakil travel in 6 min=360s again equating time for both 1000/r=(2000-360s)/s.......(2) solving (1) &(2) we get s=20/6 putting value in first we get time =480sec=8min ANSWER:D The answer is: D

D

mathematics

If f(a)=4a-6, what is the value of (f(5a)-f(a))/2 ?

[ "12a-6", "10a+5", "5a/6", "4a-6", "20a+6" ]

f(a)=4a-6 f(5a) = 20a-6 (f(5a)-f(a))/2 = (20a-6+4a-6)/2 = 12a-6 Answer is The answer is: A

A

mathematics

In expressing a length 810472 km as nearly as possible with three significant digits, find the percentage error.

[ "0.034", "0.024", "0.352", "0.063", "0.026" ]

Error = (81.5 – 81.472)km = 0.028. Required percentage = [(0.028/81.472)*100]% = 0.034%. Answer A. The answer is: A

A

mathematics

In an apartment building that has 490 units, 4 out of every 7 units are currently rented, including 1/6 of the one-bedroom units. If, of the rented apartments, there is a 6:1 ratio of two-bedroom units to one-bedroom units, and the building only consists of two-bedroom and one-bedroom units, how many two-bedroom units are not rented?

[ "50", "70", "100", "105", "10" ]

Rented = 4/7*490 = 280. Rented two-bedroom = 6/7*280 = 240; Rented one-bedroom = 1/7*280 = 40 (or 280-240=40). Rented one-bedroom units are 1/5 of all one-bedroom: 1/6*{All one bedroom} = 40 --> {All one-bedroom} = 240. {All two-bedroom} = 490 - 240 = 250. Two-bedroom not rented = 250 - 240 = 10 Answer: E The answer is: E

E

mathematics

What is the sum of the greatest common factor and the lowest common multiple of 36 and 56?

[ "592", "520", "508", "560", "584" ]

Prime factorization of the given numbers 36= 2^2 * 3^2 56= 2^3 *7 Greatest common factor = 4 Lowest common multiple = 504 Sum = 4+ 504 = 508 Answer C The answer is: C

C

mathematics

When the integer k is divided by 7, the remainder is 1. Which of the following expressions below when divided by 7, will have a remainder of 5? I. 4k + 1 II. 6k + 6 III. 8k + 2

[ "I only", "II only", "III only", "I and II only", "I, II and III" ]

k = 7j + 1 4k + 1 = 28j + 4 + 1 = 28j + 5 6k + 6 = 42j + 6 + 6 = 42j + 7 + 5 8k + 2 = 56j + 8 + 2 = 56j + 7 + 3 The answer is D. The answer is: D

D

mathematics

The average salary of a person for the months of January, February, March and April is Rs.8000 and that for the months February, March, April and May is Rs.8500. If his salary for the month of May is Rs.6500, find his salary for the month of January?

[ "2177", "2876", "4500", "2981", "2711" ]

Sum of the salaries of the person for the months of January, February, March and April = 4 * 8000 = 32000 ----(1) Sum of the salaries of the person for the months of February, March, April and May = 4 * 8500 = 34000 ----(2) (2)-(1) i.e. May - Jan = 2000 Salary of May is Rs.6500 Salary of January = Rs.4500.Answer: C The answer is: C

C

mathematics

The cost of 2 benchs and 3 tables is Rs.1300. The cost of 3 benchs and 2 tables is Rs.1200. The cost of each table is more than that of each bench by?

[ "900", "200", "100", "400", "600" ]

C 100 2C + 3T = 1300 --- (1) 3C + 3T = 1200 --- (2) Subtracting 2nd from 1st, we get -C + T = 100 => T - C = 100 The answer is: C

C

mathematics

A person can row at 9 kmph and still water. He takes 3 1/2 hours to row from A to B and back. What is the distance between A and B if the speed of the stream is 1 kmph?

[ "16 km", "87 km", "89 km", "67 km", "20 km" ]

Let the distance between A and B be x km. Total time = x/(9 + 1) + x/(9 - 1) = 3.5 => x/10 + x/8 = 7/2 => (4x + 5x)/40 = 7/2 => x = 16 km. Answer:A The answer is: A

A

mathematics

A soccer team played 160 games and won 65 percent of them. How many games did it win?

[ "84", "94", "104", "114", "124" ]

65% of 160 =x 0.65*160 = x 104=x answer :C The answer is: C

C

mathematics

. In a certain city, 60 percent of the registered voters are Democrats and the rest are Republicans. In a mayoral race, if 70 percent of the registered voters who are Democrats and 20 percent of the registered voters who are Republicans are expected to vote for Candidate A, what percent of the registered voters are expected to vote for Candidate A ?

