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	The contents of two vessels containing copper and tin in the ratio 2:3 and 5:7 are mixed in the ratio 3:5. The resulting mixture will have copper and tin in the ratio?	[ "210:283", "312:433", "178:213", "197:283", "145:256" ]	The ratio of copper and tin the new vessel= (2/53/8 + 5/125/8) : (3/53/8 + 7/125/8) = 197/480 : 283/480 = 197:283 Answer is D The answer is: D	D
mathematics	If a code word is defined to be a sequence of different letters chosen from the 10 letters A, B, C, D, E, F, G, H, I, and J, what is the ratio of the number of 5-letter code words to the number of 6-letter code words?	[ "1", "1/4", "1/5", "1/3", "1/2" ]	Method #1: Using the permutation formula # of 5 letter code words: nPr = n! / (n – r)! = 10! / (10 – 5)! = 109876 # of 6 letter code words: nPr = 10! / (10 – 6)! = 1098765 # of 5 words / # of 4 words = (109876)/(1098765) = 1/5 C The answer is: C	C
mathematics	The sum of two numbers is 16. The difference is 10. What are the two numbers?	[ "10-6", "8-8", "9-7", "11-5", "13-3" ]	13+3 = 16 13 - 3 = 10 The Answer is E The answer is: E	E
mathematics	9 men or 6 women can do a piece of work in 20 days. In how many days will 12 men and 8 women do the same work?	[ "12/9 days", "15/2 days", "82/8 days", "22/76 days", "22/2 days" ]	9M = 6W ---- 20 days 12M + 8W -----? 8W + 8 W = 16W ---? 6W ---- 20 16 -----? 6 * 20 = 16 * x => x = 15/2 days Answer:B The answer is: B	B
mathematics	One side of a rectangle is 3 cm shorter than the other side. If we increase the length of each side by 1 cm, then the area of the rectangle will increase by 16 cm2. Find the lengths of all sides.	[ "10 and 3", "9 and 6", "10 and 7", "3 and 10", "10 and 10" ]	Let x be the length of the longer side x>3, then the other side's length is x−3 cm. Then the area is S1 = x(x - 3) cm2. After we increase the lengths of the sides they will become (x+1) and (x−3+1)=(x−2) cm long. Hence the area of the new rectangle will be A2=(x+1)⋅(x−2) cm2, which is 16 cm2 more than the first area. Therefore A1+16=A2 x(x−3)+16=(x+1)(x−2) x2−3x+16=x2+x−2x−2 2x=18 x=9. So, the sides of the rectangle are 9 cm and (9−3)=6 cm long. So answer is B. The answer is: B	B
mathematics	Last year a worker saved 5% of her annual salary. This year, she made 20% more money than last year and she saved 6% of her salary. The amount she saved this year was what percent of the amount she saved last year?	[ "136%", "140%", "144%", "148%", "152%" ]	Let x be the worker's salary last year. Last year, she saved 0.05x. This year, she saved 0.06(1.2x)=0.072x 0.072x/0.05x=144% The answer is C. The answer is: C	C
mathematics	The length of a train and that of a platform are equal. If with a speed of 90 k/hr, the train crosses the platform in one minute, then the length of the train (in meters) is:	[ "700", "780", "760", "750", "459" ]	Speed = [90 * 5/18] m/sec = 25 m/sec; Time = 1 min. = 60 sec. Let the length of the train and that of the platform be x meters. Then, 2x/60 = 25 è x = 25 * 60 / 2 = 750 Answer: Option D The answer is: D	D
mathematics	A fruit seller sells mangoes at the rate of Rs.12 per kg and thereby loses 15%. At what price per kg, he should have sold them to make a profit of 5%	[ "Rs 8.82", "Rs 9.82", "Rs 10.82", "Rs 14.82", "None of these" ]	Explanation: 85 : 12 = 105 : x x= (12×105/85) = Rs 14.82 Option D The answer is: D	D
mathematics	A straight pipe 1 meter in length was marked off in halves and also in thirds. If the pipe was then cut into separate pieces at each of these markings, which of the following gives all the different lengths of the pieces, in fractions of a meter?	[ "1/6 and 1/3 only", "1/4 and 1/3 only", "1/6, 1/4, and 1/3", "1/12, 1/6 and 1/4", "1/12, 1/6, and 1/3" ]	Generally fast way to solve such problem is writing the different marks in ascending/descending order with same denominator: Here 4th : 0/4, 1/4, 2/4, 3/4, 4/4 and 3rd : 0/3, 1/3, 2/3, 3/3 Generally fast way to solve such problem is writing the different marks in ascending/descending order with same denominator: Here 2th : 0/2, 1/2, 2/2 and 3rd : 0/3, 1/3, 2/3, 3/3 Now with understood common denominator 6 write the numbers : for 2th : 0,3,6 and for 3rd : 0,2,4,6 Now comine : 0,2,3,4,6 Now find the cut with denominator 6 (Substracrt adjacent terms : 1/3, 1/6, 1/6, 1/3 i.e. 1/3 and 1/6 after removing duplicates. answer : A The answer is: A	A
mathematics	In one hour, a boat goes 11 km along the stream and 5 km against the stream. The speed of the boat in still water in ( km/hr) is	[ "3", "5", "8", "9", "7" ]	Solution Speed in still water = 1/2(11+5) km/hr = 8 km/hr. Answer C The answer is: C	C
mathematics	Which of these must the factor W of the product of four consecutive even integers:- 1) 48 2) 64 3) 96 4) 192 5) 80	[ "W=1,2 only", "W=2,3 only", "W=1,2,3 only", "W=1,2,3,4 only", "All of them" ]	Let the four variables be a< b< c< d. Assume a worst case scenario where the a equal to a prime number (hence odd). therefore a = divisible by 1 b = a + 1 (divisible by 2) c = a + 3 (divisible by 3) d = a + 4 (divisible by 4) therefore each answer choice must be divisible by 2 x 3 x 4 = 24 only 80 is not divisible. Therefore answer = D The answer is: D	D
mathematics	A rectangular park 60 m long and 40 m wide has two concrete crossroads running in the middle of the park and rest of the park has been used as a lawn. If the area of the lawn is 2109 sq. m, then what is the width of the road?	[ "3", "4", "5", "7", "8" ]	Area of the park = (60 x 40) m2 = 2400 m2. Area of the lawn = 2109 m2. Area of the crossroads = (2400 - 2109) m2 = 291 m2. Let the width of the road be x metres. Then, 60x + 40x - x2 = 291 x2 - 100x + 291 = 0 (x - 97)(x - 3) = 0 x = 3. A The answer is: A	A
mathematics	John invested part of his savings into a investment X that earned a profit of 10% and the rest of the savings into an investment E that lost 15%. If John neither made a profit nor a loss, then what fraction of his savings was invested in investment X?	[ "a. 3/5", "b.2/3", "c.7/10", "d.3/4", "e.4/5" ]	X(10) --- Net(0) --- E(-15) = -15/-10 = 3/2. So, John invested 3/3+2 = 3/5 of his savings in investment X. Ans (A). The answer is: A	A
mathematics	The distance between Delhi and Mathura is 120 kms. A starts from Delhi with a speed of 20 kmph at 7 a.m. for Mathura and B starts from Mathura with a speed of 25 kmph at 8 p.m. from Delhi. When will they meet?	[ "40.00 a.m.", "10.13 a.m.", "12.00 a.m.", "18.00 a.m.", "19.00 a.m." ]	Explanation: D = 120 â€“ 20 = 100 RS = 20 + 25 = 45 T = 100/45 = 2 hours 13 minutes 8 a.m. + 2 hours 13 minutes = 10:13 a.m. Answer: Option B The answer is: B	B
mathematics	What is the probability that the sum of two dice will yield a 5, and then when both are thrown again, their sum will again yield a 5? assume that each die has 4 sides with faces numbered 1 to 4.	[ "1/144", "1/36", "1/12", "1/16", "1/3" ]	Solution - Rolling dices is an independent event. The combinations to get 5 are (1,4), (4,1), (2,3), (3,2), and total combinations of both dices is 16. The probability of getting 5 in first attempt is 4/16=1/4. Probability of getting 5 again in second attempt = (1/4)*(1/4) = 1/16. ANS D The answer is: D	D
mathematics	A can do half the work in one day where as B can do it full. B can also do half the work of C in one day. Ratio in their efficiency will be?	[ "1:2:8", "1:2:0", "1:2:5", "1:2:4", "1:2:1" ]	WC of A: B = 1:2 B: C = 1:2 --------------------- A: B: C = 1:2:4 Answer:D The answer is: D	D
mathematics	The sum of number of boys and girls in a school is 300. If the number of boys is x, then the number of girls becomes x% of the total number of students. The number of boys is?	[ "50", "40", "60", "100", "75" ]	We have x+x% of 300 = 300 x + x/100 * 300 = 300 4 * x = 300 x = 75 Answer is E The answer is: E	E
mathematics	If taxi fares were $1.00 for the first 1/5 mile and $0.40 for each 1/5 mile there after, then the taxi fare for a 3-mile ride was	[ "$1.56", "$2.40", "$3.80", "$4.20", "$6.60" ]	In 3 miles , initial 1/5 mile charge is $1 rest of the distance = 3 - (1/5) = 14/5 rest of the distance charge = 14(0.4) = $5.6 (as the charge is 0.4 for every 1/5 mile) => total charge for 3 miles = 1+5.6 = 6.6 Answer is E. The answer is: E	E
mathematics	Cricket match is conducted in US. The run rate of a cricket game was only 3.2 in first 10 over. What should be the run rate in the remaining 40 overs to reach the target of 262 runs?	[ "6", "6.25", "5.75", "7.5", "8" ]	Required run rate = 262 - (3.2 x 10) = 230 = 5.75 40 40 C The answer is: C	C
mathematics	The perimeter of an equilateral triangle is 60. If one of the sides of the equilateral triangle is the side of an isosceles triangle of perimeter 70, then how long is the base of isosceles triangle?	[ "15", "20", "25", "30", "35" ]	The base of the isosceles triangle is 70-20-20= 30 units The answer is D. The answer is: D	D
mathematics	In a rare coin collection, all coins are either pure gold or pure silver, and there is initially one gold coin for every three silver coins. With the addition of 12 more gold coins to the collection, the ratio of gold coins to silver coins is 1 to 2. Based on this information, how many total coins are there now in this collection (after the acquisition)?	[ "72", "84", "96", "108", "120" ]	Initially the number of gold coins and silver coins is 2k and 6k. After adding gold coins, the number of coins is 3k and 6k. Thus k = 12 and the total number of coins is 9k = 108. The answer is D. The answer is: D	D
mathematics	Find the odd man out. 1, 27, 216, 512, 1024, 1331	[ "1024", "512", "27", "1", "2" ]	Explanation : All given numbers except 1024 are perfect cubes. Answer : Option A The answer is: A	A
mathematics	The price of 5 kilograms of premium fertilizer is the same as the price of 10 kilograms of regular fertilizer. If the price of premium fertilizer is y cents per kilogram more than the price of regular fertilizer, what is the price, in cents, per kilogram of premium fertilizer?	[ "y/30", "5/6y", "6/5y", "2y", "6y" ]	Usingpfor premium andrfor regular, I got two equations from the question stem: 5p = 10r and p = r+y Substitute for p: 5(r+y) = 10r Distribute: 5r + 5y = 10r Subtract 5r from both sides: 5y = 5r Plug back into the first equation: 5p = 10(y) Distribute: 5p = 10y Divide both sides by 5: p = 2y The answer is D. The answer is: D	D
mathematics	If books bought at prices ranging from Rs. 90 to Rs. 190 are sold at prices ranging from Rs. 120 to Rs 260, what is the greatest possible profit that might be made in selling 21 books ?	[ "Rs. 2500", "Rs. 3000", "Rs. 3570", "Rs. 3200", "Rs. 3600" ]	The greatest profit is possible only if the cost price of the books are minimum and selling prices are maximum. Let lowest cost price of the 21 books = 9021 = Rs. 1,890 Maximum selling price of 21 books = 260 21 = Rs. 5,460 So, maximum profit = 5460 - 1890 = Rs. 3,570 ANSWER : OPTION C The answer is: C	C
mathematics	If Janice was 21 years old z years ago and Lisa will be 19 years old in p years, what was the average (arithmetic mean) of their ages 8 years ago?	[ "(z + p)/2", "(z - p + 24)/4", "(z - p + 14)/4", "(z + p + 34)/2", "(z - p + 24)/2" ]	Today, J = z+21 and L = 19-p 8 years ago, J = z+13 and L = 11-p The average of their ages was (z-p+24) / 2 The answer is E. The answer is: E	E
