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	Mike weighs twice as much as Mary. Mike's weight is 150% of Michelle's weight. Alan weighs 20% more than Charlie. Charlie weighs 160% of Mary's weight. Which of these 5 people weighs the highest?	[ "Mary", "Mike", "Michelle", "Alan", "Charlie" ]	Mary < Michelle < Mike Charlie < Alan Let x be Mary's weight. Mike's weight is 2x and Alan's weight is 1.2*1.6x = 1.92x. The answer is B. The answer is: B	B
mathematics	The value of (8x10^7)(8x10^8) is closest to which of the following?	[ "10^17", "10^14", "10^18", "10^19", "10^20" ]	multiplying these we get, 64 x 10^7 x 10^8 = 6.4 x 10^16 which is closer to 10^17 Answer: A The answer is: A	A
mathematics	Its festive time and all big companies are offering the big discount especially on iPhone whose price is staggering Rs. 65,000. Following is the offer from the three major companies in India. : Amazon offers Flat 65% discount : Flipkart offers 10% discount over and over again. : Snapdeal offers RS 42,000 off. Which is the best offer for you ?	[ "Flipkart", "Amazon", "Snapdeal", "All", "None of Above" ]	A Explanation: Flipkart : 22664, Amazon: 22750 and Snapdeal: 23000 SnapDeal discount : 65000 - 42000 = 23000 Amazon 65% discount : 35/100 * 65000 = 22750 Flipkart 10% recursive discount: After 1st 10% discount, Amount is 58500 After 2nd 10% discount, Amount is 52650 After 3rd 10% discount, Amount is 47385 After 4th 10% discount, Amount is 42646.5 After 5th 10% discount, Amount is 38381.85 After 6th 10% discount, Amount is 34543.665 After 7th 10% discount, Amount is 31089.2985 After 8th 10% discount, Amount is 27980.36865 After 9th 10% discount, Amount is 25182.331785 After 10th 10% discount, Amount is 22664.0986065 The answer is: A	A
mathematics	If a, b, and c are consecutive odd positive integers and a < b < c, which of the following could be equal to c - b - a+4 ?	[ "-2", "5", "-3", "-4", "-5" ]	let we put values. a=1, b=3, c=5 5-3-1=1 1+4 =5 Answer :B The answer is: B	B
mathematics	Find the value of sin 75° + sin 15° = ?	[ "0", "1/2", "1", "3/2", "2" ]	sin A + sin B = 2 sin [ (A + B) / 2 ] cos [ (A - B) / 2 ] =2 sin [ (75 +15) / 2 ] cos [ (75 - 15) / 2 ] =2 sin90cos60=21(1/2)=1 ANSWER:C The answer is: C	C
mathematics	In how many ways can the letters of the word REPEATED be arranged?	[ "1206", "1348", "6720", "3000", "3478" ]	REPEATED has 8 words, but E is repeated three times. Thus ways = 8! / 3! = 6720 ways C The answer is: C	C
mathematics	In the manufacture of a certain product, 7 percent of the units produced are defective and 4 percent of the defective units are shipped for sale. What percent of the units produced are defective units that are shipped for sale?	[ "0.125%", "0.28%", "0.8%", "1.25%", "2.0%" ]	Percent of defective produced = 7% Percent of the defective units that are shipped for sale = 4% Percent of units produced are defective units that are shipped for sale = (4/100)(7/100)100% = (28/10000)*100% = (28/100)% = .28 % Answer B The answer is: B	B
mathematics	David and Rachel are getting married. The extended family wants to have its picture taken, but David's father is unwilling to stand next to Rachel's mother. How many options does the photographer have to arrange the 6 family members in a row for the picture?	[ "9!", "9×8!", "4x5!", "10!/2!", "10!" ]	In how many ways David's father and Rachel's mother can stand together? Consider them as one unit: {F, M}. So, we'd have 9 units {F, M}, 1, 2, 3, 4, which can be arranged in 9! ways. David's father and Rachel's mother within their unit can be arranged in 2! ways. Therefore, David's father and Rachel's mother can stand together in 5!2! ways. Total - Restriction = = 6! - 5!2! = = 5!(6- 2!) = = 4*5!. Answer: C. The answer is: C	C
mathematics	Difference between the length &breadth of a rectangle is 23 m. If its perimeter is 206 m, then its area is?? We have: (l - b) = 23 and 2(l + b) = 206 or (l + b) = 103?	[ "2400 m^2", "2420 m^2", "2520 m^2", "2600 m^2", "2630 m^2" ]	Solving the two equations, we get: l = 63 and b = 40. Area = (l x b) = (63 x 40) m2 = 2520 m^2 C The answer is: C	C
mathematics	It is required to fix a pipe such that water flowing through it at a speed of 7 metres per minute fills a tank of capacity 1760 cubic metres in 10 minutes. The inner radius of the pipe should be :	[ "√2 m", "2 m", "1⁄2 m", "2√2 m", "None of these" ]	Let inner radius of the pipe be r. Then, 1760 = 22⁄7 × r2 × 7 × 10 or r2=1760/22×10=8 or r = 2√2 m Answer D The answer is: D	D
mathematics	A certain restaurant offers 6 different salads, 4 different main courses, and 7 different desserts. If customers choose one salad, one main course, and two different desserts for their meal, how many different meals are possible?	[ "260", "388", "436", "504", "520" ]	The number of possible choices for desserts is 7C2 = 21 The number of possible meals is 6421 = 504 The answer is D. The answer is: D	D
mathematics	George has 8 candies in a bag, 3 of which are sweet while the other 5 are sour. He pulls out 2 of the candies simultaneously, and at random. What is the probability that exactly one of the candies he picked is sour?	[ "2/8", "3/15", "2/28", "3/5", "15/28" ]	The probability is equal to the number of desired choices divided by the total number of possibilities. Probability = Favorable/Total Total = 8C2 = 87/2 = 28 Favorable: Pick 1 sour out of 3 sour AND pick 1 sweet out of 5 sweet. 3C15C1=3*5=15 P=15/28 When you use combination method, it is picking all possible cases and the order doesn't matter. Whereas, upon choosing probability method to solve, order matters. Thus, Total Probability: Probability of choosing sour candy first AND Probability of choosing sweet candy OR Probability of choosing sweet candy first AND Probability of choosing sour candy Answer: E The answer is: E	E
mathematics	If 6th March, 2005 is Monday, what was the day of the week on 6th March, 2004?	[ "Sunday", "Saturday", "Tuesday", "Wednesday", "Monday" ]	The year 2004 is a leap year. So, it has 2 odd days. But, Feb 2004 not included because we are calculating from March 2004 to March 2005. So it has 1 odd day only. The day on 6th March, 2005 will be 1 day beyond the day on 6th March, 2004. Given that, 6th March, 2005 is Monday. 6th March, 2004 is Sunday (1 day before to 6th March, 2005). Answer A The answer is: A	A
mathematics	How many odd 4-digit positive integers Q that are multiples of 5 can be formed without using the digit 3?	[ "648", "729", "900", "1296", "3240" ]	I choose A. Possible n° of 1st digit: 8 (0 can't be the first number, or else it wouldn't have 4 digits. 3 is exlcuded) Possible n° of 2nd digit: 9 (3 is excluded) Possible n° of 3rd digit: 9 (3 is excluded) Possible n° of 4th digit: 1 (a number is a multiple of 5 if it ends in 5 or 0, here we are asked for the odd numbers, hence the last digit can't be 0) So, Q=899*1=648 (A) The answer is: A	A
mathematics	A father said to his son, "I was as old as you are at the present at the time of your birth". If the father's age is 44 years now, the son's age five years back was?	[ "17years", "18years", "19years", "20years", "21years" ]	Let the son's present age be x years. Then, (44 - x) = x 2x = 44. x = 22. Son's age 5 years back (22 - 5) = 17 years. A) The answer is: A	A
mathematics	Set S consists of integers {2,3,4,5}. If two numbers are chosen from set S at random, what is the probability that the sum of 2 numbers is more than 5?	[ "5/6", "1/2", "2/3", "1/4", "2/7" ]	Number of ways you can choose 2 from 4 = 4C2 = 6 E = event of getting the 2 numbers is more than 5 = (2,4),(2,5),(3,4)(3,5),(4,5) = 5 probability = 5/6 Answer is A The answer is: A	A
mathematics	Last month, John rejected 0.7% of the products that he inspected and Jane rejected 0.8 percent of the products that she inspected. If total of 0.75 percent of the products produced last month were rejected, what fraction of the products did Jane inspect?	[ "1/6", "1/2", "5/8", "5/6", "15/16" ]	X - fraction of products Jane inspected (1 - X) - fraction of products John inspected 0.8(X) + 0.7(1-X) = 0.75 0.1X = 0.75 - 0.7 X = 0.05/0.1 X = 1/2 Therefore the answer is B: 1/2. The answer is: B	B
mathematics	A building is to be completed in 48 days. To meet the deadline 54 men were employed and were made to work for 10 hours a day. After 30 days 5/9th of the work was completed. How many more workers should be employed to meet the deadline if each workers are now made to work 8 hours a day?	[ "36", "55", "40", "45", "None of these" ]	Explanation : 54 men work 10 hours a day for 30 days and 5/9th of the work is completed. Now, let x workers be employed to work 8 hours a day for the rest 18 days to complete 4/9th of the work. M1D1T1W2 = M2D2T2W1 5430104/9 = x1885/9 x = 90 Hence, 36 more workers should be employed. Answer : A The answer is: A	A
mathematics	12 members were present at a board meeting. Each member shake hands with all of the other members before and after the meeting .How many hand shakes were there?	[ "237", "268", "132", "827", "261" ]	Explanation: In order to have a hand shake there must be two members. Therefore to select 2 out of 12 we have 12C2. This happens twice that is before and after the meeting Answer = 12C2 ×2 = 132 Answer: C The answer is: C	C
mathematics	what is the units digit of the expression 17^7-2?	[ "1", "2", "3", "7", "9" ]	7^1=7 7^2=49 7^3=343 7^4=1(last digit) 7^5=7(last digit) and the cycle repeats after every 4 powers Therefore, last digit of 17^7=3 3-2=1 Answer A The answer is: A	A
mathematics	A certain sum is invested at simple interest at 18% p.a. for two years instead of investing at 12% p.a. for the same time period. Therefore the interest received is more by Rs. 840. Find the sum?	[ "7000", "7029", "2778", "2800", "2791" ]	Let the sum be Rs. x. (x * 18 * 2)/100 - (x * 12 * 2)/100 = 840 => 36x/100 - 24x/100 =840 => 12x/100 = 840 => x = 7000.Answer:A The answer is: A	A
mathematics	The value of ((x – y)³ + (y - z)³ + (z – x)³)/(12 (x – y) (y – z) (z – x)) is equal to :	[ "0", "1/12", "1", "1/4", "1/3" ]	Since (x – y) + (y – z) + (z – x) = 0, so (x – y)³ + (y – z)³ + (z – x)³= 3 (x – y) (y – z) (z – x). (3 (x – y) (y – z) (z – x))/(12(x – y) (y – z) (z – x)) = 1/4. ANSWER:D The answer is: D	D
mathematics	If P is a prime number greater than 100, what is the remainder when P^2 is divided by 4.	[ "4", "Cannot be determined", "2", "3", "1" ]	take square of any prime number remainder will be 1 Ans E The answer is: E	E
mathematics	Three numbers are in the ratio of 2 : 3 : 4 and their L.C.M. is 300. What is their H.C.F.?	[ "20", "25", "30", "60", "75" ]	Let the numbers be 2x, 3x, and 4x. LCM of 2x, 3x and 4x is 12x. 12x = 300 x = 25 HCF of 2x, 3x and 4x = x = 25 The answer is B. The answer is: B	B
mathematics	A can do a piece of work in 30 days. He works at it for 5 days and then B finishes it in 20 days. In what time can A and B together it?	[ "13 1/7 days", "13 1/3 days", "13 1/8 days", "13 8/3 days", "12 1/3 days" ]	5/30 + 20/x = 1 x = 24 1/30 + 1/24 = 3/40 40/3 = 13 1/3 days Answer:B The answer is: B	B
mathematics	The mall charges 40 cents for the first hour of parking and $3 for each additional hour until the customer reaches 4 hours, after that the parking fee is $2 per hour. If Mr.Park parked his car in the mall for 7 hours and 30 minutes, how much is he going to pay?	[ "$6.8", "$12.", "$13.", "$14.5.", "$15." ]	0.40+22+12+0.40= $6.8 Answer : $6.8 The answer is: A	A
