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	Ram, who is half as efficient as Krish, will take 36 days to complete a task if he worked alone. If Ram and Krish worked together, how long will they take to complete the task?	[ "16 days", "12 days", "8 days", "6 days", "18 days" ]	Number of days taken by Ram to complete task = 36 Since Ram is half as efficient as Krish , Amount of work done by Krish in 1 day = Amount of work done by Ram in 2 days If total work done by Ram in 36 days is 36w Amount of work done by Ram in 1 day = w Amount of work done by Krish in 1 day = 2w Total amount of work done by Krish and Ram in a day = 3w Total amount of time needed by Krish and Ram to complete task = 36w/3w = 12 days Answer B The answer is: B	B
mathematics	If the difference between compound interest (interest compounded yearly)and simple interest on a sum for 2 years at 10% p.a. is Rs.150 then sum is	[ "Rs.12,000", "Rs.15,000", "Rs.13,000", "Rs.10,000", "Rs.14,000" ]	compund interest = p[1+r/100]^t-p CI = p[21/100] simple interest = ptr/100 SI = p[20/100] difference p[21/100]-p[20/100] = 150 p=15,000 ANSWER:B The answer is: B	B
mathematics	A sock drawer contains seven socks, each one a different solid color. The colors of the socks are white,black, red, orange, yellow, green, blue, indigo, and violet. A person reaches into the drawer, pulls out two socks, and puts a single sock on each foot. If each sock can fit either the left or the right foot, and if it matters whether a particular sock is on the left or the right foot, how many different sock fashion combinations could the person make from the nine socks?	[ "12", "15", "21", "36", "72" ]	It's a question of permutation since order matters here .... It can be deduced to- 9P2 = 9!/7! = 9*8 = 72 .........Answer is - E The answer is: E	E
mathematics	The present ages of three persons in proportions 4 : 7 : 9. Eight years ago, the sum of their ages was 16. Find their present ages (in years).	[ "8, 14, 18", "8, 28, 36", "20, 35, 45", "33,42,43", "23,42,43" ]	Let their present ages be 4x, 7x and 9x years respectively. Then, (4x - 8) + (7x - 8) + (9x - 8) = 16 20x = 40 x = 2. Their present ages are 4x = 8 years, 7x = 14 years and 9x = 18 years respectively. ANSWER:A The answer is: A	A
mathematics	If Rs.450 amount to Rs.540 in 4 years, what will it amount to in 6 years at the same rate % per annum?	[ "227", "887", "585", "2679", "27" ]	90 = (4504R)/100 R = 5% I = (45065)/100 = 135 450 + 135 = 585 Answer:C The answer is: C	C
mathematics	What positive number, when squared, is equal to the cube of the positive square root of 12?	[ "64", "32", "8", "4", "2" ]	Let the positive number be x x^2 = ((12)^(1/2))^3 =>x^2 = 4^3 = 16 => x = 4 Answer D The answer is: D	D
mathematics	Average age of boys in a class is 16 years and average age of girls is 15 years, what is the average age of all	[ "15.5", "15", "16", "17", "Cant be computed" ]	Explanation: As number of girls and boys is not given so result cant be computed Option D The answer is: D	D
mathematics	If the ratio of the roots of the equation x2 – 2ax + b = 0 is equal to that of the roots x2 – 2cx + d = 0, then:	[ "a2b = c2d", "a2c = b2d", "a2d = c2b", "d2 b = c2 a", "none" ]	x^2-2ax+b=0 for this eqn..roots r....R1=2a/1,R2=b/1; x^2-2cx+d=0 for this eqn ..roots r...R3=2c/1,R4=d; As per question ,2a/b=2c/d =>2ad=2bc ANSWER:C The answer is: C	C
mathematics	A metered rikshaw charges Rs 13.50 for the first 1 Km and 2.50 per 1/3 km there after. What would the charge if this rikshaw is hired for 13 Kms? In approx??	[ "103.5 Rs", "104.5 Rs", "105.5 Rs", "106.5 Rs", "107.5 Rs" ]	For 1st Km: Rs.13.50 Ramaining distance:13-1=12 KM 1/3 km costs 2.5 rs 1 km costs (2.53) Remaining 12KM costs (2.53)*12=90 Rs total cost=90+13.5=103.5 Rs ANSWER:A The answer is: A	A
mathematics	Evaluate 35 / .07	[ "400", "500", "505", "None of these", "506" ]	Explanation: 35/.07 = 3500/7 = 500 Option B The answer is: B	B
mathematics	A train running at the speed of 60 km/hr crosses a pole in 9 sec. What is the length of the train?	[ "535 m", "178 m", "186 m", "168 m", "150 m" ]	Speed = 60 * 5/18 = 50/3 m/sec Length of the train = speed * time = 50/3 * 9 = 150 m Answer:E The answer is: E	E
mathematics	A restaurant spends one quarter of its monthly budget for rent and quarter of the rest for food and beverages. What percentage of the budget does the restaurant spend for food and beverages?	[ "23.5%", "32.5%", "35%", "18.75%", "20%" ]	Spend on rent = 1/4 Spend on food and beverage= 1/4 of remaining = 1/4*3/4= 3/16 so 3/16= 18.75% D is the answer The answer is: D	D
mathematics	A cistern has a leak which would empty the cistern in 20 minutes. A tap is turned on which admits 1 liters a minute into the cistern, and it is emptied in 24 minutes. How many liters does the cistern hold?	[ "480", "120", "289", "270", "927" ]	1/x - 1/20 = -1/24 x = 120 120 * 1 = 120 Answer: B The answer is: B	B
mathematics	The average weight of 25 persons sitting in a boat had some value. A new person added to them whose weight was 46 kg only. Due to his arrival, the average weight of all the persons decreased by 5 kg. Find the average weight of first 25 persons?	[ "56 kg", "56 kg", "56 kg", "176 kg", "739 kg" ]	25x + 46 = 26(x – 5) x = 176 Answer:D The answer is: D	D
mathematics	Several people are sitting around a round table playing a card game with a deck of 51 cards. Each person is dealt one card per deal, and the cards are dealt in a clockwise fashion. If Martin is dealt both the first card of the deck and the last card of the deck, which of the following could be the total number of people sitting at the table?	[ "4", "5", "7", "11", "13" ]	Let n be the number of people at the table. If Martin gets the first and the last card, it means Martin got one more card than the others. Thus 51/n has a remainder of 1 and so 51-1 = 50 is a multiple of n. The answer is B. The answer is: B	B
mathematics	Out of 10 persons working on a project, 4 are graduates. If 3 are selected, what is the probability that there is at least one graduate among them?	[ "5/5", "5/8", "5/1", "5/6", "5/2" ]	P(at least one graduate) = 1 - P(no graduates) = 1 - 6C3/10C3 = 1 - (6 * 5 * 4)/(10 * 9 * 8) = 5/6 Answer:D The answer is: D	D
mathematics	During the first week of performances of a certain play, 5,400 tickets were sold, all at reduced price. During the remaining weeks of performances, 5 times as many tickets were sold at full price as were sold at reduced price. If the total number of tickets R sold was 25,200, how many of them were sold at full price?	[ "21,000", "19,800", "16,500", "15,800", "8,700" ]	Given: The question tells us about the number of tickets sold in the first week at reduced price = 5,400. It also tells us that during the remaining weeks, the number of tickets sold at full price was 5 times the no. of tickets sold at reduced price. The total tickets sold was 25,200, and we are asked to find the number of tickets that where sold at full price. Approach: The question asks us to find the number of ticket sold at full price. We know that the number of tickets sold at full price was 5 times the no. of tickets sold at reduced price in remaining weeks. Hence, assuming tickets sold at reduced price in remaining weeks to be x would give us the no. of tickets sold at full price to be 5x. Tickets sold in first week + Tickets sold in remaining weeks = Total no. of tickets soldi.e. Tickets sold in first week + Tickets sold at full price in remaining weeks + Tickets sold at reduced price in remaining weeks = Total no. of tickets sold We know the no. of tickets sold during first week and the total no. of tickets sold. We will use this relation to get to our answer. Working Out: Tickets sold in first week + Tickets sold at full price in remaining weeks + Tickets sold at reduced price in remaining weeks = Total no. of tickets sold Substituting values in the equation, we get 5,400 + 5x + x = 25,200 x= 3,300 Tickets sold at full price = 5x = 16,500 Answer: Option C The answer is: C	C
mathematics	If, 1 * 3 * 5 = 16 3 * 5 * 7 = 38 Then find, 5 * 6 * 9 =?	[ "65", "59", "72", "80", "77" ]	(9 * 6) + 5 = 59 B The answer is: B	B
mathematics	A basketball player succeeds with 60% of her free throws. If she has a set of three free throws, what is the probability that she succeeds at least once?	[ "0.856", "0.872", "0.936", "0.952", "0.985" ]	P(missing all 3 free throws) = 0.4^3 = 0.064 P(succeeding at least once) = 1 - 0.064 = 0.936 The answer is C. The answer is: C	C
mathematics	A train sets off at 2 p.m. at the speed of 50 kmph. Another train starts at 3:30 p.m. in the same direction at the rate of 65 kmph. At what time the trains will meet?	[ "8.37 p.m", "8.20 p.m", "8.30 p.m", "8.38 p.m", "8.10 p.m" ]	D = 50 * 1 Â½ = 75 km RS = 65 â€“ 50 = 15 T = 75/15 = 5 h 3.30 + 7 h = 8.30 p.m. Answer: C The answer is: C	C