mathematics	What is the tens digit of 7^1213?	[ "0", "1", "2", "3", "4" ]	7^1 = 7 7^2 = 49 7^3 = 343 7^4 = 2401 7^5 = 16807 7^6 = 117649 We should see this as pattern recognition . We have a cycle of 4 . (We can multiply the last 2 digits only as we care about ten's digit ) 0 , 4 , 4 , 0 . 1213= 4*304 + 1 The ten's digit will be 0 . Answer A The answer is: A	A
mathematics	In a certain store, the profit is 320% of the cost. If the cost increases by 25% but the selling price remains constant, approximately what percentage of the selling price is the profit?	[ "20", "70", "77", "26", "12" ]	Let C.P. = Rs. 100. Then, profit = Rs. 320, S.P. = Rs. 420 New C.P. = 125% of Rs. 100 = Rs. 125. New S.P. = Rs. 420 Profit = 420 - 125 = Rs. 295 Required percentage = 295/420 * 100 = 1475/21 = 70% Answer:B The answer is: B	B
mathematics	The average age of 39 students in a group is 10 years. When teacher’s age is included to it, the average increases by one. What is the teacher’s age in years?	[ "50", "55", "60", "cannot be determined", "None of these" ]	Age of the teacher = (40 × 11 – 39 × 10) years = 50 years. Answer A The answer is: A	A
mathematics	If the true discount on a certain sum due 6 months hence at 15% is Rs. 120, what is the banker’s discount on the same sum for the same time and at the same rate?	[ "100", "115", "120", "129", "None" ]	Sol. B.G. = S.I. on T.D. = Rs. [120 * 15 * 1/2 * 1/100] = Rs. 9. ∴ (B.D.) - (T.D.) = Rs.9. ∴ B.D. = Rs. (120 + 9) = Rs. 129 Answer D The answer is: D	D
mathematics	Lamp A flashes every 6 seconds, Lamp B flashes every 8 seconds, Lamp C flashes every 10 seconds. At a certain instant of time all three lamps flash simultaneously. During the period of 10 minutes after that how many times will exactly two lamps flash? (Please include any flash of exactly two lights which occurs at the 10 minute mark.)	[ "41", "42", "43", "44", "45" ]	10 minutes is 600 seconds. Lamp A and Lamp B will flash together every 24 seconds. 600/24=25. In the time period, Lamp A and Lamp B will flash together 25 times. Lamp A and Lamp C will flash together every 30 seconds. 600/30=20. In the time period, Lamp A and Lamp C will flash together 20 times. Lamp B and Lamp C will flash together every 40 seconds. 600/40=15. In the time period, Lamp B and Lamp C will flash together 15 times. All three lights will flash together every 22235=120 seconds. 600/120=5. We have counted these triple flashes three times, so we need to subtract three times the number of times that all three lights flash together. The number of times that exactly two lights flash together is 25+20+15-15=45 times. The answer is E. The answer is: E	E
mathematics	If a large pizza has a radius that is 60% larger that that of a medium pizza, what is the percent increase in area between a medium and a large pizza?	[ "30%", "60%", "98%", "120%", "156%" ]	Let the radius of medium pizza be r. Then the radius of large pizza is 1.6r. The area of the medium pizza is pir^2 The area of the large pizza is pi(1.6r)^2 = 2.56pi*r^2, an increase of 156%. The answer is E. The answer is: E	E
mathematics	If a book is sold at 9% profit instead of 9% loss, it would have brought Rs 9 more. Find out the cost price of the book	[ "75", "72", "50", "70", "80" ]	Let C.P. of the book be Rs. ’X’ Given, 1.09 X - 0.91X = 9 => 0.18 X = 9 = 9/0.18 = Rs 50 ANSWER:C The answer is: C	C
mathematics	HOW MANY KGS OF TEA WORTH RS.25/KG MUST BE BLENDED WITH 30 KGS OF TEA WORTH RS.30/KG SO THAT BY SELLING THE BLENDED VARIETY AT RS.30/KG THERE SHOULD BE A GAIN OF 3%	[ "36", "8", "7", "6", "6.3" ]	(x+30)30=(103/100)(25x+3030) Solving we get 6.3. Answer is E. The answer is: E	E
mathematics	Stacy and Heather are 15 miles apart and walk towards each other along the same route. Stacy walks at constant rate that is 1 mile per hour fast than heather's constant rate of 5 miles/hour. If Heather starts her journey 24 minutes after Stacy, how far from the original destination has Heather walked when the two meet?.	[ "6.5mile", "5.7mile", "7.0mile", "8.0mile", "12 mile" ]	Ss - Stacy's speed = 6m/hr Sh - Heather's speed = 5m/hr In 24 minutes Stacy will cover = (24/60)6 = 2.4miles Now since both are walking in opposite directions, add their speeds - 6+5 =11m/hr and distance to cover is 15 -2.4 = 12.6 Time taken = Distance/ Speed = 12.6/11 = 1.145 hrs Heather will cover = 51.145 = 5.72miles. Answer B The answer is: B	B
mathematics	If an integer n is to be chosen at random from the integers 1 to 96, inclusive, what is the probability that n(n + 1)(n + 2) will be divisible by 4?	[ "1/4", "3/8", "1/2", "5/8", "3/4" ]	I get 5/8 as well 1 to 96 inclusive means we have 48 odd and 48 even integers E O E / 4 = Integer, therefore we have 48 / 96 numbers divisible by 8 O E O / 4 = Not Integer We cannot forget multiples of 8 from 1 to 96 We have 24 numbers that are multiple of 4 Therefore, 48/96 + 24/96 = 72/96 = 3/4 answer : E The answer is: E	E
mathematics	42573y is exactly divisible by 72, then what is the minimum value of y?	[ "3", "4", "6", "8", "9" ]	72 = 9 x8, where 9 and 8 are co-prime. The minimum value of x for which 73x for which 73x is divisible by 8 is, x = 6. Sum of digits in 425736 = (4 + 2 + 5 + 7 + 3 + 6) = 27, which is divisible by 9. Required value of y is 6 C The answer is: C	C
mathematics	The ratio of the ages of a man and his wife is 4:3. After 4 years,the ratio will be 9:7.If at the time of marriage the ratio was 5:3,then how many years ago were they married ?	[ "8", "10", "12", "14", "15" ]	let the present ages of the man and his wife be 4x and 3x then (4x+4)/(3x+4)= 9/7 [since given that after four years their ages will be 9/7] by solving it we have x=8 so their present ages are 32 and 24 respectively now suppose if they were married X years ago, then (32-X)/(24-X)=5/3 by solving it we have 2X=24 so X=12 so they were married 12 years ago ANSWER:C The answer is: C	C
mathematics	60 percent of movie theatres in Town X have 3 screens or less. 20% of those theatres sell an average of more than $300 worth of popcorn per showing. 56 percent of all the movie theatres in Town X sell $300 or less of popcorn per showing. What percent of all the stores on the street have 4 or more screens and sell an average of more than $300 worth of popcorn per day?	[ "12", "18", "32", "40", "44" ]	let's take numbers here. Assume that the total number of movie theaters in the town = 100 Then number of movie theaters with 3 screens or less = 60 => Number of movie theaters with 4 screens or more = 40 Movie theaters with 3 screens or less selling popcorn at more than $300 = 20% of 60 = 12 Number of movie theaters selling popcorn at $300 or less = 56 => Number of movie theaters selling popcorn at more than $300 = 100-56 = 44 Of these 44 theaters, 12 are those with 3 screens or less Therefore 32 (44-12) must be those with four screens or more C is the answer The answer is: C	C
mathematics	If the units digit of n^43 is 7, which of the following could be the value of n? I. n = 41 II. n = 43 III. n = 47	[ "Only I", "Only II", "Only III", "I and II", "II and III" ]	I tried in this way. Given n^43 units digit is 7. If at all we have to get 7 as units digits only 3 and 7 series has 7 3^! = 3 , 3^2 = 9 , 3^3 = 27 , 3^4 = 81 7^1 = 7, 7^2 = 49 , 7^3 = 3 (units ) , 7^4 = 1 (units) We have n^43 - then divide 43 by 4 = reminder 3. Then we have for only 7^3 - we have units digit as 7. Hence 47^43 = 7 (units). Option A is correct answer , and with 41^43 we always get 1 as units digit and 43^43 - we get units as 3. The answer is: A	A
mathematics	40 men shake hands with each other. Maximum no of handshakes without cyclic handshakes.	[ "780", "200", "210", "220", "230" ]	or, if there are n persons then no. of shakehands = nC2 = 40C2 = 780 ANSWER:A The answer is: A	A
mathematics	The average price of three items of furniture is Rs. 30000. If their prices are in the ratio 3:5:7, the price of the cheapest item is?	[ "2379", "2889", "9288", "9000", "6000" ]	Let their prices be 3x, 5x and 7x. Then, 3x + 5x + 7x = (15000 * 3) or x = 2000. Cost of cheapest item = 3x = Rs. 6000. Answer: E The answer is: E	E
mathematics	A wheel that has 6 cogs is meshed with a larger wheel of 7 cogs. When the smaller wheel has made 21 revolutions, then the number of revolutions made by the larger wheel is:	[ "9", "10", "6", "18", "7" ]	Explanation : Let the required number of revolutions made by larger wheel be x. Then, More cogs, Less revolutions (Indirect Proportion) 7:6::21:x => 7 * x = 21 * 6 => x = (21 * 6)/7 => x = 18 Answer : D The answer is: D	D
mathematics	4, 6, 12, 14, 28, 30, ?	[ "32", "64", "62", "60", "52" ]	The given sequence is a combination of two series 4, 12, 28, .... and 6, 14, 30, .... The pattern is +8, +16, +32. So, the missing number = (28 + 32) = 60 Answer : D. The answer is: D	D
mathematics	Murali travelled from city A to city B at a speed of 40 kmph and from city B to city C at 60 kmph. What is the average speed of Murali from A to C given that the ratio of distances between A to B and B to C is 2 : 3?	[ "17 kmph", "50 kmph", "18 kmph", "17 kmph", "11 kmph" ]	Let the distances between city A to B and B to C be 2x km and 3x km respectively. Total time taken to cover from A to C = (2x)/40 + (3x)/60 = (6x + 6x)/120 = 12x/120 = x/10 Average speed = (2x + 3x)/(x/10) = 50 kmph. Answer:B The answer is: B	B
mathematics	The total monthly income of four men and two women is 46,000. If every woman earns 500 more than a man then what is the monthly income of a woman?	[ "7,500", "8,000", "9,000", "6,500", "None of these" ]	4M + 2W = 46000; Again, W = M + 500 or, M = W – 500 ∴ (W – 500) + 2W = 46000 or, 6W = 46000 + 2000 = 48000 ∴ W = 8000 Answer B The answer is: B	B
mathematics	Arun got 30% of the maximum marks in an examination and failed by 10 marks. However, Sujith who took the same examination got 40% of the total marks and got 15 marks more than the passing marks. What were the passing marks in the examination?	[ "90", "250", "75", "85", "95" ]	Explanation : Let x is the maximum marks of the examination Marks that Arun got = 30 % of x = 30x/100 Given that Arun failed by 10 marks ⇒Minimum Pass Mark = (30x/100) + 10......(Equation 1)=85 ANSWER IS D The answer is: D	D
mathematics	The ratio between the length and the breadth of a rectangular plot is 7 : 5. If the perimeter of the plot is 216 metres, what is its area?	[ "1325 sq.metres", "1260 sq.metres", "2835 sq.metres", "3380 sq.metres", "None of these" ]	Let the length and breadth be 7x and 5x respectively. Then, P = 2(7x + 5x) = 216 â‡’ x = 9 Area = 7 Ã— 9 Ã— 5 Ã— 9 = 2835 sq.m. Answer C The answer is: C	C
mathematics	The sides of a triangle are in the ratio 5: 12: 13 and its perimeter is 300 m, its area is?	[ "150", "377", "297", "266", "971" ]	5x + 12x + 13x = 300 => x = 10 a = 50, b = 120, c = 130 S = (50 + 120 + 130)/2 = 150 Answer: A The answer is: A	A
mathematics	A group of 10 representatives is to be selected out of 12 seniors and 10 juniors. In how many different ways can the group be selected if it should have at least one senior?	[ "²²C₉", "²²C₁₀", "²²C₉ + ¹⁰C₁", "²²C₁₀ - 1", "¹⁰C₁" ]	The total number of ways of forming the group of ten representatives is ²²C₁₀. The total number of ways of forming the group that consists of no seniors is ¹⁰C₁₀ = 1 way The required number of ways = ²²C₁₀ - 1 Answer:D The answer is: D	D