mathematics	If a and b are each greater than x and y, which of the following must be true? I. ab > xy II. \|a\| + \|b\| > \|x\| + \|y\| III.a + b > x + y	[ "I only", "II only", "I and II", "I and III", "I, II and III" ]	I. a + b > x + y. Since a and b are each greater than x and y, then the sum of a and b will also be greater than the sum of x and y. II. ab > xy. Not necessarily true, consider a = b = 0 and x = y = -1 --> ab = 0 < 1 = xy. III. \|a\| + \|b\| > \|x\| + \|y\|. Not necessarily true, consider a = b = 0 and x = y = -1 --> \|a\| + \|b\| = 0 < 2 = \|x\| + \|y\|. Answer: B. The answer is: B	B
mathematics	If each participant of a chess tournament plays exactly one game with each of the remaining participants, then 171 games will be played during the tournament. Find the number of participants.	[ "15", "16", "17", "18", "19" ]	Let P be the number of participants. PC2 = 171 (P)(P-1) = 342 = 19*18 P = 19 The answer is E. The answer is: E	E
mathematics	If 5^29 * 4^15 = 2 * 10^n, what is the value of n?	[ "11", "21", "22", "29", "32" ]	My attempt: 5^(29) * 4^(15) = 210^p 5^(29) 2 ^ (30) = 2 * (25)^p 5^(29) 2 ^ (30) = 2 * 2^(p) * 5^(p) 5^(29) * 2 ^ (30) = 2^(p+1) * 5^(p) => (p+1) = 30 => p = 29 Answer: 29 (D) The answer is: D	D
mathematics	John must arrange 2 different physics books and 3 different mathematics books on one shelf. If the first book on the leftmost side is a mathematics book and no physics book is next to another physics book. How many different arrangements exist?	[ "6", "12", "36", "120", "720" ]	First Place, is reserved for Math book. There are 3 Math books which can be arranged in3 ways Restriction comes into playhysics book cannot be together. Hence, the maththe physics books take alternate places Second Place, Physics Book - in 3 ways Third Place, Math Book - in 2 ways (only 2 books left) Fourth Place, Physics - in 2 ways (only 2 Physics book left) Rest two places can be arranged in one way only. Total no of ways = 32211 = 12 ways B The answer is: B	B
mathematics	If the sides of a triangle are 30 cm, 28 cm and 12 cm, what is its area?	[ "120 cm2", "112 cm2", "776 cm2", "666 cm2", "168 cm2" ]	The triangle with sides 30 cm, 28 cm and 12 cm is right angled, where the hypotenuse is 30 cm. Area of the triangle = 1/2 * 28 * 12 = 168 cm2 Answer: E The answer is: E	E
mathematics	If a^5 ≤ a, which of the following must be true? I. –1 ≤ a ≤ 0 II. a=0 III. 0 ≤ a ≤ 1	[ "None of the above", "I only", "II only", "III only", "I and III only" ]	The trick here is more on the answer choices. Look at I II and III. all are right (pick out some numbers). Therefore I was totally confused because non of the answers had the right answer (I II and III) I finally chose D, but hesitate between A and D quite a long time... This is a tricky tricky question, since it takes into consideration that the answers are correct but they do not cover all the POSSIBLE answers. Therefore it is A. The answer is: A	A
mathematics	A can do a piece of work in 20 days. B in 15 days A and C in 12 days. In how many days can A finish the work if he is assisted by B on one day and C on the next, alternately?	[ "2 days", "5 days", "8 days", "7 days", "9 days" ]	C 8 days A + B = 1/20 + 1/15 = 7/60 A + C = 1/20 + 1/12 = 8/60 7/60 + 8/60 = 15/60 = 1/4 4 days * 2 = 8 days The answer is: C	C
mathematics	A shopkeeper loses 15%,if an article is sold for Rs. 102. What should be the selling price of the article to gain 20%?	[ "128", "144", "176", "186", "111" ]	Explanation: Given that SP = Rs. 102 and loss = 15% CP = [100(SP)]/(100 - l%) = (100 * 102)/85 = 20 * 6 = Rs. 120. To get 20% profit, New SP = [(100 + p%)CP]/100 = (120 * 120)/100 = Rs. 144 Answer:B The answer is: B	B
mathematics	The letters of the word 'SURITE' are written in all possible orders and these words are written in alphabetical order. Then what is the rank of the word 'SURITI'	[ "- 236", "- 245", "- 307", "- 315", "- 475" ]	Total Number of Words = 6! = 720 [(number of characters)/(repeating group )!] After S, we have T and U. Number of words starting with T = 5! = 120 Number of words starting with U = 5! = 120 So any word starting with S will have rank < 720 - 120(for Us) - 120(for Ts) = 480 Only option A < 480, so Answer is E The answer is: E	E
mathematics	Machine A and machine B are each used to manufacture 880 sprockets. It takes machine A 10 hours longer to produce 880 sprockets than machine B. Machine B produces 10% more sprockets per hour than machine A. How many sprockets per hour does machineAproduce?	[ "6", "6.6", "8.8", "100", "110" ]	time taken by B = t time taken by A = t+10 qty produced by A = q qty produced by B = 1.1 q for B: t(1.1q) =880 qt=800 for A: (t+10)(q) = 880 qt+10q=880 800+10q=880 q=8 so A can produce 8/hour. then B can produce = 8(1.1)=8.8/hour. C The answer is: C	C
mathematics	If P(A) = 2/15, P(B) = 4/15, and P(A âˆª B) = 12/15 Find P(B\|A)	[ "1/2", "2/3", "3/2", "4/5", "6" ]	P(B\|A) = P(A âˆª B)/P(A) P(B\|A) = (12/15)/(2/15) = 6. E The answer is: E	E
mathematics	A cashier mentally reversed the digits of one customer's correct amount of change and thus gave the customer an incorrect amount of change. If the cash register contained 27 cents more than it should have as a result of this error, which of the following could have been the correct amount of change in cents?	[ "14", "45", "54", "65", "52" ]	Just check the answers and reverse the numbers until you get 27. 52 - 25 = 27 Answer E The answer is: E	E
mathematics	An amount of Rs. 100000 is invested in two types of shares. The first yields an interest of 9% p.a and the second, 11% p.a. If the total interest at the end of one year is 9 2/3 %, then the amount invested in each share was?	[ "23777", "35000", "29977", "26777", "19871" ]	Let the sum invested at 9% be Rs. x and that invested at 11% be Rs. (100000 - x). Then, (x * 9 * 1)/100 + [(100000 - x) * 11 * 1]/100 = (100000 * 29/3 * 1/100) (9x + 1100000 - 11x)/100 = 29000/3 = 9700 (9x + 1100000 - 11x) = 970000 x = 65000 Sum invested at 9% = Rs. 65000 Sum invested at 11% = Rs. (100000 - 65000) = Rs. 35000. Answer: B The answer is: B	B
mathematics	Hal bought walnuts at 5 for $1 and apples at 4 for $1.He spent a total of $19.50 . He sells both at 20 for $5 and as a result gains $3 .How many walnuts did Hal buy ?	[ "50", "45", "60", "80", "55" ]	Let's start with the concrete information: He buys everything for $19.50 and earns $3 after selling so he sells everything for $22.50 (= 2250 cents). He sells each item for 5/20 = 25 cents so in all he sells 2250/25 = 90 items Cost of each walnut = 1/5 = $.2 = 20 cents Cost of each apple = 1/4 = $.25 = 25 cents Now we have one equation to solve: 20w + 25(90 - w) = 1950 (w is the number of walnuts he buys) 4w + 5(90 - w) = 390 w = 60 Answer (C) The answer is: C	C
mathematics	A survey was sent to 80 customers, 9 of whom responded. Then the survey was redesigned and sent to another 63 customers, 12 of whom responded. By approximately what percent did the response rate increase from the original survey to the redesigned survey?	[ "2%", "5%", "14%", "28%", "69%" ]	Rate of first survey = 9/80 Rate of second survey = 12/63 % Response rate increase (12/63-9/80)/(9/80) = 69% Answer is E = 69% The answer is: E	E
mathematics	If the average marks of three batches of 55, 60 and 45 students respectively is 50, 55, 60, then the average marks of all the students is	[ "54.48", "54.68", "54.6", "54.58", "None of these" ]	Explanation: (55×50)+(60×55)+(45×60)55+60+45 8750160=54.68 Answer: Option B The answer is: B	B
mathematics	From a pack of cards two cards are drawn one after the other, with replacement. The probability that the first is a red card and the second is a king is ?	[ "1/26", "1/07", "1/22", "1/29", "1/21" ]	Let E1 be the event of drawing a red card. Let E2 be the event of drawing a king . P(E1 ∩ E2) = P(E1) . P(E2) (As E1 and E2 are independent) = 1/2 * 1/13 = 1/26 Answer:A The answer is: A	A
mathematics	An bus covers a certain distance at a speed of 140 kmph in 5 hours. To cover the samedistance in 1hr, it must travel at a speed of?	[ "520 km/hr", "640 km/hr", "656 km/hr", "731 km/hr", "700 km/hr" ]	Distance = (140 x 5) = 700 km. Required speed = 700 km/hr. E The answer is: E	E
mathematics	The current of a stream at 1 kmph. A motor boat goes 35 km upstream and back to the starting point in 12 hours. The speed of the motor boat in still water is?	[ "6", "9", "8", "3", "1" ]	S = 1 M = x DS = x + 1 US = x - 1 35/(x + 1) + 35/(x - 1) = 12 x = 6 Answer: A The answer is: A	A
mathematics	If two numbers are in the ratio 2:3. If 10 is added to both of the numbers then the ratio becomes 3:4 then find the smallest number?	[ "10", "20", "24", "26", "29" ]	2:3 2x + 10 : 3x + 10 = 3 : 4 4[2x + 10] = 3[3x + 10] 8x + 40 = 9x + 30 9x - 8x = 40 - 30 x = 10 Then smallest number is = 2 2x = 20 Short cut method: a:b = 2:3 c:d = 3:4 1.Cross multiplication with both ratios a * d ~ b * c = 2 * 4 ~ 3 * 3 = 8 ~ 9 = 1 2. If 10 is added both the number means 10 * 3 = 30 and 10 * 4 = 40, Then 30 ~ 40 = 10 ===> 1 -----> 10 ===> 2 -----> 20 B The answer is: B	B
mathematics	A train overtakes 2 girls who are walking inthe opposite direction in which the train is going at the rate of 3 km/hour & 6km/hour and passes them completely in 36sec & 30 sec respectively. Find the length of the train is?	[ "120 m", "130 m", "150 m", "200 m", "250 m" ]	Let the length of the train e x meter, and let the speed of train be y km/h, then \inline x=\left ( y+3 \right )\frac{5}{18}\times 36 ........(1) and \inline x=\left ( y+6\right )\frac{5}{18}\times 30 ........(2) From eq (1) and (2), we get \inline (y+3)\times 36 = ( y+6)\times 30 y = 12 km/h \inline \therefore \inline x=(y+3)\times \frac{5}{18}\times 36 x= 150 m C The answer is: C	C
mathematics	If a man reduces the selling price of a fan from Rs. 420 to Rs. 402, his loss increases by 3%. The cost price of the fan is :	[ "Rs.600", "Rs.650", "Rs.475", "Rs.525", "None of these" ]	Explanation : Solution: let C.P. be Rs. X. then, 3% of x = (420-402) =18 => 3x/100 = 18 => x =Rs.600. Answer : A The answer is: A	A
mathematics	A pump can fill a tank with a water in 2 hours. Because of a leak, it took 3 hours to fill the tank. The leak can drain all the water of the full tank in how many hours?	[ "2", "3", "4", "5", "6" ]	The rate of the pump + leak = 1/3 1/2 - leak's rate = 1/3 leak's rate = 1/2 - 1/3 = 1/6 The leak will empty the tank in 6 hours. The answer is E. The answer is: E	E
mathematics	A and B started a partnership business investing some amount in the ratio of 4 : 5. C joined then after six months with an amount equal to that of B. In what proportion should the profit at the end of one year be distributed among A, B and C?	[ "4 : 9 : 8", "5 : 7 : 4", "6 : 10 : 5", "7 : 9: 4", "8 : 10 : 5" ]	Let the initial investments of A and B be 4x and 5x. A : B : C = (4x x 12) : (5x x 12) : (5x x 6) = 48 : 60 : 30 = 8 : 10 : 5. ANSWER :E The answer is: E	E
mathematics	Today John, who is 38 years old, and his daughter, who is 13 years old, celebrate their birthdays. How many years will pass before John’s age is twice his daughter’s age?	[ "13", "14", "15", "16", "12" ]	Forget conventional ways of solving math questions. In PS, IVY approach is the easiest and quickest way to find the answer. After x years passes John’s age will be (38+x) years old, and his daughter’s age will be (13+x) years old. Since the John’s age is twice his daughter’s age (38+x)= 2 * (13+x) ---> 38+x=26+2x ---> x= 12 The answer is (E). The answer is: E	E
mathematics	On my sister's birthday, she was 132 cm in height, having grown 10% since the year before. How tall was she the previous year?	[ "130 cm", "126 cm", "120 cm", "116 cm", "112 cm" ]	Let the previous year's height be x. 1.1x = 132 x = 120 The answer is C. The answer is: C	C