[ "50%", "53%", "54%", "55%", "57%" ]

Registered voters = 100 D = 60 R = 40 70% of D ( 60) = 42 20% of R ( 40 ) = 8 Total voter% of registered voters = 50 / 100 50% Ans A The answer is: A

A

mathematics

Birbal is a witty trader who trade of a mystical fruit grown far in north. He travels from one place to another with three sacks which can hold 30 fruits each. None of the sack can hold more than 30 fruits. On his way, he has to pass through thirty check points and at each check point, he has to give one fruit for each sack to the authorities. How many mystical fruits remain after he goes through all the thirty check points?

[ "23", "24", "25", "26", "27" ]

Solution: 25 Fruits Remember we told you that Birbal is a witty trader. So his sole motive is to get rid of the sacks as fast as he can. For the first sack: He must be able to fill fruits from one sack to other two sacks. Assume that he is able to do that after M check points. Now to find M, (Space in first sack) M + (Space in second sack) M = (Remaining fruits in Third Sack) 30 – M M = 10 Thus after 10 checkpoints, Birbal will be left with only 2 sacks containing 30 fruits each. Now he must get rid of the second sack. For that, he must fill the fruits from second sack to the first sack. Assume that he manages to do that after N checkpoints. (Space in First Sack) N = (Remaining fruits in second sack) 30 – N N = 15 Thus after he has crossed 25 checkpoints, he will be left be one sack with 30 fruits in it. He has to pass five more checkpoints where he will have to give five fruits and he will be left with twenty five fruits once he has crossed all thirty check points. Answer C The answer is: C

C

mathematics

For integers x and y, if 91x = 8y, which of the following must be true? I. y > x II. y/7 is an integer III. The cube root of x is an integer

[ "I only", "II only", "III only", "I and II", "II and III" ]

Given 91*x=8*y It can be equal when x = 8 or -8 and y = 91 or -91 So Statement (I) y < x if we take x = -8 and y =-91 but y > x if we take x = 8 and y = -91, so (I) is not true always Statement (2) in any case 91/7 or -91/7 is an integer that is 13 or -13. So it is true Statement (3) cube root of 8 or -8 is 2 and -2 respectively. So it is true always. answer is E The answer is: E

E

mathematics

How many positive integers arethere from 0 to 1000 that leave a remainder of 3 on division by 7 & a remainder of 2 on division by 4?

[ "30", "36", "38", "42", "46" ]

Number should be of the form 7n + 3 and 4m + 2. The LCM of 7 and 4 is 28. So, let us see what are the possible remainders when we divide this number by 28. A number of the form 7n + 3 can be written as 28K + 3 or 28k + 10 or 28 + 17 or 28k + 24. A number of the form 4m + 2 can be written as 28l + 2, 28l + 6, 28l + 10, 28l + 14, 28l + 18, 28l + 22, 28l + 26. For a detailed discussion on how we get to this, look at this post. Within these, the only common term is 28K + 10. The numbers in this sequence are 10, 38, 66.....990. We still need to figure out how many numbers are there in this sequence. We are going in steps of 28, so let us see if we can write these numbers in terms of 28p + r. 10 = 28 * 0 + 10 38 = 28 * 1 + 10 66 = 28 * 2 + 10 94 = 28 * 3 + 10 ........................... 990 = 28 * 35 + 10 There are 36 numbers in this sequence. Correct Answer: 36 B The answer is: B

B

mathematics

Two varieties of wheat - A and B costing Rs. 9 per kg and Rs. 15 per kg were mixed in the ratio 3 : 7. If 5 kg of the mixture is sold at 25% profit, find the profit made?

[ "Rs. 16.58", "Rs. 16.51", "Rs. 16.59", "Rs. 16.50", "Rs. 16.52" ]

Explanation: Let the quantities of A and B mixed be 3x kg and 7x kg. Cost of 3x kg of A = 9(3x) = Rs. 27x Cost of 7x kg of B = 15(7x) = Rs. 105x Cost of 10x kg of the mixture = 27x + 105x = Rs. 132x Cost of 5 kg of the mixture = 132x/10x (5) = Rs. 66 Profit made in selling 5 kg of the mixture = 25/100 (cost of 5 kg of the mixture) = 25/100 * 66 = Rs. 16.50 Answer:D The answer is: D

D

mathematics

The least number which should be added to 2497 so that the sum is exactly divisible by 5, 6, 4 and 3 is:

[ "21", "23", "26", "29", "30" ]

L.C.M. of 5, 6, 4 and 3 = 60. On dividing 2497 by 60, the remainder is 37. Number to be added = (60 - 37) = 23. answer :B The answer is: B

B

mathematics

A tank has 5 inlet pipes. Three pipes are narrow and two are wide. Each of the three narrow pipes works at 1/2 the rate of each of the wide pipes. All the pipes working together will take what fraction R of time taken by the two wide pipes working together to fill the tank?