mathematics	How much water must be added to 60 litres of milk at 1.5 litres for Rs. 20 So as to have a mixture worth Rs.32/3 a litre?	[ "10 litres", "12 litres", "15 litres", "18 litres", "21 litres" ]	C.P. of 1 litre of milk = Rs. 20×2/3 = Rs. 40/3. C.P. of 1 litre of water =Rs 0. Mean price = Rs. 32/3. By the rule of alligation, we have : C.P of 1 litre C.P of 1 litre of water of milk (0) (Rs. 40/3) \ / Mean Price (Rs. 32/3) / \ 40/3−32/3 32/(3−0) 8/3 32/3 The ratio of water and milk =8/3:32/3. =8:32=1:4. Thus, Quantity of water to be added to 60 litres of milk: =(1/4)×60 litres. =15 litres. ANSWER : C The answer is: C	C
mathematics	If x^2 = 231, which of the following is closest to a potential value of x?	[ "-127", "-11", "12", "13", "15" ]	Here the thing we must not forget is that X^even has two potential solutions => x =+- √231 => +- 15 (approx) this value is closer to 15 Hence E is correct. The answer is: E	E
mathematics	Walking 7/6 of his usual rate, a boy reaches his school 2 min early. Find his usual time to reach the school?	[ "14", "28", "99", "77", "66" ]	Speed Ratio = 1:7/6 = 6:7 Time Ratio = 7:6 1 -------- 7 2 --------- ? 14 m Answer:A The answer is: A	A
mathematics	If 10 bulls can plough 20 identical fields in 3 days working 10 hours a day, then in how many days can 30 bulls plough 32 same identical fields working 8 hours a day?	[ "8", "7", "5", "2.0", "1" ]	Explanation: M1D1W2 = M2D2W1 1031032 = 30d820 d = 2 days ANSWER: D The answer is: D	D
mathematics	In a nationwide poll, N people were interviewed. If 1/6 of them answered yes to question 1, and of those, 1/2 answered yes to question 2, which of the following expressions represents the number of people interviewed who did NOT answer yes to both questions?	[ "N/8", "7N/8", "11N/12", "17N/24", "41N/48" ]	The number of people who answered yes to both questions is (1/2)(1/6)N = N/12 The number of people who did not answer yes to both is 1 - N/12 = 11N/12 The answer is C. The answer is: C	C
mathematics	What approximate value should come in place of the question mark (?) in the following equation?47.05 Ã— 8.65 â€“ 25.22 Ã— 6.4 = (28 + ?) Ã— 5	[ "28.1149", "24.1149", "21.1149", "22.1149", "31.1149" ]	Solve using approximation Answer C The answer is: C	C
mathematics	Two pipes A and B can separately fill a cistern in 10 and 15 minutes respectively. A person opens both the pipes together when the cistern should have been was full he finds the waste pipe open. He then closes the waste pipe and in another 4 minutes the cistern was full. In what time can the waste pipe empty the cistern when fill?	[ "7", "9", "5", "4", "8" ]	1/10 + 1/15 = 1/6 * 4 = 2/3 1 - 2/3 = 1/3 1/10 + 1/15 - 1/x = 1/3 x = 8 ANSWER E The answer is: E	E
mathematics	With out any halt a train travels a certain distance with an average speed of 75 km ph , and with halts it covers the same distance at an average speed of 60 kmph. When it is traveling with halts, how many minutes/per hour does the train halt on an average ?	[ "48 min.", "12min.", "15min.", "18min.", "19min." ]	With halt in 1 hour the train travels 60km With out halt for traveling same distance it take 60/75 = 4/5 = 48 minutes :. 12 minutes is the halting time per hour ANSWER:B The answer is: B	B
mathematics	The price of a certain product increased by the same percent from 1960 to 1970 as from 1970 to 1980. If its price of $1.10 in 1970 was 150 percent of its price in 1960, what was its price in 1980?	[ "a) $ 1.65", "b) $ 2.00", "c) $ 2.40", "d) $ 2.70", "e) $ 3.00" ]	The price in 1970 was 150 percent of its price in 1960, means that the percent increase was 50% from 1960 to 1970 (and from 1970 to 1980). Therefore the price in 1980 = $1.1*1.5 = $1.65. Answer: A. The answer is: A	A
mathematics	The value of a machine depreciates at 20% per annum. If its present value is Rs. 1,50,000, at what price should it be sold after two years such that a profit of Rs. 24,000 is made?	[ "328897", "120000", "877888", "277768", "188871" ]	The value of the machine after two years = 0.8 * 0.8 * 1,50,000 = Rs. 96,000 SP such that a profit of Rs. 24,000 is made = 96,000 + 24,000 = Rs. 1,20,000 Answer: B The answer is: B	B
mathematics	An escalator moves towards the top level at the rate of 8 ft.sec and its length is 160 feet. If a person walks on the moving escalator at the rate of 2 feet per second towards the top level, how much time does he take to cover the entire length.	[ "14 sec", "10 sec", "16 sec", "8 sec", "9 sec" ]	Time taken to cover the entire length = tot.dist/resultant speed = 160/ (8+2) = 16sec ANSWER:C The answer is: C	C
mathematics	Present ages of Sameer and Anand are in the ratio of 5 : 4 respectively. Seven years hence, the ratio of their ages will become 11 : 9 respectively. What is Anand's present age in years?	[ "A)84", "B)89", "C)67", "D)56", "E)45" ]	Let the present ages of Sameer and Anand be 5x years and 4x years respectively. Then, (5x + 7/4x + 7)=11/9 9(5x + 7) = 11(4x + 7) 45x + 63 = 44x + 77 45x - 44x = 77 - 63 x = 14. Anand's present age = 4x = 84 years. Answer:A The answer is: A	A
mathematics	A boat with still water speed of a is traveling upstream where the streams speed is b. After covering certain distance s, the boat turns back and tries to come to the starting place. But the boat stops at 3/4th of the intended distance due to a technical fault. What is the ratio of the time taken for the return journey to that of the upstream journey.	[ "3(a - b)/4(a + b)", "4(a - b)/3(a + b)", "3(a + b)/4(a - b)", "4/3", "4/8" ]	speed of boat upstream = a - b speed of boat downstream = a + b For upstream journey, time taken = distance / speed = s / (a - b) During return journey, the boat had covered on 3/4th of s : Therefore for return journey, time taken = distance / speed = (3s/4)/(a+b) Ratio of time taken for return journey to the upstream journey = (3s/4)/(a+b)/ (s/(a - b)) = 3(a - b)/4(a + b) ANSWER:A The answer is: A	A
mathematics	HDFC bank offers an interest of 5% per annum compounded annually on all its deposits. If $10,000 is deposited, what will be the ratio of the interest earned in the 4th year to the interest earned in the 5th year?	[ "1:5", "625:3125", "100:105", "100^4:105^4", "725:3225" ]	Hi Bunuel, Here is my approach: is this correct? HDFC bank offers an interest of 5% per annum compounded annually on all its deposits. Interest earned in 4 year= 10000(1+0.05)^4 Interest earned in 5 year= 10000(1+0.05)^5 Ratio= {10000(1.05)^4}/{10000(1.05^5)} =>1.05^4/1.05^5 =>1/1.05 Multiplied by 100 in both numerator and denominator gives 100:105 Hence Ans:C The answer is: C	C
mathematics	Each book on a certain shelf is labeled by a single category. For every 2 history books, there are 7 fantasy books and for every 3 fantasy books, there are 8 reference books. If the proportion of history to reference books is doubled, while the proportion of fantasy to reference books is maintained, which of the following could be the number of history books if there are fewer than 60 fantasy books on the shelf after the changes?	[ "12", "21", "27", "35", "36" ]	For every 2 history books, there are 7 fantasy books: Originally H:F = 2:7 = 6:21. For every 3 fantasy books, there are 8 reference books: F:R = 3:8 = 21:56 H:F:R = 6:21:56 After the changes, H:F:R = 12:21:56 There are fewer than 60 fantasy books, so there are 21 or 42 fantasy books. The number of history books could be 12 or 24. The answer is A. The answer is: A	A
mathematics	Seven children — A, B, C, D, E, F, G and H— are going to sit in seven chairs in a row. The children CF have to sit next to each other, and the others can sit in any order in any remaining chairs. How many possible configurations are there for the children?	[ "600", "720", "1440", "10080", "4800" ]	for such questions , we can treat both as one then total person=7.. these 7 can be arranged in 7! ways.. but within these 7, one consists of two people who can be arranged in 2 ways CF or FC.. so ans =7!*2=10080 ans D The answer is: D	D
mathematics	In the xy-plane, the points (c, d), (c, -d), and (-c, -d) are three vertices of a certain square. If c < 0 and d > 0, which of the following points N is in the same quadrant as the fourth vertex of the square?	[ "(-5, -3)", "(-5, 3)", "(5, -3)", "(3, -5)", "(3, 5)" ]	The question:In the xy-plane, the points N=(c, d), (c, -d), and (-c, -d) are three vertices of a certain square.If c < 0 and d > 0,which of the following points is in the same quadrant as the fourth vertex of the square? I marked the tricky part in red. It seems c is anegativenumber and d is a positive number. This means Vertex #1 = (c, d) is in QII (that is, negative x and positive y) Vertex #2 = (c, -d) is in QIII (that is, both xy negative) Vertex #3 = (-c, -d) is in QIV (that is y is negative, but x is positive) That means the last vertex should be in the first quadrant --- the only first quadrant point is (5, 3), answer =E. The answer is: E	E
mathematics	In the equation a = 36.12b, b and a are integers. If a/b leaves a remainder of r, which of the following must divide into r?	[ "2", "3", "4", "6", "12" ]	1) It says it is a equation, so a=36.12b should be 36.12 * b.. 2) It says b is an integer, again it means 36.12 * b.. Otherwise b would be just a digit and it would be mentioned.. Although not clearly mentioned that 36.12b is actually 36.12 * b, BUT entire info points towards that.. and that is why I have taken a/b = 36.12 The answer is: B	B
mathematics	A merchant marks his goods up in such a way that the profit made on selling 30 articles is equal to the cost price of 20 articles. What is the W % profit made by the merchant?	[ "66.67 %", "50 %", "200 %", "100 %", "33.33 %" ]	C.P of 1 article= $30(say) C.P of 20 articles=3020=$600 Now, C.P of 20 articles=Profit on 30 articles Therefore, profit on 1 article=$600/30=$20 Profit W%=(20/30)100=66.67% Answer A The answer is: A	A
mathematics	When the positive integer x is divided by 9,the remainder is 5.What is the remainder when 8x is divided by 9?	[ "0", "1", "3", "4", "6" ]	i tried plugging in numbers x = 9q+5 x = 14 8x = 112 8x/9= 9*12+4 remainder is 4. Answer is D. The answer is: D	D
mathematics	In a college, 1 percent of students hate math, 2 percent of students hate English, 1 percent hate French and 4 percent hate German. Can you find out the percentage of students who hate all 4 subjects ?	[ "8%", "5%", "7%", "12%", "19%" ]	A 8% of student hate all four subjects. The answer is: A	A
mathematics	Choose the missing terms out of the given alternatives. QPO, SRQ, UTS, WVU, ?	[ "XVZ", "ESD", "ZYA", "VWX", "YXW" ]	E YXW Each term consists of three consecutive letters in reverse order. The first letter and the last letter of the next term are the same. The answer is: E	E
mathematics	The sum of two consecutive integers is 15. Find the numbers.	[ "17, 18", "7, 8", "5, 6", "1, 2", "8, 9" ]	n + (n + 1) = 15 2n + 1 = 15 2n = 14 n = 7 Answer: B The answer is: B	B
mathematics	A and B’s salaries together amount to Rs. 3,000. A spends 95% of his salary and B spends 85% of his. If now their savings are the same, what is B’s salary?	[ "777", "750", "789", "776", "881" ]	(5/100) A = (15/100) B A = 3B A + B =3000 4B = 3000 => B = 750 Answer B The answer is: B	B
mathematics	If a·b·c·d=360, where a, b, c and d are positive integers, and a<b<c<d, which of the following could be the value of d−a?	[ "9", "10", "11", "13", "15" ]	prime factorize : 360 = 235*12 Hence a = 2 and d = 12 . Hence answer is 12 - 2 = 10 Answer B The answer is: B	B