mathematics	A seller has 1000kg of rice part of which he sells at 8% profit and the rest at 18% profit. He gains 14%. The quantity sold at 18% profit is?	[ "200 kg", "300 kg", "400 kg", "600 kg", "800 kg" ]	By rule of alligation, Profit% by selling 1st part Profit% by selling 2nd part 8 18 Net % profit 14 18-14=4 14-8=6 => Quantity of part1 : Quantity of part2 = 4 : 6 = 2 : 3 Total quantity is given as 1000 kg. So quantity of part2 (quantity sold at 18% profit) =1000×35 = 600 kg D The answer is: D	D
mathematics	The number 0.5 is how much greater than 1/3 ?	[ "1/6", "2/10", "1/50", "1/500", "2/500" ]	let x be the difference then .5-1/3=x 5/10-1/3=x x=1/6 ans A The answer is: A	A
mathematics	A train running at the speed of 60 km/hr crosses a pole in 9 seconds. What is the length of the train?	[ "277", "266", "288", "150", "332" ]	Speed=(60 * 5/18) m/sec = (50/3) m/sec Length of the train = (Speed x Time) = (50/3 * 9) m = 150 m . Answer: D The answer is: D	D
mathematics	Suresh started a business with Rs.20,000. Kiran joined him after 4 months with Rs.30,000. After 2 more months, Suresh withdrew Rs.5,000 of his capital and 2 more months later, Kiran brought in Rs.20,000 more. What should be the ratio in which they should share their profits at the end of the year?	[ "17:12", "12:17", "21:32", "32:21", "17:32" ]	Here capital is not the same. Suresh invested 20000 for initial 6 months and 15000 for the next 6 months. Hence his term of ratio =(20000×6+15000×6) Kiran invested Rs.30000 for 4 months and Rs.50000 for next 4 months. Hence his term of ratio =(30000×4+50000×4) Suresh : Kiran =(20000×6+15000×6) :(30000×4+50000×4) =(20×6+15×6):(30×4+50×4)=(20×3+15×3):(30×2:50×2) =105:160=21:32 Answer is C. The answer is: C	C
mathematics	A wire in the form of a circle of radius 3.5 m is bent in the form of a rectangule, whose length and breadth are in the ratio of 6 : 5. What is the area of the rectangle?	[ "19 cm2", "30 cm2", "17 cm2", "18 cm2", "12 cm2" ]	The circumference of the circle is equal to the permeter of the rectangle. Let l = 6x and b = 5x 2(6x + 5x) = 2 * 22/7 * 3.5 => x = 1 Therefore l = 6 cm and b = 5 cm Area of the rectangle = 6 * 5 = 30 cm2 Answer:B The answer is: B	B
mathematics	The length of a rectangular plot is thrice its breadth. If the area of the rectangular plot is 867 sq m, then what is the breadth of the rectangular plot?	[ "12", "17", "10", "12", "19" ]	Let the breadth of the plot be b m. Length of the plot = 3 b m (3b)(b) = 867 3b2 = 867 b2 = 289 = 172 (b > 0) b = 17 m. Answer:B The answer is: B	B
mathematics	There are 4 more women than there are men on a local co-ed softball team. If there are a total of 20 players on the team, what is the ratio of men to women?	[ "10/16", "6/16", "4/16", "6/10", "8/12" ]	w = m+4 w+m = 20 m+4+m = 20 2m = 16 m = 8 w = 12 ratio:8:12 Ans: E The answer is: E	E
mathematics	Efficiency with which Adam and Mike work is in the ratio 2:1. How much time will they, working together, take to complete a job which Adam alone could have done in 10 days?	[ "15 days", "20 days", "6 days", "6 1â„3 days", "None of these" ]	Ratio of times taken by Adam and Mike = 100 : 200 = 1 : 2. Suppose Mike takes x days to do the work. Then, 1 : 2 : : 10 : x â‡’ x = (10Ã—2)/1 â‡’ x = 20 Adamâ€™s 1 dayâ€™s work = 1â„10; Mikeâ€™s 1 days work = 1â„20 (Adam + Mike)â€™s 1 dayâ€™s work = (1â„10 + 1â„20) = 3â„20 âˆ´ Adam and Mike together can complete the job in 20â„3 days or 6 2â„3 days. Answer E The answer is: E	E
mathematics	Two trains of equal length are running on parallel lines in the same directions at 46km/hr. and 36km/hr. The faster trains pass the slower train in 72 seconds. The length of each train is:	[ "82m", "50m", "72m", "100m", "None of these" ]	Explanation: The relative speed of train is 46-36 = 10 Km/hr = (10 X 5) / 18 = 25/9 m/s10×518=259m/s In 72 secs the total distance traveled is 72x25/9 = 200 m. Therefore the length of each train is = 200/2 = 100 m. Answer D The answer is: D	D
mathematics	A train running at a speed of 60 kmph crosses a pole in 6 seconds.What is the length of the train?	[ "120 m", "180 m", "100 m", "150 m", "160 m" ]	60 kmph=50/3 m/sec 50/3*6=100 m ANSWER:C The answer is: C	C
mathematics	The ratio of ducks and frogs in a pond is 37 : 39 respectively. The average number of ducks and frogs in the pond is 132. What is the number of frogs in the pond ?	[ "148", "134", "156", "144", "None" ]	Solution: Ratio of Ducks and Frogs in Pond, = 37 : 39. Average of Ducks and Frogs in Pond, = 132. So, total number of Ducks and Frogs in the Pond, = 2* 132 = 262. Therefore, Number of Frogs, = (262*39)/76 = 134. Answer: Option B The answer is: B	B
mathematics	Excluding stoppages, the speed of a bus is 80 km/hr and including stoppages, it is 70 km/hr. For how many minutes does the bus stop per hour?	[ "11 min", "10 min", "8 min", "6 min", "5 min" ]	Due to stoppages, it covers 10 km less. Time taken to cover 10 km = 10/80 * 60 = 8 min. Answer:C The answer is: C	C
mathematics	1,3,5,7,9,..50 find term of sequnce	[ "1234", "1456", "1456", "1678", "2500" ]	This is an arithmetic progression, and we can write down a=1a=1 ,d=2d=2 , n=50n=50 . We now use the formula, so that Sn=12n(2a+(n−1)l)Sn=12n(2a+(n−1)l) S50=12×50×(2×1+(50−1)×2)S50=12×50×(2×1+(50−1)×2) =25×(2+49×2)=25×(2+49×2) =25×(2+98)=25×(2+98) =2500=2500 . E The answer is: E	E
mathematics	Integer X represents the product of all integers between 1 to 24 (inclusive). The smallest prime factor of (x+1) must be	[ "Between 1 to 10", "Between 11 to 15", "Between 15 to 20", "Between 20 to 25", "Greater than 24" ]	Answer = E = Greater than 24 This problem is asking smallest prime factor of (24!+1) 25! already have there prime factors 2,3,5,7,11,13.......... so on upto 23 (1 cannot be considered prime factor) Just adding 1 to 24! will remove all the factors stated above; so the smallest possible prime factor has to be greater than 24 Answer = E The answer is: E	E
mathematics	You have been given a physical balance and 7 weights of 52, 50, 48, 44, 45, 46 and 78 kgs. Keeping weights on one pan and object on the other, what is the maximum you can weigh less than 183 kgs.	[ "180", "181", "182", "178", "168" ]	add the max weights 52+50+78=180 ANSWER:A The answer is: A	A
mathematics	Three competing juice makers conducted a blind taste test with mall shoppers. The shoppers could choose to taste any number of the three brands of juices but had to select at least one juice that they liked. If 100 shoppers liked brand J, 200 shoppers liked brand K, 700 shoppers liked brand L, 250 shoppers liked exactly 2 juices, and 50 shoppers liked all three juices, how many shoppers took the taste test?	[ "1,300", "1,000", "900", "700", "650" ]	Given: Atleast 1 juice was liked by the participants. --> Neither = 0 Assume, I -->No overlap between the sets II --> Overlap between 2 sets III --> Overlap between 3 sets I + 2(II) + 3(III) = 100 + 200 + 700 I + 2(250) + 3(50) = 1000 I = 350 Total number of shoppers who took the taste test = I + II + III = 350 + 250 + 50 = 650 Answer: E The answer is: E	E
mathematics	An gun can take a maximum of four shotsat an enemyplane moving away from it. The probability of hitting the plane at the 1st, 2nd, third and 4th shots are 1.4, 1.3, 1.2 & 1.1 respectively. What is the probability that the plane is hit when all the four shots are fired?	[ "0.6976", "0.7893", "0.8212", "0.7541", "0.9847" ]	Required probability: =(0.4×0.7×0.8×0.9)+(0.6×0.3×0.8×0.9)+(0.6×0.7×0.2×0.9)+(0.6×0.7×0.8×0.1)+(0.4×0.3×0.8×0.9)+(0.4×0.7×0.2×0.9)+(0.4×0.7×0.8×0.1)+(0.6×0.3×0.2×0.9)+(0.6×0.3×0.8×0.1)+(0.6×0.7×0.2×0.1)+(0.4×0.3×0.2×0.9)+(0.6×0.3×0.2×0.1)+(0.4×0.3×0.8×0.1)+(0.4×0.7×0.2×0.1)+(0.4×0.3×0.2×0.1)=(0.4×0.7×0.8×0.9)+(0.6×0.3×0.8×0.9)+(0.6×0.7×0.2×0.9)+(0.6×0.7×0.8×0.1)+(0.4×0.3×0.8×0.9)+(0.4×0.7×0.2×0.9)+(0.4×0.7×0.8×0.1)+(0.6×0.3×0.2×0.9)+(0.6×0.3×0.8×0.1)+(0.6×0.7×0.2×0.1)+(0.4×0.3×0.2×0.9)+(0.6×0.3×0.2×0.1)+(0.4×0.3×0.8×0.1)+(0.4×0.7×0.2×0.1)+(0.4×0.3×0.2×0.1) =0.2016+0.1296+0.756+0.336+0.864+0.504+0.224+0.324+0.144+0.0084+0.0216+0.0036+0.0096+0.0056+0.002=0.2016+0.1296+0.756+0.336+0.864+0.504+0.224+0.324+0.144+0.0084+0.0216+0.0036+0.0096+0.0056+0.002 =0.6976=0.6976 Edit: Thank you Vaibhav for providing an alternative method. Alternate Method: probability that the plane is hit when all the four shots are fired, P=1−probability of not hitting the targetP=1−probability of not hitting the target =1−(0.6×0.7×0.8×0.9)=1−(0.6×0.7×0.8×0.9) =1−0.3024=1−0.3024 =0.6976 A The answer is: A	A
mathematics	What is the remainder when 6990990900032 is divided by 32 ?	[ "5", "0", "4", "2", "3" ]	Though i was unaware of the divisibility test for 32 but i guessed the pattern!! divisibility rule for 4- last two digits must be divisible by 4 divisibility rule for 8- last three digits must be divisible by 8 similarly, divisibility rule for 32 - last five digits must be divisible by 32 Hence, Ans B The answer is: B	B
mathematics	If x and y are positive integers and 12x=21y what is the least possible value of xy?	[ "9", "28", "63", "84", "252" ]	12x=21y => x/y = 7/4 => 4x=7y 4(3)=7(3) => x*y=9 A The answer is: A	A
mathematics	A train running at the speed of 60 km/hr crosses a pole in 12 seconds. What is the length of the train?	[ "186 m", "176 m", "300 m", "150 m", "200 m" ]	Speed=(60 * 5/18) m/sec = (50/3) m/sec Length of the train = (Speed x Time) = (50/3 * 12) m = 200 m. Answer: E The answer is: E	E
mathematics	At a restaurant, glasses are stored in two different-sized boxes. One box contains 12 glasses, and the other contains 16 glasses. If the average number of glasses per box is 15, and there are 16 more of the larger boxes, what is the total number of glasses E at the restaurant? (Assume that all boxes are filled to capacity.)	[ "96", "240", "E=256", "E=384", "E=480" ]	Most Test Takers would recognize thesystemof equations in this prompt and just do algebra to get to the solution (and that's fine). The wording of the prompt and the 'spread' of the answer choices actually provide an interesting 'brute force' shortcut that you can take advantage of to eliminate the 4 wrong answers.... We're told that there are 2 types of boxes: those that hold 12 glasses and those that hold 16 glasses. Since the AVERAGE number of boxes is 15, we know that there MUST be at least some of each. We're also told that that there are 16 MORE of the larger boxes. This means, at the minimum, we have... 1 small box and 17 large boxes = 1(12) + 17(16) = 12 + 272 = 284 glasses at the MINIMUM Since the question asks for the total number of glasses, we can now eliminate Answers A, B and C.... The difference in the number of boxes MUST be 16 though, so we could have.... 2 small boxes and 18 large boxes 3 small boxes and 19 large boxes etc. With every additional small box + large box that we add, we add 12+16= 28 MORE glasses. Thus, we can justadd 28suntil we hit the correct answer.... 284+28 = 312 312+28 = 340 340+28 = 368 368+28 = 396 At this point, we've 'gone past' Answer D, so the correct answer MUST be Answer E.....But here's the proof.... 396+28 = 424 424+28 = 452 452+28 = 480 Final Answer: E The answer is: E	E
mathematics	A local bank that has 12 branches uses a two-digit code to represent each of its branches. The same integer can be used for both digits of a code, and a pair of two-digit numbers that are the reverse of each other (such as 17 and 71) are considered as two separate codes. What is the fewest number of different integers required for the 12 codes?	[ "3", "4", "12 ( 2 integers 4 codes)", "6", "7" ]	Pick any two integer. Integers: 12 Code: 11, 12, 21, 22 = 4 Codes Add one more integer: 3 13, 31, 33, 23, 32 = 5 Codes Add one more integer: 4 44, 14, 41, 24, 42, 34, 43 = 7 Codes Total = 16 Codes. Enough. Answer: C 4 integers create 12 codes. The answer is: C	C
