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	Rs.8000 become Rs.10210 in a certain interval of time at the rate of 5% per annum of C.I. Find the time?	[ "6 YEARS", "7", "5", "3", "4" ]	Explanation: 10210 = 8000(21/20)N (21/20)5 = (21/20)N => N = 5 Answer: Option C The answer is: C	C
mathematics	What is the sum of the multiples of 4 between 34 and 135 inclusive?	[ "2000", "2100", "2150", "2200", "2500" ]	the fastest way in an AP is to find the average and multiply with total integers.. between 34 and 135, the smallest multiple of 4 is 36 and largest =132.. average=(36+132)/2=84.. total numbers = (132-36)/4 + 1= 24+1=25.. sum=25*84=2100 ans B The answer is: B	B
mathematics	In a garden, 26 trees are planted at equal distances along a yard 600 metres long, one tree being at each end of the yard. What is the distance between two consecutive trees?	[ "10", "8", "12", "24", "16" ]	26 trees have 25 gaps between them. Length of each gap = 600/25 = 24 i.e., distance between two consecutive trees = 24 Answer is D. The answer is: D	D
mathematics	If the ratio of the sum of the first 6 terms of a G.P. to the sum of the first 3 terms of the G.P. is 126, what is the common ratio of the G.P?	[ "3", "1/3", "2", "5", "1/5" ]	126=(a1+a2+a3+a4+a5+a6)/(a1+a2+a3) Factorize the same terms 126=1+(a4+a5+a6)/(a1+a2+a3) Write every term with respect to r a1=a1 a2=a1r^1 a3=a1r^2 ......... 126=1+(a1(r^3+r^4+r^5))/(a1(1+r^1+r^2)) 125=(r^3 (1+r^1+r^2))/((1+r^1+r^2)) 125=r^3 r=5 D The answer is: D	D
mathematics	A sun is divided among X, Y and Z in such a way that for each rupee X gets, Y gets 45 paisa and Z gets 30 paisa. If the share of Y is RS. 27, what is the total amount?	[ "166", "105", "178", "177", "169" ]	x:y:z = 100:45:30 20:9:6 9 --- 27 35 --- ? => 105 Answer: B The answer is: B	B
mathematics	Two goods trains each 500 m long are running in opposite directions on parallel tracks. Their speeds are 45 km/hr and 30 km/hr respectively. Find the time taken by the slower train to pass the driver of the faster one?	[ "12 sec", "24 sec", "48 sec", "60 sec", "65 sec" ]	Explanation: Relative speed = 45 + 30 = 75 km/hr. 75 * 5/18 = 125/6 m/sec. Distance covered = 500 + 500 = 1000 m. Required time = 1000 * 6/125 = 48 sec. ANSWER IS C The answer is: C	C
mathematics	A, B and C jointly thought of engaging themselves in a business venture. It was agreed that A would invest Rs. 6500 for 6 months, B, Rs. 8400 for 5 months and C, Rs. 10,000 for 3 months. A wants to be the working member for which, he was to receive 5% of the profits. The profit earned was Rs. 7400. What is the share of B in the profit.	[ "2670", "2560", "2440", "2550", "2660" ]	A is a working member and for that, he receives 5% of the profit = 5% of 7400 =(5×7400)/100=370 Remaining amount =7400−370=7030 Ratio of their investments =6500×6:8400×5:10000×3=65×6:84×5:100×3=13×6:84:20×3=13×2:28:20=13:14:10 Share of B in the profit =7030×14/37=190×14=2660 Answer is E. The answer is: E	E
mathematics	Three houses of the same type were advertised to be let in a locality. Two men made separate applications for a house. What is the probability that each of them applied for the same house.	[ "1/3", "2/3", "1/6", "1/9", "1/27" ]	Since each of the house has same probability of getting selected so for each men proability of selecting a house out of 3 houses 1/3 Let us consider case where all 2 men choose House no 1 So for First men it will be 1/3,second men 1/3 So probability of selecting house no 1 is 1/31/3= 1/9 And since there are 3 such house so probability that each men select the same house is 31/9 or 1/3 Ans is A The answer is: A	A
mathematics	After increasing 20% in the price of a Book costs Rs.240. Find the actual cost of an article?	[ "100", "150", "200", "220", "250" ]	CP* (120/100) = 240 CP= 2* 100 => CP = 200 Answer:C The answer is: C	C
mathematics	A bag contains 6 white marbles and 6 black marbles. If each of 6 girls and 6 boys randomly selects and keeps a marble, what is the probability that all of the girls select the same colored marble?	[ "1/35", "1/10", "1/3", "1/462", "1/252" ]	first, total ways to select for all boys and girls, i.e 12!/(6!6!) = 121110987/65432 =924 then there are one two way girls can have all same colors, either white or black. The number of ways in which 6 girls can select 6 white balls = 6C6 = 1 The number of ways in which 6 girls can select 6 black balls = 6C6 = 1 Therefore, total favorable outcomes/total outcomes = 2/924 = 1/462 D The answer is: D	D
mathematics	If 6 men and 8 boys can do a piece of work in 10 days while 26 men and 48 boys can do the same in 2 days, the time taken by 15 men and 20 boys in doing the same type of work will be?	[ "4", "5", "6", "7", "8" ]	Let 1 men's 1 day work = x and 1 boy's 1 day work = y. Then, 6x + 8y = 1/10 and 26x + 48y = 1/2 Solving these two equations, we get: x = 1/100 and y = 1/200 (15 men + 20 boys)'s 1 day work = (15/100 + 20/200) = 1/4 15 men and 20 boys can do the work in 4 days. Answer:A The answer is: A	A
mathematics	A new tower has just been built at the Verbico military hospital; the number of beds available for patients at the hospital is now 4 times the number available before the new tower was built. Currently, 1/3 of the hospital's original beds, as well as 1/5 of the beds in the new tower, are occupied. For the purposes of renovating the hospital's original wing, all of the patients in the hospital's original beds must be transferred to beds in the new tower. If patients are neither admitted nor discharged during the transfer, what fraction of the beds in the new tower will be unoccupied once the transfer is complete?	[ "11/30", "29/60", "17/30", "31/45", "11/15" ]	I think D - 31/45 is the correct answer. Here goes: Lets assume originally the number of beds = x After the new tower, the total combined no of beds = 4x So old = x, New = 3x Now 1/3 of x are occupied and 1/5 of 3x are occupied which simplifies to (3/5)x We are shifting 1/3 of x to the new ward so there will now be: 1/3 of x plus 3/5 of x occupied in the new ward. Add them up to get 14/15 of x There are 3x beds in New Tower so ratio is: (14/15)x / 3x = 14/45 of x Subtract that from 45/45 of x and you get the number of un-occupied beds to total capacity of New Tower =31/45 D The answer is: D	D
mathematics	On a game show, a contestant is given three keys, each of which opens exactly one of three identical boxes. The contestant assigns each key to one of the boxes and wins the amount of money contained in any box that is opened by the key assigned to it. The first box contains $1.5, the second $150, and the third $1500. What is the probability that a contestant will win more than $1500?	[ "1/9", "2/3", "1/6", "1/3", "1/2" ]	Let's call the boxes that contain $1.5, $150, and $1500, respectively, Box A, Box B, Box C. These are opened, respectively, by Key A, Key B, and Key C. We want to know the probability of winning more than $1500. Notice that if the distribution of keys is: Box A = Key B Box B = Key A Box C = Key C then the contestant wins exactly $1500, not more than $1500. The only configuration that leads to winning more than $1000 is: Box A = Key A Box B = Key B Box C = Key C i.e., getting all three keys correct. That's the only way to be more than $1500. So, really, the question can be rephrased: what is the probability of guessing the order of keys so that each key matches the correct box? Well, for a set of three items, the number of possible permutations is 3! = 321 = 6. Of those 6 possible permutations, only one of them leads to all three keys being paired with the right box. So, the answer is Probability = 1/6 Answer = C The answer is: C	C
mathematics	The ratio between the number of sheep and the number of horses at the Stewar farm is 2 to 7. If each of horse is fed 230 ounces of horse food per day and the farm needs a total 12880 ounces of horse food per day. what is number sheep in the form??	[ "18", "16", "32", "56", "58" ]	et no of sheep and horses are 2k and 7k no of horses= 12880/230=56 now 7K=56 and k=8 no of sheep=(2*8) =16 ANSWER:B The answer is: B	B
mathematics	Jason's team scored 60 points in a game basketball and he accounted for 60 percent of their points. How much did he score?	[ "42", "38", "36", "44", "40" ]	600/10 x (6/10) = 3600/100 or 36 Answer is C The answer is: C	C
mathematics	Two cyclist start from the same places in opposite directions. One is going towards north at 18kmph and the other is going towards south 20kmph. What time will they take to be 190km apart?	[ "1 1/4 hours", "5 hours", "4hours", "3 3/4 hours", "6hours" ]	To be (18+20) km apart, they take 1 hour To be 190 km apart, they take 1/38 * 190 = 5 hrs Answer is B The answer is: B	B
mathematics	Distance between two stations A and B is 778 km. A train covers the journey from A to B at 84 km per hour and returns back to A with a uniform speed of 56km per hour. Find the average speed of the train during the whole journey?	[ "67.0 km /hr", "67.2 km /hr", "69.0 km /hr", "69.2 km /hr", "None" ]	Solution Required average speed =(2xy / x+y)km/hr = 2 x 84 x 56 /(84 + 56) = (2 x 84 x 85 /140) = 67.2 km/hr. Answer B The answer is: B	B
mathematics	The angle of elevation of the sun, when the length of the shadow of a tree is √3 times the height of the tree is	[ "30°", "45°", "60°", "90°", "None" ]	Solution Let AB be the tree and AC be its shadow. Then, < ABC = θ. Then, AC/AB = √3 cotθ= √3 θ=30° Answer A The answer is: A	A
mathematics	The ratio between the length and the breadth of a rectangular park is 3 : 2. If a man cycling along the boundary of the park at the speed of 12 km/hr completes one round in 8 minutes, then the area of the park (in sq. m) is:	[ "153601", "153600", "153602", "153603", "153604" ]	Perimeter = Distance covered in 8 min. =(12000/60) x 8m = 1600 m. Let length = 3x metres and breadth = 2x metres. Then, 2(3x + 2x) = 1600 or x = 160. Length = 480 m and Breadth = 320 m. Area = (480 x 320) m2 = 153600 m2. Answer: B The answer is: B	B
mathematics	The tax on a commodity is diminished by 15% and its consumption increased by 10%. The effect on revenue is?	[ "8.5", "6.5", "5.5", "5.6", "4.4" ]	100 * 100 = 10000 85 * 110 = 9350 ----------- 10000-----------650 100-----------? => 6.5% decrease Answer:B The answer is: B	B
mathematics	A tap can fill a tank in 8 hours. After half the tank is filled three more similar taps are opened. What is the total time taken to fill the tank completely?	[ "5 hrs", "6 hrs", "8 hrs", "7.5 hrs", "4 hrs" ]	Time taken by one tap to fill the tank = 4 hrs. Part filled by the taps in 1 hour = 4 * 1/8 = 1/2 Remaining part = 1 - 1/2 = 1/2 1/2 : 1/2 :: 1 : x x = 1/2 * 1 * 2 = 1 hrs. i.e., 60 min So, total time taken = 3 hrs 60 min = 4 hrs ANSWER: E The answer is: E	E
mathematics	Mr. Smith calculated the average of 10three digit numbers. But due to a mistake he reversed the digits of a number and thus his average increased by 49.5. The difference between the unit digit and hundreds digit of that number is :	[ "a) 4", "b) 3", "c) 2", "d) 1", "e) 5" ]	Since the average increased by 49.5 and there were a total of 10 numbers, it means the incorrect number was 495 greater than the correct number. Say, the correct number was abc (where a, b and c are the digits of the 3 digit number) Then the incorrect number was cba. 100c + 10b + a - (100a + 10b + c) = 495 99c - 99a = 99(c - a) = 495 495 = 99*5 = 99(c - a) So c - a = 5 Answer (E) The answer is: E	E