mathematics	If the speed of a man is 45 km per hour, then what is the distance traveled by him in 30 seconds ?	[ "275m", "360m", "375 m", "420 m", "480 m" ]	The distance traveled in 30 sec = 45(5/18) 30 =375m Answer: C The answer is: C	C
mathematics	Lilly has 10 fish and Rosy has 9 fish. In total, how many fish do they have in all?	[ "16", "17", "18", "19", "20" ]	10+9=19 The answer is D. The answer is: D	D
mathematics	9548 + 7314 = 7362 + (?)	[ "8300", "8400", "8500", "8700", "9500" ]	9548 16862 = 7362 + x + 7314 x = 16862 - 7362 ----- = 9500 16862 ----- E) The answer is: E	E
mathematics	Pipe A can fill a tank in 8 hours, pipe B in 10 hours and pipe C in 40 hours. If all the pipes are open, in how many hours will the tank be filled?	[ "2", "2.5", "3", "4", "None" ]	Sol. Part filled by (A + B + C) in 1 hour = (1/8 + 1/10 + 1/40) = 1/4. âˆ´ All the three pipes together will fill the tank in 4 hours. Answer D The answer is: D	D
mathematics	The ages of Rahul and Madhan differ by 16 years. Six years ago, Madhan’s age was thrice as that of Rahul’s,find their present ages	[ "14 years, 30 years", "12 years, 28 years", "16 years, 34 years", "18 years, 38 years", "none of these" ]	Let Rahul’s age = x years So, Madhan’s age = ( x + 16 )years Also, 3(x - 6) = x + 16 - 6 or, x = 14 Rahul’s age = 14 years And, Madhan’s age 14 + 16 = 30 years ANSWER:A The answer is: A	A
mathematics	There is a 10% chance that Tigers will not win at all during the whole season. There is a 20% chance that Federer will not play at all in the whole season. What is the greatest possible probability that the Tigers will win and Federer will play during the season?	[ "55%", "60%", "70%", "72%", "80%" ]	There is a 10% chance that Tigers will not win at all during the whole season We can infer that there is 90% chance Tigers will win . Similarly There is a 20% chance that Federer will not play at all in the whole season We can also infer that there is 80% chance that Federer will play. Answer E The answer is: E	E
mathematics	If Tim had lunch at $50.50 and he gave 20% tip, how much did he spend?	[ "$57.45", "$35.42", "$60.60", "$21.56", "$78.45" ]	The tip is 20% of what he paid for lunch. tip = 20% of 50.50 = (20/100)*50.50 = 101/100 = $10.10 Total spent 50.50 + 10.10 = $60.60 correct answer is C)$60.60 The answer is: C	C
mathematics	Which one of the given numbers is divisible by 11?	[ "4823718", "8423718", "8432718", "4238718", "4852718" ]	Explanation: 4238718 = (4+3+7+8) – (2+8+1) = 11 So, the given number is divisible by 11 Answer:D The answer is: D	D
mathematics	If 2^z is a factor of 30!, which of the following could be the value of z? I. 23 II. 26 III. 24	[ "I ONLY", "II ONLY", "BOTH I AND II", "III ONLY", "NONE OF THE ABOVE" ]	2^z is a factor of 30!, what values can z take. Powers of 2 in 30! = [30/2] + [30/4] +[30/8] + [30/16] , where [x] is the integral part of x Powers of 2 in 30! = 15 + 7 + 3 + 1 = 26 Hence the maximum value of 2^z in 30! = 2^26 Only Statement II satisfies Correct Option: B The answer is: B	B
mathematics	The difference between 3/5 of 2/3 of a number and 2/5 of 1/4 of the same number is 288. What is the number?	[ "960", "850", "895", "955", "975" ]	according to the given condition x(2/3)(3/5) - x(2/5)(1/4) = 288 so 2x/5 - x/10 = 288 or 3x/10 = 288 or x = 2880/3 = 960 ANSWER:A The answer is: A	A
mathematics	Four people are to be seated on a bench. How many different sitting arrangements are possible if Erik must sit next to Joe?	[ "4", "6", "8", "12", "16" ]	Consider E and J one. But, in this arrangement they can sit in two different combinations. E first and J second or J first and E second. Total we have (E and J) and the two other persons= 4 arrangements to do. Total arrangements= 4*2= 8 C is the answer The answer is: C	C
mathematics	Find the value of 1.5 x [(3.6 x 0.48 x 2.50) / (0.12 x 0.09 x 0.5)]	[ "800", "500", "900", "1200", "None" ]	Answer 1.5 x [(3.6 x 0.48 x 2.50) / (0.12 x 0.09 x 0.5)] = 1.5 x [(36 x 48 x 250) / (12 x 9 x 5)] = 1.5 x 4 x 4 x 50 = 1200 Correct Option: D The answer is: D	D
mathematics	In store A there are 10 pairs of pants for every 30 store B has. The price ratio between the pants in store B and the pants in store A is 3:4. If all the pants were sold in both places until the stock ran out, what is the ratio between the total amount stores A earned to the total amount store B earned?	[ "3:16.", "2:3.", "4:9", "3:4.", "2:5." ]	1st statement : ratio of pants Store A : Store B 10x : 30x X:3X Price : 4y:3y Total revenue 4xy : 9xy 4:9 Answer : C The answer is: C	C
mathematics	A glass was filled with 12 ounces of water, and 0.03 ounce of the water evaporated each day during a 22-day period. What percent of the original amount of water evaporated during this period?	[ "5.002%", "5.5%", "0.5%", "5%", "20%" ]	In 22 days 22*0.03=0.66 ounces of water evaporated, which is 0.66/12âˆ—100=5.5 of the original amount of water. Answer: B. The answer is: B	B
mathematics	A, B and C rents a pasture for Rs.435. A put in 12 horses for 8 months, B 16 horses for 9 months and 18 horses for 6 months. How much should B pay?	[ "180", "227", "268", "198", "176" ]	128 :169 = 186 8: 12: 9 12/29 435 = 180 Answer:A The answer is: A	A
mathematics	If x=2, which of the following is(are) true? I. x^2=2x II x/-4 = 1 III \|x\|=-x	[ "II only", "III only", "II,III only", "I only", "I,III only" ]	2^2 = 2 * 2 Answer : D The answer is: D	D
mathematics	In a box, there are 8 red, 7 blue and 6 green balls. One ball is picked up randomly. What is the probability that it is neither red nor green?	[ "3/4", "1/3", "7/19", "8/21", "9/21" ]	7C1/21C1=7/21=1/3 ANSWER:B The answer is: B	B
mathematics	Ronald and Elan are working on an assignment. Ronald takes 6 hrs to type 32 pages on a computer, while Elan takes 5 hrs to type 40 pages. How much time will they take, working together on two different computers to type an assignment of 110 pages?	[ "8 hrs 19 min", "8 hrs 18 min", "8 hrs 15 min", "8 hrs 65 min", "8 hrs 18 min" ]	Number of pages typed by Ronald in 1 hour = 32/6 = 16/3 Number of pages typed by Elan in 1 hour = 40/5 = 8 Number of pages typed by both in 1 hour = (16/3 + 8) = 40/3 Time taken by both to type 110 pages = (110 * 3/40) = 8 1/4 = 8 hrs 15 min Answer:C The answer is: C	C
mathematics	If the difference between the compound interest & simple interest of a certain sum of money is Rs.72 at 12% p.a. per two year. Find the sum(in Rs.)?	[ "200/15", "200/17", "220/17", "240/17", "260/17" ]	200/17 C.I=A-P A=p(1+12/100)^2 S.I=p212/100 C.I-S.I=72 given substitute and solve p=200/17 ANSWER:B The answer is: B	B
mathematics	The average age of the mother and her 6 children is 12 years which is reduced by 5 years if the age of the mother is excluded. How old is the mother?	[ "42 years", "40 years", "48 years", "50 years", "None of these" ]	Total age of the mother and six children = 12 × 7 = 84 years. Total age of six children = 7 × 6 = 42 years. (since average is reduced by 5) Mother is 42 years old. ANSWER:A The answer is: A	A
mathematics	Raj and Roshan has some money with them in the ratio 5:4 respectively. If Raj has Rs. 45. How much money Raj has more than Roshan?	[ "5", "9", "16", "12", "18" ]	Let the money Roshan has be x then (45/x)=5/4 Upon cross multiplication and solving for x we get x=36 So Raj has Rs. 9 more than Roshan Answer:B The answer is: B	B
mathematics	Find the one which does not belong to that group ?	[ "30", "82", "27", "62", "11" ]	Explanation: 27, 36, 72 and 45 are divisible by 9, but not 30. Answer: A The answer is: A	A
mathematics	A wholesaler wishes to sell 100 pounds of mixed nuts at $2.00 a pound. She mixes peanuts worth $1.50 a pound with cashews worth $4.00 a pound. How many pounds of cashews must she use?	[ "40", "45", "50", "55", "60" ]	From the question stem we know that we need a mixture of 100 pounds of peanuts and cashews. If we represent peanuts as x and cashews as y, we get x + y = 100. Since the wholesaler wants to sell the mixture of 100 pounds @ $2.50, we can write this as: $2.5 * (x + y) = $1.5x + $4y From the equation x + y = 100, we can rewrite y as y = 100 - x and substitute this into our equation to get: $2.5 * (x + 100 - x) = $1.5x + $4(100 - x) If you solve for x, you will get x = 60, and therefore y = 40. So the wholesaler must use 40 pounds of cashews. You can substitute into the original equation to see that: $250 = $1.5(60) + $4(40) Answer is C. The answer is: C	C
mathematics	A part-time employee’s hourly wage was increased by 25%. She decided to decrease the number of hours worked per week so that her total income did not change. By approximately what percent should the number of hours worked be decreased?	[ "9%", "15%", "20%", "50%", "100%" ]	Let's plug in somenicenumbers and see what's needed. Let's say the employee used to make $1/hour and worked 100 hours/week So, the TOTAL weekly income was $100/week After the 25% wage increase, the employee makes $1.25/hour We want the employee's income to remain at $100/week. So, we want ($1.25/hour)(new # of hours) = $100 Divide both sides by 1.25 to get: new # of hours = 100/1.25 ≈ 80 hours So, the number of hours decreases from 100 hours to (approximately) 80 hours. This represents a 20% decrease (approximately) . Answer : C The answer is: C	C
mathematics	If a, f, and c are consecutive even integers and a < f < c, all of the following must be divisible by 4 EXCEPT	[ "a + c", "f + c", "ac", "(bc)/2", "(abc)/4" ]	I did get the correct answer within 80 seconds and it was not by luck either. I did not pick numbers but just used the concept stated by Ian. The 3 numbers can be written as a, (a + 2)(a + 4). If 'a' is divisible by 4, then even 'c' or 'a + 4' is divisible by 4. However, is 'b' is divisible by 4, then both 'a' and 'a + 4' are still divisible by 2. A - (a + c) = a + (a + 4) = 2a + 4 = 2(a + 2) = 2b. 2b will always be divisible by 4 even if 'b' is not divisible by 4. Reason: 'b' already has a prime factorization of at least a '2'. Hence '2b' has two 2s. C - ac = a(a+4). If, as stated above, one of them is divisible by 4, then the product is divisible. If both of them are not divisible by 4, then the product is still divisible by 4 because of the presence of two 2s again in the prime factorization. D - bc/2 = (a + 2)(a + 4)/2. Either b or c is divisible by 2. Hence, if we assume that b is divisible by 2 and not divisible by 4, then it leaves us just one possibility. Is c divisible by 4? It has to be because c is the next consecutive even integer. E - abc/4 = a(a + 2)(a + 4)/4. One of these integers is divisible by 4 already. If we again assume 'b' to be that integer divisible by 4, then we are left with the question - Is a(a + 4) divisible by 4? This is the same as option C. B - f + c = (a + 2) + (a + 4) = 2a + 6 = 2(a + 3). (a + 3) will never be divisible by 2 because it is an odd integer. Hence, 2(a + 3), although divisible by 2, will not be divisible by 4 because it has just one 2 in its prime factorization. As a whole, whether you choose numbers (2, 46 being the easiest) or solve conceptually, the answer is still easily obtainable within 2 minutes.B The answer is: B	B
mathematics	If 40% of a certain number is 160, then what is 20% of that number?	[ "75", "100", "120", "30", "80" ]	Explanation: 40% = 404 = 160 20% = 204 = 80 Answer: Option E The answer is: E	E