mathematics	Cars emerging from a motorway arrive at a junction that splits the road into two separate lanes. The number of cars per hour that continue in either lane is constant. If 7 cars per hour were diverted from the left lane to the right lane, the number of cars entering the right lane per hour would be twice as big as the number of cars entering the left lane per hour. Alternatively, if 7 cars per hour were diverted from the right lane to the left lane, the number of cars entering the left lane per hour would be four times as great as the number of cars entering the right lane per hour. How many cars enter the left lane per hour?	[ "21", "18", "17", "19", "28" ]	as per question 7 cars diverted from left lane to right lane. Thus we get equation R+7=2(L-7) as per question 7 cars diverted from right lane to left lane .thus we get equation L+7=4(R-7) by solving two equation i.e R +7 =2L-14 OR. R =2L -21 AND L+7= 4R -28 OR L= 4R -35 BY SOLVING WE GET L= 4( 2L -21) -35 OR L= 8L -84-35 OR 119 =7L THUS L =17 C The answer is: C	C
mathematics	Find the fraction which has the same ratio to 2/6 that 3/4 has to 1/2	[ "1/2", "2/5", "6/8", "9/4", "7/5" ]	P : 2/6 = 3/4 : 1/2 As the product of the means is equal to the product of the extremes. P1/2 = 2/6 3/4 P*1/2 = 6/24 P = 1/2 => P = 1/2 ANSWER:A The answer is: A	A
mathematics	Workers at a campaign office have 2000 fliers to send out. If they send out 1/10 of them in the morning and 1/4 of the remaining ones out during the afternoon, how many are left for the next day?	[ "300", "1350", "1100", "1200", "1900" ]	(1/10)2000 = 200 Remaining = 2000-200 = 1800 (1/4) of remaining = (1/4)1800 = 450 Remaining now = 1800-450 = 1350 Answer: Option B The answer is: B	B
mathematics	a batmans runs just before the last match of the season adds up750 in his last two innings his scores only 6 scores and his avg drop by 2 fond his final avg of the season?	[ "21", "22", "23", "24", "25" ]	Formula for this question is 6 = 2avg-2(N+2) 6 = 2(750/n) - 2(n+2) n*n+5n-750 = 0 n= 25 so final ans 23 ANSWER:C The answer is: C	C
mathematics	The speed of a train is 70 kmph excluding stoppages and including stoppages it is 63 kmph. Of how many minutes does the train stop per hour?	[ "3", "6", "7", "9", "14" ]	Explanation: T = 7/70 * 60 = 6 Answer: Option B The answer is: B	B
mathematics	An bus covers a certain distance at a speed of 240 kmph in 5 hours. To cover the samedistance in 1hr, it must travel at a speed of?	[ "520 km/hr", "640 km/hr", "656 km/hr", "731 km/hr", "720 km/hr" ]	Distance = (240 x 5) = 1200 km. Speed = Distance/Time Speed = 1200/(5/3) km/hr. [We can write 1 hours as 5/3 hours] Required speed = 1200 x 3 km/hr = 720 km/hr. 5 E The answer is: E	E
mathematics	The cash realised on selling a 14% stock is Rs.106.25, brokerage being 1/4% is	[ "123", "106", "100", "156", "240" ]	Explanation: Cash realised= Rs. (106.25 - 0.25) = Rs. 106. Answer: B The answer is: B	B
mathematics	Two numbers are in the ratio 3:5. If 9 be subtracted from each, they are in the ratio of 9:17. The first number is?	[ "36", "67", "87", "56", "51" ]	(3x-9):(5x-9) = 9:17 x = 12 => 3x = 36 Answer:A The answer is: A	A
mathematics	What will come in place of the x in the following Number series? 46080, 3840, 384, 48, 8, 2, x	[ "1", "3", "5", "6", "7" ]	46080 /12 = 3840 3840 /10 = 384 384 /8 = 48 48 /6 = 8 8/4 = 2 2 /2 = 1 A The answer is: A	A
mathematics	How many bricks, each measuring 25 cm x 11.25 cm x 6 cm, will be needed to build a wall of 8.5 m x 6 m x 22.5 cm?	[ "6400", "6410", "6440", "6500", "6800" ]	Number of bricks = Volume of Wall/Volume of Bricks =850x600x22.5/25x11.25x6= = 6800 answer :E The answer is: E	E
mathematics	2 chairs and 1 table cost $110. 4 chairs and 1 table cost $166. How much does one chair cost?	[ "26", "56", "110", "28", "54" ]	Let the cost of 1 chair = x, let the cost of 1 table = y 2x + y = 110 y = 110 - 2x Again, 4x + y = 166 4x + (110 - 2x) = 166 4x + 110 - 2x = 166 2x + 110 = 166 2x = 56 x = 28 Answer: D The answer is: D	D
mathematics	Sekar started a business investing Rs.25,000 in 1999. In 2000, he invested an additional amount of Rs.10,000 and Rajeev joined him with an amount of Rs.35,000. In 2001, Sekar invested another additional amount of Rs.10,000 and Jatin joined them with an amount of Rs.35,000. What will be Rajeev's share in the profit of Rs.2,40,000 earned at the end of 3 years from the start of the business in 1999?	[ "Rs.45,000", "Rs.80,000", "Rs.70,000", "Rs.75,000", "none" ]	Solution Sekar:Rajeev:Jatin= (25000×12+35000×12+45000×12):(35000×24) : (35000×12) = 1260000 : 840000 : 420000 = 3 : 2 : 1. Rajeev's share =Rs.(240000×2/6) = Rs.80000. Answer B The answer is: B	B
mathematics	The list price of an article is Rs.65. A customer pays Rs.56.16 for it. He was given two successive discounts, one of them being 10%. The other discount is?	[ "8%", "4%", "6%", "3%", "1%" ]	65(90/100)((100-x)/100) = 56.16 x = 4% Answer: B The answer is: B	B
mathematics	In a group of 24 students, each student is registered for at least one of three classes – History, Math and English. 15 students are registered for History, 15 students are registered for Math, and 20 students are registered for English. If only three students are registered for all three classes, how many students are registered for exactly two classes?	[ "13", "10", "9", "20", "7" ]	Each student is registered forat least one of three classesmeans thatthere are no students who are registered for none of the classes. Total = {people in group A} + {people in group B} + {people in group C} - {people in exactly 2 groups} - 2{people in exactly 3 groups} + {people in none of the groups}: 24 = 15 + 15 + 20 - {people in exactly 2 groups} - 23 + 0-->{people in exactly 2 groups}=20 Answer: D The answer is: D	D
mathematics	Tough and Tricky questions: Combinations. Five contestants representing four different countries advance to the finals of a fencing championship. Assuming all competitors have an equal chance of winning, how many possibilities are there with respect to how a first-place and second-place medal can be awarded?	[ "6", "7", "12", "15", "24" ]	Four contestants representing four different countries advance to the finals of a fencing championship. Assuming all competitors have an equal chance of winning, how many possibilities are there with respect to how a first-place and second-place medal can be awarded? We have 2 slots to be filled using 5 contestants:5 options for slot13 option for slot2 = 5 3 = 15 Ans. D) 15 The answer is: D	D
mathematics	If the average (arithmetic mean) of a list of numbers is 12 and the standard deviation of that list of numbers is 1.3, then which of the following numbers is more than two standard deviations from the mean? I. 13.7 II. 12.3 III. 9.3	[ "I only", "I and II only", "II only", "III only", "I and III only" ]	Mean = 12 SD = 1.3 2 SD above mean = 12+21.3 = 14.6 2 SD below mean = 12-21.3 = 9.4 12.3 and 13.7 lies in the range of 2SD from mean Answer: Option D The answer is: D	D
mathematics	If the length of an edge of cube P is twice the length of an edge of cube Q, what is the ratio of the volume of cube Q to the volume of cube P?	[ "1/8", "1/4", "1/3", "1/7", "1/9" ]	The length of cube Q = 1; The length of cube P = 2; The ratio of the volume of cube Q to the volume of cube P = 1^3/2^3 = 1/8. Answer: A The answer is: A	A
mathematics	A rectangular-shaped carpet that measures x feet by y feet is priced at $12. What is the cost of the carpet, in dollars per square yard? (1 square yard = 9 square feet)	[ "108/(xy)", "90xy", "xy/90", "xy/10", "10/(xy)" ]	The area of the carpet in feet is xy. The area in square yards is xy / 9. The price per square yard is 12 / (xy/9) = 108/(xy). The answer is A. The answer is: A	A
mathematics	In what time will a train 180 meters long cross an electric pole, if its speed is 154 km/hr	[ "5 seconds", "4.3 seconds", "3 seconds", "2.5 seconds", "None of these" ]	Explanation: First convert speed into m/sec Speed = 154*(5/18) = 42 m/sec Time = Distance/speed = 180/42 = 4.3 seconds Option B The answer is: B	B
mathematics	One out of every 300 light bulbs are defected. If 2 out of every 10 defected light bulbs have a broken glass and there are 20 broken glass light bulbs in the shipment, how many light bulbs total are there in the shipment?	[ "2,000", "30000", "10,000", "50,000", "52,000" ]	20 broken glasses indicates that 1010= 100 defected bulbs are present. 100 defected bulbs indicates that 100300= 30,000 light bulbs are present. B is the answer The answer is: B	B
mathematics	40 onions on a scale weigh 7.68 kg. When 5 onions are removed from the scale, the average weight of the 35 onions is 190 grams. What is the average weight (in grams) of the 5 onions which were removed?	[ "200", "202", "204", "206", "208" ]	35*190=6650. The other 5 onions weigh a total of 1030 grams. The average weight is 1030/5 = 206 grams. The answer is D. The answer is: D	D
mathematics	Of 70 players on a football team, 43 are throwers. The rest of the team is divided so one third are left- handed and the rest are right handed. Assuming that all throwers are right handed, how many right- handed players are there total?	[ "54", "59", "63", "61", "92" ]	Total = 70 Thrower = 43 Rest = 70 - 43 = 27 Left Handed = 27/3 = 9 Right handed = 18 If all Thrower are right handed then total right handed is 43 + 18 = 61 so D. 61 is the right answer The answer is: D	D
mathematics	A train 125 m long passes a man, running at 5 km/hr in the same direction in which the train is going, in 10 seconds. The speed of the train is:	[ "10 km/hr", "50 km/hr", "14 km/hr", "17 km/hr", "77 km/hr" ]	Speed of the train relative to man = (125/10) m/sec = (25/2) m/sec. [(25/2) * (18/5)] km/hr = 45 km/hr. Let the speed of the train be x km/hr. Then, relative speed = (x - 5) km/hr. x - 5 = 45 ==> x = 50 km/hr. Answer: B The answer is: B	B
mathematics	Find the odd man out. 187, 264, 316, 473, 682, 781	[ "187", "316", "781", "682", "473" ]	In all numbers except 316, the middle digit is the sum of other two digits. Answer is B The answer is: B	B
mathematics	At a meeting, 3 people are to be seated around a circular table. Two seating arrangements are considered different only when the positions of the people are different relative to each other. What is the total number of different possible seating arrangements for the group?	[ "2", "7", "C)120", "D)144", "E)720" ]	The number of arrangements of n distinct objects in a row is given by n! The number of arrangements of n distinct objects in a circle is given by (n−1)! "The difference between placement in a row and that in a circle is following: if we shift all object by one position, we will get different arrangement in a row but the same relative arrangement in a circle. So, for the number of circular arrangements of n objects we have: R=n!-n=(n−1)! (n−1)!=(7−1)!=720 Answer: E The answer is: C	C
mathematics	A tank is filled in eight hours by three pipes A, B and C. Pipe A is twice as fast as pipe B, and B is twice as fast as C. How much time will pipe B alone take to fill the tank?	[ "17 hours", "28 hours", "19 hours", "14 hours", "14 hours" ]	1/A + 1/B + 1/C = 1/8 (Given) Also given that A = 2B and B = 2C => 1/2B + 1/B + 2/B = 1/8 => (1 + 2 + 4)/2B = 1/8 => 2B/7 = 8 => B = 28 hours. Answer: B The answer is: B	B