mathematics	A welder received an order to make a 1 million liter cube-shaped tank. If he has only 4x2 meter sheets of metal that can be cut, how many metal sheets will be required for this orderT? (1 cubic meter = 1,000 liters)	[ "92", "90", "82", "78", "75" ]	I get 75. A cube with 1 million liters cube would be a cube with the dimensions of 100100100. 42 covers 8 sq liters so 100/8 = 12.5. T=12.56 = 75.E The answer is: E	E
mathematics	If 638521 is to be divisible by 5, what is the least whole number that should be added to?	[ "8", "7", "5", "4", "3" ]	A number is divisible by 5 if the last digit is either 0 or 5. Here, 638521=1(last digit is neither 0 or 5). the next multiple of 5 i.e to make the last digit 0 or 5 add 4 4 must be added to 638521 to make it divisible by 5 D The answer is: D	D
mathematics	0.999999+0.111111=?	[ "1", "1.0001", "1.0021", "1.111", "1.11111" ]	0.999999 + 0.111111 = 0.999999 + 0.11111 + 0.000001 = (0.999999 + 0.000001) + 0.11111 = 1 + 0.11111 = 1.11111 E The answer is: E	E
mathematics	A furniture manufacturer has two machines, but only one can be used at a time. Machine K is utilized during the first shift and Machine B during the second shift, while both work half of the third shift. If Machine K can do the job in 12 days working two shifts and Machine B can do the job in 15 days working two shifts, how many days will it take to do the job with the current work schedule?	[ "14", "13", "11", "9", "7" ]	'Approximately' could actually make such a question ambiguous. Not this one though but a similar question with the answer as 9.2 days. You round off 8.89 days as 9 days and everything is fine in this question. What do you do when you get 9.2 days? Do you need 9 days or 10 days? Can you round off 9.2 as 9 even though that is what you do with numbers? No, because in 9 days your work is not over. You do need 10 days. To finish a work say Machine K you need to work full 9 days and a part of the 10th day. If I ask you how many days do you need to complete the work, will you say 9 or 10? You will say 10 even if you don't use the 10th day fully=D The answer is: D	D
mathematics	There are 300 seniors at Morse High School, and 50% of them have cars. Of the remaining grades (freshmen, sophomores, and juniors), only 10% of them have cars. If 25% of all the students at Morse have cars, how many students are in the three lower grades?	[ "500", "900", "1200", "1350", "1500" ]	Let x be the number of students in the lower three grades. 0.1x + 150 = 0.25(x+300) 0.15x = 75 x = 500 The answer is A. The answer is: A	A
mathematics	The total age of A and B is 16 years more than the total age of B and C. C is how many year younger than	[ "14 years", "12 years", "56 years", "16 years", "55 years" ]	Given that A+B = 16 + B + C => A â€“ C = 16 + B â€“ B = 16 => C is younger than A by 16 years Answer:D The answer is: D	D
mathematics	If by selling an article for Rs.60, a person loses 1/7 of money, what would he have gained or lost % by selling it for Rs.77?	[ "5%", "10%", "15%", "20%", "25%" ]	Sol. CP - = EC7 = 70 1-7 6 77-70 % Profit = 100 = 10% B The answer is: B	B
mathematics	A cycle is bought for Rs.900 and sold for Rs.1080, find the gain percent?	[ "20%", "30%", "15%", "10%", "35%" ]	900---- 180 100---- 20% ANSWER A The answer is: A	A
mathematics	If a > 1, which of the following is equal to (2a + 6)/(a^2 + 2a - 3)?	[ "a", "a + 3", "2/(a - 1)", "2a/(a - 3)", "(a - 1)/2" ]	(2a + 6)/(a^2 + 2a - 3) = 2(a + 3) / (a + 3)(a - 1) = 2/(a - 1) Option C The answer is: C	C
mathematics	The speed of a boat in upstream is 30 kmph and the speed of the boat downstream is 70 kmph. Find the speed of the boat in still water and the speed of the stream?	[ "22 kmph", "20 kmph", "21 kmph", "26 kmph", "28 kmph" ]	Speed of the boat in still water = (30+70)/2 = 50 kmph. Speed of the stream = (70-30)/2 = 20 kmph. Answer:B The answer is: B	B
mathematics	325 metres long yard, 26 trees are palnted at equal distances, one tree being at each end of the yard. What is the distance between 2consecutive trees	[ "13", "12", "14", "16", "18" ]	26 trees have 25 gaps between them, Required distance (325/25) = 13 A The answer is: A	A
mathematics	For each color copy, Print Shop X charges $1.25 and Print Shop Y charges $2.75. How much greater is the charge for 80 color copies at Print Shop Y than at Print Shop X?	[ "$120", "$125", "$130", "$135", "$140" ]	The difference in the two prices is $2.75 - $1.25 = $1.50 for each color copy. Each color copy will cost an extra $1.50 at Print Shop Y. 80*$1.50 = $120 The answer is A. The answer is: A	A
mathematics	A dog takes 10 leaps for every 2 leaps of a hare. If one leap of the dog is equal to 2 leaps of the hare, the ratio of the speed of the dog to that of the hare is :	[ "5:1", "10:1", "15:1", "20:1", "25:1" ]	Explanation: Dog : Hare = (10*2) leaps of hare : 2 leaps of hare = 20 : 2. Answer: B) 10:1 The answer is: B	B
mathematics	2y - x = 2xy . If x and y are integers, which of the following could equal y?	[ "2", "1", "0", "3", "4" ]	Plug in the answer choices in the equation from the question stem. A) y = 2 >>> 4-x = 4x >>> No value of x will satisfy this, not even 0. POE B) y = 1 >>> 2 - x = 2x >>> Same, POE C) y = 0 >>> -x = 0 >>> x This is the answer Answer C The answer is: C	C
mathematics	Three investors, A, B, and C, divide the profits from a business enterprise in the ratio of 5 : 7 : 8, respectively. If investor A earned $ 5,000, how much money did investors B and C earn in total?	[ "$15,000", "$4,900", "$5,600", "$9,500", "$10,500" ]	Let profit for A = 5x profit for B = 7x profit for C = 8x Investor A earned = 5000 5x = 5000=>x=1000 Total profit for B and C = 7x+ 8x = 15x Therefore , 15x =15*1000= 15,000 Answer A The answer is: A	A
mathematics	What annual instalment will discharge a debt of Rs 1092 due in 3 years at 12% simple interest?	[ "Rs.325", "Rs.545", "Rs.560", "Rs.550", "Rs.450" ]	Let each instalment be Rs.x . 1st year = [x + (x * 12 * 2)/100] 2nd year = [ x + (x 12 1)/100] 3rd year = x Then, [x + (x * 12 * 2)/100] + [ x + (x 12 1)/100] + x =1092 3x + ( 24x/100 ) + ( 12x/100 ) = 1092 336x =109200 x = 325 Each instalment = Rs. 325 Answer: A The answer is: A	A
mathematics	I sold a book at a profit of 10%. Had I sold it for $100 more, 15% would have been gained. Find the cost price?	[ "$2000", "$2500", "$3000", "$3120", "$1540" ]	115% of cost - 110% of cost = $100 5% of cost = $100 cost = 100*100/5 = $2000 Answer is A The answer is: A	A
mathematics	The difference of the squares of two consecutive even integers is divisible by which of the following integers ?	[ "6", "4", "2", "5", "1" ]	Let the two consecutive even integers be 2n and (2n + 2). Then, (2n + 2)^2 = (2n + 2 + 2n)(2n + 2 - 2n) = 2(4n + 2) = 4(2n + 1), which is divisible by 4. ANSWER B The answer is: B	B
mathematics	A tradesman by means of his false balance defrauds to the extent of 20%? in buying goods as well as by selling the goods. What percent does he gain on his outlay?	[ "74%", "94%", "44%", "24%", "74%" ]	g% = 20 + 20 + (20*20)/100 = 44% Answer:C The answer is: C	C
mathematics	A man can swim in still water at 12 km/h, but takes twice as long to swim upstream than downstream. The speed of the stream is?	[ "4", "4.2", "5.3", "1.5", "5.2" ]	M = 12 S = x DS = 12 + x US = 12 - x 12 + x = (12 - x)2 12 + x = 24 -2x 3x = 12 x = 4 Answer:A The answer is: A	A
mathematics	What is the greatest possible value of integer n if 100! is divisible by 15^n	[ "20", "21", "22", "23", "24" ]	15^n = 5^n * 3^n Highest prime factor will be the limiting factor. 100/5 +100/25 =20+4 = 24 ANSWER:E The answer is: E	E
mathematics	An uneducated retailer marks all his goods at 55% above the cost price and thinking that he will still make 25% profit, offers a discount of 25% on the marked price. What is his actual profit on the sales?	[ "12.50 %", "13.50 %", "14 %", "14.50 %", "None" ]	Sol. Let C.P. = Rs. 100. Then, marked price = Rs. 155. S.P. = 75% of Rs. 155 = Rs. 116.25. ∴ Gain% = 16.25%. Answer E The answer is: E	E
mathematics	There are three rooms in a motel: one single, one double and one for four persons. How many ways are there to house seven persons in these rooms ?	[ "7! / 1! 2! 3!", "7!", "7! / 3", "7! / 3!", "7! / 4" ]	Choose 1 person for the single room & from the remaining choose 2 for the double room & from the remaining choose 4 people for the four person room, Then, 7C1 x 6C2 x 4C4 = 7! / 1! 2! 3! ANSWER:A The answer is: A	A
mathematics	The probability of a team winning a match given Matt is playing the match is 0.7. The probability of the team winning a match given Matt is not playing the match is 0.5. The probability of Matt playing any match is 0.8. If it is known that the team has won the last match, what is the probability that Matt played the match?	[ "A)0.848", "B)0.7", "C)0.8571", "D)0.7531", "E)0.8213" ]	Out of 100 matches: Matt is plays in 80 and not plays in 20. Out of 80 matches Matt plays in, team wins 0.7080 = 56. Out of 20 matches Matt does not play in, team wins 0.520 = 10. So, out of 100 matches 56 + 10 = 66 are won. It is known that the team has won the last match. Out of 66 matches won, Matt is in 56: 56/66 = 0.848... Answer: A. The answer is: A	A
mathematics	The sum of the ages of a father and son is 45 years. Five years ago, the product of their ages was four times the fathers age at that time. The present age of father and son	[ "6", "7", "9", "2", "5" ]	Let sons age = x years. Then fathers age = (45 - x)years. (x—5)(45—x—5) = 4(45- x - 5) hence (x—5) = 4 so x = 9 Their ages are 36 years and 9 years. Answer: C The answer is: C	C
mathematics	100 people are standing in a circle. The person standing at number 1 is having a sword. He kills the person next to him with the sword and then gives the sword to the third person. This process is carried out till there is just one person left. Can you find out who survives?	[ "93", "73", "90", "75", "87" ]	B The person on 73rd number will survive. Till the number is the power of 2, the last person to survive will be the one who started it. But since the number here is not the power of 2, we will take the greatest power of 2 that is less than the number which is 64. 100 - 64 = 36 36 people are killed as 2, 4, 6, ..., 72. Thus the sword will now be given to the 73rd person. Now he is the first person to start in the remaining 64 people. Thus he will be the one to survive. The answer is: B	B
mathematics	If A, B and C together can finish a piece of work in 4 days. A alone in 12 days and B in 18 days, then C alone can do it in?	[ "1", "7", "8", "9", "6" ]	C = 1/4 - 1/12 – 1/18 = 1/9 => 9 days' Answer: D The answer is: D	D