mathematics

The contents of two vessels containing copper and tin in the ratio 2:3 and 5:7 are mixed in the ratio 3:5. The resulting mixture will have copper and tin in the ratio?

[ "210:283", "312:433", "178:213", "197:283", "145:256" ]

The ratio of copper and tin the new vessel= (2/5*3/8 + 5/12*5/8) : (3/5*3/8 + 7/12*5/8) = 197/480 : 283/480 = 197:283 Answer is D The answer is: D

D

mathematics

If a code word is defined to be a sequence of different letters chosen from the 10 letters A, B, C, D, E, F, G, H, I, and J, what is the ratio of the number of 5-letter code words to the number of 6-letter code words?

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

Method #1: Using the permutation formula # of 5 letter code words: nPr = n! / (n – r)! = 10! / (10 – 5)! = 10*9*8*7*6 # of 6 letter code words: nPr = 10! / (10 – 6)! = 10*9*8*7*6*5 # of 5 words / # of 4 words = (10*9*8*7*6)/(10*9*8*7*6*5) = 1/5 C The answer is: C

C

mathematics

The sum of two numbers is 16. The difference is 10. What are the two numbers?

[ "10-6", "8-8", "9-7", "11-5", "13-3" ]

13+3 = 16 13 - 3 = 10 The Answer is E The answer is: E

E

mathematics

9 men or 6 women can do a piece of work in 20 days. In how many days will 12 men and 8 women do the same work?

[ "12/9 days", "15/2 days", "82/8 days", "22/76 days", "22/2 days" ]

9M = 6W ---- 20 days 12M + 8W -----? 8W + 8 W = 16W ---? 6W ---- 20 16 -----? 6 * 20 = 16 * x => x = 15/2 days Answer:B The answer is: B

B

mathematics

One side of a rectangle is 3 cm shorter than the other side. If we increase the length of each side by 1 cm, then the area of the rectangle will increase by 16 cm2. Find the lengths of all sides.

[ "10 and 3", "9 and 6", "10 and 7", "3 and 10", "10 and 10" ]

Let x be the length of the longer side x>3, then the other side's length is x−3 cm. Then the area is S1 = x(x - 3) cm2. After we increase the lengths of the sides they will become (x+1) and (x−3+1)=(x−2) cm long. Hence the area of the new rectangle will be A2=(x+1)⋅(x−2) cm2, which is 16 cm2 more than the first area. Therefore A1+16=A2 x(x−3)+16=(x+1)(x−2) x2−3x+16=x2+x−2x−2 2x=18 x=9. So, the sides of the rectangle are 9 cm and (9−3)=6 cm long. So answer is B. The answer is: B

B

mathematics

Last year a worker saved 5% of her annual salary. This year, she made 20% more money than last year and she saved 6% of her salary. The amount she saved this year was what percent of the amount she saved last year?

[ "136%", "140%", "144%", "148%", "152%" ]

Let x be the worker's salary last year. Last year, she saved 0.05x. This year, she saved 0.06(1.2x)=0.072x 0.072x/0.05x=144% The answer is C. The answer is: C

C

mathematics

The length of a train and that of a platform are equal. If with a speed of 90 k/hr, the train crosses the platform in one minute, then the length of the train (in meters) is:

[ "700", "780", "760", "750", "459" ]

Speed = [90 * 5/18] m/sec = 25 m/sec; Time = 1 min. = 60 sec. Let the length of the train and that of the platform be x meters. Then, 2x/60 = 25 è x = 25 * 60 / 2 = 750 Answer: Option D The answer is: D

D

mathematics

A fruit seller sells mangoes at the rate of Rs.12 per kg and thereby loses 15%. At what price per kg, he should have sold them to make a profit of 5%

[ "Rs 8.82", "Rs 9.82", "Rs 10.82", "Rs 14.82", "None of these" ]

Explanation: 85 : 12 = 105 : x x= (12×105/85) = Rs 14.82 Option D The answer is: D

D

mathematics

A straight pipe 1 meter in length was marked off in halves and also in thirds. If the pipe was then cut into separate pieces at each of these markings, which of the following gives all the different lengths of the pieces, in fractions of a meter?

[ "1/6 and 1/3 only", "1/4 and 1/3 only", "1/6, 1/4, and 1/3", "1/12, 1/6 and 1/4", "1/12, 1/6, and 1/3" ]

Generally fast way to solve such problem is writing the different marks in ascending/descending order with same denominator: Here 4th : 0/4, 1/4, 2/4, 3/4, 4/4 and 3rd : 0/3, 1/3, 2/3, 3/3 Generally fast way to solve such problem is writing the different marks in ascending/descending order with same denominator: Here 2th : 0/2, 1/2, 2/2 and 3rd : 0/3, 1/3, 2/3, 3/3 Now with understood common denominator 6 write the numbers : for 2th : 0,3,6 and for 3rd : 0,2,4,6 Now comine : 0,2,3,4,6 Now find the cut with denominator 6 (Substracrt adjacent terms : 1/3, 1/6, 1/6, 1/3 i.e. 1/3 and 1/6 after removing duplicates. answer : A The answer is: A

A

mathematics

In one hour, a boat goes 11 km along the stream and 5 km against the stream. The speed of the boat in still water in ( km/hr) is

[ "3", "5", "8", "9", "7" ]

Solution Speed in still water = 1/2(11+5) km/hr = 8 km/hr. Answer C The answer is: C

C

mathematics

Which of these must the factor W of the product of four consecutive even integers:- 1) 48 2) 64 3) 96 4) 192 5) 80

[ "W=1,2 only", "W=2,3 only", "W=1,2,3 only", "W=1,2,3,4 only", "All of them" ]

Let the four variables be a< b< c< d. Assume a worst case scenario where the a equal to a prime number (hence odd). therefore a = divisible by 1 b = a + 1 (divisible by 2) c = a + 3 (divisible by 3) d = a + 4 (divisible by 4) therefore each answer choice must be divisible by 2 x 3 x 4 = 24 only 80 is not divisible. Therefore answer = D The answer is: D

D

mathematics

A rectangular park 60 m long and 40 m wide has two concrete crossroads running in the middle of the park and rest of the park has been used as a lawn. If the area of the lawn is 2109 sq. m, then what is the width of the road?

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

Area of the park = (60 x 40) m2 = 2400 m2. Area of the lawn = 2109 m2. Area of the crossroads = (2400 - 2109) m2 = 291 m2. Let the width of the road be x metres. Then, 60x + 40x - x2 = 291 x2 - 100x + 291 = 0 (x - 97)(x - 3) = 0 x = 3. A The answer is: A

A

mathematics

John invested part of his savings into a investment X that earned a profit of 10% and the rest of the savings into an investment E that lost 15%. If John neither made a profit nor a loss, then what fraction of his savings was invested in investment X?

[ "a. 3/5", "b.2/3", "c.7/10", "d.3/4", "e.4/5" ]

X(10) --- Net(0) --- E(-15) = -15/-10 = 3/2. So, John invested 3/3+2 = 3/5 of his savings in investment X. Ans (A). The answer is: A

A

mathematics

The distance between Delhi and Mathura is 120 kms. A starts from Delhi with a speed of 20 kmph at 7 a.m. for Mathura and B starts from Mathura with a speed of 25 kmph at 8 p.m. from Delhi. When will they meet?

[ "40.00 a.m.", "10.13 a.m.", "12.00 a.m.", "18.00 a.m.", "19.00 a.m." ]

Explanation: D = 120 â€“ 20 = 100 RS = 20 + 25 = 45 T = 100/45 = 2 hours 13 minutes 8 a.m. + 2 hours 13 minutes = 10:13 a.m. Answer: Option B The answer is: B

B

mathematics

What is the probability that the sum of two dice will yield a 5, and then when both are thrown again, their sum will again yield a 5? assume that each die has 4 sides with faces numbered 1 to 4.

[ "1/144", "1/36", "1/12", "1/16", "1/3" ]

Solution - Rolling dices is an independent event. The combinations to get 5 are (1,4), (4,1), (2,3), (3,2), and total combinations of both dices is 16. The probability of getting 5 in first attempt is 4/16=1/4. Probability of getting 5 again in second attempt = (1/4)*(1/4) = 1/16. ANS D The answer is: D

D

mathematics

A can do half the work in one day where as B can do it full. B can also do half the work of C in one day. Ratio in their efficiency will be?

[ "1:2:8", "1:2:0", "1:2:5", "1:2:4", "1:2:1" ]

WC of A: B = 1:2 B: C = 1:2 --------------------- A: B: C = 1:2:4 Answer:D The answer is: D

D

mathematics

The sum of number of boys and girls in a school is 300. If the number of boys is x, then the number of girls becomes x% of the total number of students. The number of boys is?

[ "50", "40", "60", "100", "75" ]

We have x+x% of 300 = 300 x + x/100 * 300 = 300 4 * x = 300 x = 75 Answer is E The answer is: E

E

mathematics

If taxi fares were $1.00 for the first 1/5 mile and $0.40 for each 1/5 mile there after, then the taxi fare for a 3-mile ride was

[ "$1.56", "$2.40", "$3.80", "$4.20", "$6.60" ]

In 3 miles , initial 1/5 mile charge is $1 rest of the distance = 3 - (1/5) = 14/5 rest of the distance charge = 14(0.4) = $5.6 (as the charge is 0.4 for every 1/5 mile) => total charge for 3 miles = 1+5.6 = 6.6 Answer is E. The answer is: E

E

mathematics

Cricket match is conducted in US. The run rate of a cricket game was only 3.2 in first 10 over. What should be the run rate in the remaining 40 overs to reach the target of 262 runs?

[ "6", "6.25", "5.75", "7.5", "8" ]

Required run rate = 262 - (3.2 x 10) = 230 = 5.75 40 40 C The answer is: C

C

mathematics

The perimeter of an equilateral triangle is 60. If one of the sides of the equilateral triangle is the side of an isosceles triangle of perimeter 70, then how long is the base of isosceles triangle?

[ "15", "20", "25", "30", "35" ]

The base of the isosceles triangle is 70-20-20= 30 units The answer is D. The answer is: D

D

mathematics

In a rare coin collection, all coins are either pure gold or pure silver, and there is initially one gold coin for every three silver coins. With the addition of 12 more gold coins to the collection, the ratio of gold coins to silver coins is 1 to 2. Based on this information, how many total coins are there now in this collection (after the acquisition)?

[ "72", "84", "96", "108", "120" ]

Initially the number of gold coins and silver coins is 2k and 6k. After adding gold coins, the number of coins is 3k and 6k. Thus k = 12 and the total number of coins is 9k = 108. The answer is D. The answer is: D

D

mathematics

Find the odd man out. 1, 27, 216, 512, 1024, 1331

[ "1024", "512", "27", "1", "2" ]

Explanation : All given numbers except 1024 are perfect cubes. Answer : Option A The answer is: A

A

mathematics

The price of 5 kilograms of premium fertilizer is the same as the price of 10 kilograms of regular fertilizer. If the price of premium fertilizer is y cents per kilogram more than the price of regular fertilizer, what is the price, in cents, per kilogram of premium fertilizer?

[ "y/30", "5/6*y", "6/5*y", "2y", "6y" ]

Usingpfor premium andrfor regular, I got two equations from the question stem: 5p = 10r and p = r+y Substitute for p: 5(r+y) = 10r Distribute: 5r + 5y = 10r Subtract 5r from both sides: 5y = 5r Plug back into the first equation: 5p = 10(y) Distribute: 5p = 10y Divide both sides by 5: p = 2y The answer is D. The answer is: D

D

mathematics

If books bought at prices ranging from Rs. 90 to Rs. 190 are sold at prices ranging from Rs. 120 to Rs 260, what is the greatest possible profit that might be made in selling 21 books ?

[ "Rs. 2500", "Rs. 3000", "Rs. 3570", "Rs. 3200", "Rs. 3600" ]

The greatest profit is possible only if the cost price of the books are minimum and selling prices are maximum. Let lowest cost price of the 21 books = 90*21 = Rs. 1,890 Maximum selling price of 21 books = 260 *21 = Rs. 5,460 So, maximum profit = 5460 - 1890 = Rs. 3,570 ANSWER : OPTION C The answer is: C

C

mathematics

If Janice was 21 years old z years ago and Lisa will be 19 years old in p years, what was the average (arithmetic mean) of their ages 8 years ago?