mathematics	What profit percent is made by selling an article at a certain price, if by selling at 2/3rd of that price, there would be a loss of 20%?	[ "20%", "26%", "80%", "10%", "50%" ]	SP2 = 2/3 SP1 CP = 100 SP2 = 80 2/3 SP1 = 80 SP1 = 120 100 --- 20 => 20% Answer:A The answer is: A	A
mathematics	If 20% of a number is equal to one-third of another number, what is the ratio of first number to the second number?	[ "2:5", "1:4", "5:3", "6:11", "2:3" ]	Let 20% of A = 1/3 B then 20A/100 = 1B/3 A/5 = B/3 A/B = 5/3 A:B = 5:3 Answer is C The answer is: C	C
mathematics	6x – 5y + 3z = 26 4x + 8y – 11z = 7 5x – 6y + 2z = 12 Given the equations above, x + y + z = ?	[ "11", "12", "13", "14", "15" ]	(6x – 5y + 3z) - (5x – 6y + 2z ) = 26-12 or, x+y+z = 14 Option D is the ans The answer is: D	D
mathematics	Carrie likes to buy t-shirts at the local clothing store. They cost $9.65 each. One day, she bought 12 t-shirts. How much money did she spend?	[ "$115.8", "$248.75", "$200", "$171.6", "$190" ]	$9.65*12=$115.8. Answer is A. The answer is: A	A
mathematics	IBM and KTC quote for a tender. On the tender opening day, IBM realizes that their quotations are in the ratio 7:4 and hence decreases its price during negotiations to make it Rs 1 Lakh lower than KTC's quoted price. KTC realizes that the final quotes of the two were in the ratio 3:4. What was the price at which IBM won the bid?	[ "Rs. 7 lakh", "Rs. 3 lakh", "Rs. 4 lakh", "Rs. 1.5 lakh", "None of these" ]	Explanation : IBM initially quoted Rs 7x lakh. KTC quoted 4x lakh. IBM's final quote = (4x−1) Lakh. Thus, (4x−1)/4=3/4 i.e x=1. Hence, IBM's bid winning price = Rs 3 Lakh. Answer : B The answer is: B	B
mathematics	If 0 < a < b < c < 1 , which of the following are positive? I. b-c II. a-b III. c-a	[ "I only", "II only", "III only", "I and II", "I and III" ]	We could solve this easily using examples. I is false since b<c and both are positive II is false since b<c and both are positive III is true since c>a and both are positive So, the answer is C. The answer is: C	C
mathematics	An empty wooden vessel weighs 20% of its total weight when filled with paint. If the weight of a partially filled vessel is one half that of a completely filled vessel, what fraction of the vessel is filled.	[ "3/5", "5/9", "9/19", "4/9", "2/5" ]	An empty wooden vessel weighs 20% of its total weight when filled with paint: Vessel = 0.2(Vessel + Paint); 20V = V + P (so the weight of completely filled vessel is 10V) P = 19V (so the weight of the paint when the vessels is completely filled is 9V). The weight of a partially filled vessel is one half that of a completely filled vessel: V + P' = 1/2*20V; P' = 9V (so the weight of the paint when the vessels is partially filled is 9V). What fraction of the vessel is filled? So, we need to find the ratio of the weight of the paint when the vessel iscompletely filledto the weight of the paint when the vessel ispartially filled: P'/P = 9V/19V = 9/19. Answer: C. The answer is: C	C
mathematics	If the sum of two positive integers is 12 and the difference of their squares is 48, what is the product of the two integers?	[ "32", "119", "128", "135", "143" ]	Let the 2 positive numbers x and y x+ y = 12 -- 1 x^2 - y^2 = 48 => (x+y)(x-y)=48 -- 2 Using equation 1 in 2 , we get => x-y = 4 -- 3 Solving equation 1 and 3 , we get x= 8 y= 4 Product = 8*4 = 32 Answer A The answer is: A	A
mathematics	Three pipes of same capacity A,B,C can fill a tank in 18 hours. If there are only two pipes B and A of same capacity, the tank can be filled in?	[ "16", "19", "27", "24", "29" ]	The part of the tank filled by three pipes in one hour = 1/6 => The part of the tank filled by two pipes in 1 hour = 2/3 * 1/18= 1/27. The tank can be filled in 27 hours. Answer:C The answer is: C	C
mathematics	A shopkeeper buys mangoes at the rate of 5 a rupee and sells them at 3 a rupee. Find his net profit or loss percent?	[ "66 1/4 %", "66 9/3 %", "66 2/3 %", "66 1/5 %", "66 1/3 %" ]	The total number of mangoes bought by the shopkeeper be 15. If he buys 5 a rupee, his CP = 3 He selling at 3 a rupee, his SP = 5 Profit = SP - CP = 5 - 3 = 2 Profit Percent = 2/3 * 100 = 66 2/3 % Answer:C The answer is: C	C
mathematics	Williams works at a resort from the beginning of March to the end of September. During the month of August this past year, he made 10 times the average (arithmetic mean) of his monthly totals in tips for the other months. His total tips for August were what fraction of his total tips for all of the months he worked?	[ "5/8", "7/8", "6/8", "2/9", "1/7" ]	First notice the number of months for which he worked - March to Sept i.e. 7 months Avg of monthly totals in tips for months other than August = x Tips in August = 10x Total tips for all months = 6*x + 10x = 16x Tips for August/Total tips for all months = 10x/16x = 5/8 Answer : A The answer is: A	A
mathematics	The cross-section of a water channel is a trapezium in shape. If the channel is 12 meters wide at the top and 6 meters wide at the bottom and the area of cross-section is 630 square meters, what is the depth of the channel (in meters)?	[ "50", "60", "70", "80", "90" ]	1/2 * d * (12 + 6) = 630 d = 70 The answer is C. The answer is: C	C
mathematics	IN Common Wealth Games an athlete runs 200 meters in 32 seconds. Hisspeed is ?	[ "25 km/hr", "27 km/hr", "30 km/hr", "32 km/hr", "None of these" ]	Explanation : (200/1000)/(32/3600)=22.72 km/hr Answer : E The answer is: E	E
mathematics	How many seconds will a 800 m long train take to cross a man walking with a speed of 3 km/hr in the direction of the moving train if the speed of the train is 63 km/hr?	[ "11", "30", "99", "48", "61" ]	Speed of train relative to man = 63 - 3 = 60 km/hr. = 60 * 5/18 = 50/3 m/sec. Time taken to pass the man = 800 * 3/50 = 48 sec. Answer: D The answer is: D	D
mathematics	John weighs twice as much as Susan. Susan's weight is 60% of Sam's weight. Mark weighs 50% of Lynn's weight. Lynn weighs 160% of John's weight. Which of these 5 people weighs the least?	[ "John", "Susan", "Sam", "Mark", "Lynn" ]	John weighs twice as much as Susan --> J=2S --> John cannot weigh the least; Susan's weight is 60% of Sam's weight --> S=0.6Sam --> Sam cannot weigh the least; Mark weighs 50% of Lynn's weight --> M=0.5L --> Lynn cannot weigh the least; Lynn weighs 160% of John's weight --> L=1.9J --> John cannot weigh the least (we already know that); As you can see the answer is either Susan (S) or Mark (M). To compare their weights we should express their weights in regards of the same person: M=0.5L=0.5(1.6J)=0.8J and from J=2S, S=0.5J --> Susan weights the least: Susan's weight is 50% of that of John and Mark's weight is more than 50%of that of John. Answer: B. The answer is: B	B
mathematics	9 men went to a hotel. Eight of them spent Rs.3 each over their meals and the ninth spent Rs.2 more than the average expenditure of all the nine. Determine the total money spent by them?	[ "29.25", "30", "31.2", "34", "35" ]	Average of 9 = x 9x = 8 * 3 + x * 2 x = 3.25 Total = 9 * 3.25 = 29.25 A The answer is: A	A
mathematics	If Henry were to add 8 gallons of water to a tank that is already 3/4 full of water, the tank would be 7/8 full. How many gallons of water would the tank hold if it were full?	[ "25", "40", "64", "80", "96" ]	7/8x-3/4x=8galls 1/8*x=8gallons x=64 gallons Answer C The answer is: C	C
mathematics	Sum of two numbers is 10. Two times of the first exceeds by 5 from the three times of the other. Then the numbers will be?	[ "A)7", "B)9", "C)11", "D)13", "E)15" ]	Explanation: x + y = 10 2x – 3y = 5 x = 7 y = 3 A) The answer is: A	A
mathematics	On dividing 13698 by a certain number, we get 89 as quotient and 14 as remainder. What is the divisor?	[ "743", "154", "852", "741", "785" ]	Divisor *quotient+remainder=dividend divisor=(dividend)-(remainder)/quotient (13698-14)/89=154 Answer(B) The answer is: B	B
mathematics	If A, B and C together can finish a piece of work in 4 days. A alone in 36 days and B in 18 days, then C alone can do it in?	[ "1", "7", "8", "9", "6" ]	C = 1/4 - 1/36 – 1/18 = 1/6 => 6 days' Answer: E The answer is: E	E
mathematics	If -1<= x <= 2 and 3 <= y <= 8, which of the following represents the range of all possible values of y-x?	[ "5 <= y-x <= 6", "1 <= y-x <= 5", "1 <= y-x <= 6", "1 <= y-x <= 9", "1 <= y-x <= 10" ]	Maximum value of y-x= 8 - (-1)= 9 Minimum value of y-x= 3-2= 1 D mentions the correct range The answer is: D	D
mathematics	Find the odd man out. 187, 264, 336, 473, 682, 781	[ "187", "336", "781", "682", "473" ]	In all numbers except 336, the middle digit is the sum of other two digits. Answer is B The answer is: B	B