[ "1/2", "2/3", "3/4", "3/7", "4/7" ]

I always plug in for these questions.. I find them easier Let 2 large pipes each work fill 10lts/hr small ones = 1/2*10 = 5 total 5 = 10+10+5+5+5 = 35 lts/hrs now assume the total capacity = 140 lts ( LCM of 20,35) Qn :All the pipes working together will take what fraction of time taken by the two wide pipes working together to fill the tank all working together will take 140/35 = 4 hrs two large pipes working will take 140/20 = 7 hrs hence ratio R= 4/7 = E The answer is: E

E

mathematics

On rainy mornings, Mo drinks exactly N cups of hot chocolate (assume that N is an integer). On mornings that are not rainy, Mo drinks exactly 2 cups of tea. Last week Mo drank a total of 16 cups of tea and hot chocolate together. If during that week Mo drank 4 more tea cups than hot chocolate cups, then how many rainy days were there last week?

[ "6", "3", "4", "5", "2" ]

T= the number of cups of tea C= the number of cups of hot chocolate T+C = 16 T-C=4 -> T= 10. C=6. Mo drinks 5 cups of tea a day then number of days that are not rainy = 10/2 = 5 So number of rainy days = 7-5 = 2 E is the answer. The answer is: E

E

mathematics

An empty pool being filled with water at a constant rate takes 7 hours to fill to 3/5 of its capacity. How much more time will it take to finish filling the pool?

[ "5 hr 30 min", "5 hr 20 min", "4 hr 40 min", "3 hr 12 min", "2 hr 40 min" ]

(3/5) of a pool/ 7 hours = 3/35 (the rate) (3 pools/35 hours) = (2/5* pool)/ x hours Cross multiply 3x = (2/5) 35 x = 4 2/3 2/3 of an hour = 40 minutes C The answer is: C

C

mathematics

If K is the sum of reciprocals of the consecutive integers from 33 to 38, inclusive, then K is closest in value to which of the following?

[ "1/12", "1/10", "1/8", "1/7", "1/4" ]

1/33 , 1/34 , 1/35 , 1/36 , 1/37 , 1/38 Hypothetically , assume all 6 Numbers to be 1/33 Hence sum of it would result in = 6/33 ( almost equals 1/6 , or slightly more than 1/6 - ) If all 6 nos were to be 1/38 ... Sum of which would result in 6/38 = 3/19 . Hence answer should lie between 1/6 and 1/7 (3/21) D i.e 1/7 The answer is: D

D

mathematics

Robert is travelling on his cycle and has calculated to reach point A at 2 P.M. if he travels at 10 kmph, he will reach there at 12 noon if he travels at 15 kmph. At what speed must he travel to reach A at 1 P.M.?

[ "9 km/hour", "10 km/hour", "11 km/hour", "12 km/hour", "None of these" ]

Explanation: We need to calculate the distance, then we can calculate the Ɵme and finally our answer. Lets solve this, Let the distance travelled by x km Time = Distance/Speed x10−x15=2[because, 2 pm - 12 noon = 2 hours]3x−2x=60x=60.Time=DistanceSpeedTime@10km/hr=6010=6hours So 2 P.M. - 6 = 8 A.M Robert starts at 8 A.M. He have to reach at 1 P.M. i.e, in 5 hours So, Speed = 60/5 = 12 km/hr Answer: D The answer is: D

D

mathematics

What are the number of ways to select 3 men and 2 women such that one man and one woman are always selected?

[ "12", "10", "30", "99", "123" ]

The number of ways to select three men and two women such that one man and one woman are always selected = Number of ways selecting two men and one woman from men and five women = ⁴C₂ * ⁵C₁ = (4 * 3)/(2 * 1) * 5 = 30 ways. Answer:C The answer is: C

C

mathematics

If you divide a number into 3 equal groups and then divide each group in half, you end up with 13. What number did you start with?

[ "76", "77", "78", "79", "None of these" ]

Solution: Suppose the start number is x Division into 3 equal groups is: x/3, and then in half is (x/3)/2 = 13 x/6 = 13 x = 13 * 6 = 78 Answer C The answer is: C

C

mathematics

A boy has six trousers and 13 shirts. In how many different ways can he select a trouser and a shirt?

[ "238 ways", "87 ways", "66 ways", "78 ways", "121 ways" ]

Explanation: The boy can select one trouser in six ways. The boy can select one shirt in 13 ways. The number of ways in which he can select one trouser and one shirt is 6 * 13 = 78 ways. Answer: D The answer is: D

D