mathematics	5 friends visited a fruit stall, and everyone decided to contribute equally to the total bill of $100. If one of the friends had a coupon for 6% off the total bill, and if each friend still contributed equally after the coupon was applied to the bill, how much did each friend pay?	[ "18", "18.8", "19", "17.8", "17.9" ]	At the non-discounted price, each friend would pay $20, as $100 divided by 5 friends is $20 per friend. But if the bill is 6% off, then each friend would pay 6% less. 6% of $20 is $1.2, so each friend saves $1.2 and pays the remaining 18.8 CORRECT OPTION:OPTION B The answer is: B	B
mathematics	There are 35 students in a hostel. If the no. of students increases by 7, the expenses of the mess increase by Rs.42/day while the average expenditure per head diminishes by Rs1. Find the original expenditure of the mess?	[ "Rs. 34", "Rs. 39", "Rs. 42", "Rs. 49", "Rs. 51" ]	Suppose the average join the mess , total expenditure = 35x + 42 Now, the average expenditure = (35x + 42)/ (35 + 7) = x – 1 or, 35x + 42 = 42x – 42 or, x = 12 Thus the original expenditure of the mess = 35 x 12 = Rs. 42 C The answer is: C	C
mathematics	In a shop, 40% socks are white and rest are black. 60% socks are made of cotton and rest are made of wool. 25% white socks are made of cotton and 20 of the black socks are made of wool. How many black socks D are made of cotton?	[ "100", "80", "60", "50", "25" ]	I'll prefer to solve this with plug n play method. As we know, White Cotton socks are only 25% and Total Cotton socks is 60% - Hence Black Cotton socks D has to be [highlight]HIGH[/highlight]number. Thats why we've to pick high number... say 100 or 80. 100 fits perfectly after relevant calculations. Hence answer A. The answer is: A	A
mathematics	The median of a triangle is the line from any vertex to the midpoint of the opposite side. Triangle ABC has vertices A = (0, 5), B = (–1, –1), and C = (5, 2). What is the slope of the median from A to the midpoint of BC?	[ "–3/4", ">–4/3", "–5", "–5/2", "–9/4" ]	First to find the midpoint of B & C — average the x-coordinates: (–1+ 5)/2 = 2; and average the y-coordinates: (–1 + 2)/2 = 1/2. Thus, the midpoint has coordinates (2, 1/2). We want the slope from A = (0, 5) to (2, 1/2). The rise is the change in the y-coordinates: 1/2 – 5 = -9/2. The run is the change in the x-coordinates: 2 – 0 = 2. Slope = rise/run = [–9/2]/2 = –9/4. Answer = (E) The answer is: E	E
mathematics	The inner circumference of a circular race track, 14 m wide, is 440 m. Find radius of the outer circle?	[ "22", "37", "87", "84", "82" ]	Let inner radius be r metres. Then, 2 r = 440 ; r = = 70 m. Radius of outer circle = (70 + 14) m = 84 m. Answer: D The answer is: D	D
mathematics	Convert 100 inches into centimeter?	[ "112cm", "120cm", "150cm", "210cm", "254cm" ]	1 inch = 2.54cm 100 inches = 100*2.54 = 254cm Answer is E The answer is: E	E
mathematics	If A : B = 4 : 7 and B : C = 5 : 9 then A : B : C is :	[ "ratio 20 : 35 : 63", "35 : 36 : 63", "30 : 35 : 65", "25 :34: 68", "None of these" ]	A : B = 4 : 7 B : C = 5 :9 = 57/5 : 9 7/5 = 7 : 63/5 A : B : C = 4 : 7 : 63/5 = 20 : 35 : 63 ANSWER: A The answer is: A	A
mathematics	40% of a number is more than 20% of 650 by 190. Find the number?	[ "299", "277", "800", "289", "271" ]	(40/100) * X – (20/100) * 650 = 190 2/5 X = 320 X = 800 Answer:C The answer is: C	C
mathematics	Two trains of length 140 m and 280 m are running towards each other on parallel lines at 42 kmph and 30 kmph respectively. In what time will they be clear of each other from the moment they meet?	[ "28", "266", "990", "20", "21" ]	Relative speed = (42 + 30) * 5/18 = 4 * 5 = 20 mps. Distance covered in passing each other = 140 + 280 = 420 m. The time required = d/s = 420/20 = 21 sec. Answer: E The answer is: E	E
mathematics	In what time will a railway train 20 m long moving at the rate of 36 kmph pass a telegraph post on its way?	[ "8 sec", "1 sec", "9 sec", "6 sec", "2 sec" ]	T = 20/36 * 18/5 = 2 sec Answer:E The answer is: E	E
mathematics	In a certain random experiment, exactly one of the outcomes A, B, and C will occur. In each random experiment, the probability that outcome A will occur is 1/3 , and the probability that outcome B will occur is 1/3. What is the probability that when the random experiment is conducted 6 independent times, each of outcomes A, B, and C will occur twice?	[ "5/243", "1/12", "10/81", "1/6", "16/81" ]	Given that P(A) = P(B) = P(C) = 1/3. P(AABBCC) = (13)^6∗6!2!2!2!=1081 we multiply by 6!/(2!2!2!) because AABBCC scenario can occur in several ways: AABBCC, AABCBC, AACBBC, ... (the number of permutations of 6 letters AABBCC is 6!(2!2!2!)). Answer: C. The answer is: C	C
mathematics	If 2x-1 + 2x+1 = 1280, then find the value of x.	[ "0", "2", "4", "9", "6" ]	Sol. 2x-1 + 2x+1 = 1280 ⇔ 2x-1 (1+22) = 1280 ⇔ 2x-1 = 1280 / 5 = 256 = 28 ⇔ x - 1 = 8 ⇔ x = 9. Hence, x = 9. Answer D The answer is: D	D
mathematics	Find the compound interest on $800 for 1year at 10% p.a. if CI is component yearly?	[ "$40", "$400", "$840", "$800", "$80" ]	A = P(1 + R/100)^T = 800(1 + 10/100)^1 = 800*21/20 =$840 CI = A-P = 840-800 = $40 Answer is A The answer is: A	A
mathematics	If the average of ten numbers is 30, then which of the following could be the standard deviation of the ten numbers? I. 0 II. 30 III. 20	[ "I", "all three options", "II", "III", "I&II" ]	We know that we have 10 numbers (and they could be ANY values - including negatives and non-integers) and we know that the average of those numbers is 10. This is meant to say that there are an INFINITE number of possible sets of 10 numbers that fit this prompt. IF all ten numbers were the same (meaning that we had ten 10s), then the SD would be 0. The more 'spread out' those ten numbers get, the higher the SD becomes. Since there's no limit to the 'spread', then there's no limit to what the SD could be either. Thus, it could be 10 or 20 or any other number. B The answer is: B	B
mathematics	7 baseball players each stand at different corners of a baseball diamond. The sides of the diamond are all of equal length. Two arrangements of baseball players are considered different only when the relative positions of the players differ. How many different ways can the baseball players arrange themselves around the diamond?	[ "4", "6", "16", "24", "720" ]	it is like a circular arrangement. total ways for n people to arrange in a circle is = factorial (n-1) in this case n= 7 hence ans = 6 factorial = 720 hence E The answer is: E	E
mathematics	A man said to his son, "I was two-third of your present age when you were born". If the present age of the man is 48 years, find the present age of the son?	[ "25.7 years", "28 years", "29.3 years", "28.8 years", "28.9 years" ]	Present age of the son be P, he was born P years ago. The age of the man was: (48 - P). His age when the son was born should be equal to 2/3 of P. (48 - P) = 2/3 P 5P = 144 => P = 28.8 ANSWER:D The answer is: D	D
mathematics	In the city of San Durango, 60 people own cats, dogs, or rabbits. If 34 people owned cats, 40 owned dogs, 10 owned rabbits, and 12 owned exactly two of the three types of pet, how many people owned all three?	[ "2", "6", "8", "12", "32" ]	Total = C + D + R - (CD + DR + CR) - 2CDR 60 = 34 + 40 + 10 - (12) - 2x x = 6 So, answer will be B The answer is: B	B
mathematics	When processing flower-nectar into honey bees' extract, a considerable amount of water gets reduced. How much flower-nectar must be processed to yield 1kg of honey, if nectar contains 50% water, and the honey obtained from this nectar contains 25% water?	[ "1.2 kg", "1.5 kg", "1.7 kg", "1.9 kg", "None of these" ]	Explanation : Flower-nectar contains 50% of non-water part. In honey this non-water part constitutes 75% (100-25). Therefore 0.5 X Amount of flower-nectar = 0.75 X Amount of honey = 0.75 X 1 kg Therefore amount of flower-nectar needed = (0.75/0.51)kg=1.5 kgs Answer : B The answer is: B	B
mathematics	In how many ways 8 different tickets Q can be distributed between Jane and Bill if each is to receive any even number of tickets and all 8 tickets to be distributed.	[ "From 2 to 6 inclusive.", "From 98 to 102 inclusive.", "From 122 to 126 inclusive.", "From 128 to 132 inclusive.", "From 196 to 200 inclusive." ]	Possibilities J 8 6 4 2 0 B 0 2 4 6 8 # of ways 8C8 8C6 8C4 8C2 8C0 Q=1+28+70+28+1 = 128 Answer is D. The answer is: D	D
mathematics	A and B walk around a circular track. A and B walk at a speed of 2 rounds per hour and 3 rounds per hour respectively. If they start at 8 a.m. from the same point in opposite directions, how many times shall they cross each other before 9.30 a.m.?	[ "9.39 am", "9.80 am", "9.30 am", "9.32 am", "5.30 am" ]	Relative speed = Speed of A + Speed of B (∴ they walk in opposite directions) = 2 + 3 = 5 rounds per hour => They cross each other 5 times in 1 hour and 2 times in 1/2 hour Time duration from 8 am to 9.30 am = 1.5 hour Hence they cross each other 7 times before 9.30 am Answer : C The answer is: C	C
mathematics	Rs.8000 become Rs.8652.8 in a certain interval of time at the rate of 4% per annum of C.I. Find the time?	[ "6 years", "8 years", "9 years", "3 years", "2 years" ]	8652.8 = 8000(26/25)N (26/25)^2 = (26/25)N => N = 2 At the end of two years what will be the comp.Answer: E The answer is: E	E
mathematics	5358 x 53 = ?	[ "283974", "283758", "273298", "273258", "277382" ]	A 5358 x 53 = 5358 x (50 + 3) = 5358 x 50 + 5358 x 3 = 267900 + 16074 = 283974. The answer is: A	A
mathematics	A student chose a number, multiplied it by 2, then subtracted 138 from the result and got 112. What was the number he chose?	[ "123", "267", "125", "267", "120" ]	Let xx be the number he chose, then 2â‹…xâˆ’138=112 x=125 Answer:C The answer is: C	C
mathematics	A can finish a work in 10 days and B can do same work in half the time taken by A. then working together, what part of same work they can finish in a day?	[ "1/5", "1/6", "1/7", "3/10", "None of these" ]	Explanation: Please note in this question, we need to answer part of work for a day rather than complete work. It was worth mentioning here because many do mistake at this point in hurry to solve the question So lets solve now, A's 1 day work = 1/10 B's 1 day work = 1/5 [because B take half the time than A] (A+B)'s one day work = (1/10+1/5)=3/10 So in one day 3/10 work will be done Answer: D The answer is: D	D
mathematics	The number of bacteria in a petri dish increased by 50 percent every 2 hours. If there were 108 million bacteria in the dish at 2: 30 p.m., at what time were there 32 million bacteria in the dish?	[ "6: 00 p.m.", "8: 00 p.m.", "6: 00 a.m.", "8: 30 a.m.", "10: 00 a.m." ]	Given: The number of bacteria in a petri dish increased by 50 percent every 2 hours There were 108 million bacteria in the dish at 2: 00 p.m Since the bacteria is increasing by 50% every 2 hours, this means that the number is multiplied by 1.5 every 2 hours. Required: At what time were there 32 million bacteria in the dish? Assume that there were n intervals of 2 hours between 32 million and 108 million. 32 * (1.5)^n = 108 (3/2)^n = 108/32 = 27/8 = (3/2)^3 Hence n = 3 intervals. Each interval was of 2 hours. Therefore, the number of hours = 6 Subtracting 6 hours from 2H30 PM, we get 8H30 AM as the answer. Option D The answer is: D	D