mathematics

Mike weighs twice as much as Mary. Mike's weight is 150% of Michelle's weight. Alan weighs 20% more than Charlie. Charlie weighs 160% of Mary's weight. Which of these 5 people weighs the highest?

[ "Mary", "Mike", "Michelle", "Alan", "Charlie" ]

Mary < Michelle < Mike Charlie < Alan Let x be Mary's weight. Mike's weight is 2x and Alan's weight is 1.2*1.6x = 1.92x. The answer is B. The answer is: B

B

mathematics

The value of (8x10^7)(8x10^8) is closest to which of the following?

[ "10^17", "10^14", "10^18", "10^19", "10^20" ]

multiplying these we get, 64 x 10^7 x 10^8 = 6.4 x 10^16 which is closer to 10^17 Answer: A The answer is: A

A

mathematics

Its festive time and all big companies are offering the big discount especially on iPhone whose price is staggering Rs. 65,000. Following is the offer from the three major companies in India. : Amazon offers Flat 65% discount : Flipkart offers 10% discount over and over again. : Snapdeal offers RS 42,000 off. Which is the best offer for you ?

[ "Flipkart", "Amazon", "Snapdeal", "All", "None of Above" ]

A Explanation: Flipkart : 22664, Amazon: 22750 and Snapdeal: 23000 SnapDeal discount : 65000 - 42000 = 23000 Amazon 65% discount : 35/100 * 65000 = 22750 Flipkart 10% recursive discount: After 1st 10% discount, Amount is 58500 After 2nd 10% discount, Amount is 52650 After 3rd 10% discount, Amount is 47385 After 4th 10% discount, Amount is 42646.5 After 5th 10% discount, Amount is 38381.85 After 6th 10% discount, Amount is 34543.665 After 7th 10% discount, Amount is 31089.2985 After 8th 10% discount, Amount is 27980.36865 After 9th 10% discount, Amount is 25182.331785 After 10th 10% discount, Amount is 22664.0986065 The answer is: A

A

mathematics

If a, b, and c are consecutive odd positive integers and a < b < c, which of the following could be equal to c - b - a+4 ?

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

let we put values. a=1, b=3, c=5 5-3-1=1 1+4 =5 Answer :B The answer is: B

B

mathematics

Find the value of sin 75° + sin 15° = ?

[ "0", "1/2", "1", "3/2", "2" ]

sin A + sin B = 2 sin [ (A + B) / 2 ] cos [ (A - B) / 2 ] =2 sin [ (75 +15) / 2 ] cos [ (75 - 15) / 2 ] =2 sin90cos60=2*1*(1/2)=1 ANSWER:C The answer is: C

C

mathematics

In how many ways can the letters of the word REPEATED be arranged?

[ "1206", "1348", "6720", "3000", "3478" ]

REPEATED has 8 words, but E is repeated three times. Thus ways = 8! / 3! = 6720 ways C The answer is: C

C

mathematics

In the manufacture of a certain product, 7 percent of the units produced are defective and 4 percent of the defective units are shipped for sale. What percent of the units produced are defective units that are shipped for sale?

[ "0.125%", "0.28%", "0.8%", "1.25%", "2.0%" ]

Percent of defective produced = 7% Percent of the defective units that are shipped for sale = 4% Percent of units produced are defective units that are shipped for sale = (4/100)*(7/100)*100% = (28/10000)*100% = (28/100)% = .28 % Answer B The answer is: B

B

mathematics

David and Rachel are getting married. The extended family wants to have its picture taken, but David's father is unwilling to stand next to Rachel's mother. How many options does the photographer have to arrange the 6 family members in a row for the picture?

[ "9!", "9×8!", "4x5!", "10!/2!", "10!" ]

In how many ways David's father and Rachel's mother can stand together? Consider them as one unit: {F, M}. So, we'd have 9 units {F, M}, 1, 2, 3, 4, which can be arranged in 9! ways. David's father and Rachel's mother within their unit can be arranged in 2! ways. Therefore, David's father and Rachel's mother can stand together in 5!*2! ways. Total - Restriction = = 6! - 5!*2! = = 5!(6- 2!) = = 4*5!. Answer: C. The answer is: C

C

mathematics

Difference between the length &breadth of a rectangle is 23 m. If its perimeter is 206 m, then its area is?? We have: (l - b) = 23 and 2(l + b) = 206 or (l + b) = 103?

[ "2400 m^2", "2420 m^2", "2520 m^2", "2600 m^2", "2630 m^2" ]

Solving the two equations, we get: l = 63 and b = 40. Area = (l x b) = (63 x 40) m2 = 2520 m^2 C The answer is: C

C

mathematics

It is required to fix a pipe such that water flowing through it at a speed of 7 metres per minute fills a tank of capacity 1760 cubic metres in 10 minutes. The inner radius of the pipe should be :

[ "√2 m", "2 m", "1⁄2 m", "2√2 m", "None of these" ]

Let inner radius of the pipe be r. Then, 1760 = 22⁄7 × r2 × 7 × 10 or r2=1760/22×10=8 or r = 2√2 m Answer D The answer is: D

D

mathematics

A certain restaurant offers 6 different salads, 4 different main courses, and 7 different desserts. If customers choose one salad, one main course, and two different desserts for their meal, how many different meals are possible?

[ "260", "388", "436", "504", "520" ]

The number of possible choices for desserts is 7C2 = 21 The number of possible meals is 6*4*21 = 504 The answer is D. The answer is: D

D

mathematics

George has 8 candies in a bag, 3 of which are sweet while the other 5 are sour. He pulls out 2 of the candies simultaneously, and at random. What is the probability that exactly one of the candies he picked is sour?

[ "2/8", "3/15", "2/28", "3/5", "15/28" ]

The probability is equal to the number of desired choices divided by the total number of possibilities. Probability = Favorable/Total Total = 8C2 = 8*7/2 = 28 Favorable: Pick 1 sour out of 3 sour AND pick 1 sweet out of 5 sweet. 3C1*5C1=3*5=15 P=15/28 When you use combination method, it is picking all possible cases and the order doesn't matter. Whereas, upon choosing probability method to solve, order matters. Thus, Total Probability: Probability of choosing sour candy first AND Probability of choosing sweet candy OR Probability of choosing sweet candy first AND Probability of choosing sour candy Answer: E The answer is: E

E

mathematics

If 6th March, 2005 is Monday, what was the day of the week on 6th March, 2004?

[ "Sunday", "Saturday", "Tuesday", "Wednesday", "Monday" ]

The year 2004 is a leap year. So, it has 2 odd days. But, Feb 2004 not included because we are calculating from March 2004 to March 2005. So it has 1 odd day only. The day on 6th March, 2005 will be 1 day beyond the day on 6th March, 2004. Given that, 6th March, 2005 is Monday. 6th March, 2004 is Sunday (1 day before to 6th March, 2005). Answer A The answer is: A

A

mathematics

How many odd 4-digit positive integers Q that are multiples of 5 can be formed without using the digit 3?

[ "648", "729", "900", "1296", "3240" ]

I choose A. Possible n° of 1st digit: 8 (0 can't be the first number, or else it wouldn't have 4 digits. 3 is exlcuded) Possible n° of 2nd digit: 9 (3 is excluded) Possible n° of 3rd digit: 9 (3 is excluded) Possible n° of 4th digit: 1 (a number is a multiple of 5 if it ends in 5 or 0, here we are asked for the odd numbers, hence the last digit can't be 0) So, Q=8*9*9*1=648 (A) The answer is: A

A

mathematics

A father said to his son, "I was as old as you are at the present at the time of your birth". If the father's age is 44 years now, the son's age five years back was?

[ "17years", "18years", "19years", "20years", "21years" ]

Let the son's present age be x years. Then, (44 - x) = x 2x = 44. x = 22. Son's age 5 years back (22 - 5) = 17 years. A) The answer is: A

A

mathematics

Set S consists of integers {2,3,4,5}. If two numbers are chosen from set S at random, what is the probability that the sum of 2 numbers is more than 5?

[ "5/6", "1/2", "2/3", "1/4", "2/7" ]

Number of ways you can choose 2 from 4 = 4C2 = 6 E = event of getting the 2 numbers is more than 5 = (2,4),(2,5),(3,4)(3,5),(4,5) = 5 probability = 5/6 Answer is A The answer is: A

A

mathematics

Last month, John rejected 0.7% of the products that he inspected and Jane rejected 0.8 percent of the products that she inspected. If total of 0.75 percent of the products produced last month were rejected, what fraction of the products did Jane inspect?

[ "1/6", "1/2", "5/8", "5/6", "15/16" ]

X - fraction of products Jane inspected (1 - X) - fraction of products John inspected 0.8(X) + 0.7(1-X) = 0.75 0.1X = 0.75 - 0.7 X = 0.05/0.1 X = 1/2 Therefore the answer is B: 1/2. The answer is: B

B

mathematics

A building is to be completed in 48 days. To meet the deadline 54 men were employed and were made to work for 10 hours a day. After 30 days 5/9th of the work was completed. How many more workers should be employed to meet the deadline if each workers are now made to work 8 hours a day?

[ "36", "55", "40", "45", "None of these" ]

Explanation : 54 men work 10 hours a day for 30 days and 5/9th of the work is completed. Now, let x workers be employed to work 8 hours a day for the rest 18 days to complete 4/9th of the work. M1D1T1W2 = M2D2T2W1 54*30*10*4/9 = x*18*8*5/9 x = 90 Hence, 36 more workers should be employed. Answer : A The answer is: A

A

mathematics

12 members were present at a board meeting. Each member shake hands with all of the other members before and after the meeting .How many hand shakes were there?

[ "237", "268", "132", "827", "261" ]

Explanation: In order to have a hand shake there must be two members. Therefore to select 2 out of 12 we have 12C2. This happens twice that is before and after the meeting Answer = 12C2 ×2 = 132 Answer: C The answer is: C

C

mathematics

what is the units digit of the expression 17^7-2?

[ "1", "2", "3", "7", "9" ]

7^1=7 7^2=49 7^3=343 7^4=1(last digit) 7^5=7(last digit) and the cycle repeats after every 4 powers Therefore, last digit of 17^7=3 3-2=1 Answer A The answer is: A

A

mathematics

A certain sum is invested at simple interest at 18% p.a. for two years instead of investing at 12% p.a. for the same time period. Therefore the interest received is more by Rs. 840. Find the sum?

[ "7000", "7029", "2778", "2800", "2791" ]

Let the sum be Rs. x. (x * 18 * 2)/100 - (x * 12 * 2)/100 = 840 => 36x/100 - 24x/100 =840 => 12x/100 = 840 => x = 7000.Answer:A The answer is: A

A

mathematics

The value of ((x – y)³ + (y - z)³ + (z – x)³)/(12 (x – y) (y – z) (z – x)) is equal to :

[ "0", "1/12", "1", "1/4", "1/3" ]

Since (x – y) + (y – z) + (z – x) = 0, so (x – y)³ + (y – z)³ + (z – x)³= 3 (x – y) (y – z) (z – x). (3 (x – y) (y – z) (z – x))/(12(x – y) (y – z) (z – x)) = 1/4. ANSWER:D The answer is: D

D

mathematics

If P is a prime number greater than 100, what is the remainder when P^2 is divided by 4.

[ "4", "Cannot be determined", "2", "3", "1" ]

take square of any prime number remainder will be 1 Ans E The answer is: E

E

mathematics

Three numbers are in the ratio of 2 : 3 : 4 and their L.C.M. is 300. What is their H.C.F.?

[ "20", "25", "30", "60", "75" ]

Let the numbers be 2x, 3x, and 4x. LCM of 2x, 3x and 4x is 12x. 12x = 300 x = 25 HCF of 2x, 3x and 4x = x = 25 The answer is B. The answer is: B

B

mathematics

A can do a piece of work in 30 days. He works at it for 5 days and then B finishes it in 20 days. In what time can A and B together it?

[ "13 1/7 days", "13 1/3 days", "13 1/8 days", "13 8/3 days", "12 1/3 days" ]

5/30 + 20/x = 1 x = 24 1/30 + 1/24 = 3/40 40/3 = 13 1/3 days Answer:B The answer is: B

B

mathematics

The mall charges 40 cents for the first hour of parking and $3 for each additional hour until the customer reaches 4 hours, after that the parking fee is $2 per hour. If Mr.Park parked his car in the mall for 7 hours and 30 minutes, how much is he going to pay?

[ "$6.8", "$12.", "$13.", "$14.5.", "$15." ]

0.40+2*2+1*2+0.40= $6.8 Answer : $6.8 The answer is: A

A

mathematics

If a and b are each greater than x and y, which of the following must be true? I. ab > xy II. |a| + |b| > |x| + |y| III.a + b > x + y

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

I. a + b > x + y. Since a and b are each greater than x and y, then the sum of a and b will also be greater than the sum of x and y. II. ab > xy. Not necessarily true, consider a = b = 0 and x = y = -1 --> ab = 0 < 1 = xy. III. |a| + |b| > |x| + |y|. Not necessarily true, consider a = b = 0 and x = y = -1 --> |a| + |b| = 0 < 2 = |x| + |y|. Answer: B. The answer is: B

B

mathematics

If each participant of a chess tournament plays exactly one game with each of the remaining participants, then 171 games will be played during the tournament. Find the number of participants.