mathematics	in how many ways u can form a group of 11 members from 5 men and 11 women if the men member not more than 3?	[ "2256 ways", "2356", "3456", "4456", "1554" ]	we need team members=11 such that there should not be more than 3 men so the conditions are (3M,8W),(2M,9W),(1M,10W) Now, no. of ways=11c11+5c311c8+5c211c9+5c1*11c10=2256 ANSWER:A The answer is: A	A
mathematics	40% of all students in a class commute by public transportation. If 25% of the students aspire to be scientists, which of the following can be the percentage of students who do not commute by public transportation and do not aspire to be scientists? I. 7% II. 20% III. 45%	[ "I ONLY", "II ONLY", "III ONLY", "I AND II", "I AND III" ]	40% Students use public transportation. This means 60% students do not use public transportation. 25% students aspire to be scientists means even if all these students use public transportation, minimum 60% - 25% = 35% students do not use public transportation and do not aspire to be scientists.This means correct answer is between 35% and 60% Answer :C. The answer is: C	C
mathematics	One hour after Adrienne started walking the 60 miles from X to Y, Harold started walking from X to Y as well. Adrienne walks 3 miles per hour and Harold walks 1 mile per hour faster than Adrienne. How far from X will Harold be when he catches up to Adrienne?	[ "8 miles", "12 miles", "10 miles", "11 miles", "14 miles" ]	First, determine how far Adrienne has walked in the one hour. She has walked three miles which means she is three miles ahead of Harold when he sets off. Harold walks at four miles/hour which means that every hour, Harold will get one mile closer to Adrienne. If he gets one mile closer every hour, it will take him three hours to catch up to her which means he travels 3hours * 4 miles/hour = 12 miles and she travels 4 hours * 3 miles/hour = 12 miles. He will be 12 miles from X when he catches up to her. A slightly different way to solve... We don't know how long they will walk before they catch up to one another but we do know that A walks for one hour more than J. J = T and A = T+1. We are looking for the distance at which they meet up which means the distance will be the same. D=rt so, rt (Harold ) = rt (adrienne) r(t) = r(t+1) 4t = 3t+3 t=3 d=rt d=4*3 d=12 B) 12 miles The answer is: B	B
mathematics	A train moves with a speed of 108 kmph. Its speed in metres per second is	[ "10.8", "18", "30", "38.8", "None" ]	Solution Speed = 108 Kmph = (108 x 5/18)m/sec = 30 m/sec. Answer C The answer is: C	C
mathematics	A company pays 15.5% dividend to its investors. If an investor buys Rs.50 shares and gets 25% on investment, at what price did the investor buy the shares?	[ "25", "31", "18", "19", "01" ]	Explanation: Dividend on 1 share = (15.5 * 50)/100 = Rs.7.75 Rs.25 is income on an investment of Rs.100 Rs.7.75is income on an investment of Rs. (7.75 * 100)/25 = Rs.31 ANSWER: B The answer is: B	B
mathematics	If the annual interest on a principal is 8%, how many years before the amount is double?	[ "11.3", "12", "12.5", "10.2", "11.2" ]	P = (P8R)/100 R = 12.5 Answer: C The answer is: C	C
mathematics	How many 3-digit even numbers are possible such that if one of the digits is 5, the next/succeeding digit to it should be 1?	[ "5", "305", "365", "405", "495" ]	510, 512, 514, 516, and 518, so total 5. Hence Option A. The answer is: A	A
mathematics	If a function f is defined by f(x)= (2x-1)/3 for all non zero numbers x. If f(a) = 1 and f(ab) = 1/9 then b= ?	[ "3", "1/3", "-1/3", "-3", "-12" ]	Given that f(x)= (2x-1)/3 and f(a) = 1, then f(a) =(2a-1)/3=1 ===> a=2, then backsolve using the answer choices: f(ab) = f(2b) = 1/6 A) 3 ===> f(23) = f(6) = (12-1)/3 = 11/3 B) 1/3 ===> f((21/3) = f(2/3) = (4/3-1)/3 = 1/9 WINS C) -1/3 ===> f(2-1/3) = f(-2/3) = (-4/3-1)/3 = -7/9 D) -3 ===> f(2-3) = f(-6) = (-12-1)/3 = -13/3 E) -12 ===> f(2*-12) = f(-24) = (-24-1)/3 = -25/3 Answer: B The answer is: B	B
mathematics	A train passes a station platform in 36 seconds and a man standing on the platform in 20 seconds. If the speed of the train is 54 km/hr, what is the length of the platform?	[ "299", "200", "240", "111", "161" ]	Speed = [54 * 5/18] m/sec = 15 m/sec. Length of the train = (15 * 20) m = 300 m. Let the length of the platform be x meters. Then, x + 300 / 36 = 15 x + 300 = 540 x = 240 m. Answer:C The answer is: C	C
mathematics	Reena took a loan of Rs. 1200 with simple interest for as many years as the rate of interest. If she paid Rs. 432 as interest at the end of the loan period, what was the rate of interest?	[ "2", "6", "5", "4", "8" ]	Explanation: Explanation: Let rate = R% and time = R years. Then, Answer: B) 6 The answer is: B	B
mathematics	If y = x^2 + cx + d, y is minimum when x is:	[ "c/d", "-c/d", "-c/2", "-d/2", "d/c" ]	We're given the equation Y = X^2 + cX + d. IF.. we use a simple Classic Quadratic.... c = 2 d = 1 Y = X^2 + 2X + 1 We can then go about finding the answer that yields the MINIMUM result when X = ... Answer A: c/d = 2/1 = 2 --> 4+4+1 = +9 Answer B: -c/d = -2/1 = -2 --> 4-4+1 = +1 Answer C: -c/2 = -2/2 = -1 --> 1-2+1 = 0 Answer D: -d/2 = -1/2 -->(1/4)-1+1 = +1/4 Answer E: d/c = 1/2 --> (1/4)+1+1 = +2 1/4 From these results, we can see the minimum result: C The answer is: C	C
mathematics	To furnish a kitchen in a model home an interior decorator is to select 2 chairs and 2 tables from the collection of chairs and tables in a warehouse that are all different from each other. If there are 5 chairs in the warehouse and if 120 different combinations are possible, how many tables are there in the warehouse?	[ "A)5", "B)8", "C)10", "D)15", "E)30" ]	Total number of ways to choose 2 chairs from 5= 5C2=10 Total number of combination=100 That means we need get 10 combinations from the selection of tables.... Screening through the answers.... 5C2=10..... 10*10=100 Answer is 6... A The answer is: A	A
mathematics	The cost price of an article is 25% of the marked price. Calculate the gain percent after allowing a discount of 50%.	[ "25%", "50%", "100%", "150%", "none" ]	Sol. Let marked price = Rs. 100. Then, C.P. = Rs. 25. S.P = Rs. 50. âˆ´ Gain % = [25/25 * 100]% = 100.0%. Answer C The answer is: C	C
mathematics	On a partly cloudy day, Derek decides to walk back from work. When it is sunny, he walks at a speed of s miles/hr (s is an integer) and when it gets cloudy, he increases his speed to (s + 1) miles/hr. If his average speed for the entire distance is 2.8 miles/hr, what fraction T of the total distance did he cover while the sun was shining on him?	[ "1/4", "4/5", "1/5", "1/6", "1/7" ]	If s is an integer and we know that the average speed is 2.8, s must be = 2. That meanss+1= 3. This implies that the ratio of time for s=2 is 1/4 of the total time. The formula for distance/rate is D=Rt...so the distance travelled when s=2 is 2t. The distance travelled for s+1=3 is 3*4t or 12t. Therefore, total distance covered while the sun was shining over him is T=2/14 = 1/7. Answer: E The answer is: E	E
mathematics	A trained covered x km at 40 kmph and another 2x km at 20 kmph. Find the average speed of the train in covering the entire 3x km?	[ "43 kmph", "65 kmph", "24 kmph", "14 kmph", "61 kmph" ]	Total time taken = x/40 + 2x/20 hours = 5x/40 = x/8 hours Average speed = 3x/(x/8) = 24 kmph Answer:C The answer is: C	C
mathematics	A herd of goats consists of A males and B females. In that herd, half of the goats that have horns are females. If C goats of the herd do not have horns, then the total number of male goats in the herd that do NOT have horns, in terms of A, B and C is -	[ "(A−B+C)/2", "(A−B−C)/2", "(A+B+C)/2", "(A+B−C)/2", "(2A−B+C)/2" ]	Male Goats = A Female Goats = B 1/2 of Horn Goats = Females = x (say) Therefore, other half will be Male = x Now, Male Goats without horn = A -x -- (1) Also, Total Goats without horn = C = (A -x) + (B-x) or x = (A+B - C)/2 Substituting the value of x in equation (1) We will have A - x =(A−B+C)/2. Answer A. The answer is: A	A
mathematics	There are 3 department available in XYZ company,namely Finance, Marketing, HR.The total expenditure of the company $69700.the ratio of department expenditure are 11:14:16.Then find out the total expenditure of marketing department?	[ "$27560", "$28900", "$27250", "$15600", "$23800" ]	Finance:Marketing:HR ratio of expenditure = 11+14+16=41; Expenditure of marketing department = 14/41 * $69700 = $23800. Answer =E The answer is: E	E
mathematics	The average of five numbers is 27. If one number is excluded, the average becomes 25. The excluded number is?	[ "25", "35", "38", "29", "22" ]	excluded number = (27 x 5) - (25 x 4) = 135 - 100 = 35. Answer: B The answer is: B	B
mathematics	A 260 m long train running at the speed of 120 km/hr crosses another train running in opposite direction at the speed of 80 km/hr in 9 sec. What is the length of the other train ?	[ "240 mts", "270 mts", "260 mts", "250 mts", "230 mts" ]	Explanation: Relative speed = 120 + 80 = 200 km/hr. = 200 x 5/18 = 500/9 m/sec. Let the length of the other train be L mts. Then, (L + 260)/9 = 500/9 => L = 240 mts. ANSWER IS A The answer is: A	A