mathematics	If a(a + 7) = 18 and b(b + 7) = 18, where a ≠ b, then a + b =	[ "−48", "−5", "2", "-7", "48" ]	i.e. if a = 2 then b = -9 or if a = -9 then b = 2 But in each case a+b = -9+2 = -7 Answer: option D The answer is: D	D
mathematics	A chair is bought for Rs.600/- and sold at a loss of 10% find its selling price	[ "Rs.540/-", "Rs.550/-", "Rs.560/-", "Rs.590/-", "Rs.580/-" ]	100 % ------> 600 (100 * 6 = 600) 90 % ------> 540 (90 * 6 = 540) Selling price = Rs.540/- A) The answer is: A	A
mathematics	A tank is 25 m long, 12 m wide and 6 m deep. The cost of plastering its walls and bottom at 75 paise per sq. m, is:	[ "Rs. 456", "Rs. 458", "Rs. 558", "Rs. 568", "None of these" ]	Explanation: Area to be plastered = [2(l + b) x h] + (l x b) = {[2(25 + 12) x 6] + (25 x 12)} m2 = (444 + 300) m2 = 744 m2. Cost of plastering = Rs. 744 x 75 / 100 = Rs. 558 Answer: C The answer is: C	C
mathematics	Three friends Dhoni, Rahul and Aswin divide $1540 amongs them in such a way that if $10, $12 and $18 are removed from the sums that Dhoni, Rahul and Aswin received respectively, then the share of the sums that they got will be in the ratio of 15: 17: 18. How much did Aswin receive?	[ "$560", "$562", "$564", "$558", "$570" ]	A+B+C = 1540 Given ratio 15:17:18 Let us say the shares of A,B,C deducting 10,12,18 be a,b,c a+b+c = 1540-40= 1500 = 50K c share = (1500X18)/50 = 540 C = Aswin share = 540+18= 558 Option D The answer is: D	D
mathematics	There are 600 boys in a hostel. Each plays either hockey or football or both. If 75% play hockey and 55% play football, how many play both?	[ "120", "150", "200", "180", "160" ]	n(A) = 75600/100 = 450 n(B) = 55600/100 = 330 n(AUB) = 600 n(AnB) = 450+330-600 = 180 Answer is D The answer is: D	D
mathematics	What is the are of an equilateral triangle of side 16 cm?	[ "64√6 cm2", "84√3 cm2", "64√9 cm2", "64√3 cm2", "66√3 cm2" ]	Area of an equilateral triangle = √3/4 S2 If S = 16, Area of triangle = √3/4 * 16 * 16 = 64√3 cm2; Answer: D The answer is: D	D
mathematics	The pages of a report are numbered consecutively from 1 to 13. If the sum of the page numbers up to and including page number x of the report is equal to one less than the sum of the page numbers following page number x, then x =	[ "5", "6", "7", "8", "9" ]	sum of the first few numbers =1+2+3+4+5+6+7+8+9 =45 sum of the last few = 10 +11+12+13 =46 page no.9 answer .E The answer is: E	E
mathematics	Of the 20 members of a kitchen crew, 17 can use the meat-cutting machine, 18 can use the bread-slicing machine, and 15 can use both machines. If one member is chosen at random, what is the probability that the member chosen will be someone who cannot use either machine?	[ "0", "1/10", "1/7", "1/4", "1/3" ]	You know how to solve for Total number of people who can use at least one machine: Total = n(A) + n(B) - n(A and B) Total people who can use at least one machine = 17 + 18 - 15 = 20 So all 20 people know how to use at least one machine. Hence, if you pick anyone, the probability is 0 that he wouldn't know how to use any machine. Answer A The answer is: A	A
mathematics	If q = 20! + 17, then q is divisible by which of the following? I. 15 II. 17 III. 19	[ "None", "I only", "II only", "I and II", "II and II" ]	Another crude way to answer this, if you did not know the properties above would be to consider that that 20! will have the number ending in 00 due to 10 and 20 being included. So q!+17 = xxxx00 +17 = xxxx17 which is only possibly divisible by 17. Hence Option C is the answer. The answer is: C	C
mathematics	In the number 11,0AB, A and B represent the tens and units digits, respectively. If 11,0AB is divisible by 52, what is the greatest possible value of B × A?	[ "0", "5", "10", "15", "22" ]	You should notice that 522=110 so 11,000 is divisible by 55: 55200=11,000 (or you can notice that 11,000 is obviously divisible by both 5 and 11 so by 55) --> BA=00=0. Next number divisible by 55 is 11,000+55=11,055: BA=55=22 (next number won't have 110 as the first 3 digits so we have only two options 0 and 25). Answer: E. ! Please post PS questions in the PS subforum:gmat-problem-solving-ps-140/ Please post DS questions in the DS subforum:gmat-data-sufficiency-ds-141/ No posting of PS/DS questions is allowed in the mainMath forum. E The answer is: E	E
mathematics	The speed of a boat in still water is 60kmph and the speed of the current is 25kmph. Find the speed downstream and upstream?	[ "80,47 kmph", "80,80 kmph", "85,35 kmph", "80,40 kmph", "83,40 kmph" ]	Speed downstream = 60 + 25 = 85 kmph Speed upstream = 60 - 25 = 35 kmph.Answer:C The answer is: C	C
mathematics	If the domain of function f given by f(x) = -x 2 + 6x is given by the interval [0 , 6], then the range of f is given by the interval	[ "[0 , 9]", "[0 , 6]", "[0 , 3]", "[3 , 6]", "None" ]	If the domain of function f given by f(x) = -x 2 + 6x is given by the interval [0 , 6], then the range of f is given by the interval Answer B The answer is: B	B
mathematics	If Y > X and XM < YM, what must be true?	[ "M >0.", "M < Y.", "X < 0.", "M < 0.", "Y < 0." ]	X>Y, bus as soon as M is multiplied to both sides inequality sign changes. This is only possible when -ve is multiplied on both sides. That means M is -ve A is the answer The answer is: A	A
mathematics	Right triangle ABC is to be drawn in the xy-plane so that the right angle is at A and AB is parallel to the y-axis. If the x- and y-coordinates of A, B, and C are to be integers that are consistent with the inequalities -4 ≤ x ≤ 2 and 4 ≤ y ≤ 9 , then how many different triangles can be drawn that will meet these conditions?	[ "54", "432", "864", "2,916", "148,824" ]	We have the rectangle with dimensions 94 (9 horizontal dots and 4 vertical). AB is parallel to y-axis and AC is parallel to x-axis. Choose the (x,y) coordinates for vertex A: 9C14C1; Choose the x coordinate for vertex C (as y coordinate is fixed by A): 8C1, (9-1=8 as 1 horizontal dot is already occupied by A); Choose the y coordinate for vertex B (as x coordinate is fixed by A): 3C1, (4-1=3 as 1 vertical dot is already occupied by A). 9C14C18C1*3C1=864. Answer: C. The answer is: C	C
mathematics	A certain sum amounts to Rs.1550 in 2 years and Rs.1700 in 3 years. Find the rate % per annum?	[ "5.67%", "7.67%", "6.67%", "4.67%", "8.67%" ]	2 --- 1550 3 --- 1700 -------------- 1 --- 150 N = 1 I = 150 R = ? P = 1550 - 300= 1250 150 = (12501R)/100 R = 6.67% Answer: C The answer is: C	C
mathematics	How many terms are there in 2, 4, 8, 16,..., 2048?	[ "14", "11", "12", "10", "8" ]	2, 4, 8, 16, ...,2048 is a G.P with a =2 and r =4/2 =2 Let the number of terms be n. Then 2 x 2 ^n-1 = 2048 or 2^n-1 = 1024= 2^10 Thus n - 1 =10 n= 11 ANSWER:B The answer is: B	B
mathematics	In the following sequence: [x, y, z, 6, 8, 16, 28] each number is equal to the sum of the three numbers preceding it. What is x+y?	[ "2", "3", "4", "5", "-2" ]	lets start from z, as per the question stem z + 6 + 8 = 16 -->> z= 2 similarly, y +2 + 6 = 8 --> y = 0 similarly,, x + 0 + 2 = 6 --> x = 4 hence , x+y = 4-0 = 4 --> x+y=4 ANSWER:C The answer is: C	C
mathematics	In a 1000 m race Usha beats Shiny by 50 m. In the same race, by what time margin Shiny beat Mercy. who runs at 4 m/s ?	[ "100 sec.", "50 sec", "25 sec", "Data not sufficient", "None of these" ]	Explanation: Speed of Shiny = 50/ 10 = 5m/s Time taken by shiny to complete the race is B = 1000/5 = 200 sec. Time taken by Baley to complete the race is D = 1000/4 = 250 sec. Hence, D-B = 50 sec Answer : B The answer is: B	B
mathematics	Of 30 applicants for a job, 12 had at least 4 years' experience, 18 had degrees, and 3 had less than 4 years' experience and did not have a degree.How many of the applicants had at least 4 years' experience and a degree?	[ "14", "13", "9", "7", "5" ]	D. 7 30 - 3 = 27 27 - 12 - 18 = -7 Then 7 are in the intersection between 4 years experience and degree. Answer D The answer is: D	D
mathematics	For any integer k greater than 1, the symbol k* denotes the product of all integers between 1 and k, inclusive. If k* is a multiple of 2835 what is the least possible value of k?	[ "5", "7", "9", "11", "13" ]	2835 = 333357 Thus k must include numbers at least up to the number 9 so that there are at least four appearances of 3 (that is: 3, 6, and 9=33). The answer is C. The answer is: C	C
mathematics	Eddy and Freddy start simultaneously from city A and they travel to City B and City C respectively. Eddy takes 3 hours and Freddy takes 4 hours to complete the journey. If the distance between City A and City B is 480 kms and City A and City C is 300 kms. What is the ratio of their average speed of travel? (Eddy: Freddy)	[ "32/15", "3/8", "8/5", "5/8", "5/3" ]	Distance traveled by Eddy = 480 km Time taken by Eddy = 3 hours Average speed of Eddy = 480/3 = 160 km/hour Distance traveled by Freddy = 300 km Time taken by Freddy = 4 hours Average speed of Freddy = 300/4 = 75 km/hour Ratio of average speed of Eddy to Freddy = 160/75 = 32/15 Answer A The answer is: A	A
mathematics	Angelina walked 100 meters from her home to the grocery at a constant speed. She then walked 180 meters to the gym at double the speed. She spent 40 seconds less on her way from the grocery to the gym than on her way from home to the grocery. What was Angelina's speed, in meters per second, from the grocery to the gym?	[ "2", "3", "0.5", "6", "12" ]	let the speed be X... so time taken from home to grocery= 100/x.. the speed to gym = 2x.. so time taken = 180/2x=90/x.. its given 100/x-90/x=40.. 10/x=40.. x=0.25m/secs.. so grocery to gym=2*0.25=0.5m/s... Answer : C The answer is: C	C
mathematics	A started a business with an investment of Rs. 70000 and after 6 months B joined him investing Rs. 120000. If the profit at the end of a year is Rs. 91000, then the share of B is?	[ "A)44500", "B)42000", "C)44098", "D)43007", "E)44098" ]	Ratio of investments of A and B is (70000 * 12) : (120000 * 6) = 7 : 6 Total profit = Rs. 91000 Share of B = 6/13 (91000) = Rs. 42000 Answer:B The answer is: B	B
mathematics	A copy machine, working at a constant rate, makes 30 copies per minute. A second copy machine, working at a constant rate, makes 55 copies per minute. Working together at their respective rates, how many copies do the two machines make in half an hour ?	[ "90", "2,700", "4,500", "2,550", "324,000" ]	Together the two machines make 30+55=85 copies per minute. So, in half an hour they will make 85*30=2,550 copies. Answer: D. The answer is: D	D
mathematics	Two trains of equal lengths take 10 sec and 18 sec respectively to cross a telegraph post. If the length of each train be 120 m, in what time will they cross other travelling in opposite direction?	[ "11", "9", "13", "14", "12.8" ]	Speed of the first train = 120/10 = 12 m/sec. Speed of the second train = 120/18 = 6.7 m/sec. Relative speed = 12 + 6.7 = 18.7 m/sec. Required time = (120 + 120)/18.7 = 12.8 sec. Answer: Option E The answer is: E	E
mathematics	What is the maximum value of vx - yz. If the value of v,x,y,z have to be chosen from the set A where A(-3,-2,-1,0,1,2,3)	[ "15", "66", "25", "88", "17" ]	Explanation: To maximize the value of vx - yz, we make yz negative and vx as maximum as possible using given value. vx−yz=(−3)2−(−3×2)vx−yz=(−3)2−(−3×2) = 15 Answer:A The answer is: A	A