[ "15", "16", "17", "18", "19" ]

Let P be the number of participants. PC2 = 171 (P)(P-1) = 342 = 19*18 P = 19 The answer is E. The answer is: E

E

mathematics

If 5^29 * 4^15 = 2 * 10^n, what is the value of n?

[ "11", "21", "22", "29", "32" ]

My attempt: 5^(29) * 4^(15) = 2*10^p 5^(29) * 2 ^ (30) = 2 * (2*5)^p 5^(29) * 2 ^ (30) = 2 * 2^(p) * 5^(p) 5^(29) * 2 ^ (30) = 2^(p+1) * 5^(p) => (p+1) = 30 => p = 29 Answer: 29 (D) The answer is: D

D

mathematics

John must arrange 2 different physics books and 3 different mathematics books on one shelf. If the first book on the leftmost side is a mathematics book and no physics book is next to another physics book. How many different arrangements exist?

[ "6", "12", "36", "120", "720" ]

First Place, is reserved for Math book. There are 3 Math books which can be arranged in3 ways Restriction comes into playhysics book cannot be together. Hence, the maththe physics books take alternate places Second Place, Physics Book - in 3 ways Third Place, Math Book - in 2 ways (only 2 books left) Fourth Place, Physics - in 2 ways (only 2 Physics book left) Rest two places can be arranged in one way only. Total no of ways = 3*2*2*1*1 = 12 ways B The answer is: B

B

mathematics

If the sides of a triangle are 30 cm, 28 cm and 12 cm, what is its area?

[ "120 cm2", "112 cm2", "776 cm2", "666 cm2", "168 cm2" ]

The triangle with sides 30 cm, 28 cm and 12 cm is right angled, where the hypotenuse is 30 cm. Area of the triangle = 1/2 * 28 * 12 = 168 cm2 Answer: E The answer is: E

E

mathematics

If a^5 ≤ a, which of the following must be true? I. –1 ≤ a ≤ 0 II. a=0 III. 0 ≤ a ≤ 1

[ "None of the above", "I only", "II only", "III only", "I and III only" ]

The trick here is more on the answer choices. Look at I II and III. all are right (pick out some numbers). Therefore I was totally confused because non of the answers had the right answer (I II and III) I finally chose D, but hesitate between A and D quite a long time... This is a tricky tricky question, since it takes into consideration that the answers are correct but they do not cover all the POSSIBLE answers. Therefore it is A. The answer is: A

A

mathematics

A can do a piece of work in 20 days. B in 15 days A and C in 12 days. In how many days can A finish the work if he is assisted by B on one day and C on the next, alternately?

[ "2 days", "5 days", "8 days", "7 days", "9 days" ]

C 8 days A + B = 1/20 + 1/15 = 7/60 A + C = 1/20 + 1/12 = 8/60 7/60 + 8/60 = 15/60 = 1/4 4 days * 2 = 8 days The answer is: C

C

mathematics

A shopkeeper loses 15%,if an article is sold for Rs. 102. What should be the selling price of the article to gain 20%?

[ "128", "144", "176", "186", "111" ]

Explanation: Given that SP = Rs. 102 and loss = 15% CP = [100(SP)]/(100 - l%) = (100 * 102)/85 = 20 * 6 = Rs. 120. To get 20% profit, New SP = [(100 + p%)CP]/100 = (120 * 120)/100 = Rs. 144 Answer:B The answer is: B

B

mathematics

The letters of the word 'SURITE' are written in all possible orders and these words are written in alphabetical order. Then what is the rank of the word 'SURITI'

[ "- 236", "- 245", "- 307", "- 315", "- 475" ]

Total Number of Words = 6! = 720 [(number of characters)/(repeating group )!] After S, we have T and U. Number of words starting with T = 5! = 120 Number of words starting with U = 5! = 120 So any word starting with S will have rank < 720 - 120(for Us) - 120(for Ts) = 480 Only option A < 480, so Answer is E The answer is: E

E

mathematics

Machine A and machine B are each used to manufacture 880 sprockets. It takes machine A 10 hours longer to produce 880 sprockets than machine B. Machine B produces 10% more sprockets per hour than machine A. How many sprockets per hour does machineAproduce?

[ "6", "6.6", "8.8", "100", "110" ]

time taken by B = t time taken by A = t+10 qty produced by A = q qty produced by B = 1.1 q for B: t(1.1q) =880 qt=800 for A: (t+10)(q) = 880 qt+10q=880 800+10q=880 q=8 so A can produce 8/hour. then B can produce = 8(1.1)=8.8/hour. C The answer is: C

C

mathematics

If P(A) = 2/15, P(B) = 4/15, and P(A âˆª B) = 12/15 Find P(B|A)

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

P(B|A) = P(A âˆª B)/P(A) P(B|A) = (12/15)/(2/15) = 6. E The answer is: E

E

mathematics

A cashier mentally reversed the digits of one customer's correct amount of change and thus gave the customer an incorrect amount of change. If the cash register contained 27 cents more than it should have as a result of this error, which of the following could have been the correct amount of change in cents?

[ "14", "45", "54", "65", "52" ]

Just check the answers and reverse the numbers until you get 27. 52 - 25 = 27 Answer E The answer is: E

E

mathematics

An amount of Rs. 100000 is invested in two types of shares. The first yields an interest of 9% p.a and the second, 11% p.a. If the total interest at the end of one year is 9 2/3 %, then the amount invested in each share was?

[ "23777", "35000", "29977", "26777", "19871" ]

Let the sum invested at 9% be Rs. x and that invested at 11% be Rs. (100000 - x). Then, (x * 9 * 1)/100 + [(100000 - x) * 11 * 1]/100 = (100000 * 29/3 * 1/100) (9x + 1100000 - 11x)/100 = 29000/3 = 9700 (9x + 1100000 - 11x) = 970000 x = 65000 Sum invested at 9% = Rs. 65000 Sum invested at 11% = Rs. (100000 - 65000) = Rs. 35000. Answer: B The answer is: B

B

mathematics

Hal bought walnuts at 5 for $1 and apples at 4 for $1.He spent a total of $19.50 . He sells both at 20 for $5 and as a result gains $3 .How many walnuts did Hal buy ?

[ "50", "45", "60", "80", "55" ]

Let's start with the concrete information: He buys everything for $19.50 and earns $3 after selling so he sells everything for $22.50 (= 2250 cents). He sells each item for 5/20 = 25 cents so in all he sells 2250/25 = 90 items Cost of each walnut = 1/5 = $.2 = 20 cents Cost of each apple = 1/4 = $.25 = 25 cents Now we have one equation to solve: 20*w + 25*(90 - w) = 1950 (w is the number of walnuts he buys) 4w + 5(90 - w) = 390 w = 60 Answer (C) The answer is: C

C

mathematics

A survey was sent to 80 customers, 9 of whom responded. Then the survey was redesigned and sent to another 63 customers, 12 of whom responded. By approximately what percent did the response rate increase from the original survey to the redesigned survey?

[ "2%", "5%", "14%", "28%", "69%" ]

Rate of first survey = 9/80 Rate of second survey = 12/63 % Response rate increase (12/63-9/80)/(9/80) = 69% Answer is E = 69% The answer is: E

E

mathematics

If the average marks of three batches of 55, 60 and 45 students respectively is 50, 55, 60, then the average marks of all the students is

[ "54.48", "54.68", "54.6", "54.58", "None of these" ]

Explanation: (55×50)+(60×55)+(45×60)55+60+45 8750160=54.68 Answer: Option B The answer is: B

B

mathematics

From a pack of cards two cards are drawn one after the other, with replacement. The probability that the first is a red card and the second is a king is ?

[ "1/26", "1/07", "1/22", "1/29", "1/21" ]

Let E1 be the event of drawing a red card. Let E2 be the event of drawing a king . P(E1 ∩ E2) = P(E1) . P(E2) (As E1 and E2 are independent) = 1/2 * 1/13 = 1/26 Answer:A The answer is: A

A

mathematics

An bus covers a certain distance at a speed of 140 kmph in 5 hours. To cover the samedistance in 1hr, it must travel at a speed of?

[ "520 km/hr", "640 km/hr", "656 km/hr", "731 km/hr", "700 km/hr" ]

Distance = (140 x 5) = 700 km. Required speed = 700 km/hr. E The answer is: E

E

mathematics

The current of a stream at 1 kmph. A motor boat goes 35 km upstream and back to the starting point in 12 hours. The speed of the motor boat in still water is?

[ "6", "9", "8", "3", "1" ]

S = 1 M = x DS = x + 1 US = x - 1 35/(x + 1) + 35/(x - 1) = 12 x = 6 Answer: A The answer is: A

A

mathematics

If two numbers are in the ratio 2:3. If 10 is added to both of the numbers then the ratio becomes 3:4 then find the smallest number?

[ "10", "20", "24", "26", "29" ]

2:3 2x + 10 : 3x + 10 = 3 : 4 4[2x + 10] = 3[3x + 10] 8x + 40 = 9x + 30 9x - 8x = 40 - 30 x = 10 Then smallest number is = 2 2x = 20 Short cut method: a:b = 2:3 c:d = 3:4 1.Cross multiplication with both ratios a * d ~ b * c = 2 * 4 ~ 3 * 3 = 8 ~ 9 = 1 2. If 10 is added both the number means 10 * 3 = 30 and 10 * 4 = 40, Then 30 ~ 40 = 10 ===> 1 -----> 10 ===> 2 -----> 20 B The answer is: B

B

mathematics

A train overtakes 2 girls who are walking inthe opposite direction in which the train is going at the rate of 3 km/hour & 6km/hour and passes them completely in 36sec & 30 sec respectively. Find the length of the train is?

[ "120 m", "130 m", "150 m", "200 m", "250 m" ]

Let the length of the train e x meter, and let the speed of train be y km/h, then \inline x=\left ( y+3 \right )\frac{5}{18}\times 36 ........(1) and \inline x=\left ( y+6\right )\frac{5}{18}\times 30 ........(2) From eq (1) and (2), we get \inline (y+3)\times 36 = ( y+6)\times 30 y = 12 km/h \inline \therefore \inline x=(y+3)\times \frac{5}{18}\times 36 x= 150 m C The answer is: C

C

mathematics

If a man reduces the selling price of a fan from Rs. 420 to Rs. 402, his loss increases by 3%. The cost price of the fan is :

[ "Rs.600", "Rs.650", "Rs.475", "Rs.525", "None of these" ]

Explanation : Solution: let C.P. be Rs. X. then, 3% of x = (420-402) =18 => 3x/100 = 18 => x =Rs.600. Answer : A The answer is: A

A

mathematics

A pump can fill a tank with a water in 2 hours. Because of a leak, it took 3 hours to fill the tank. The leak can drain all the water of the full tank in how many hours?

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

The rate of the pump + leak = 1/3 1/2 - leak's rate = 1/3 leak's rate = 1/2 - 1/3 = 1/6 The leak will empty the tank in 6 hours. The answer is E. The answer is: E

E

mathematics

A and B started a partnership business investing some amount in the ratio of 4 : 5. C joined then after six months with an amount equal to that of B. In what proportion should the profit at the end of one year be distributed among A, B and C?

[ "4 : 9 : 8", "5 : 7 : 4", "6 : 10 : 5", "7 : 9: 4", "8 : 10 : 5" ]

Let the initial investments of A and B be 4x and 5x. A : B : C = (4x x 12) : (5x x 12) : (5x x 6) = 48 : 60 : 30 = 8 : 10 : 5. ANSWER :E The answer is: E

E

mathematics

Today John, who is 38 years old, and his daughter, who is 13 years old, celebrate their birthdays. How many years will pass before John’s age is twice his daughter’s age?

[ "13", "14", "15", "16", "12" ]

Forget conventional ways of solving math questions. In PS, IVY approach is the easiest and quickest way to find the answer. After x years passes John’s age will be (38+x) years old, and his daughter’s age will be (13+x) years old. Since the John’s age is twice his daughter’s age (38+x)= 2 * (13+x) ---> 38+x=26+2x ---> x= 12 The answer is (E). The answer is: E

E

mathematics

On my sister's birthday, she was 132 cm in height, having grown 10% since the year before. How tall was she the previous year?

[ "130 cm", "126 cm", "120 cm", "116 cm", "112 cm" ]

Let the previous year's height be x. 1.1x = 132 x = 120 The answer is C. The answer is: C

C

mathematics

A seller has 1000kg of rice part of which he sells at 8% profit and the rest at 18% profit. He gains 14%. The quantity sold at 18% profit is?