[ "(z + p)/2", "(z - p + 24)/4", "(z - p + 14)/4", "(z + p + 34)/2", "(z - p + 24)/2" ]

Today, J = z+21 and L = 19-p 8 years ago, J = z+13 and L = 11-p The average of their ages was (z-p+24) / 2 The answer is E. The answer is: E

E

mathematics

What is the tens digit of 7^1213?

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

7^1 = 7 7^2 = 49 7^3 = 343 7^4 = 2401 7^5 = 16807 7^6 = 117649 We should see this as pattern recognition . We have a cycle of 4 . (We can multiply the last 2 digits only as we care about ten's digit ) 0 , 4 , 4 , 0 . 1213= 4*304 + 1 The ten's digit will be 0 . Answer A The answer is: A

A

mathematics

In a certain store, the profit is 320% of the cost. If the cost increases by 25% but the selling price remains constant, approximately what percentage of the selling price is the profit?

[ "20", "70", "77", "26", "12" ]

Let C.P. = Rs. 100. Then, profit = Rs. 320, S.P. = Rs. 420 New C.P. = 125% of Rs. 100 = Rs. 125. New S.P. = Rs. 420 Profit = 420 - 125 = Rs. 295 Required percentage = 295/420 * 100 = 1475/21 = 70% Answer:B The answer is: B

B

mathematics

The average age of 39 students in a group is 10 years. When teacher’s age is included to it, the average increases by one. What is the teacher’s age in years?

[ "50", "55", "60", "cannot be determined", "None of these" ]

Age of the teacher = (40 × 11 – 39 × 10) years = 50 years. Answer A The answer is: A

A

mathematics

If the true discount on a certain sum due 6 months hence at 15% is Rs. 120, what is the banker’s discount on the same sum for the same time and at the same rate?

[ "100", "115", "120", "129", "None" ]

Sol. B.G. = S.I. on T.D. = Rs. [120 * 15 * 1/2 * 1/100] = Rs. 9. ∴ (B.D.) - (T.D.) = Rs.9. ∴ B.D. = Rs. (120 + 9) = Rs. 129 Answer D The answer is: D

D

mathematics

Lamp A flashes every 6 seconds, Lamp B flashes every 8 seconds, Lamp C flashes every 10 seconds. At a certain instant of time all three lamps flash simultaneously. During the period of 10 minutes after that how many times will exactly two lamps flash? (Please include any flash of exactly two lights which occurs at the 10 minute mark.)

[ "41", "42", "43", "44", "45" ]

10 minutes is 600 seconds. Lamp A and Lamp B will flash together every 24 seconds. 600/24=25. In the time period, Lamp A and Lamp B will flash together 25 times. Lamp A and Lamp C will flash together every 30 seconds. 600/30=20. In the time period, Lamp A and Lamp C will flash together 20 times. Lamp B and Lamp C will flash together every 40 seconds. 600/40=15. In the time period, Lamp B and Lamp C will flash together 15 times. All three lights will flash together every 2*2*2*3*5=120 seconds. 600/120=5. We have counted these triple flashes three times, so we need to subtract three times the number of times that all three lights flash together. The number of times that exactly two lights flash together is 25+20+15-15=45 times. The answer is E. The answer is: E

E

mathematics

If a large pizza has a radius that is 60% larger that that of a medium pizza, what is the percent increase in area between a medium and a large pizza?

[ "30%", "60%", "98%", "120%", "156%" ]

Let the radius of medium pizza be r. Then the radius of large pizza is 1.6r. The area of the medium pizza is pi*r^2 The area of the large pizza is pi*(1.6*r)^2 = 2.56*pi*r^2, an increase of 156%. The answer is E. The answer is: E

E

mathematics

If a book is sold at 9% profit instead of 9% loss, it would have brought Rs 9 more. Find out the cost price of the book

[ "75", "72", "50", "70", "80" ]

Let C.P. of the book be Rs. ’X’ Given, 1.09 X - 0.91X = 9 => 0.18 X = 9 = 9/0.18 = Rs 50 ANSWER:C The answer is: C

C

mathematics

HOW MANY KGS OF TEA WORTH RS.25/KG MUST BE BLENDED WITH 30 KGS OF TEA WORTH RS.30/KG SO THAT BY SELLING THE BLENDED VARIETY AT RS.30/KG THERE SHOULD BE A GAIN OF 3%

[ "36", "8", "7", "6", "6.3" ]

(x+30)*30=(103/100)(25x+30*30) Solving we get 6.3. Answer is E. The answer is: E

E

mathematics

Stacy and Heather are 15 miles apart and walk towards each other along the same route. Stacy walks at constant rate that is 1 mile per hour fast than heather's constant rate of 5 miles/hour. If Heather starts her journey 24 minutes after Stacy, how far from the original destination has Heather walked when the two meet?.

[ "6.5mile", "5.7mile", "7.0mile", "8.0mile", "12 mile" ]

Ss - Stacy's speed = 6m/hr Sh - Heather's speed = 5m/hr In 24 minutes Stacy will cover = (24/60)*6 = 2.4miles Now since both are walking in opposite directions, add their speeds - 6+5 =11m/hr and distance to cover is 15 -2.4 = 12.6 Time taken = Distance/ Speed = 12.6/11 = 1.145 hrs Heather will cover = 5*1.145 = 5.72miles. Answer B The answer is: B

B

mathematics

If an integer n is to be chosen at random from the integers 1 to 96, inclusive, what is the probability that n(n + 1)(n + 2) will be divisible by 4?

[ "1/4", "3/8", "1/2", "5/8", "3/4" ]

I get 5/8 as well 1 to 96 inclusive means we have 48 odd and 48 even integers E O E / 4 = Integer, therefore we have 48 / 96 numbers divisible by 8 O E O / 4 = Not Integer We cannot forget multiples of 8 from 1 to 96 We have 24 numbers that are multiple of 4 Therefore, 48/96 + 24/96 = 72/96 = 3/4 answer : E The answer is: E

E

mathematics

42573y is exactly divisible by 72, then what is the minimum value of y?

[ "3", "4", "6", "8", "9" ]

72 = 9 x8, where 9 and 8 are co-prime. The minimum value of x for which 73x for which 73x is divisible by 8 is, x = 6. Sum of digits in 425736 = (4 + 2 + 5 + 7 + 3 + 6) = 27, which is divisible by 9. Required value of y is 6 C The answer is: C

C

mathematics

The ratio of the ages of a man and his wife is 4:3. After 4 years,the ratio will be 9:7.If at the time of marriage the ratio was 5:3,then how many years ago were they married ?

[ "8", "10", "12", "14", "15" ]

let the present ages of the man and his wife be 4x and 3x then (4x+4)/(3x+4)= 9/7 [since given that after four years their ages will be 9/7] by solving it we have x=8 so their present ages are 32 and 24 respectively now suppose if they were married X years ago, then (32-X)/(24-X)=5/3 by solving it we have 2X=24 so X=12 so they were married 12 years ago ANSWER:C The answer is: C

C

mathematics

60 percent of movie theatres in Town X have 3 screens or less. 20% of those theatres sell an average of more than $300 worth of popcorn per showing. 56 percent of all the movie theatres in Town X sell $300 or less of popcorn per showing. What percent of all the stores on the street have 4 or more screens and sell an average of more than $300 worth of popcorn per day?

[ "12", "18", "32", "40", "44" ]

let's take numbers here. Assume that the total number of movie theaters in the town = 100 Then number of movie theaters with 3 screens or less = 60 => Number of movie theaters with 4 screens or more = 40 Movie theaters with 3 screens or less selling popcorn at more than $300 = 20% of 60 = 12 Number of movie theaters selling popcorn at $300 or less = 56 => Number of movie theaters selling popcorn at more than $300 = 100-56 = 44 Of these 44 theaters, 12 are those with 3 screens or less Therefore 32 (44-12) must be those with four screens or more C is the answer The answer is: C

C

mathematics

If the units digit of n^43 is 7, which of the following could be the value of n? I. n = 41 II. n = 43 III. n = 47

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

I tried in this way. Given n^43 units digit is 7. If at all we have to get 7 as units digits only 3 and 7 series has 7 3^! = 3 , 3^2 = 9 , 3^3 = 27 , 3^4 = 81 7^1 = 7, 7^2 = 49 , 7^3 = 3 (units ) , 7^4 = 1 (units) We have n^43 - then divide 43 by 4 = reminder 3. Then we have for only 7^3 - we have units digit as 7. Hence 47^43 = 7 (units). Option A is correct answer , and with 41^43 we always get 1 as units digit and 43^43 - we get units as 3. The answer is: A

A

mathematics

40 men shake hands with each other. Maximum no of handshakes without cyclic handshakes.

[ "780", "200", "210", "220", "230" ]

or, if there are n persons then no. of shakehands = nC2 = 40C2 = 780 ANSWER:A The answer is: A

A

mathematics

The average price of three items of furniture is Rs. 30000. If their prices are in the ratio 3:5:7, the price of the cheapest item is?

[ "2379", "2889", "9288", "9000", "6000" ]

Let their prices be 3x, 5x and 7x. Then, 3x + 5x + 7x = (15000 * 3) or x = 2000. Cost of cheapest item = 3x = Rs. 6000. Answer: E The answer is: E

E

mathematics

A wheel that has 6 cogs is meshed with a larger wheel of 7 cogs. When the smaller wheel has made 21 revolutions, then the number of revolutions made by the larger wheel is:

[ "9", "10", "6", "18", "7" ]

Explanation : Let the required number of revolutions made by larger wheel be x. Then, More cogs, Less revolutions (Indirect Proportion) 7:6::21:x => 7 * x = 21 * 6 => x = (21 * 6)/7 => x = 18 Answer : D The answer is: D

D

mathematics

4, 6, 12, 14, 28, 30, ?

[ "32", "64", "62", "60", "52" ]

The given sequence is a combination of two series 4, 12, 28, .... and 6, 14, 30, .... The pattern is +8, +16, +32. So, the missing number = (28 + 32) = 60 Answer : D. The answer is: D

D

mathematics

Murali travelled from city A to city B at a speed of 40 kmph and from city B to city C at 60 kmph. What is the average speed of Murali from A to C given that the ratio of distances between A to B and B to C is 2 : 3?

[ "17 kmph", "50 kmph", "18 kmph", "17 kmph", "11 kmph" ]

Let the distances between city A to B and B to C be 2x km and 3x km respectively. Total time taken to cover from A to C = (2x)/40 + (3x)/60 = (6x + 6x)/120 = 12x/120 = x/10 Average speed = (2x + 3x)/(x/10) = 50 kmph. Answer:B The answer is: B

B

mathematics

The total monthly income of four men and two women is 46,000. If every woman earns 500 more than a man then what is the monthly income of a woman?

[ "7,500", "8,000", "9,000", "6,500", "None of these" ]

4M + 2W = 46000; Again, W = M + 500 or, M = W – 500 ∴ (W – 500) + 2W = 46000 or, 6W = 46000 + 2000 = 48000 ∴ W = 8000 Answer B The answer is: B

B

mathematics

Arun got 30% of the maximum marks in an examination and failed by 10 marks. However, Sujith who took the same examination got 40% of the total marks and got 15 marks more than the passing marks. What were the passing marks in the examination?

[ "90", "250", "75", "85", "95" ]

Explanation : Let x is the maximum marks of the examination Marks that Arun got = 30 % of x = 30x/100 Given that Arun failed by 10 marks ⇒Minimum Pass Mark = (30x/100) + 10......(Equation 1)=85 ANSWER IS D The answer is: D

D

mathematics

The ratio between the length and the breadth of a rectangular plot is 7 : 5. If the perimeter of the plot is 216 metres, what is its area?

[ "1325 sq.metres", "1260 sq.metres", "2835 sq.metres", "3380 sq.metres", "None of these" ]

Let the length and breadth be 7x and 5x respectively. Then, P = 2(7x + 5x) = 216 â‡’ x = 9 Area = 7 Ã— 9 Ã— 5 Ã— 9 = 2835 sq.m. Answer C The answer is: C

C

mathematics

The sides of a triangle are in the ratio 5: 12: 13 and its perimeter is 300 m, its area is?

[ "150", "377", "297", "266", "971" ]

5x + 12x + 13x = 300 => x = 10 a = 50, b = 120, c = 130 S = (50 + 120 + 130)/2 = 150 Answer: A The answer is: A

A

mathematics

A group of 10 representatives is to be selected out of 12 seniors and 10 juniors. In how many different ways can the group be selected if it should have at least one senior?