mathematics	An IT company wants to hire 500 candidate, and each candidate is either engineer, manager, or peon . If it wants to hire 300 more engineers than managers, and twice as many peons as managers. how many engineers does The company want to hire ?	[ "310", "320", "330", "340", "350" ]	x = the number of engineers y = the number of managers z = the number of peons From the first sentence we have Equation #1: x + y + z = 500 ...It wants to hire 300 more engineers than managers... Equation #2: x = 300 + y ...twice as many peons as managers... Equation #3: z = 2y by reshuffling of equation #2 : x - y = 300 Now, we can replace z with y in Equation #1 equation #4 : x + y + 2y= 500 x+3y = 500 by adding equation #4 and equation #5 we get y = 50 There are 50 managers.This is 300 less than the number of engineers, so x = 350. That's the answer. Just as a check, z = 100, and 350 + 50 + 100 = 500. Answer = 350,(E) The answer is: E	E
mathematics	Working alone, pump A can empty a pool in 4 hours. Working alone, pump B can empty the same pool in 2 hours. Working together, how many minutes will it take pump A and pump B to empty the pool?	[ "65", "70", "75", "80", "85" ]	Pump A can empty (1/4) of the pool per hour. Pump B can empty (1/2) of the pool per hour. Together the pumps can empty 1/4+1/2=3/4 of the pool per hour. 1 pool / (3/4) pool per hour = 4/3 hours = 80 minutes. The answer is D. The answer is: D	D
mathematics	From the sale of sleeping bags, a retailer made a gross profit of 17% of the wholesale cost. If each sleeping bag was sold for $28, what was the wholesale cost per bag?	[ "3.0", "3.36", "23.93", "25.0", "31.36" ]	Cost price * 1.17 = Selling price --> Cost price * 1.17= $28 --> Cost price = $23.93. Answer: C. The answer is: C	C
mathematics	How many positive integers less than 5,000 are evenly divisible by neither 16 nor 21?	[ "4,514", "4,475", "4,521", "4,428", "4,349" ]	integers less than 5000 divisible by 16 5000/16 =333.something , so 333 integers less than 5000 divisible by 21 5000/21 = 238.## , so 238 we have double counted some, so take LCM of 16 and 21 =105 and divide by 5000, we get 47. so all numbers divisible by 16 and 21 = 333 +238 -47 =524 now subtract that from 4999. 4999- 524 = 4514 answer A. The answer is: A	A
mathematics	A pupil's marks were wrongly entered as 83 instead of 63. Due to the average marks for the class got increased by half. The number of pupils in the class is?	[ "13", "18", "40", "82", "43" ]	Let there be x pupils in the class. Total increase in marks = (x * 1/2) = x/2 x/2 = (83 - 63) => x/2 = 20 => x = 40 Answer:C The answer is: C	C
mathematics	A jogger running at 9 km/hr along side a railway track is 200 m ahead of the engine of a 120 m long train running at 45 km/hr in the same direction. In how much time will the train pass the jogger?	[ "32", "20", "36", "88", "34" ]	Speed of train relative to jogger = 45 - 9 = 36 km/hr. = 36 * 5/18 = 10 m/sec. Distance to be covered = 200 + 120 = 320 m. Time taken = 320/10 = 32 sec. Answer: Option A The answer is: A	A
mathematics	If x and y are multiples of 2 then which are all the multiples of 2 1) x*y 2) x^y 3) x+y 4) x-y 5) x/y	[ "1,3", "1,2,4,5", "1,2,5", "1,2,3,4", "all of these" ]	x*y,x^y,x+y, x-Y are even numbers ANSWER:D The answer is: D	D
mathematics	Julie put half of her savings in a savings account that pays an annual simple interest and half in a savings account that pays an annual compound interest. After two years she earned $112 and $120 from the simple interest account and the compound interest account respectively. If the interest rates for both accounts were the same, what was the amount of Julie's initial savings?	[ "600", "784", "1080", "1200", "1440" ]	$112 for 2 years = $56 per year. Extra $8 yearned with the compound interest is the percent yearned on percent. So, $8 is yearned on $56, which means that the interest = 7%. This on the other hand means that half of the savings = 56*7 = $392. Twice of that = $784. Answer: B. The answer is: B	B
mathematics	What is the greatest positive integer n such that 3^n is a factor of 36^50?	[ "100", "200", "300", "600", "900" ]	36 = 3^2 * 2^2. 36^50 = 3^100 * 2^100 The answer is A. The answer is: A	A
mathematics	Let us say that a table tennis tournament was going on with knock out terms which means the one who loses the match is out of the tournament. 101 players took part in that tournament. How many matches were played?	[ "90 matches", "95 matches", "99 matches", "100 matches", "87 matches" ]	D 100 matches. The number of matches will always sum up to one less than the number of players in a knock out tournament. You may calculate it in any manner. Thus 100 matches were played. The answer is: D	D
mathematics	The denominator of a fraction is 8 greater than the numerator. If the numerator and the denominator are increased by 5, the resulting fraction is equal to 6â„7. What is the value of the original fraction?	[ "25/33", "31/39", "37/45", "43/51", "53/61" ]	Let the numerator be x. Then the denominator is x+8. x+5 / x+13 = 6/7. 7x+35=6x+78. x=43. The original fraction is 43/51. The answer is D. The answer is: D	D
mathematics	Two pipes can separately fill a tank in 20 and 30 hours respectively. Both the pipes are opened to fill the tank but when the tank is full, a leak develops in the tank through which one-third of water supplied by both the pipes goes out. What is the total time taken to fill the tank?	[ "17 hrs", "16 hrs", "15 hrs", "13 hrs", "12 hrs" ]	1/20 + 1/30 = 1/12 1 + 1/3 = 4/3 1 --- 12 4/3 --- ? 4/3 * 12 = 16 hrs Answer:B The answer is: B	B
mathematics	You and your friend spent a total of $15 for lunch. Your friend spent $5 more than you. How much did your friend spend on their lunch?	[ "$9", "$3", "$4", "$6", "$10" ]	My lunch = l, my friends lunch = l+5 (l)+(l+5)=15 l+l+5-5=15-5 2l=10 l=5 My friends lunch l+5 = 5+5=$10, the answer is E The answer is: E	E
mathematics	Tanks X and Y contain 500 and 200 gallons of water respectively. If water is being pumped out of tank X at a rate of K gallons per minute and water is being added to tank Y at a rate of M gallons per minute, how many hours will elapse before the two tanks contain equal amounts of water?	[ "5/M+K hours", "6(M+K) hours", "300/M+K hours", "300/M−K hours", "60/M−K hours" ]	Consider k=1,m=2 Then per the question, 500 - 1x = 200 + 2x x=100 Check answer options for No. of hours (x)=100 for k=1 and m=2 ANSWER:C The answer is: C	C
mathematics	Which of the following are divisible by both 2 and 3? I. 234,124,422 II. 88,865,544,264 III. 5,555,554,674	[ "I only", "I, II & III", "II and III", "II Only", "I and III" ]	I. is divisible by 3 since sum of the digits is 24 , which is divisible by 3 II. is divisible by 3 since sum of the digits is 60 , which is divisible by 3 III. is divisible by 3 since sum of the digits is divisible by 3 Thus among the given options only (B) holds true. The answer is: B	B
mathematics	Sarah made $45 more than Kara yesterday. Today, they each made the same amount of money as yesterday and it totaled $834. How much would Kara make in 5 days if she continues to make the same amount of money every day.	[ "$225", "$879", "$930", "$2,085", "None of the above" ]	S-K=45 2(S+K)=834 Solving the 2 equations, you get, S=$231 and K=$186 So $186x5=$930 Correct Answer: C The answer is: C	C
mathematics	How many positive integer solutions does the equation 4x+5y = 100 have?	[ "50", "33", "16", "5", "14" ]	formula: (constant)/(lcm of two nos) =100/(4*5)=5 ANSWER:D The answer is: D	D
mathematics	11 persons are sitting ina row. how many ways can 11persons be arranged in a row such that 3 persons should always be together?	[ "7!×3!", "7!×2!", "9!×3!", "7!×1!", "6!×2!" ]	Given that three particular persons should always be together. Hence, just group these three persons together and consider as a single person. Therefore we can take total number of persons as 9. These 9 persons can be arranged in 9! ways. We had grouped three persons together. These three persons can be arranged among themselves in 3! ways. Hence, required number of ways =9!×3! C The answer is: C	C
mathematics	A computer manufacturer produces a certain electronic component at a cost of $150 per component. Shipping costs for delivering the components are $1 per unit. Further, the manufacturer has costs of $19,500 a month related to the electronic component regardless of how many it produces. If the manufacturer produces and sells 250 components a month, what is the lowest price it can sell them for such that the costs don't exceed the revenues?	[ "199", "249", "233", "215", "229" ]	$19500 is a fixed cost Each component is $151 ($150 to produce, $1 to ship) Manufacturer will be producing and selling 250 components so therefore the equation to find price would be 250p = 19500+(250150)+(250*1) p = (19500+37500+250)/250 p = 229 Answer: E The answer is: E	E