[ "200 kg", "300 kg", "400 kg", "600 kg", "800 kg" ]

By rule of alligation, Profit% by selling 1st part Profit% by selling 2nd part 8 18 Net % profit 14 18-14=4 14-8=6 => Quantity of part1 : Quantity of part2 = 4 : 6 = 2 : 3 Total quantity is given as 1000 kg. So quantity of part2 (quantity sold at 18% profit) =1000×35 = 600 kg D The answer is: D

D

mathematics

The number 0.5 is how much greater than 1/3 ?

[ "1/6", "2/10", "1/50", "1/500", "2/500" ]

let x be the difference then .5-1/3=x 5/10-1/3=x x=1/6 ans A The answer is: A

A

mathematics

A train running at the speed of 60 km/hr crosses a pole in 9 seconds. What is the length of the train?

[ "277", "266", "288", "150", "332" ]

Speed=(60 * 5/18) m/sec = (50/3) m/sec Length of the train = (Speed x Time) = (50/3 * 9) m = 150 m . Answer: D The answer is: D

D

mathematics

Suresh started a business with Rs.20,000. Kiran joined him after 4 months with Rs.30,000. After 2 more months, Suresh withdrew Rs.5,000 of his capital and 2 more months later, Kiran brought in Rs.20,000 more. What should be the ratio in which they should share their profits at the end of the year?

[ "17:12", "12:17", "21:32", "32:21", "17:32" ]

Here capital is not the same. Suresh invested 20000 for initial 6 months and 15000 for the next 6 months. Hence his term of ratio =(20000×6+15000×6) Kiran invested Rs.30000 for 4 months and Rs.50000 for next 4 months. Hence his term of ratio =(30000×4+50000×4) Suresh : Kiran =(20000×6+15000×6) :(30000×4+50000×4) =(20×6+15×6):(30×4+50×4)=(20×3+15×3):(30×2:50×2) =105:160=21:32 Answer is C. The answer is: C

C

mathematics

A wire in the form of a circle of radius 3.5 m is bent in the form of a rectangule, whose length and breadth are in the ratio of 6 : 5. What is the area of the rectangle?

[ "19 cm2", "30 cm2", "17 cm2", "18 cm2", "12 cm2" ]

The circumference of the circle is equal to the permeter of the rectangle. Let l = 6x and b = 5x 2(6x + 5x) = 2 * 22/7 * 3.5 => x = 1 Therefore l = 6 cm and b = 5 cm Area of the rectangle = 6 * 5 = 30 cm2 Answer:B The answer is: B

B

mathematics

The length of a rectangular plot is thrice its breadth. If the area of the rectangular plot is 867 sq m, then what is the breadth of the rectangular plot?

[ "12", "17", "10", "12", "19" ]

Let the breadth of the plot be b m. Length of the plot = 3 b m (3b)(b) = 867 3b2 = 867 b2 = 289 = 172 (b > 0) b = 17 m. Answer:B The answer is: B

B

mathematics

There are 4 more women than there are men on a local co-ed softball team. If there are a total of 20 players on the team, what is the ratio of men to women?

[ "10/16", "6/16", "4/16", "6/10", "8/12" ]

w = m+4 w+m = 20 m+4+m = 20 2m = 16 m = 8 w = 12 ratio:8:12 Ans: E The answer is: E

E

mathematics

Efficiency with which Adam and Mike work is in the ratio 2:1. How much time will they, working together, take to complete a job which Adam alone could have done in 10 days?

[ "15 days", "20 days", "6 days", "6 1â„3 days", "None of these" ]

Ratio of times taken by Adam and Mike = 100 : 200 = 1 : 2. Suppose Mike takes x days to do the work. Then, 1 : 2 : : 10 : x â‡’ x = (10Ã—2)/1 â‡’ x = 20 Adamâ€™s 1 dayâ€™s work = 1â„10; Mikeâ€™s 1 days work = 1â„20 (Adam + Mike)â€™s 1 dayâ€™s work = (1â„10 + 1â„20) = 3â„20 âˆ´ Adam and Mike together can complete the job in 20â„3 days or 6 2â„3 days. Answer E The answer is: E

E

mathematics

Two trains of equal length are running on parallel lines in the same directions at 46km/hr. and 36km/hr. The faster trains pass the slower train in 72 seconds. The length of each train is:

[ "82m", "50m", "72m", "100m", "None of these" ]

Explanation: The relative speed of train is 46-36 = 10 Km/hr = (10 X 5) / 18 = 25/9 m/s10×518=259m/s In 72 secs the total distance traveled is 72x25/9 = 200 m. Therefore the length of each train is = 200/2 = 100 m. Answer D The answer is: D

D

mathematics

A train running at a speed of 60 kmph crosses a pole in 6 seconds.What is the length of the train?

[ "120 m", "180 m", "100 m", "150 m", "160 m" ]

60 kmph=50/3 m/sec 50/3*6=100 m ANSWER:C The answer is: C

C

mathematics

The ratio of ducks and frogs in a pond is 37 : 39 respectively. The average number of ducks and frogs in the pond is 132. What is the number of frogs in the pond ?

[ "148", "134", "156", "144", "None" ]

Solution: Ratio of Ducks and Frogs in Pond, = 37 : 39. Average of Ducks and Frogs in Pond, = 132. So, total number of Ducks and Frogs in the Pond, = 2* 132 = 262. Therefore, Number of Frogs, = (262*39)/76 = 134. Answer: Option B The answer is: B

B

mathematics

Excluding stoppages, the speed of a bus is 80 km/hr and including stoppages, it is 70 km/hr. For how many minutes does the bus stop per hour?

[ "11 min", "10 min", "8 min", "6 min", "5 min" ]

Due to stoppages, it covers 10 km less. Time taken to cover 10 km = 10/80 * 60 = 8 min. Answer:C The answer is: C

C

mathematics

1,3,5,7,9,..50 find term of sequnce

[ "1234", "1456", "1456", "1678", "2500" ]

This is an arithmetic progression, and we can write down a=1a=1 ,d=2d=2 , n=50n=50 . We now use the formula, so that Sn=12n(2a+(n−1)l)Sn=12n(2a+(n−1)l) S50=12×50×(2×1+(50−1)×2)S50=12×50×(2×1+(50−1)×2) =25×(2+49×2)=25×(2+49×2) =25×(2+98)=25×(2+98) =2500=2500 . E The answer is: E

E

mathematics

Integer X represents the product of all integers between 1 to 24 (inclusive). The smallest prime factor of (x+1) must be

[ "Between 1 to 10", "Between 11 to 15", "Between 15 to 20", "Between 20 to 25", "Greater than 24" ]

Answer = E = Greater than 24 This problem is asking smallest prime factor of (24!+1) 25! already have there prime factors 2,3,5,7,11,13.......... so on upto 23 (1 cannot be considered prime factor) Just adding 1 to 24! will remove all the factors stated above; so the smallest possible prime factor has to be greater than 24 Answer = E The answer is: E

E

mathematics

You have been given a physical balance and 7 weights of 52, 50, 48, 44, 45, 46 and 78 kgs. Keeping weights on one pan and object on the other, what is the maximum you can weigh less than 183 kgs.

[ "180", "181", "182", "178", "168" ]

add the max weights 52+50+78=180 ANSWER:A The answer is: A

A

mathematics

Three competing juice makers conducted a blind taste test with mall shoppers. The shoppers could choose to taste any number of the three brands of juices but had to select at least one juice that they liked. If 100 shoppers liked brand J, 200 shoppers liked brand K, 700 shoppers liked brand L, 250 shoppers liked exactly 2 juices, and 50 shoppers liked all three juices, how many shoppers took the taste test?

[ "1,300", "1,000", "900", "700", "650" ]

Given: Atleast 1 juice was liked by the participants. --> Neither = 0 Assume, I -->No overlap between the sets II --> Overlap between 2 sets III --> Overlap between 3 sets I + 2*(II) + 3*(III) = 100 + 200 + 700 I + 2*(250) + 3*(50) = 1000 I = 350 Total number of shoppers who took the taste test = I + II + III = 350 + 250 + 50 = 650 Answer: E The answer is: E

E

mathematics

An gun can take a maximum of four shotsat an enemyplane moving away from it. The probability of hitting the plane at the 1st, 2nd, third and 4th shots are 1.4, 1.3, 1.2 & 1.1 respectively. What is the probability that the plane is hit when all the four shots are fired?

[ "0.6976", "0.7893", "0.8212", "0.7541", "0.9847" ]

Required probability: =(0.4×0.7×0.8×0.9)+(0.6×0.3×0.8×0.9)+(0.6×0.7×0.2×0.9)+(0.6×0.7×0.8×0.1)+(0.4×0.3×0.8×0.9)+(0.4×0.7×0.2×0.9)+(0.4×0.7×0.8×0.1)+(0.6×0.3×0.2×0.9)+(0.6×0.3×0.8×0.1)+(0.6×0.7×0.2×0.1)+(0.4×0.3×0.2×0.9)+(0.6×0.3×0.2×0.1)+(0.4×0.3×0.8×0.1)+(0.4×0.7×0.2×0.1)+(0.4×0.3×0.2×0.1)=(0.4×0.7×0.8×0.9)+(0.6×0.3×0.8×0.9)+(0.6×0.7×0.2×0.9)+(0.6×0.7×0.8×0.1)+(0.4×0.3×0.8×0.9)+(0.4×0.7×0.2×0.9)+(0.4×0.7×0.8×0.1)+(0.6×0.3×0.2×0.9)+(0.6×0.3×0.8×0.1)+(0.6×0.7×0.2×0.1)+(0.4×0.3×0.2×0.9)+(0.6×0.3×0.2×0.1)+(0.4×0.3×0.8×0.1)+(0.4×0.7×0.2×0.1)+(0.4×0.3×0.2×0.1) =0.2016+0.1296+0.756+0.336+0.864+0.504+0.224+0.324+0.144+0.0084+0.0216+0.0036+0.0096+0.0056+0.002=0.2016+0.1296+0.756+0.336+0.864+0.504+0.224+0.324+0.144+0.0084+0.0216+0.0036+0.0096+0.0056+0.002 =0.6976=0.6976 Edit: Thank you Vaibhav for providing an alternative method. Alternate Method: probability that the plane is hit when all the four shots are fired, P=1−probability of not hitting the targetP=1−probability of not hitting the target =1−(0.6×0.7×0.8×0.9)=1−(0.6×0.7×0.8×0.9) =1−0.3024=1−0.3024 =0.6976 A The answer is: A

A

mathematics

What is the remainder when 6990990900032 is divided by 32 ?

[ "5", "0", "4", "2", "3" ]

Though i was unaware of the divisibility test for 32 but i guessed the pattern!! divisibility rule for 4- last two digits must be divisible by 4 divisibility rule for 8- last three digits must be divisible by 8 similarly, divisibility rule for 32 - last five digits must be divisible by 32 Hence, Ans B The answer is: B

B

mathematics

If x and y are positive integers and 12x=21y what is the least possible value of xy?

[ "9", "28", "63", "84", "252" ]

12x=21y => x/y = 7/4 => 4x=7y 4(3)=7(3) => x*y=9 A The answer is: A

A

mathematics

A train running at the speed of 60 km/hr crosses a pole in 12 seconds. What is the length of the train?

[ "186 m", "176 m", "300 m", "150 m", "200 m" ]

Speed=(60 * 5/18) m/sec = (50/3) m/sec Length of the train = (Speed x Time) = (50/3 * 12) m = 200 m. Answer: E The answer is: E

E

mathematics

At a restaurant, glasses are stored in two different-sized boxes. One box contains 12 glasses, and the other contains 16 glasses. If the average number of glasses per box is 15, and there are 16 more of the larger boxes, what is the total number of glasses E at the restaurant? (Assume that all boxes are filled to capacity.)

[ "96", "240", "E=256", "E=384", "E=480" ]

Most Test Takers would recognize thesystemof equations in this prompt and just do algebra to get to the solution (and that's fine). The wording of the prompt and the 'spread' of the answer choices actually provide an interesting 'brute force' shortcut that you can take advantage of to eliminate the 4 wrong answers.... We're told that there are 2 types of boxes: those that hold 12 glasses and those that hold 16 glasses. Since the AVERAGE number of boxes is 15, we know that there MUST be at least some of each. We're also told that that there are 16 MORE of the larger boxes. This means, at the minimum, we have... 1 small box and 17 large boxes = 1(12) + 17(16) = 12 + 272 = 284 glasses at the MINIMUM Since the question asks for the total number of glasses, we can now eliminate Answers A, B and C.... The difference in the number of boxes MUST be 16 though, so we could have.... 2 small boxes and 18 large boxes 3 small boxes and 19 large boxes etc. With every additional small box + large box that we add, we add 12+16= 28 MORE glasses. Thus, we can justadd 28suntil we hit the correct answer.... 284+28 = 312 312+28 = 340 340+28 = 368 368+28 = 396 At this point, we've 'gone past' Answer D, so the correct answer MUST be Answer E.....But here's the proof.... 396+28 = 424 424+28 = 452 452+28 = 480 Final Answer: E The answer is: E

E

mathematics

A local bank that has 12 branches uses a two-digit code to represent each of its branches. The same integer can be used for both digits of a code, and a pair of two-digit numbers that are the reverse of each other (such as 17 and 71) are considered as two separate codes. What is the fewest number of different integers required for the 12 codes?