[ "²²C₉", "²²C₁₀", "²²C₉ + ¹⁰C₁", "²²C₁₀ - 1", "¹⁰C₁" ]

The total number of ways of forming the group of ten representatives is ²²C₁₀. The total number of ways of forming the group that consists of no seniors is ¹⁰C₁₀ = 1 way The required number of ways = ²²C₁₀ - 1 Answer:D The answer is: D

D

mathematics

How much water must be added to 60 litres of milk at 1.5 litres for Rs. 20 So as to have a mixture worth Rs.32/3 a litre?

[ "10 litres", "12 litres", "15 litres", "18 litres", "21 litres" ]

C.P. of 1 litre of milk = Rs. 20×2/3 = Rs. 40/3. C.P. of 1 litre of water =Rs 0. Mean price = Rs. 32/3. By the rule of alligation, we have : C.P of 1 litre C.P of 1 litre of water of milk (0) (Rs. 40/3) \ / Mean Price (Rs. 32/3) / \ 40/3−32/3 32/(3−0) 8/3 32/3 The ratio of water and milk =8/3:32/3. =8:32=1:4. Thus, Quantity of water to be added to 60 litres of milk: =(1/4)×60 litres. =15 litres. ANSWER : C The answer is: C

C

mathematics

If x^2 = 231, which of the following is closest to a potential value of x?

[ "-127", "-11", "12", "13", "15" ]

Here the thing we must not forget is that X^even has two potential solutions => x =+- √231 => +- 15 (approx) this value is closer to 15 Hence E is correct. The answer is: E

E

mathematics

Walking 7/6 of his usual rate, a boy reaches his school 2 min early. Find his usual time to reach the school?

[ "14", "28", "99", "77", "66" ]

Speed Ratio = 1:7/6 = 6:7 Time Ratio = 7:6 1 -------- 7 2 --------- ? 14 m Answer:A The answer is: A

A

mathematics

If 10 bulls can plough 20 identical fields in 3 days working 10 hours a day, then in how many days can 30 bulls plough 32 same identical fields working 8 hours a day?

[ "8", "7", "5", "2.0", "1" ]

Explanation: M1*D1*W2 = M2*D2*W1 10*3*10*32 = 30*d*8*20 d = 2 days ANSWER: D The answer is: D

D

mathematics

In a nationwide poll, N people were interviewed. If 1/6 of them answered yes to question 1, and of those, 1/2 answered yes to question 2, which of the following expressions represents the number of people interviewed who did NOT answer yes to both questions?

[ "N/8", "7N/8", "11N/12", "17N/24", "41N/48" ]

The number of people who answered yes to both questions is (1/2)(1/6)N = N/12 The number of people who did not answer yes to both is 1 - N/12 = 11N/12 The answer is C. The answer is: C

C

mathematics

What approximate value should come in place of the question mark (?) in the following equation?47.05 Ã— 8.65 â€“ 25.22 Ã— 6.4 = (28 + ?) Ã— 5

[ "28.1149", "24.1149", "21.1149", "22.1149", "31.1149" ]

Solve using approximation Answer C The answer is: C

C

mathematics

Two pipes A and B can separately fill a cistern in 10 and 15 minutes respectively. A person opens both the pipes together when the cistern should have been was full he finds the waste pipe open. He then closes the waste pipe and in another 4 minutes the cistern was full. In what time can the waste pipe empty the cistern when fill?

[ "7", "9", "5", "4", "8" ]

1/10 + 1/15 = 1/6 * 4 = 2/3 1 - 2/3 = 1/3 1/10 + 1/15 - 1/x = 1/3 x = 8 ANSWER E The answer is: E

E

mathematics

With out any halt a train travels a certain distance with an average speed of 75 km ph , and with halts it covers the same distance at an average speed of 60 kmph. When it is traveling with halts, how many minutes/per hour does the train halt on an average ?

[ "48 min.", "12min.", "15min.", "18min.", "19min." ]

With halt in 1 hour the train travels 60km With out halt for traveling same distance it take 60/75 = 4/5 = 48 minutes :. 12 minutes is the halting time per hour ANSWER:B The answer is: B

B

mathematics

The price of a certain product increased by the same percent from 1960 to 1970 as from 1970 to 1980. If its price of $1.10 in 1970 was 150 percent of its price in 1960, what was its price in 1980?

[ "a) $ 1.65", "b) $ 2.00", "c) $ 2.40", "d) $ 2.70", "e) $ 3.00" ]

The price in 1970 was 150 percent of its price in 1960, means that the percent increase was 50% from 1960 to 1970 (and from 1970 to 1980). Therefore the price in 1980 = $1.1*1.5 = $1.65. Answer: A. The answer is: A

A

mathematics

The value of a machine depreciates at 20% per annum. If its present value is Rs. 1,50,000, at what price should it be sold after two years such that a profit of Rs. 24,000 is made?

[ "328897", "120000", "877888", "277768", "188871" ]

The value of the machine after two years = 0.8 * 0.8 * 1,50,000 = Rs. 96,000 SP such that a profit of Rs. 24,000 is made = 96,000 + 24,000 = Rs. 1,20,000 Answer: B The answer is: B

B

mathematics

An escalator moves towards the top level at the rate of 8 ft.sec and its length is 160 feet. If a person walks on the moving escalator at the rate of 2 feet per second towards the top level, how much time does he take to cover the entire length.

[ "14 sec", "10 sec", "16 sec", "8 sec", "9 sec" ]

Time taken to cover the entire length = tot.dist/resultant speed = 160/ (8+2) = 16sec ANSWER:C The answer is: C

C

mathematics

Present ages of Sameer and Anand are in the ratio of 5 : 4 respectively. Seven years hence, the ratio of their ages will become 11 : 9 respectively. What is Anand's present age in years?

[ "A)84", "B)89", "C)67", "D)56", "E)45" ]

Let the present ages of Sameer and Anand be 5x years and 4x years respectively. Then, (5x + 7/4x + 7)=11/9 9(5x + 7) = 11(4x + 7) 45x + 63 = 44x + 77 45x - 44x = 77 - 63 x = 14. Anand's present age = 4x = 84 years. Answer:A The answer is: A

A

mathematics

A boat with still water speed of a is traveling upstream where the streams speed is b. After covering certain distance s, the boat turns back and tries to come to the starting place. But the boat stops at 3/4th of the intended distance due to a technical fault. What is the ratio of the time taken for the return journey to that of the upstream journey.

[ "3(a - b)/4(a + b)", "4(a - b)/3(a + b)", "3(a + b)/4(a - b)", "4/3", "4/8" ]

speed of boat upstream = a - b speed of boat downstream = a + b For upstream journey, time taken = distance / speed = s / (a - b) During return journey, the boat had covered on 3/4th of s : Therefore for return journey, time taken = distance / speed = (3s/4)/(a+b) Ratio of time taken for return journey to the upstream journey = (3s/4)/(a+b)/ (s/(a - b)) = 3(a - b)/4(a + b) ANSWER:A The answer is: A

A

mathematics

HDFC bank offers an interest of 5% per annum compounded annually on all its deposits. If $10,000 is deposited, what will be the ratio of the interest earned in the 4th year to the interest earned in the 5th year?

[ "1:5", "625:3125", "100:105", "100^4:105^4", "725:3225" ]

Hi Bunuel, Here is my approach: is this correct? HDFC bank offers an interest of 5% per annum compounded annually on all its deposits. Interest earned in 4 year= 10000(1+0.05)^4 Interest earned in 5 year= 10000(1+0.05)^5 Ratio= {10000(1.05)^4}/{10000(1.05^5)} =>1.05^4/1.05^5 =>1/1.05 Multiplied by 100 in both numerator and denominator gives 100:105 Hence Ans:C The answer is: C

C

mathematics

Each book on a certain shelf is labeled by a single category. For every 2 history books, there are 7 fantasy books and for every 3 fantasy books, there are 8 reference books. If the proportion of history to reference books is doubled, while the proportion of fantasy to reference books is maintained, which of the following could be the number of history books if there are fewer than 60 fantasy books on the shelf after the changes?

[ "12", "21", "27", "35", "36" ]

For every 2 history books, there are 7 fantasy books: Originally H:F = 2:7 = 6:21. For every 3 fantasy books, there are 8 reference books: F:R = 3:8 = 21:56 H:F:R = 6:21:56 After the changes, H:F:R = 12:21:56 There are fewer than 60 fantasy books, so there are 21 or 42 fantasy books. The number of history books could be 12 or 24. The answer is A. The answer is: A

A

mathematics

Seven children — A, B, C, D, E, F, G and H— are going to sit in seven chairs in a row. The children CF have to sit next to each other, and the others can sit in any order in any remaining chairs. How many possible configurations are there for the children?

[ "600", "720", "1440", "10080", "4800" ]

for such questions , we can treat both as one then total person=7.. these 7 can be arranged in 7! ways.. but within these 7, one consists of two people who can be arranged in 2 ways CF or FC.. so ans =7!*2=10080 ans D The answer is: D

D

mathematics

In the xy-plane, the points (c, d), (c, -d), and (-c, -d) are three vertices of a certain square. If c < 0 and d > 0, which of the following points N is in the same quadrant as the fourth vertex of the square?

[ "(-5, -3)", "(-5, 3)", "(5, -3)", "(3, -5)", "(3, 5)" ]

The question:In the xy-plane, the points N=(c, d), (c, -d), and (-c, -d) are three vertices of a certain square.If c < 0 and d > 0,which of the following points is in the same quadrant as the fourth vertex of the square? I marked the tricky part in red. It seems c is anegativenumber and d is a positive number. This means Vertex #1 = (c, d) is in QII (that is, negative x and positive y) Vertex #2 = (c, -d) is in QIII (that is, both xy negative) Vertex #3 = (-c, -d) is in QIV (that is y is negative, but x is positive) That means the last vertex should be in the first quadrant --- the only first quadrant point is (5, 3), answer =E. The answer is: E

E

mathematics

In the equation a = 36.12b, b and a are integers. If a/b leaves a remainder of r, which of the following must divide into r?

[ "2", "3", "4", "6", "12" ]

1) It says it is a equation, so a=36.12b should be 36.12 * b.. 2) It says b is an integer, again it means 36.12 * b.. Otherwise b would be just a digit and it would be mentioned.. Although not clearly mentioned that 36.12b is actually 36.12 * b, BUT entire info points towards that.. and that is why I have taken a/b = 36.12 The answer is: B

B

mathematics

A merchant marks his goods up in such a way that the profit made on selling 30 articles is equal to the cost price of 20 articles. What is the W % profit made by the merchant?

[ "66.67 %", "50 %", "200 %", "100 %", "33.33 %" ]

C.P of 1 article= $30(say) C.P of 20 articles=30*20=$600 Now, C.P of 20 articles=Profit on 30 articles Therefore, profit on 1 article=$600/30=$20 Profit W%=(20/30)*100=66.67% Answer A The answer is: A

A

mathematics

When the positive integer x is divided by 9,the remainder is 5.What is the remainder when 8x is divided by 9?

[ "0", "1", "3", "4", "6" ]

i tried plugging in numbers x = 9q+5 x = 14 8x = 112 8x/9= 9*12+4 remainder is 4. Answer is D. The answer is: D

D

mathematics

In a college, 1 percent of students hate math, 2 percent of students hate English, 1 percent hate French and 4 percent hate German. Can you find out the percentage of students who hate all 4 subjects ?

[ "8%", "5%", "7%", "12%", "19%" ]

A 8% of student hate all four subjects. The answer is: A

A

mathematics

Choose the missing terms out of the given alternatives. QPO, SRQ, UTS, WVU, ?

[ "XVZ", "ESD", "ZYA", "VWX", "YXW" ]

E YXW Each term consists of three consecutive letters in reverse order. The first letter and the last letter of the next term are the same. The answer is: E

E

mathematics

The sum of two consecutive integers is 15. Find the numbers.

[ "17, 18", "7, 8", "5, 6", "1, 2", "8, 9" ]

n + (n + 1) = 15 2n + 1 = 15 2n = 14 n = 7 Answer: B The answer is: B

B

mathematics

A and B’s salaries together amount to Rs. 3,000. A spends 95% of his salary and B spends 85% of his. If now their savings are the same, what is B’s salary?

[ "777", "750", "789", "776", "881" ]

(5/100) A = (15/100) B A = 3B A + B =3000 4B = 3000 => B = 750 Answer B The answer is: B

B

mathematics

If a·b·c·d=360, where a, b, c and d are positive integers, and a<b<c<d, which of the following could be the value of d−a?