mathematics	A train covers a distance of 10 km in 20 min. If it takes 6 sec to pass a telegraph post, then the length of the train is?	[ "50", "80", "120", "100", "40" ]	Speed = (10/20 * 60) km/hr = (30 * 5/18) m/sec = 8.333333 m/sec. Length of the train = 8.333333 * 6 = 50 m.Answer: A The answer is: A	A
mathematics	Pipes A and B can fill a cistern in 8 and 24 minutes respectively. They are opened an alternate minutes. Find how many minutes, the cistern shall be full?	[ "16", "12", "14", "61", "51" ]	1/8 + 1/24 = 1/6 6 * 2 = 12 Answer:B The answer is: B	B
mathematics	Of the three- digit integers greater than 700, how many have two digits Q that are equal to each other and the remaining digit different from the other two?	[ "90", "82", "80", "45", "36" ]	three-digit integers greater than 700: 701 to 999, inclusive. possible values for hundreds-digit--> 7,8,9 possible values for tens-digit and ones-digit --> 0, 1,2,3,4,5,6,7,8,9 when hundreds-digit and tens-digit are the same: (3x1x10)-3=27 ---> we minus three to exclude 777, 888 and 999 when hundreds-digit and ones-digit are the same: (3x10x1)-3=27 ---> we minus three to exclude 777, 888 and 999 when tens-digit and hundreds-digit are the same:[(3x10x1)-3]-1=26 ---> we minus three to exclude 777, 888 and 999; we minus one to exclude 700 Q=27+27+26 = 80 Answer: C The answer is: C	C
mathematics	I walk a certain distance and ride back taking a total time of 37 minutes. I could walk both ways in 55 minutes. How long would it take me to ride both ways?	[ "20mins", "19mins", "5mins", "4mins", "12mins" ]	Let the distance be x km. Then, ( Time taken to walk x km) + (time taken to ride x km) =37 min. ( Time taken to walk 2x km ) + ( time taken to ride 2x km )= 74 min. But, the time taken to walk 2x km = 55 min. Time taken to ride 2x km = (74-55)min =19 min. Ans: B The answer is: B	B
mathematics	A 340-liter solution of Kola is made from 64% water, 9% concentrated Kola and the rest is made from sugar. If 3.2 liters of sugar, 8 liter of water and 6.8 liters of concentrated Kola were added to the solution, what percent of the solution is made from sugar?	[ "6%.", "7.5%.", "9.2%.", "10.5%.", "26.5%." ]	Denominator: 340+8+3.2+6.8=358 Numerator: 340(1-.64-.09)+3.2 340(0.27)+3.2 91.8+3.2 95 Ratio: 95/358=0.265 Answer: E The answer is: E	E
mathematics	Marcus deposited $8,000 to open a new savings account that earned five percent annual interest, compounded semi-annually. If there were no other transactions in the account, what the amount of money in Marcuss account one year after the account was opened?	[ "$8,200", "$8,205", "$8,400", "$8,405", "$8,500" ]	Approach #1: 5 percent annual interest compounded semi-annually --> 2.5% in 6 moths. For the first 6 moths interest was 2.5% of $8,000, so $200; For the next 6 moths interest was 2.5% of $8,000, plus 2.5% earned on previous interest of $200, so $200+$5=$205; Total interest for one year was $200+$205=$405, hence balance after one year was $8,000+ $405=$8,405. Answer: D. The answer is: D	D
mathematics	10^25 - 760 is divisible by all of the following except:	[ "A.12", "B.8", "C.5", "D.4", "E.7" ]	The last three digits ( 1000 - 760 ) 240 240 is divisible by 12,4,8,5 240 is not evenly divisible by 7 so the answer is E) 7 The answer is: E	E
mathematics	The bacteria have the probability of split into 3 and probability to die is 1/3rd of the total bacteria. Let the probability is P. Some of them survived with probability 1/5.Then which among the following relation is true?	[ "P=1/3+1/53", "P=1/3+1/54", "P=1/3+1/52", "P=1/8(1/8-3)", "P=1/5*(1/4-3)" ]	The bacteria have the probability of split into 3 and probability to die is 1/3rd of the total bacteria. Let the probability is P. Some of them survived with probability 1/5.Then which among the following relation is true? a)P=1/3+1/53 b)P=1/5(1/8-3) P=1/3+1/5*3 is true. ANSWER:A The answer is: A	A
mathematics	If \|5x-10\| = 100, then find the sum of the values of x?	[ "1", "-2", "3", "-3", "4" ]	\|5x-10\| = 100 5x-10 = 100 or 5x-10 = -100 5x = 110 or 5x = -90 x = 22 or x = -18 sum = 21-18 = 3 Answer is C The answer is: C	C
mathematics	12 men can complete a piece of work in 4 days, while 15 women can complete the same work in 4 days. 6 men start working on the job and after working for 2 days, all of them stopped working. How many women should be put on the job to complete the remaining work, if it is to be completed in 3 days.	[ "15", "18", "22", "25", "26" ]	One man’s one day’s work = 1/48 One woman’s one day’s work = 1/60 6 men’s 2 day’s work = ((6/48) x 2) = 1/4 Remaining work = 3/4 Now, 1/60 work s done in 1 day by 1 woman. Thus, 3/4 work will be done in 3 days by (60 x (3/4) x (1/3)) = 15 women. ANSWER:A The answer is: A	A
mathematics	A walks with a speed of 6 km/hr and after 5 hr of his start, B starts running towards A at a speed of 8 km/hr. At what distance from start will B catch A.	[ "100 Km", "110 Km", "120 Km", "140 Km", "NONE" ]	Explanation : In 5hrs, A will cover 30 km. Now, at some distance ‘x’. So A will cover X distance and B will cover 30 + X. x/6 = (30+x)/8 x = 90. So distance from start after which B will catch A = 90+30 =120km Answer – C The answer is: C	C
mathematics	How many of the following numbers are divisible by 14 ? 264, 396, 462, 792, 968, 2178, 5184, 6336	[ "3", "4", "5", "6", "1" ]	By using your calculator you can calculate that the following numbers are divisible by 14 : 462. Required number of number = 1. E The answer is: E	E
mathematics	David used part of $100,000 to purchase a house. Of the remaining portion, he invested 1/3 of it at 4 percent simple annual interest and 2/3 of it at 6 percent simple annual interest. If after a year the income from the two investments totaled $320, what was the purchase price of the house?	[ "$96,000", "$94,000", "$88,000", "$75,000", "$40,000" ]	Of all the answer choices, (A) and (D) do not offer a number divisible by 3. (E) can be eliminated easily because when you invest 1/3 of $60,000 ($20,000) @ 4% interest rate, you earn $800 interest, which is definitely more than $320. But, if you calculate 2/3 of $60,000 ($40,000) @ 6% interest rate, you earn $2400 interest. Total interest when $60,000 is the remaining amount: $800 + $2400 = $3200. We need $320. It means the remaining amount should be $6000. Therefore, (B) is the answer. The answer is: B	B
mathematics	Of the five numbers in a sequence, the first term is 15,000, and each of the following terms is 20% of the previous term. What is the value range of the five numbers?	[ "9,375", "9,750", "9,975", "9,984", "14,976" ]	1st number= 15,000 2nd number = 20% of 15,000= 3000 3rd number= 20% of 3000= 600 4th number = 20% of 600= 120 5th number= 20% of 120= 24 Range = 15,000-24= 14976 E is the answer The answer is: E	E
mathematics	The area of a triangle is with base 10m and height 10m?	[ "11", "10", "50", "122", "12" ]	1/2 * 10 *10= 50 m2 Answer: C The answer is: C	C
mathematics	Kim purchased n items from a catalog for $8 each. Postage and handling charges consisted of $3 for the first item and $1 for each additional item. Which of the following gives the total dollar amount for Kim’s purchase, including postage and handling, in terms of n ?	[ "8n + 2", "8n + 4", "9n + 2", "9n + 3", "9n + 4" ]	n items for $8 each total price $8n postage and handling of $3 for 1st item and $1 for the rest total postage and handling = $ [3+ (n-1)] = $ n+2 total cost 8n+n+2 = 9n+2 ; ANSWER:C The answer is: C	C
mathematics	The area of a parallelogram is 72 sq m and its base is 12m . Then the length of the height is?	[ "6m", "7m", "60m", "13m", "none" ]	bh=72. h12=72 =>h=6m. Answer: (A) The answer is: A	A
mathematics	Find the least number must be subtracted from 427398 so that remaining no.is divisible by 15?	[ "3", "5", "7", "8", "9" ]	On dividing 427398 by 15 we get the remainder 3, so 3 should be subtracted A The answer is: A	A
mathematics	Two trains of length 160 m and 200 m are 100 m apart. They start moving towards each other on parallel tracks, at speeds 54 kmph and 72 kmph. In how much time will the trains cross each other?	[ "100/7 sec", "80/7 sec", "112/7 sec", "120/7 sec", "50/7 sec" ]	Relative speed = (54 + 72)* 5/18 = 7 * 5 = 35 mps. The time required = d/s = (160 + 100 + 300)/35 = 560/35 = 112/7 sec. ANSWER:C The answer is: C	C
mathematics	Find the odd man out. 742, 743, 633, 581, 871, 990, 532	[ "532", "990", "581", "743", "None of these" ]	Explanation : In all numbers except 581, the difference of third and first digit is the middle digit. Answer : Option C The answer is: C	C