[ "3", "4", "12 ( 2 integers 4 codes)", "6", "7" ]

Pick any two integer. Integers: 12 Code: 11, 12, 21, 22 = 4 Codes Add one more integer: 3 13, 31, 33, 23, 32 = 5 Codes Add one more integer: 4 44, 14, 41, 24, 42, 34, 43 = 7 Codes Total = 16 Codes. Enough. Answer: C 4 integers create 12 codes. The answer is: C

C

mathematics

Cars emerging from a motorway arrive at a junction that splits the road into two separate lanes. The number of cars per hour that continue in either lane is constant. If 7 cars per hour were diverted from the left lane to the right lane, the number of cars entering the right lane per hour would be twice as big as the number of cars entering the left lane per hour. Alternatively, if 7 cars per hour were diverted from the right lane to the left lane, the number of cars entering the left lane per hour would be four times as great as the number of cars entering the right lane per hour. How many cars enter the left lane per hour?

[ "21", "18", "17", "19", "28" ]

as per question 7 cars diverted from left lane to right lane. Thus we get equation R+7=2(L-7) as per question 7 cars diverted from right lane to left lane .thus we get equation L+7=4(R-7) by solving two equation i.e R +7 =2L-14 OR. R =2L -21 AND L+7= 4R -28 OR L= 4R -35 BY SOLVING WE GET L= 4( 2L -21) -35 OR L= 8L -84-35 OR 119 =7L THUS L =17 C The answer is: C

C

mathematics

Find the fraction which has the same ratio to 2/6 that 3/4 has to 1/2

[ "1/2", "2/5", "6/8", "9/4", "7/5" ]

P : 2/6 = 3/4 : 1/2 As the product of the means is equal to the product of the extremes. P*1/2 = 2/6 * 3/4 P*1/2 = 6/24 P = 1/2 => P = 1/2 ANSWER:A The answer is: A

A

mathematics

Workers at a campaign office have 2000 fliers to send out. If they send out 1/10 of them in the morning and 1/4 of the remaining ones out during the afternoon, how many are left for the next day?

[ "300", "1350", "1100", "1200", "1900" ]

(1/10)*2000 = 200 Remaining = 2000-200 = 1800 (1/4) of remaining = (1/4)*1800 = 450 Remaining now = 1800-450 = 1350 Answer: Option B The answer is: B

B

mathematics

a batmans runs just before the last match of the season adds up750 in his last two innings his scores only 6 scores and his avg drop by 2 fond his final avg of the season?

[ "21", "22", "23", "24", "25" ]

Formula for this question is 6 = 2*avg-2(N+2) 6 = 2*(750/n) - 2(n+2) n*n+5n-750 = 0 n= 25 so final ans 23 ANSWER:C The answer is: C

C

mathematics

The speed of a train is 70 kmph excluding stoppages and including stoppages it is 63 kmph. Of how many minutes does the train stop per hour?

[ "3", "6", "7", "9", "14" ]

Explanation: T = 7/70 * 60 = 6 Answer: Option B The answer is: B

B

mathematics

An bus covers a certain distance at a speed of 240 kmph in 5 hours. To cover the samedistance in 1hr, it must travel at a speed of?

[ "520 km/hr", "640 km/hr", "656 km/hr", "731 km/hr", "720 km/hr" ]

Distance = (240 x 5) = 1200 km. Speed = Distance/Time Speed = 1200/(5/3) km/hr. [We can write 1 hours as 5/3 hours] Required speed = 1200 x 3 km/hr = 720 km/hr. 5 E The answer is: E

E

mathematics

The cash realised on selling a 14% stock is Rs.106.25, brokerage being 1/4% is

[ "123", "106", "100", "156", "240" ]

Explanation: Cash realised= Rs. (106.25 - 0.25) = Rs. 106. Answer: B The answer is: B

B

mathematics

Two numbers are in the ratio 3:5. If 9 be subtracted from each, they are in the ratio of 9:17. The first number is?

[ "36", "67", "87", "56", "51" ]

(3x-9):(5x-9) = 9:17 x = 12 => 3x = 36 Answer:A The answer is: A

A

mathematics

What will come in place of the x in the following Number series? 46080, 3840, 384, 48, 8, 2, x

[ "1", "3", "5", "6", "7" ]

46080 /12 = 3840 3840 /10 = 384 384 /8 = 48 48 /6 = 8 8/4 = 2 2 /2 = 1 A The answer is: A

A

mathematics

How many bricks, each measuring 25 cm x 11.25 cm x 6 cm, will be needed to build a wall of 8.5 m x 6 m x 22.5 cm?

[ "6400", "6410", "6440", "6500", "6800" ]

Number of bricks = Volume of Wall/Volume of Bricks =850x600x22.5/25x11.25x6= = 6800 answer :E The answer is: E

E

mathematics

2 chairs and 1 table cost $110. 4 chairs and 1 table cost $166. How much does one chair cost?

[ "26", "56", "110", "28", "54" ]

Let the cost of 1 chair = x, let the cost of 1 table = y 2x + y = 110 y = 110 - 2x Again, 4x + y = 166 4x + (110 - 2x) = 166 4x + 110 - 2x = 166 2x + 110 = 166 2x = 56 x = 28 Answer: D The answer is: D

D

mathematics

Sekar started a business investing Rs.25,000 in 1999. In 2000, he invested an additional amount of Rs.10,000 and Rajeev joined him with an amount of Rs.35,000. In 2001, Sekar invested another additional amount of Rs.10,000 and Jatin joined them with an amount of Rs.35,000. What will be Rajeev's share in the profit of Rs.2,40,000 earned at the end of 3 years from the start of the business in 1999?

[ "Rs.45,000", "Rs.80,000", "Rs.70,000", "Rs.75,000", "none" ]

Solution Sekar:Rajeev:Jatin= (25000×12+35000×12+45000×12):(35000×24) : (35000×12) = 1260000 : 840000 : 420000 = 3 : 2 : 1. Rajeev's share =Rs.(240000×2/6) = Rs.80000. Answer B The answer is: B

B

mathematics

The list price of an article is Rs.65. A customer pays Rs.56.16 for it. He was given two successive discounts, one of them being 10%. The other discount is?

[ "8%", "4%", "6%", "3%", "1%" ]

65*(90/100)*((100-x)/100) = 56.16 x = 4% Answer: B The answer is: B

B

mathematics

In a group of 24 students, each student is registered for at least one of three classes – History, Math and English. 15 students are registered for History, 15 students are registered for Math, and 20 students are registered for English. If only three students are registered for all three classes, how many students are registered for exactly two classes?

[ "13", "10", "9", "20", "7" ]

Each student is registered forat least one of three classesmeans thatthere are no students who are registered for none of the classes. Total = {people in group A} + {people in group B} + {people in group C} - {people in exactly 2 groups} - 2*{people in exactly 3 groups} + {people in none of the groups}: 24 = 15 + 15 + 20 - {people in exactly 2 groups} - 2*3 + 0-->{people in exactly 2 groups}=20 Answer: D The answer is: D

D

mathematics

Tough and Tricky questions: Combinations. Five contestants representing four different countries advance to the finals of a fencing championship. Assuming all competitors have an equal chance of winning, how many possibilities are there with respect to how a first-place and second-place medal can be awarded?

[ "6", "7", "12", "15", "24" ]

Four contestants representing four different countries advance to the finals of a fencing championship. Assuming all competitors have an equal chance of winning, how many possibilities are there with respect to how a first-place and second-place medal can be awarded? We have 2 slots to be filled using 5 contestants:5 options for slot1*3 option for slot2 = 5* 3 = 15 Ans. D) 15 The answer is: D

D

mathematics

If the average (arithmetic mean) of a list of numbers is 12 and the standard deviation of that list of numbers is 1.3, then which of the following numbers is more than two standard deviations from the mean? I. 13.7 II. 12.3 III. 9.3

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

Mean = 12 SD = 1.3 2 SD above mean = 12+2*1.3 = 14.6 2 SD below mean = 12-2*1.3 = 9.4 12.3 and 13.7 lies in the range of 2SD from mean Answer: Option D The answer is: D

D

mathematics

If the length of an edge of cube P is twice the length of an edge of cube Q, what is the ratio of the volume of cube Q to the volume of cube P?

[ "1/8", "1/4", "1/3", "1/7", "1/9" ]

The length of cube Q = 1; The length of cube P = 2; The ratio of the volume of cube Q to the volume of cube P = 1^3/2^3 = 1/8. Answer: A The answer is: A

A

mathematics

A rectangular-shaped carpet that measures x feet by y feet is priced at $12. What is the cost of the carpet, in dollars per square yard? (1 square yard = 9 square feet)

[ "108/(xy)", "90xy", "xy/90", "xy/10", "10/(xy)" ]

The area of the carpet in feet is xy. The area in square yards is xy / 9. The price per square yard is 12 / (xy/9) = 108/(xy). The answer is A. The answer is: A

A

mathematics

In what time will a train 180 meters long cross an electric pole, if its speed is 154 km/hr

[ "5 seconds", "4.3 seconds", "3 seconds", "2.5 seconds", "None of these" ]

Explanation: First convert speed into m/sec Speed = 154*(5/18) = 42 m/sec Time = Distance/speed = 180/42 = 4.3 seconds Option B The answer is: B

B

mathematics

One out of every 300 light bulbs are defected. If 2 out of every 10 defected light bulbs have a broken glass and there are 20 broken glass light bulbs in the shipment, how many light bulbs total are there in the shipment?

[ "2,000", "30000", "10,000", "50,000", "52,000" ]

20 broken glasses indicates that 10*10= 100 defected bulbs are present. 100 defected bulbs indicates that 100*300= 30,000 light bulbs are present. B is the answer The answer is: B

B

mathematics

40 onions on a scale weigh 7.68 kg. When 5 onions are removed from the scale, the average weight of the 35 onions is 190 grams. What is the average weight (in grams) of the 5 onions which were removed?

[ "200", "202", "204", "206", "208" ]

35*190=6650. The other 5 onions weigh a total of 1030 grams. The average weight is 1030/5 = 206 grams. The answer is D. The answer is: D

D

mathematics

Of 70 players on a football team, 43 are throwers. The rest of the team is divided so one third are left- handed and the rest are right handed. Assuming that all throwers are right handed, how many right- handed players are there total?

[ "54", "59", "63", "61", "92" ]

Total = 70 Thrower = 43 Rest = 70 - 43 = 27 Left Handed = 27/3 = 9 Right handed = 18 If all Thrower are right handed then total right handed is 43 + 18 = 61 so D. 61 is the right answer The answer is: D

D

mathematics

A train 125 m long passes a man, running at 5 km/hr in the same direction in which the train is going, in 10 seconds. The speed of the train is:

[ "10 km/hr", "50 km/hr", "14 km/hr", "17 km/hr", "77 km/hr" ]

Speed of the train relative to man = (125/10) m/sec = (25/2) m/sec. [(25/2) * (18/5)] km/hr = 45 km/hr. Let the speed of the train be x km/hr. Then, relative speed = (x - 5) km/hr. x - 5 = 45 ==> x = 50 km/hr. Answer: B The answer is: B

B

mathematics

Find the odd man out. 187, 264, 316, 473, 682, 781

[ "187", "316", "781", "682", "473" ]

In all numbers except 316, the middle digit is the sum of other two digits. Answer is B The answer is: B

B

mathematics

At a meeting, 3 people are to be seated around a circular table. Two seating arrangements are considered different only when the positions of the people are different relative to each other. What is the total number of different possible seating arrangements for the group?

[ "2", "7", "C)120", "D)144", "E)720" ]

The number of arrangements of n distinct objects in a row is given by n! The number of arrangements of n distinct objects in a circle is given by (n−1)! "The difference between placement in a row and that in a circle is following: if we shift all object by one position, we will get different arrangement in a row but the same relative arrangement in a circle. So, for the number of circular arrangements of n objects we have: R=n!-n=(n−1)! (n−1)!=(7−1)!=720 Answer: E The answer is: C

C

mathematics

A tank is filled in eight hours by three pipes A, B and C. Pipe A is twice as fast as pipe B, and B is twice as fast as C. How much time will pipe B alone take to fill the tank?

[ "17 hours", "28 hours", "19 hours", "14 hours", "14 hours" ]

1/A + 1/B + 1/C = 1/8 (Given) Also given that A = 2B and B = 2C => 1/2B + 1/B + 2/B = 1/8 => (1 + 2 + 4)/2B = 1/8 => 2B/7 = 8 => B = 28 hours. Answer: B The answer is: B

B