mathematics

Rs.8000 become Rs.10210 in a certain interval of time at the rate of 5% per annum of C.I. Find the time?

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

Explanation: 10210 = 8000(21/20)N (21/20)5 = (21/20)N => N = 5 Answer: Option C The answer is: C

C

mathematics

What is the sum of the multiples of 4 between 34 and 135 inclusive?

[ "2000", "2100", "2150", "2200", "2500" ]

the fastest way in an AP is to find the average and multiply with total integers.. between 34 and 135, the smallest multiple of 4 is 36 and largest =132.. average=(36+132)/2=84.. total numbers = (132-36)/4 + 1= 24+1=25.. sum=25*84=2100 ans B The answer is: B

B

mathematics

In a garden, 26 trees are planted at equal distances along a yard 600 metres long, one tree being at each end of the yard. What is the distance between two consecutive trees?

[ "10", "8", "12", "24", "16" ]

26 trees have 25 gaps between them. Length of each gap = 600/25 = 24 i.e., distance between two consecutive trees = 24 Answer is D. The answer is: D

D

mathematics

If the ratio of the sum of the first 6 terms of a G.P. to the sum of the first 3 terms of the G.P. is 126, what is the common ratio of the G.P?

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

126=(a1+a2+a3+a4+a5+a6)/(a1+a2+a3) Factorize the same terms 126=1+(a4+a5+a6)/(a1+a2+a3) Write every term with respect to r a1=a1 a2=a1*r^1 a3=a1*r^2 ......... 126=1+(a1(r^3+r^4+r^5))/(a1(1+r^1+r^2)) 125=(r^3 (1+r^1+r^2))/((1+r^1+r^2)) 125=r^3 r=5 D The answer is: D

D

mathematics

A sun is divided among X, Y and Z in such a way that for each rupee X gets, Y gets 45 paisa and Z gets 30 paisa. If the share of Y is RS. 27, what is the total amount?

[ "166", "105", "178", "177", "169" ]

x:y:z = 100:45:30 20:9:6 9 --- 27 35 --- ? => 105 Answer: B The answer is: B

B

mathematics

Two goods trains each 500 m long are running in opposite directions on parallel tracks. Their speeds are 45 km/hr and 30 km/hr respectively. Find the time taken by the slower train to pass the driver of the faster one?

[ "12 sec", "24 sec", "48 sec", "60 sec", "65 sec" ]

Explanation: Relative speed = 45 + 30 = 75 km/hr. 75 * 5/18 = 125/6 m/sec. Distance covered = 500 + 500 = 1000 m. Required time = 1000 * 6/125 = 48 sec. ANSWER IS C The answer is: C

C

mathematics

A, B and C jointly thought of engaging themselves in a business venture. It was agreed that A would invest Rs. 6500 for 6 months, B, Rs. 8400 for 5 months and C, Rs. 10,000 for 3 months. A wants to be the working member for which, he was to receive 5% of the profits. The profit earned was Rs. 7400. What is the share of B in the profit.

[ "2670", "2560", "2440", "2550", "2660" ]

A is a working member and for that, he receives 5% of the profit = 5% of 7400 =(5×7400)/100=370 Remaining amount =7400−370=7030 Ratio of their investments =6500×6:8400×5:10000×3=65×6:84×5:100×3=13×6:84:20×3=13×2:28:20=13:14:10 Share of B in the profit =7030×14/37=190×14=2660 Answer is E. The answer is: E

E

mathematics

Three houses of the same type were advertised to be let in a locality. Two men made separate applications for a house. What is the probability that each of them applied for the same house.

[ "1/3", "2/3", "1/6", "1/9", "1/27" ]

Since each of the house has same probability of getting selected so for each men proability of selecting a house out of 3 houses 1/3 Let us consider case where all 2 men choose House no 1 So for First men it will be 1/3,second men 1/3 So probability of selecting house no 1 is 1/3*1/3= 1/9 And since there are 3 such house so probability that each men select the same house is 3*1/9 or 1/3 Ans is A The answer is: A

A

mathematics

After increasing 20% in the price of a Book costs Rs.240. Find the actual cost of an article?

[ "100", "150", "200", "220", "250" ]

CP* (120/100) = 240 CP= 2* 100 => CP = 200 Answer:C The answer is: C

C

mathematics

A bag contains 6 white marbles and 6 black marbles. If each of 6 girls and 6 boys randomly selects and keeps a marble, what is the probability that all of the girls select the same colored marble?

[ "1/35", "1/10", "1/3", "1/462", "1/252" ]

first, total ways to select for all boys and girls, i.e 12!/(6!*6!) = 12*11*10*9*8*7/6*5*4*3*2 =924 then there are one two way girls can have all same colors, either white or black. The number of ways in which 6 girls can select 6 white balls = 6C6 = 1 The number of ways in which 6 girls can select 6 black balls = 6C6 = 1 Therefore, total favorable outcomes/total outcomes = 2/924 = 1/462 D The answer is: D

D

mathematics

If 6 men and 8 boys can do a piece of work in 10 days while 26 men and 48 boys can do the same in 2 days, the time taken by 15 men and 20 boys in doing the same type of work will be?

[ "4", "5", "6", "7", "8" ]

Let 1 men's 1 day work = x and 1 boy's 1 day work = y. Then, 6x + 8y = 1/10 and 26x + 48y = 1/2 Solving these two equations, we get: x = 1/100 and y = 1/200 (15 men + 20 boys)'s 1 day work = (15/100 + 20/200) = 1/4 15 men and 20 boys can do the work in 4 days. Answer:A The answer is: A

A

mathematics

A new tower has just been built at the Verbico military hospital; the number of beds available for patients at the hospital is now 4 times the number available before the new tower was built. Currently, 1/3 of the hospital's original beds, as well as 1/5 of the beds in the new tower, are occupied. For the purposes of renovating the hospital's original wing, all of the patients in the hospital's original beds must be transferred to beds in the new tower. If patients are neither admitted nor discharged during the transfer, what fraction of the beds in the new tower will be unoccupied once the transfer is complete?

[ "11/30", "29/60", "17/30", "31/45", "11/15" ]

I think D - 31/45 is the correct answer. Here goes: Lets assume originally the number of beds = x After the new tower, the total combined no of beds = 4x So old = x, New = 3x Now 1/3 of x are occupied and 1/5 of 3x are occupied which simplifies to (3/5)x We are shifting 1/3 of x to the new ward so there will now be: 1/3 of x plus 3/5 of x occupied in the new ward. Add them up to get 14/15 of x There are 3x beds in New Tower so ratio is: (14/15)x / 3x = 14/45 of x Subtract that from 45/45 of x and you get the number of un-occupied beds to total capacity of New Tower =31/45 D The answer is: D

D

mathematics

On a game show, a contestant is given three keys, each of which opens exactly one of three identical boxes. The contestant assigns each key to one of the boxes and wins the amount of money contained in any box that is opened by the key assigned to it. The first box contains $1.5, the second $150, and the third $1500. What is the probability that a contestant will win more than $1500?

[ "1/9", "2/3", "1/6", "1/3", "1/2" ]

Let's call the boxes that contain $1.5, $150, and $1500, respectively, Box A, Box B, Box C. These are opened, respectively, by Key A, Key B, and Key C. We want to know the probability of winning more than $1500. Notice that if the distribution of keys is: Box A = Key B Box B = Key A Box C = Key C then the contestant wins exactly $1500, not more than $1500. The only configuration that leads to winning more than $1000 is: Box A = Key A Box B = Key B Box C = Key C i.e., getting all three keys correct. That's the only way to be more than $1500. So, really, the question can be rephrased: what is the probability of guessing the order of keys so that each key matches the correct box? Well, for a set of three items, the number of possible permutations is 3! = 3*2*1 = 6. Of those 6 possible permutations, only one of them leads to all three keys being paired with the right box. So, the answer is Probability = 1/6 Answer = C The answer is: C

C

mathematics

The ratio between the number of sheep and the number of horses at the Stewar farm is 2 to 7. If each of horse is fed 230 ounces of horse food per day and the farm needs a total 12880 ounces of horse food per day. what is number sheep in the form??

[ "18", "16", "32", "56", "58" ]

et no of sheep and horses are 2k and 7k no of horses= 12880/230=56 now 7K=56 and k=8 no of sheep=(2*8) =16 ANSWER:B The answer is: B

B

mathematics

Jason's team scored 60 points in a game basketball and he accounted for 60 percent of their points. How much did he score?

[ "42", "38", "36", "44", "40" ]

600/10 x (6/10) = 3600/100 or 36 Answer is C The answer is: C

C

mathematics

Two cyclist start from the same places in opposite directions. One is going towards north at 18kmph and the other is going towards south 20kmph. What time will they take to be 190km apart?

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

To be (18+20) km apart, they take 1 hour To be 190 km apart, they take 1/38 * 190 = 5 hrs Answer is B The answer is: B

B

mathematics

Distance between two stations A and B is 778 km. A train covers the journey from A to B at 84 km per hour and returns back to A with a uniform speed of 56km per hour. Find the average speed of the train during the whole journey?

[ "67.0 km /hr", "67.2 km /hr", "69.0 km /hr", "69.2 km /hr", "None" ]

Solution Required average speed =(2xy / x+y)km/hr = 2 x 84 x 56 /(84 + 56) = (2 x 84 x 85 /140) = 67.2 km/hr. Answer B The answer is: B

B

mathematics

The angle of elevation of the sun, when the length of the shadow of a tree is √3 times the height of the tree is

[ "30°", "45°", "60°", "90°", "None" ]

Solution Let AB be the tree and AC be its shadow. Then, < ABC = θ. Then, AC/AB = √3 cotθ= √3 θ=30° Answer A The answer is: A

A

mathematics

The ratio between the length and the breadth of a rectangular park is 3 : 2. If a man cycling along the boundary of the park at the speed of 12 km/hr completes one round in 8 minutes, then the area of the park (in sq. m) is:

[ "153601", "153600", "153602", "153603", "153604" ]

Perimeter = Distance covered in 8 min. =(12000/60) x 8m = 1600 m. Let length = 3x metres and breadth = 2x metres. Then, 2(3x + 2x) = 1600 or x = 160. Length = 480 m and Breadth = 320 m. Area = (480 x 320) m2 = 153600 m2. Answer: B The answer is: B

B

mathematics

The tax on a commodity is diminished by 15% and its consumption increased by 10%. The effect on revenue is?

[ "8.5", "6.5", "5.5", "5.6", "4.4" ]

100 * 100 = 10000 85 * 110 = 9350 ----------- 10000-----------650 100-----------? => 6.5% decrease Answer:B The answer is: B

B

mathematics

A tap can fill a tank in 8 hours. After half the tank is filled three more similar taps are opened. What is the total time taken to fill the tank completely?

[ "5 hrs", "6 hrs", "8 hrs", "7.5 hrs", "4 hrs" ]

Time taken by one tap to fill the tank = 4 hrs. Part filled by the taps in 1 hour = 4 * 1/8 = 1/2 Remaining part = 1 - 1/2 = 1/2 1/2 : 1/2 :: 1 : x x = 1/2 * 1 * 2 = 1 hrs. i.e., 60 min So, total time taken = 3 hrs 60 min = 4 hrs ANSWER: E The answer is: E

E

mathematics

Mr. Smith calculated the average of 10three digit numbers. But due to a mistake he reversed the digits of a number and thus his average increased by 49.5. The difference between the unit digit and hundreds digit of that number is :

[ "a) 4", "b) 3", "c) 2", "d) 1", "e) 5" ]

Since the average increased by 49.5 and there were a total of 10 numbers, it means the incorrect number was 495 greater than the correct number. Say, the correct number was abc (where a, b and c are the digits of the 3 digit number) Then the incorrect number was cba. 100c + 10b + a - (100a + 10b + c) = 495 99c - 99a = 99(c - a) = 495 495 = 99*5 = 99(c - a) So c - a = 5 Answer (E) The answer is: E

E

mathematics

A welder received an order to make a 1 million liter cube-shaped tank. If he has only 4x2 meter sheets of metal that can be cut, how many metal sheets will be required for this orderT? (1 cubic meter = 1,000 liters)

[ "92", "90", "82", "78", "75" ]

I get 75. A cube with 1 million liters cube would be a cube with the dimensions of 100*100*100. 4*2 covers 8 sq liters so 100/8 = 12.5. T=12.5*6 = 75.E The answer is: E

E

mathematics

If 638521 is to be divisible by 5, what is the least whole number that should be added to?