mathematics

Ram, who is half as efficient as Krish, will take 36 days to complete a task if he worked alone. If Ram and Krish worked together, how long will they take to complete the task?

[ "16 days", "12 days", "8 days", "6 days", "18 days" ]

Number of days taken by Ram to complete task = 36 Since Ram is half as efficient as Krish , Amount of work done by Krish in 1 day = Amount of work done by Ram in 2 days If total work done by Ram in 36 days is 36w Amount of work done by Ram in 1 day = w Amount of work done by Krish in 1 day = 2w Total amount of work done by Krish and Ram in a day = 3w Total amount of time needed by Krish and Ram to complete task = 36w/3w = 12 days Answer B The answer is: B

B

mathematics

If the difference between compound interest (interest compounded yearly)and simple interest on a sum for 2 years at 10% p.a. is Rs.150 then sum is

[ "Rs.12,000", "Rs.15,000", "Rs.13,000", "Rs.10,000", "Rs.14,000" ]

compund interest = p[1+r/100]^t-p CI = p[21/100] simple interest = ptr/100 SI = p[20/100] difference p[21/100]-p[20/100] = 150 p=15,000 ANSWER:B The answer is: B

B

mathematics

A sock drawer contains seven socks, each one a different solid color. The colors of the socks are white,black, red, orange, yellow, green, blue, indigo, and violet. A person reaches into the drawer, pulls out two socks, and puts a single sock on each foot. If each sock can fit either the left or the right foot, and if it matters whether a particular sock is on the left or the right foot, how many different sock fashion combinations could the person make from the nine socks?