[ "9", "10", "11", "13", "15" ]

prime factorize : 360 = 2*3*5*12 Hence a = 2 and d = 12 . Hence answer is 12 - 2 = 10 Answer B The answer is: B

B

mathematics

If the speed of a man is 45 km per hour, then what is the distance traveled by him in 30 seconds ?

[ "275m", "360m", "375 m", "420 m", "480 m" ]

The distance traveled in 30 sec = 45*(5/18) *30 =375m Answer: C The answer is: C

C

mathematics

Lilly has 10 fish and Rosy has 9 fish. In total, how many fish do they have in all?

[ "16", "17", "18", "19", "20" ]

10+9=19 The answer is D. The answer is: D

D

mathematics

9548 + 7314 = 7362 + (?)

[ "8300", "8400", "8500", "8700", "9500" ]

9548 16862 = 7362 + x + 7314 x = 16862 - 7362 ----- = 9500 16862 ----- E) The answer is: E

E

mathematics

Pipe A can fill a tank in 8 hours, pipe B in 10 hours and pipe C in 40 hours. If all the pipes are open, in how many hours will the tank be filled?

[ "2", "2.5", "3", "4", "None" ]

Sol. Part filled by (A + B + C) in 1 hour = (1/8 + 1/10 + 1/40) = 1/4. âˆ´ All the three pipes together will fill the tank in 4 hours. Answer D The answer is: D

D

mathematics

The ages of Rahul and Madhan differ by 16 years. Six years ago, Madhan’s age was thrice as that of Rahul’s,find their present ages

[ "14 years, 30 years", "12 years, 28 years", "16 years, 34 years", "18 years, 38 years", "none of these" ]

Let Rahul’s age = x years So, Madhan’s age = ( x + 16 )years Also, 3(x - 6) = x + 16 - 6 or, x = 14 Rahul’s age = 14 years And, Madhan’s age 14 + 16 = 30 years ANSWER:A The answer is: A

A

mathematics

There is a 10% chance that Tigers will not win at all during the whole season. There is a 20% chance that Federer will not play at all in the whole season. What is the greatest possible probability that the Tigers will win and Federer will play during the season?

[ "55%", "60%", "70%", "72%", "80%" ]

There is a 10% chance that Tigers will not win at all during the whole season We can infer that there is 90% chance Tigers will win . Similarly There is a 20% chance that Federer will not play at all in the whole season We can also infer that there is 80% chance that Federer will play. Answer E The answer is: E

E

mathematics

If Tim had lunch at $50.50 and he gave 20% tip, how much did he spend?

[ "$57.45", "$35.42", "$60.60", "$21.56", "$78.45" ]

The tip is 20% of what he paid for lunch. tip = 20% of 50.50 = (20/100)*50.50 = 101/100 = $10.10 Total spent 50.50 + 10.10 = $60.60 correct answer is C)$60.60 The answer is: C

C

mathematics

Which one of the given numbers is divisible by 11?

[ "4823718", "8423718", "8432718", "4238718", "4852718" ]

Explanation: 4238718 = (4+3+7+8) – (2+8+1) = 11 So, the given number is divisible by 11 Answer:D The answer is: D

D

mathematics

If 2^z is a factor of 30!, which of the following could be the value of z? I. 23 II. 26 III. 24

[ "I ONLY", "II ONLY", "BOTH I AND II", "III ONLY", "NONE OF THE ABOVE" ]

2^z is a factor of 30!, what values can z take. Powers of 2 in 30! = [30/2] + [30/4] +[30/8] + [30/16] , where [x] is the integral part of x Powers of 2 in 30! = 15 + 7 + 3 + 1 = 26 Hence the maximum value of 2^z in 30! = 2^26 Only Statement II satisfies Correct Option: B The answer is: B

B

mathematics

The difference between 3/5 of 2/3 of a number and 2/5 of 1/4 of the same number is 288. What is the number?

[ "960", "850", "895", "955", "975" ]

according to the given condition x*(2/3)*(3/5) - x*(2/5)*(1/4) = 288 so 2x/5 - x/10 = 288 or 3x/10 = 288 or x = 2880/3 = 960 ANSWER:A The answer is: A

A

mathematics

Four people are to be seated on a bench. How many different sitting arrangements are possible if Erik must sit next to Joe?

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

Consider E and J one. But, in this arrangement they can sit in two different combinations. E first and J second or J first and E second. Total we have (E and J) and the two other persons= 4 arrangements to do. Total arrangements= 4*2= 8 C is the answer The answer is: C

C

mathematics

Find the value of 1.5 x [(3.6 x 0.48 x 2.50) / (0.12 x 0.09 x 0.5)]

[ "800", "500", "900", "1200", "None" ]

Answer 1.5 x [(3.6 x 0.48 x 2.50) / (0.12 x 0.09 x 0.5)] = 1.5 x [(36 x 48 x 250) / (12 x 9 x 5)] = 1.5 x 4 x 4 x 50 = 1200 Correct Option: D The answer is: D

D

mathematics

In store A there are 10 pairs of pants for every 30 store B has. The price ratio between the pants in store B and the pants in store A is 3:4. If all the pants were sold in both places until the stock ran out, what is the ratio between the total amount stores A earned to the total amount store B earned?

[ "3:16.", "2:3.", "4:9", "3:4.", "2:5." ]

1st statement : ratio of pants Store A : Store B 10x : 30x X:3X Price : 4y:3y Total revenue 4xy : 9xy 4:9 Answer : C The answer is: C

C

mathematics

A glass was filled with 12 ounces of water, and 0.03 ounce of the water evaporated each day during a 22-day period. What percent of the original amount of water evaporated during this period?

[ "5.002%", "5.5%", "0.5%", "5%", "20%" ]

In 22 days 22*0.03=0.66 ounces of water evaporated, which is 0.66/12âˆ—100=5.5 of the original amount of water. Answer: B. The answer is: B

B

mathematics

A, B and C rents a pasture for Rs.435. A put in 12 horses for 8 months, B 16 horses for 9 months and 18 horses for 6 months. How much should B pay?

[ "180", "227", "268", "198", "176" ]

12*8 :16*9 = 18*6 8: 12: 9 12/29 * 435 = 180 Answer:A The answer is: A

A

mathematics

If x=2, which of the following is(are) true? I. x^2=2x II x/-4 = 1 III |x|=-x

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

2^2 = 2 * 2 Answer : D The answer is: D

D

mathematics

In a box, there are 8 red, 7 blue and 6 green balls. One ball is picked up randomly. What is the probability that it is neither red nor green?

[ "3/4", "1/3", "7/19", "8/21", "9/21" ]

7C1/21C1=7/21=1/3 ANSWER:B The answer is: B

B

mathematics

Ronald and Elan are working on an assignment. Ronald takes 6 hrs to type 32 pages on a computer, while Elan takes 5 hrs to type 40 pages. How much time will they take, working together on two different computers to type an assignment of 110 pages?

[ "8 hrs 19 min", "8 hrs 18 min", "8 hrs 15 min", "8 hrs 65 min", "8 hrs 18 min" ]

Number of pages typed by Ronald in 1 hour = 32/6 = 16/3 Number of pages typed by Elan in 1 hour = 40/5 = 8 Number of pages typed by both in 1 hour = (16/3 + 8) = 40/3 Time taken by both to type 110 pages = (110 * 3/40) = 8 1/4 = 8 hrs 15 min Answer:C The answer is: C

C

mathematics

If the difference between the compound interest & simple interest of a certain sum of money is Rs.72 at 12% p.a. per two year. Find the sum(in Rs.)?

[ "200/15", "200/17", "220/17", "240/17", "260/17" ]

200/17 C.I=A-P A=p(1+12/100)^2 S.I=p*2*12/100 C.I-S.I=72 given substitute and solve p=200/17 ANSWER:B The answer is: B

B

mathematics

The average age of the mother and her 6 children is 12 years which is reduced by 5 years if the age of the mother is excluded. How old is the mother?

[ "42 years", "40 years", "48 years", "50 years", "None of these" ]

Total age of the mother and six children = 12 × 7 = 84 years. Total age of six children = 7 × 6 = 42 years. (since average is reduced by 5) Mother is 42 years old. ANSWER:A The answer is: A

A

mathematics

Raj and Roshan has some money with them in the ratio 5:4 respectively. If Raj has Rs. 45. How much money Raj has more than Roshan?

[ "5", "9", "16", "12", "18" ]

Let the money Roshan has be x then (45/x)=5/4 Upon cross multiplication and solving for x we get x=36 So Raj has Rs. 9 more than Roshan Answer:B The answer is: B

B

mathematics

Find the one which does not belong to that group ?

[ "30", "82", "27", "62", "11" ]

Explanation: 27, 36, 72 and 45 are divisible by 9, but not 30. Answer: A The answer is: A

A

mathematics

A wholesaler wishes to sell 100 pounds of mixed nuts at $2.00 a pound. She mixes peanuts worth $1.50 a pound with cashews worth $4.00 a pound. How many pounds of cashews must she use?

[ "40", "45", "50", "55", "60" ]

From the question stem we know that we need a mixture of 100 pounds of peanuts and cashews. If we represent peanuts as x and cashews as y, we get x + y = 100. Since the wholesaler wants to sell the mixture of 100 pounds @ $2.50, we can write this as: $2.5 * (x + y) = $1.5x + $4y From the equation x + y = 100, we can rewrite y as y = 100 - x and substitute this into our equation to get: $2.5 * (x + 100 - x) = $1.5x + $4(100 - x) If you solve for x, you will get x = 60, and therefore y = 40. So the wholesaler must use 40 pounds of cashews. You can substitute into the original equation to see that: $250 = $1.5(60) + $4(40) Answer is C. The answer is: C

C

mathematics

A part-time employee’s hourly wage was increased by 25%. She decided to decrease the number of hours worked per week so that her total income did not change. By approximately what percent should the number of hours worked be decreased?

[ "9%", "15%", "20%", "50%", "100%" ]

Let's plug in somenicenumbers and see what's needed. Let's say the employee used to make $1/hour and worked 100 hours/week So, the TOTAL weekly income was $100/week After the 25% wage increase, the employee makes $1.25/hour We want the employee's income to remain at $100/week. So, we want ($1.25/hour)(new # of hours) = $100 Divide both sides by 1.25 to get: new # of hours = 100/1.25 ≈ 80 hours So, the number of hours decreases from 100 hours to (approximately) 80 hours. This represents a 20% decrease (approximately) . Answer : C The answer is: C

C

mathematics

If a, f, and c are consecutive even integers and a < f < c, all of the following must be divisible by 4 EXCEPT

[ "a + c", "f + c", "ac", "(bc)/2", "(abc)/4" ]

I did get the correct answer within 80 seconds and it was not by luck either. I did not pick numbers but just used the concept stated by Ian. The 3 numbers can be written as a, (a + 2)(a + 4). If 'a' is divisible by 4, then even 'c' or 'a + 4' is divisible by 4. However, is 'b' is divisible by 4, then both 'a' and 'a + 4' are still divisible by 2. A - (a + c) = a + (a + 4) = 2a + 4 = 2(a + 2) = 2b. 2b will always be divisible by 4 even if 'b' is not divisible by 4. Reason: 'b' already has a prime factorization of at least a '2'. Hence '2b' has two 2s. C - ac = a(a+4). If, as stated above, one of them is divisible by 4, then the product is divisible. If both of them are not divisible by 4, then the product is still divisible by 4 because of the presence of two 2s again in the prime factorization. D - bc/2 = (a + 2)(a + 4)/2. Either b or c is divisible by 2. Hence, if we assume that b is divisible by 2 and not divisible by 4, then it leaves us just one possibility. Is c divisible by 4? It has to be because c is the next consecutive even integer. E - abc/4 = a(a + 2)(a + 4)/4. One of these integers is divisible by 4 already. If we again assume 'b' to be that integer divisible by 4, then we are left with the question - Is a(a + 4) divisible by 4? This is the same as option C. B - f + c = (a + 2) + (a + 4) = 2a + 6 = 2(a + 3). (a + 3) will never be divisible by 2 because it is an odd integer. Hence, 2(a + 3), although divisible by 2, will not be divisible by 4 because it has just one 2 in its prime factorization. As a whole, whether you choose numbers (2, 46 being the easiest) or solve conceptually, the answer is still easily obtainable within 2 minutes.B The answer is: B

B

mathematics

If 40% of a certain number is 160, then what is 20% of that number?

[ "75", "100", "120", "30", "80" ]

Explanation: 40% = 40*4 = 160 20% = 20*4 = 80 Answer: Option E The answer is: E

E