[ "8", "7", "5", "4", "3" ]

A number is divisible by 5 if the last digit is either 0 or 5. Here, 638521=1(last digit is neither 0 or 5). the next multiple of 5 i.e to make the last digit 0 or 5 add 4 4 must be added to 638521 to make it divisible by 5 D The answer is: D

D

mathematics

0.999999+0.111111=?

[ "1", "1.0001", "1.0021", "1.111", "1.11111" ]

0.999999 + 0.111111 = 0.999999 + 0.11111 + 0.000001 = (0.999999 + 0.000001) + 0.11111 = 1 + 0.11111 = 1.11111 E The answer is: E

E

mathematics

A furniture manufacturer has two machines, but only one can be used at a time. Machine K is utilized during the first shift and Machine B during the second shift, while both work half of the third shift. If Machine K can do the job in 12 days working two shifts and Machine B can do the job in 15 days working two shifts, how many days will it take to do the job with the current work schedule?

[ "14", "13", "11", "9", "7" ]

'Approximately' could actually make such a question ambiguous. Not this one though but a similar question with the answer as 9.2 days. You round off 8.89 days as 9 days and everything is fine in this question. What do you do when you get 9.2 days? Do you need 9 days or 10 days? Can you round off 9.2 as 9 even though that is what you do with numbers? No, because in 9 days your work is not over. You do need 10 days. To finish a work say Machine K you need to work full 9 days and a part of the 10th day. If I ask you how many days do you need to complete the work, will you say 9 or 10? You will say 10 even if you don't use the 10th day fully=D The answer is: D

D

mathematics

There are 300 seniors at Morse High School, and 50% of them have cars. Of the remaining grades (freshmen, sophomores, and juniors), only 10% of them have cars. If 25% of all the students at Morse have cars, how many students are in the three lower grades?

[ "500", "900", "1200", "1350", "1500" ]

Let x be the number of students in the lower three grades. 0.1x + 150 = 0.25(x+300) 0.15x = 75 x = 500 The answer is A. The answer is: A

A

mathematics

The total age of A and B is 16 years more than the total age of B and C. C is how many year younger than

[ "14 years", "12 years", "56 years", "16 years", "55 years" ]

Given that A+B = 16 + B + C => A â€“ C = 16 + B â€“ B = 16 => C is younger than A by 16 years Answer:D The answer is: D

D

mathematics

If by selling an article for Rs.60, a person loses 1/7 of money, what would he have gained or lost % by selling it for Rs.77?

[ "5%", "10%", "15%", "20%", "25%" ]

Sol. CP - = EC7 = 70 1-7 6 77-70 % Profit = 100 = 10% B The answer is: B

B

mathematics

A cycle is bought for Rs.900 and sold for Rs.1080, find the gain percent?

[ "20%", "30%", "15%", "10%", "35%" ]

900---- 180 100---- 20% ANSWER A The answer is: A

A

mathematics

If a > 1, which of the following is equal to (2a + 6)/(a^2 + 2a - 3)?

[ "a", "a + 3", "2/(a - 1)", "2a/(a - 3)", "(a - 1)/2" ]

(2a + 6)/(a^2 + 2a - 3) = 2(a + 3) / (a + 3)(a - 1) = 2/(a - 1) Option C The answer is: C

C

mathematics

The speed of a boat in upstream is 30 kmph and the speed of the boat downstream is 70 kmph. Find the speed of the boat in still water and the speed of the stream?

[ "22 kmph", "20 kmph", "21 kmph", "26 kmph", "28 kmph" ]

Speed of the boat in still water = (30+70)/2 = 50 kmph. Speed of the stream = (70-30)/2 = 20 kmph. Answer:B The answer is: B

B

mathematics

325 metres long yard, 26 trees are palnted at equal distances, one tree being at each end of the yard. What is the distance between 2consecutive trees

[ "13", "12", "14", "16", "18" ]

26 trees have 25 gaps between them, Required distance (325/25) = 13 A The answer is: A

A

mathematics

For each color copy, Print Shop X charges $1.25 and Print Shop Y charges $2.75. How much greater is the charge for 80 color copies at Print Shop Y than at Print Shop X?

[ "$120", "$125", "$130", "$135", "$140" ]

The difference in the two prices is $2.75 - $1.25 = $1.50 for each color copy. Each color copy will cost an extra $1.50 at Print Shop Y. 80*$1.50 = $120 The answer is A. The answer is: A

A

mathematics

A dog takes 10 leaps for every 2 leaps of a hare. If one leap of the dog is equal to 2 leaps of the hare, the ratio of the speed of the dog to that of the hare is :

[ "5:1", "10:1", "15:1", "20:1", "25:1" ]

Explanation: Dog : Hare = (10*2) leaps of hare : 2 leaps of hare = 20 : 2. Answer: B) 10:1 The answer is: B

B

mathematics

2y - x = 2xy . If x and y are integers, which of the following could equal y?

[ "2", "1", "0", "3", "4" ]

Plug in the answer choices in the equation from the question stem. A) y = 2 >>> 4-x = 4x >>> No value of x will satisfy this, not even 0. POE B) y = 1 >>> 2 - x = 2x >>> Same, POE C) y = 0 >>> -x = 0 >>> x This is the answer Answer C The answer is: C

C

mathematics

Three investors, A, B, and C, divide the profits from a business enterprise in the ratio of 5 : 7 : 8, respectively. If investor A earned $ 5,000, how much money did investors B and C earn in total?

[ "$15,000", "$4,900", "$5,600", "$9,500", "$10,500" ]

Let profit for A = 5x profit for B = 7x profit for C = 8x Investor A earned = 5000 5x = 5000=>x=1000 Total profit for B and C = 7x+ 8x = 15x Therefore , 15x =15*1000= 15,000 Answer A The answer is: A

A

mathematics

What annual instalment will discharge a debt of Rs 1092 due in 3 years at 12% simple interest?

[ "Rs.325", "Rs.545", "Rs.560", "Rs.550", "Rs.450" ]

Let each instalment be Rs.x . 1st year = [x + (x * 12 * 2)/100] 2nd year = [ x + (x *12 * 1)/100] 3rd year = x Then, [x + (x * 12 * 2)/100] + [ x + (x *12 * 1)/100] + x =1092 3x + ( 24x/100 ) + ( 12x/100 ) = 1092 336x =109200 x = 325 Each instalment = Rs. 325 Answer: A The answer is: A

A

mathematics

I sold a book at a profit of 10%. Had I sold it for $100 more, 15% would have been gained. Find the cost price?

[ "$2000", "$2500", "$3000", "$3120", "$1540" ]

115% of cost - 110% of cost = $100 5% of cost = $100 cost = 100*100/5 = $2000 Answer is A The answer is: A

A

mathematics

The difference of the squares of two consecutive even integers is divisible by which of the following integers ?

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

Let the two consecutive even integers be 2n and (2n + 2). Then, (2n + 2)^2 = (2n + 2 + 2n)(2n + 2 - 2n) = 2(4n + 2) = 4(2n + 1), which is divisible by 4. ANSWER B The answer is: B

B

mathematics

A tradesman by means of his false balance defrauds to the extent of 20%? in buying goods as well as by selling the goods. What percent does he gain on his outlay?

[ "74%", "94%", "44%", "24%", "74%" ]

g% = 20 + 20 + (20*20)/100 = 44% Answer:C The answer is: C

C

mathematics

A man can swim in still water at 12 km/h, but takes twice as long to swim upstream than downstream. The speed of the stream is?

[ "4", "4.2", "5.3", "1.5", "5.2" ]

M = 12 S = x DS = 12 + x US = 12 - x 12 + x = (12 - x)2 12 + x = 24 -2x 3x = 12 x = 4 Answer:A The answer is: A

A

mathematics

What is the greatest possible value of integer n if 100! is divisible by 15^n

[ "20", "21", "22", "23", "24" ]

15^n = 5^n * 3^n Highest prime factor will be the limiting factor. 100/5 +100/25 =20+4 = 24 ANSWER:E The answer is: E

E

mathematics

An uneducated retailer marks all his goods at 55% above the cost price and thinking that he will still make 25% profit, offers a discount of 25% on the marked price. What is his actual profit on the sales?

[ "12.50 %", "13.50 %", "14 %", "14.50 %", "None" ]

Sol. Let C.P. = Rs. 100. Then, marked price = Rs. 155. S.P. = 75% of Rs. 155 = Rs. 116.25. ∴ Gain% = 16.25%. Answer E The answer is: E

E

mathematics

There are three rooms in a motel: one single, one double and one for four persons. How many ways are there to house seven persons in these rooms ?

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

Choose 1 person for the single room & from the remaining choose 2 for the double room & from the remaining choose 4 people for the four person room, Then, 7C1 x 6C2 x 4C4 = 7! / 1! 2! 3! ANSWER:A The answer is: A

A

mathematics

The probability of a team winning a match given Matt is playing the match is 0.7. The probability of the team winning a match given Matt is not playing the match is 0.5. The probability of Matt playing any match is 0.8. If it is known that the team has won the last match, what is the probability that Matt played the match?

[ "A)0.848", "B)0.7", "C)0.8571", "D)0.7531", "E)0.8213" ]

Out of 100 matches: Matt is plays in 80 and not plays in 20. Out of 80 matches Matt plays in, team wins 0.70*80 = 56. Out of 20 matches Matt does not play in, team wins 0.5*20 = 10. So, out of 100 matches 56 + 10 = 66 are won. It is known that the team has won the last match. Out of 66 matches won, Matt is in 56: 56/66 = 0.848... Answer: A. The answer is: A

A

mathematics

The sum of the ages of a father and son is 45 years. Five years ago, the product of their ages was four times the fathers age at that time. The present age of father and son

[ "6", "7", "9", "2", "5" ]

Let sons age = x years. Then fathers age = (45 - x)years. (x—5)(45—x—5) = 4(45- x - 5) hence (x—5) = 4 so x = 9 Their ages are 36 years and 9 years. Answer: C The answer is: C

C

mathematics

100 people are standing in a circle. The person standing at number 1 is having a sword. He kills the person next to him with the sword and then gives the sword to the third person. This process is carried out till there is just one person left. Can you find out who survives?

[ "93", "73", "90", "75", "87" ]

B The person on 73rd number will survive. Till the number is the power of 2, the last person to survive will be the one who started it. But since the number here is not the power of 2, we will take the greatest power of 2 that is less than the number which is 64. 100 - 64 = 36 36 people are killed as 2, 4, 6, ..., 72. Thus the sword will now be given to the 73rd person. Now he is the first person to start in the remaining 64 people. Thus he will be the one to survive. The answer is: B

B

mathematics

If A, B and C together can finish a piece of work in 4 days. A alone in 12 days and B in 18 days, then C alone can do it in?

[ "1", "7", "8", "9", "6" ]

C = 1/4 - 1/12 – 1/18 = 1/9 => 9 days' Answer: D The answer is: D

D

mathematics

5 friends visited a fruit stall, and everyone decided to contribute equally to the total bill of $100. If one of the friends had a coupon for 6% off the total bill, and if each friend still contributed equally after the coupon was applied to the bill, how much did each friend pay?

[ "18", "18.8", "19", "17.8", "17.9" ]

At the non-discounted price, each friend would pay $20, as $100 divided by 5 friends is $20 per friend. But if the bill is 6% off, then each friend would pay 6% less. 6% of $20 is $1.2, so each friend saves $1.2 and pays the remaining 18.8 CORRECT OPTION:OPTION B The answer is: B

B

mathematics

There are 35 students in a hostel. If the no. of students increases by 7, the expenses of the mess increase by Rs.42/day while the average expenditure per head diminishes by Rs1. Find the original expenditure of the mess?