[ "12", "15", "21", "36", "72" ]

It's a question of permutation since order matters here .... It can be deduced to- 9P2 = 9!/7! = 9*8 = 72 .........Answer is - E The answer is: E

E

mathematics

The present ages of three persons in proportions 4 : 7 : 9. Eight years ago, the sum of their ages was 16. Find their present ages (in years).

[ "8, 14, 18", "8, 28, 36", "20, 35, 45", "33,42,43", "23,42,43" ]

Let their present ages be 4x, 7x and 9x years respectively. Then, (4x - 8) + (7x - 8) + (9x - 8) = 16 20x = 40 x = 2. Their present ages are 4x = 8 years, 7x = 14 years and 9x = 18 years respectively. ANSWER:A The answer is: A

A

mathematics

If Rs.450 amount to Rs.540 in 4 years, what will it amount to in 6 years at the same rate % per annum?

[ "227", "887", "585", "2679", "27" ]

90 = (450*4*R)/100 R = 5% I = (450*6*5)/100 = 135 450 + 135 = 585 Answer:C The answer is: C

C

mathematics

What positive number, when squared, is equal to the cube of the positive square root of 12?

[ "64", "32", "8", "4", "2" ]

Let the positive number be x x^2 = ((12)^(1/2))^3 =>x^2 = 4^3 = 16 => x = 4 Answer D The answer is: D

D

mathematics

Average age of boys in a class is 16 years and average age of girls is 15 years, what is the average age of all

[ "15.5", "15", "16", "17", "Cant be computed" ]

Explanation: As number of girls and boys is not given so result cant be computed Option D The answer is: D

D

mathematics

If the ratio of the roots of the equation x2 – 2ax + b = 0 is equal to that of the roots x2 – 2cx + d = 0, then:

[ "a2b = c2d", "a2c = b2d", "a2d = c2b", "d2 b = c2 a", "none" ]

x^2-2ax+b=0 for this eqn..roots r....R1=2a/1,R2=b/1; x^2-2cx+d=0 for this eqn ..roots r...R3=2c/1,R4=d; As per question ,2a/b=2c/d =>2ad=2bc ANSWER:C The answer is: C

C

mathematics

A metered rikshaw charges Rs 13.50 for the first 1 Km and 2.50 per 1/3 km there after. What would the charge if this rikshaw is hired for 13 Kms? In approx??

[ "103.5 Rs", "104.5 Rs", "105.5 Rs", "106.5 Rs", "107.5 Rs" ]

For 1st Km: Rs.13.50 Ramaining distance:13-1=12 KM 1/3 km costs 2.5 rs 1 km costs (2.5*3) Remaining 12KM costs (2.5*3)*12=90 Rs total cost=90+13.5=103.5 Rs ANSWER:A The answer is: A

A

mathematics

Evaluate 35 / .07

[ "400", "500", "505", "None of these", "506" ]

Explanation: 35/.07 = 3500/7 = 500 Option B The answer is: B

B

mathematics

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

[ "535 m", "178 m", "186 m", "168 m", "150 m" ]

Speed = 60 * 5/18 = 50/3 m/sec Length of the train = speed * time = 50/3 * 9 = 150 m Answer:E The answer is: E

E

mathematics

A restaurant spends one quarter of its monthly budget for rent and quarter of the rest for food and beverages. What percentage of the budget does the restaurant spend for food and beverages?

[ "23.5%", "32.5%", "35%", "18.75%", "20%" ]

Spend on rent = 1/4 Spend on food and beverage= 1/4 of remaining = 1/4*3/4= 3/16 so 3/16= 18.75% D is the answer The answer is: D

D

mathematics

A cistern has a leak which would empty the cistern in 20 minutes. A tap is turned on which admits 1 liters a minute into the cistern, and it is emptied in 24 minutes. How many liters does the cistern hold?

[ "480", "120", "289", "270", "927" ]

1/x - 1/20 = -1/24 x = 120 120 * 1 = 120 Answer: B The answer is: B

B

mathematics

The average weight of 25 persons sitting in a boat had some value. A new person added to them whose weight was 46 kg only. Due to his arrival, the average weight of all the persons decreased by 5 kg. Find the average weight of first 25 persons?

[ "56 kg", "56 kg", "56 kg", "176 kg", "739 kg" ]

25x + 46 = 26(x – 5) x = 176 Answer:D The answer is: D

D

mathematics

Several people are sitting around a round table playing a card game with a deck of 51 cards. Each person is dealt one card per deal, and the cards are dealt in a clockwise fashion. If Martin is dealt both the first card of the deck and the last card of the deck, which of the following could be the total number of people sitting at the table?

[ "4", "5", "7", "11", "13" ]

Let n be the number of people at the table. If Martin gets the first and the last card, it means Martin got one more card than the others. Thus 51/n has a remainder of 1 and so 51-1 = 50 is a multiple of n. The answer is B. The answer is: B

B

mathematics

Out of 10 persons working on a project, 4 are graduates. If 3 are selected, what is the probability that there is at least one graduate among them?

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

P(at least one graduate) = 1 - P(no graduates) = 1 - 6C3/10C3 = 1 - (6 * 5 * 4)/(10 * 9 * 8) = 5/6 Answer:D The answer is: D

D

mathematics

During the first week of performances of a certain play, 5,400 tickets were sold, all at reduced price. During the remaining weeks of performances, 5 times as many tickets were sold at full price as were sold at reduced price. If the total number of tickets R sold was 25,200, how many of them were sold at full price?

[ "21,000", "19,800", "16,500", "15,800", "8,700" ]

Given: The question tells us about the number of tickets sold in the first week at reduced price = 5,400. It also tells us that during the remaining weeks, the number of tickets sold at full price was 5 times the no. of tickets sold at reduced price. The total tickets sold was 25,200, and we are asked to find the number of tickets that where sold at full price. Approach: The question asks us to find the number of ticket sold at full price. We know that the number of tickets sold at full price was 5 times the no. of tickets sold at reduced price in remaining weeks. Hence, assuming tickets sold at reduced price in remaining weeks to be x would give us the no. of tickets sold at full price to be 5x. Tickets sold in first week + Tickets sold in remaining weeks = Total no. of tickets soldi.e. Tickets sold in first week + Tickets sold at full price in remaining weeks + Tickets sold at reduced price in remaining weeks = Total no. of tickets sold We know the no. of tickets sold during first week and the total no. of tickets sold. We will use this relation to get to our answer. Working Out: Tickets sold in first week + Tickets sold at full price in remaining weeks + Tickets sold at reduced price in remaining weeks = Total no. of tickets sold Substituting values in the equation, we get 5,400 + 5x + x = 25,200 x= 3,300 Tickets sold at full price = 5x = 16,500 Answer: Option C The answer is: C

C

mathematics

If, 1 * 3 * 5 = 16 3 * 5 * 7 = 38 Then find, 5 * 6 * 9 =?

[ "65", "59", "72", "80", "77" ]

(9 * 6) + 5 = 59 B The answer is: B

B

mathematics

A basketball player succeeds with 60% of her free throws. If she has a set of three free throws, what is the probability that she succeeds at least once?

[ "0.856", "0.872", "0.936", "0.952", "0.985" ]

P(missing all 3 free throws) = 0.4^3 = 0.064 P(succeeding at least once) = 1 - 0.064 = 0.936 The answer is C. The answer is: C

C

mathematics

A train sets off at 2 p.m. at the speed of 50 kmph. Another train starts at 3:30 p.m. in the same direction at the rate of 65 kmph. At what time the trains will meet?

[ "8.37 p.m", "8.20 p.m", "8.30 p.m", "8.38 p.m", "8.10 p.m" ]

D = 50 * 1 Â½ = 75 km RS = 65 â€“ 50 = 15 T = 75/15 = 5 h 3.30 + 7 h = 8.30 p.m. Answer: C The answer is: C

C

mathematics

What profit percent is made by selling an article at a certain price, if by selling at 2/3rd of that price, there would be a loss of 20%?