[ "Rs. 34", "Rs. 39", "Rs. 42", "Rs. 49", "Rs. 51" ]

Suppose the average join the mess , total expenditure = 35x + 42 Now, the average expenditure = (35x + 42)/ (35 + 7) = x – 1 or, 35x + 42 = 42x – 42 or, x = 12 Thus the original expenditure of the mess = 35 x 12 = Rs. 42 C The answer is: C

C

mathematics

In a shop, 40% socks are white and rest are black. 60% socks are made of cotton and rest are made of wool. 25% white socks are made of cotton and 20 of the black socks are made of wool. How many black socks D are made of cotton?

[ "100", "80", "60", "50", "25" ]

I'll prefer to solve this with plug n play method. As we know, White Cotton socks are only 25% and Total Cotton socks is 60% - Hence Black Cotton socks D has to be [highlight]HIGH[/highlight]number. Thats why we've to pick high number... say 100 or 80. 100 fits perfectly after relevant calculations. Hence answer A. The answer is: A

A

mathematics

The median of a triangle is the line from any vertex to the midpoint of the opposite side. Triangle ABC has vertices A = (0, 5), B = (–1, –1), and C = (5, 2). What is the slope of the median from A to the midpoint of BC?

[ "–3/4", ">–4/3", "–5", "–5/2", "–9/4" ]

First to find the midpoint of B & C — average the x-coordinates: (–1+ 5)/2 = 2; and average the y-coordinates: (–1 + 2)/2 = 1/2. Thus, the midpoint has coordinates (2, 1/2). We want the slope from A = (0, 5) to (2, 1/2). The rise is the change in the y-coordinates: 1/2 – 5 = -9/2. The run is the change in the x-coordinates: 2 – 0 = 2. Slope = rise/run = [–9/2]/2 = –9/4. Answer = (E) The answer is: E

E

mathematics

The inner circumference of a circular race track, 14 m wide, is 440 m. Find radius of the outer circle?

[ "22", "37", "87", "84", "82" ]

Let inner radius be r metres. Then, 2 r = 440 ; r = = 70 m. Radius of outer circle = (70 + 14) m = 84 m. Answer: D The answer is: D

D

mathematics

Convert 100 inches into centimeter?

[ "112cm", "120cm", "150cm", "210cm", "254cm" ]

1 inch = 2.54cm 100 inches = 100*2.54 = 254cm Answer is E The answer is: E

E

mathematics

If A : B = 4 : 7 and B : C = 5 : 9 then A : B : C is :

[ "ratio 20 : 35 : 63", "35 : 36 : 63", "30 : 35 : 65", "25 :34: 68", "None of these" ]

A : B = 4 : 7 B : C = 5 :9 = 5*7/5 : 9 *7/5 = 7 : 63/5 A : B : C = 4 : 7 : 63/5 = 20 : 35 : 63 ANSWER: A The answer is: A

A

mathematics

40% of a number is more than 20% of 650 by 190. Find the number?

[ "299", "277", "800", "289", "271" ]

(40/100) * X – (20/100) * 650 = 190 2/5 X = 320 X = 800 Answer:C The answer is: C

C

mathematics

Two trains of length 140 m and 280 m are running towards each other on parallel lines at 42 kmph and 30 kmph respectively. In what time will they be clear of each other from the moment they meet?

[ "28", "266", "990", "20", "21" ]

Relative speed = (42 + 30) * 5/18 = 4 * 5 = 20 mps. Distance covered in passing each other = 140 + 280 = 420 m. The time required = d/s = 420/20 = 21 sec. Answer: E The answer is: E

E

mathematics

In what time will a railway train 20 m long moving at the rate of 36 kmph pass a telegraph post on its way?

[ "8 sec", "1 sec", "9 sec", "6 sec", "2 sec" ]

T = 20/36 * 18/5 = 2 sec Answer:E The answer is: E

E

mathematics

In a certain random experiment, exactly one of the outcomes A, B, and C will occur. In each random experiment, the probability that outcome A will occur is 1/3 , and the probability that outcome B will occur is 1/3. What is the probability that when the random experiment is conducted 6 independent times, each of outcomes A, B, and C will occur twice?

[ "5/243", "1/12", "10/81", "1/6", "16/81" ]

Given that P(A) = P(B) = P(C) = 1/3. P(AABBCC) = (13)^6∗6!2!2!2!=1081 we multiply by 6!/(2!2!2!) because AABBCC scenario can occur in several ways: AABBCC, AABCBC, AACBBC, ... (the number of permutations of 6 letters AABBCC is 6!(2!2!2!)). Answer: C. The answer is: C

C

mathematics

If 2x-1 + 2x+1 = 1280, then find the value of x.

[ "0", "2", "4", "9", "6" ]

Sol. 2x-1 + 2x+1 = 1280 ⇔ 2x-1 (1+22) = 1280 ⇔ 2x-1 = 1280 / 5 = 256 = 28 ⇔ x - 1 = 8 ⇔ x = 9. Hence, x = 9. Answer D The answer is: D

D

mathematics

Find the compound interest on $800 for 1year at 10% p.a. if CI is component yearly?

[ "$40", "$400", "$840", "$800", "$80" ]

A = P(1 + R/100)^T = 800(1 + 10/100)^1 = 800*21/20 =$840 CI = A-P = 840-800 = $40 Answer is A The answer is: A

A

mathematics

If the average of ten numbers is 30, then which of the following could be the standard deviation of the ten numbers? I. 0 II. 30 III. 20

[ "I", "all three options", "II", "III", "I&II" ]

We know that we have 10 numbers (and they could be ANY values - including negatives and non-integers) and we know that the average of those numbers is 10. This is meant to say that there are an INFINITE number of possible sets of 10 numbers that fit this prompt. IF all ten numbers were the same (meaning that we had ten 10s), then the SD would be 0. The more 'spread out' those ten numbers get, the higher the SD becomes. Since there's no limit to the 'spread', then there's no limit to what the SD could be either. Thus, it could be 10 or 20 or any other number. B The answer is: B

B

mathematics

7 baseball players each stand at different corners of a baseball diamond. The sides of the diamond are all of equal length. Two arrangements of baseball players are considered different only when the relative positions of the players differ. How many different ways can the baseball players arrange themselves around the diamond?

[ "4", "6", "16", "24", "720" ]

it is like a circular arrangement. total ways for n people to arrange in a circle is = factorial (n-1) in this case n= 7 hence ans = 6 factorial = 720 hence E The answer is: E

E

mathematics

A man said to his son, "I was two-third of your present age when you were born". If the present age of the man is 48 years, find the present age of the son?

[ "25.7 years", "28 years", "29.3 years", "28.8 years", "28.9 years" ]

Present age of the son be P, he was born P years ago. The age of the man was: (48 - P). His age when the son was born should be equal to 2/3 of P. (48 - P) = 2/3 P 5P = 144 => P = 28.8 ANSWER:D The answer is: D

D

mathematics

In the city of San Durango, 60 people own cats, dogs, or rabbits. If 34 people owned cats, 40 owned dogs, 10 owned rabbits, and 12 owned exactly two of the three types of pet, how many people owned all three?

[ "2", "6", "8", "12", "32" ]

Total = C + D + R - (CD + DR + CR) - 2CDR 60 = 34 + 40 + 10 - (12) - 2x x = 6 So, answer will be B The answer is: B

B

mathematics

When processing flower-nectar into honey bees' extract, a considerable amount of water gets reduced. How much flower-nectar must be processed to yield 1kg of honey, if nectar contains 50% water, and the honey obtained from this nectar contains 25% water?

[ "1.2 kg", "1.5 kg", "1.7 kg", "1.9 kg", "None of these" ]

Explanation : Flower-nectar contains 50% of non-water part. In honey this non-water part constitutes 75% (100-25). Therefore 0.5 X Amount of flower-nectar = 0.75 X Amount of honey = 0.75 X 1 kg Therefore amount of flower-nectar needed = (0.75/0.51)kg=1.5 kgs Answer : B The answer is: B

B

mathematics

In how many ways 8 different tickets Q can be distributed between Jane and Bill if each is to receive any even number of tickets and all 8 tickets to be distributed.

[ "From 2 to 6 inclusive.", "From 98 to 102 inclusive.", "From 122 to 126 inclusive.", "From 128 to 132 inclusive.", "From 196 to 200 inclusive." ]

Possibilities J 8 6 4 2 0 B 0 2 4 6 8 # of ways 8C8 8C6 8C4 8C2 8C0 Q=1+28+70+28+1 = 128 Answer is D. The answer is: D

D

mathematics

A and B walk around a circular track. A and B walk at a speed of 2 rounds per hour and 3 rounds per hour respectively. If they start at 8 a.m. from the same point in opposite directions, how many times shall they cross each other before 9.30 a.m.?

[ "9.39 am", "9.80 am", "9.30 am", "9.32 am", "5.30 am" ]

Relative speed = Speed of A + Speed of B (∴ they walk in opposite directions) = 2 + 3 = 5 rounds per hour => They cross each other 5 times in 1 hour and 2 times in 1/2 hour Time duration from 8 am to 9.30 am = 1.5 hour Hence they cross each other 7 times before 9.30 am Answer : C The answer is: C

C

mathematics

Rs.8000 become Rs.8652.8 in a certain interval of time at the rate of 4% per annum of C.I. Find the time?

[ "6 years", "8 years", "9 years", "3 years", "2 years" ]

8652.8 = 8000(26/25)N (26/25)^2 = (26/25)N => N = 2 At the end of two years what will be the comp.Answer: E The answer is: E

E

mathematics

5358 x 53 = ?

[ "283974", "283758", "273298", "273258", "277382" ]

A 5358 x 53 = 5358 x (50 + 3) = 5358 x 50 + 5358 x 3 = 267900 + 16074 = 283974. The answer is: A

A

mathematics

A student chose a number, multiplied it by 2, then subtracted 138 from the result and got 112. What was the number he chose?

[ "123", "267", "125", "267", "120" ]

Let xx be the number he chose, then 2â‹…xâˆ’138=112 x=125 Answer:C The answer is: C

C

mathematics

A can finish a work in 10 days and B can do same work in half the time taken by A. then working together, what part of same work they can finish in a day?

[ "1/5", "1/6", "1/7", "3/10", "None of these" ]

Explanation: Please note in this question, we need to answer part of work for a day rather than complete work. It was worth mentioning here because many do mistake at this point in hurry to solve the question So lets solve now, A's 1 day work = 1/10 B's 1 day work = 1/5 [because B take half the time than A] (A+B)'s one day work = (1/10+1/5)=3/10 So in one day 3/10 work will be done Answer: D The answer is: D

D

mathematics

The number of bacteria in a petri dish increased by 50 percent every 2 hours. If there were 108 million bacteria in the dish at 2: 30 p.m., at what time were there 32 million bacteria in the dish?

[ "6: 00 p.m.", "8: 00 p.m.", "6: 00 a.m.", "8: 30 a.m.", "10: 00 a.m." ]

Given: The number of bacteria in a petri dish increased by 50 percent every 2 hours There were 108 million bacteria in the dish at 2: 00 p.m Since the bacteria is increasing by 50% every 2 hours, this means that the number is multiplied by 1.5 every 2 hours. Required: At what time were there 32 million bacteria in the dish? Assume that there were n intervals of 2 hours between 32 million and 108 million. 32 * (1.5)^n = 108 (3/2)^n = 108/32 = 27/8 = (3/2)^3 Hence n = 3 intervals. Each interval was of 2 hours. Therefore, the number of hours = 6 Subtracting 6 hours from 2H30 PM, we get 8H30 AM as the answer. Option D The answer is: D

D

mathematics

If a(a + 7) = 18 and b(b + 7) = 18, where a ≠ b, then a + b =

[ "−48", "−5", "2", "-7", "48" ]

i.e. if a = 2 then b = -9 or if a = -9 then b = 2 But in each case a+b = -9+2 = -7 Answer: option D The answer is: D

D

mathematics

A chair is bought for Rs.600/- and sold at a loss of 10% find its selling price

[ "Rs.540/-", "Rs.550/-", "Rs.560/-", "Rs.590/-", "Rs.580/-" ]

100 % ------> 600 (100 * 6 = 600) 90 % ------> 540 (90 * 6 = 540) Selling price = Rs.540/- A) The answer is: A

A

mathematics

A tank is 25 m long, 12 m wide and 6 m deep. The cost of plastering its walls and bottom at 75 paise per sq. m, is:

[ "Rs. 456", "Rs. 458", "Rs. 558", "Rs. 568", "None of these" ]

Explanation: Area to be plastered = [2(l + b) x h] + (l x b) = {[2(25 + 12) x 6] + (25 x 12)} m2 = (444 + 300) m2 = 744 m2. Cost of plastering = Rs. 744 x 75 / 100 = Rs. 558 Answer: C The answer is: C

C

mathematics

Three friends Dhoni, Rahul and Aswin divide $1540 amongs them in such a way that if $10, $12 and $18 are removed from the sums that Dhoni, Rahul and Aswin received respectively, then the share of the sums that they got will be in the ratio of 15: 17: 18. How much did Aswin receive?

[ "$560", "$562", "$564", "$558", "$570" ]

A+B+C = 1540 Given ratio 15:17:18 Let us say the shares of A,B,C deducting 10,12,18 be a,b,c a+b+c = 1540-40= 1500 = 50K c share = (1500X18)/50 = 540 C = Aswin share = 540+18= 558 Option D The answer is: D

D

mathematics

There are 600 boys in a hostel. Each plays either hockey or football or both. If 75% play hockey and 55% play football, how many play both?

[ "120", "150", "200", "180", "160" ]

n(A) = 75*600/100 = 450 n(B) = 55*600/100 = 330 n(AUB) = 600 n(AnB) = 450+330-600 = 180 Answer is D The answer is: D

D

mathematics

What is the are of an equilateral triangle of side 16 cm?

[ "64√6 cm2", "84√3 cm2", "64√9 cm2", "64√3 cm2", "66√3 cm2" ]

Area of an equilateral triangle = √3/4 S2 If S = 16, Area of triangle = √3/4 * 16 * 16 = 64√3 cm2; Answer: D The answer is: D

D

mathematics

The pages of a report are numbered consecutively from 1 to 13. If the sum of the page numbers up to and including page number x of the report is equal to one less than the sum of the page numbers following page number x, then x =

[ "5", "6", "7", "8", "9" ]

sum of the first few numbers =1+2+3+4+5+6+7+8+9 =45 sum of the last few = 10 +11+12+13 =46 page no.9 answer .E The answer is: E

E

mathematics

Of the 20 members of a kitchen crew, 17 can use the meat-cutting machine, 18 can use the bread-slicing machine, and 15 can use both machines. If one member is chosen at random, what is the probability that the member chosen will be someone who cannot use either machine?

[ "0", "1/10", "1/7", "1/4", "1/3" ]

You know how to solve for Total number of people who can use at least one machine: Total = n(A) + n(B) - n(A and B) Total people who can use at least one machine = 17 + 18 - 15 = 20 So all 20 people know how to use at least one machine. Hence, if you pick anyone, the probability is 0 that he wouldn't know how to use any machine. Answer A The answer is: A

A

mathematics

If q = 20! + 17, then q is divisible by which of the following? I. 15 II. 17 III. 19

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

Another crude way to answer this, if you did not know the properties above would be to consider that that 20! will have the number ending in 00 due to 10 and 20 being included. So q!+17 = xxxx00 +17 = xxxx17 which is only possibly divisible by 17. Hence Option C is the answer. The answer is: C

C

mathematics

In the number 11,0AB, A and B represent the tens and units digits, respectively. If 11,0AB is divisible by 52, what is the greatest possible value of B × A?

[ "0", "5", "10", "15", "22" ]

You should notice that 52*2=110 so 11,000 is divisible by 55: 55*200=11,000 (or you can notice that 11,000 is obviously divisible by both 5 and 11 so by 55) --> B*A=0*0=0. Next number divisible by 55 is 11,000+55=11,055: B*A=5*5=22 (next number won't have 110 as the first 3 digits so we have only two options 0 and 25). Answer: E. ! Please post PS questions in the PS subforum:gmat-problem-solving-ps-140/ Please post DS questions in the DS subforum:gmat-data-sufficiency-ds-141/ No posting of PS/DS questions is allowed in the mainMath forum. E The answer is: E

E

mathematics

The speed of a boat in still water is 60kmph and the speed of the current is 25kmph. Find the speed downstream and upstream?

[ "80,47 kmph", "80,80 kmph", "85,35 kmph", "80,40 kmph", "83,40 kmph" ]

Speed downstream = 60 + 25 = 85 kmph Speed upstream = 60 - 25 = 35 kmph.Answer:C The answer is: C

C

mathematics

If the domain of function f given by f(x) = -x 2 + 6x is given by the interval [0 , 6], then the range of f is given by the interval

[ "[0 , 9]", "[0 , 6]", "[0 , 3]", "[3 , 6]", "None" ]

If the domain of function f given by f(x) = -x 2 + 6x is given by the interval [0 , 6], then the range of f is given by the interval Answer B The answer is: B

B

mathematics

If Y > X and XM < YM, what must be true?

[ "M >0.", "M < Y.", "X < 0.", "M < 0.", "Y < 0." ]

X>Y, bus as soon as M is multiplied to both sides inequality sign changes. This is only possible when -ve is multiplied on both sides. That means M is -ve A is the answer The answer is: A

A

mathematics

Right triangle ABC is to be drawn in the xy-plane so that the right angle is at A and AB is parallel to the y-axis. If the x- and y-coordinates of A, B, and C are to be integers that are consistent with the inequalities -4 ≤ x ≤ 2 and 4 ≤ y ≤ 9 , then how many different triangles can be drawn that will meet these conditions?

[ "54", "432", "864", "2,916", "148,824" ]

We have the rectangle with dimensions 9*4 (9 horizontal dots and 4 vertical). AB is parallel to y-axis and AC is parallel to x-axis. Choose the (x,y) coordinates for vertex A: 9C1*4C1; Choose the x coordinate for vertex C (as y coordinate is fixed by A): 8C1, (9-1=8 as 1 horizontal dot is already occupied by A); Choose the y coordinate for vertex B (as x coordinate is fixed by A): 3C1, (4-1=3 as 1 vertical dot is already occupied by A). 9C1*4C1*8C1*3C1=864. Answer: C. The answer is: C

C

mathematics

A certain sum amounts to Rs.1550 in 2 years and Rs.1700 in 3 years. Find the rate % per annum?

[ "5.67%", "7.67%", "6.67%", "4.67%", "8.67%" ]

2 --- 1550 3 --- 1700 -------------- 1 --- 150 N = 1 I = 150 R = ? P = 1550 - 300= 1250 150 = (1250*1*R)/100 R = 6.67% Answer: C The answer is: C

C

mathematics

How many terms are there in 2, 4, 8, 16,..., 2048?

[ "14", "11", "12", "10", "8" ]

2, 4, 8, 16, ...,2048 is a G.P with a =2 and r =4/2 =2 Let the number of terms be n. Then 2 x 2 ^n-1 = 2048 or 2^n-1 = 1024= 2^10 Thus n - 1 =10 n= 11 ANSWER:B The answer is: B

B

mathematics

In the following sequence: [x, y, z, 6, 8, 16, 28] each number is equal to the sum of the three numbers preceding it. What is x+y?

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

lets start from z, as per the question stem z + 6 + 8 = 16 -->> z= 2 similarly, y +2 + 6 = 8 --> y = 0 similarly,, x + 0 + 2 = 6 --> x = 4 hence , x+y = 4-0 = 4 --> x+y=4 ANSWER:C The answer is: C

C

mathematics

In a 1000 m race Usha beats Shiny by 50 m. In the same race, by what time margin Shiny beat Mercy. who runs at 4 m/s ?

[ "100 sec.", "50 sec", "25 sec", "Data not sufficient", "None of these" ]

Explanation: Speed of Shiny = 50/ 10 = 5m/s Time taken by shiny to complete the race is B = 1000/5 = 200 sec. Time taken by Baley to complete the race is D = 1000/4 = 250 sec. Hence, D-B = 50 sec Answer : B The answer is: B

B

mathematics

Of 30 applicants for a job, 12 had at least 4 years' experience, 18 had degrees, and 3 had less than 4 years' experience and did not have a degree.How many of the applicants had at least 4 years' experience and a degree?

[ "14", "13", "9", "7", "5" ]

D. 7 30 - 3 = 27 27 - 12 - 18 = -7 Then 7 are in the intersection between 4 years experience and degree. Answer D The answer is: D

D

mathematics

For any integer k greater than 1, the symbol k* denotes the product of all integers between 1 and k, inclusive. If k* is a multiple of 2835 what is the least possible value of k?

[ "5", "7", "9", "11", "13" ]

2835 = 3*3*3*3*5*7 Thus k must include numbers at least up to the number 9 so that there are at least four appearances of 3 (that is: 3, 6, and 9=3*3). The answer is C. The answer is: C

C

mathematics

Eddy and Freddy start simultaneously from city A and they travel to City B and City C respectively. Eddy takes 3 hours and Freddy takes 4 hours to complete the journey. If the distance between City A and City B is 480 kms and City A and City C is 300 kms. What is the ratio of their average speed of travel? (Eddy: Freddy)

[ "32/15", "3/8", "8/5", "5/8", "5/3" ]

Distance traveled by Eddy = 480 km Time taken by Eddy = 3 hours Average speed of Eddy = 480/3 = 160 km/hour Distance traveled by Freddy = 300 km Time taken by Freddy = 4 hours Average speed of Freddy = 300/4 = 75 km/hour Ratio of average speed of Eddy to Freddy = 160/75 = 32/15 Answer A The answer is: A

A

mathematics

Angelina walked 100 meters from her home to the grocery at a constant speed. She then walked 180 meters to the gym at double the speed. She spent 40 seconds less on her way from the grocery to the gym than on her way from home to the grocery. What was Angelina's speed, in meters per second, from the grocery to the gym?

[ "2", "3", "0.5", "6", "12" ]

let the speed be X... so time taken from home to grocery= 100/x.. the speed to gym = 2x.. so time taken = 180/2x=90/x.. its given 100/x-90/x=40.. 10/x=40.. x=0.25m/secs.. so grocery to gym=2*0.25=0.5m/s... Answer : C The answer is: C

C

mathematics

A started a business with an investment of Rs. 70000 and after 6 months B joined him investing Rs. 120000. If the profit at the end of a year is Rs. 91000, then the share of B is?

[ "A)44500", "B)42000", "C)44098", "D)43007", "E)44098" ]

Ratio of investments of A and B is (70000 * 12) : (120000 * 6) = 7 : 6 Total profit = Rs. 91000 Share of B = 6/13 (91000) = Rs. 42000 Answer:B The answer is: B

B

mathematics

A copy machine, working at a constant rate, makes 30 copies per minute. A second copy machine, working at a constant rate, makes 55 copies per minute. Working together at their respective rates, how many copies do the two machines make in half an hour ?

[ "90", "2,700", "4,500", "2,550", "324,000" ]

Together the two machines make 30+55=85 copies per minute. So, in half an hour they will make 85*30=2,550 copies. Answer: D. The answer is: D

D

mathematics

Two trains of equal lengths take 10 sec and 18 sec respectively to cross a telegraph post. If the length of each train be 120 m, in what time will they cross other travelling in opposite direction?

[ "11", "9", "13", "14", "12.8" ]

Speed of the first train = 120/10 = 12 m/sec. Speed of the second train = 120/18 = 6.7 m/sec. Relative speed = 12 + 6.7 = 18.7 m/sec. Required time = (120 + 120)/18.7 = 12.8 sec. Answer: Option E The answer is: E

E

mathematics

What is the maximum value of vx - yz. If the value of v,x,y,z have to be chosen from the set A where A(-3,-2,-1,0,1,2,3)

[ "15", "66", "25", "88", "17" ]

Explanation: To maximize the value of vx - yz, we make yz negative and vx as maximum as possible using given value. vx−yz=(−3)2−(−3×2)vx−yz=(−3)2−(−3×2) = 15 Answer:A The answer is: A

A