[ "20%", "26%", "80%", "10%", "50%" ]

SP2 = 2/3 SP1 CP = 100 SP2 = 80 2/3 SP1 = 80 SP1 = 120 100 --- 20 => 20% Answer:A The answer is: A

A

mathematics

If 20% of a number is equal to one-third of another number, what is the ratio of first number to the second number?

[ "2:5", "1:4", "5:3", "6:11", "2:3" ]

Let 20% of A = 1/3 B then 20A/100 = 1B/3 A/5 = B/3 A/B = 5/3 A:B = 5:3 Answer is C The answer is: C

C

mathematics

6x – 5y + 3z = 26 4x + 8y – 11z = 7 5x – 6y + 2z = 12 Given the equations above, x + y + z = ?

[ "11", "12", "13", "14", "15" ]

(6x – 5y + 3z) - (5x – 6y + 2z ) = 26-12 or, x+y+z = 14 Option D is the ans The answer is: D

D

mathematics

Carrie likes to buy t-shirts at the local clothing store. They cost $9.65 each. One day, she bought 12 t-shirts. How much money did she spend?

[ "$115.8", "$248.75", "$200", "$171.6", "$190" ]

$9.65*12=$115.8. Answer is A. The answer is: A

A

mathematics

IBM and KTC quote for a tender. On the tender opening day, IBM realizes that their quotations are in the ratio 7:4 and hence decreases its price during negotiations to make it Rs 1 Lakh lower than KTC's quoted price. KTC realizes that the final quotes of the two were in the ratio 3:4. What was the price at which IBM won the bid?

[ "Rs. 7 lakh", "Rs. 3 lakh", "Rs. 4 lakh", "Rs. 1.5 lakh", "None of these" ]

Explanation : IBM initially quoted Rs 7x lakh. KTC quoted 4x lakh. IBM's final quote = (4x−1) Lakh. Thus, (4x−1)/4=3/4 i.e x=1. Hence, IBM's bid winning price = Rs 3 Lakh. Answer : B The answer is: B

B

mathematics

If 0 < a < b < c < 1 , which of the following are positive? I. b-c II. a-b III. c-a

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

We could solve this easily using examples. I is false since b<c and both are positive II is false since b<c and both are positive III is true since c>a and both are positive So, the answer is C. The answer is: C

C

mathematics

An empty wooden vessel weighs 20% of its total weight when filled with paint. If the weight of a partially filled vessel is one half that of a completely filled vessel, what fraction of the vessel is filled.

[ "3/5", "5/9", "9/19", "4/9", "2/5" ]

An empty wooden vessel weighs 20% of its total weight when filled with paint: Vessel = 0.2(Vessel + Paint); 20V = V + P (so the weight of completely filled vessel is 10V) P = 19V (so the weight of the paint when the vessels is completely filled is 9V). The weight of a partially filled vessel is one half that of a completely filled vessel: V + P' = 1/2*20V; P' = 9V (so the weight of the paint when the vessels is partially filled is 9V). What fraction of the vessel is filled? So, we need to find the ratio of the weight of the paint when the vessel iscompletely filledto the weight of the paint when the vessel ispartially filled: P'/P = 9V/19V = 9/19. Answer: C. The answer is: C

C

mathematics

If the sum of two positive integers is 12 and the difference of their squares is 48, what is the product of the two integers?

[ "32", "119", "128", "135", "143" ]

Let the 2 positive numbers x and y x+ y = 12 -- 1 x^2 - y^2 = 48 => (x+y)(x-y)=48 -- 2 Using equation 1 in 2 , we get => x-y = 4 -- 3 Solving equation 1 and 3 , we get x= 8 y= 4 Product = 8*4 = 32 Answer A The answer is: A

A

mathematics

Three pipes of same capacity A,B,C can fill a tank in 18 hours. If there are only two pipes B and A of same capacity, the tank can be filled in?

[ "16", "19", "27", "24", "29" ]

The part of the tank filled by three pipes in one hour = 1/6 => The part of the tank filled by two pipes in 1 hour = 2/3 * 1/18= 1/27. The tank can be filled in 27 hours. Answer:C The answer is: C

C

mathematics

A shopkeeper buys mangoes at the rate of 5 a rupee and sells them at 3 a rupee. Find his net profit or loss percent?

[ "66 1/4 %", "66 9/3 %", "66 2/3 %", "66 1/5 %", "66 1/3 %" ]

The total number of mangoes bought by the shopkeeper be 15. If he buys 5 a rupee, his CP = 3 He selling at 3 a rupee, his SP = 5 Profit = SP - CP = 5 - 3 = 2 Profit Percent = 2/3 * 100 = 66 2/3 % Answer:C The answer is: C

C

mathematics

Williams works at a resort from the beginning of March to the end of September. During the month of August this past year, he made 10 times the average (arithmetic mean) of his monthly totals in tips for the other months. His total tips for August were what fraction of his total tips for all of the months he worked?

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

First notice the number of months for which he worked - March to Sept i.e. 7 months Avg of monthly totals in tips for months other than August = x Tips in August = 10x Total tips for all months = 6*x + 10x = 16x Tips for August/Total tips for all months = 10x/16x = 5/8 Answer : A The answer is: A

A

mathematics

The cross-section of a water channel is a trapezium in shape. If the channel is 12 meters wide at the top and 6 meters wide at the bottom and the area of cross-section is 630 square meters, what is the depth of the channel (in meters)?

[ "50", "60", "70", "80", "90" ]

1/2 * d * (12 + 6) = 630 d = 70 The answer is C. The answer is: C

C

mathematics

IN Common Wealth Games an athlete runs 200 meters in 32 seconds. Hisspeed is ?

[ "25 km/hr", "27 km/hr", "30 km/hr", "32 km/hr", "None of these" ]

Explanation : (200/1000)/(32/3600)=22.72 km/hr Answer : E The answer is: E

E

mathematics

How many seconds will a 800 m long train take to cross a man walking with a speed of 3 km/hr in the direction of the moving train if the speed of the train is 63 km/hr?

[ "11", "30", "99", "48", "61" ]

Speed of train relative to man = 63 - 3 = 60 km/hr. = 60 * 5/18 = 50/3 m/sec. Time taken to pass the man = 800 * 3/50 = 48 sec. Answer: D The answer is: D

D

mathematics

John weighs twice as much as Susan. Susan's weight is 60% of Sam's weight. Mark weighs 50% of Lynn's weight. Lynn weighs 160% of John's weight. Which of these 5 people weighs the least?

[ "John", "Susan", "Sam", "Mark", "Lynn" ]

John weighs twice as much as Susan --> J=2S --> John cannot weigh the least; Susan's weight is 60% of Sam's weight --> S=0.6*Sam --> Sam cannot weigh the least; Mark weighs 50% of Lynn's weight --> M=0.5*L --> Lynn cannot weigh the least; Lynn weighs 160% of John's weight --> L=1.9*J --> John cannot weigh the least (we already know that); As you can see the answer is either Susan (S) or Mark (M). To compare their weights we should express their weights in regards of the same person: M=0.5*L=0.5*(1.6*J)=0.8*J and from J=2S, S=0.5*J --> Susan weights the least: Susan's weight is 50% of that of John and Mark's weight is more than 50%of that of John. Answer: B. The answer is: B

B

mathematics

9 men went to a hotel. Eight of them spent Rs.3 each over their meals and the ninth spent Rs.2 more than the average expenditure of all the nine. Determine the total money spent by them?

[ "29.25", "30", "31.2", "34", "35" ]

Average of 9 = x 9x = 8 * 3 + x * 2 x = 3.25 Total = 9 * 3.25 = 29.25 A The answer is: A

A

mathematics

If Henry were to add 8 gallons of water to a tank that is already 3/4 full of water, the tank would be 7/8 full. How many gallons of water would the tank hold if it were full?

[ "25", "40", "64", "80", "96" ]

7/8x-3/4x=8galls 1/8*x=8gallons x=64 gallons Answer C The answer is: C

C

mathematics

Sum of two numbers is 10. Two times of the first exceeds by 5 from the three times of the other. Then the numbers will be?

[ "A)7", "B)9", "C)11", "D)13", "E)15" ]

Explanation: x + y = 10 2x – 3y = 5 x = 7 y = 3 A) The answer is: A

A

mathematics

On dividing 13698 by a certain number, we get 89 as quotient and 14 as remainder. What is the divisor?

[ "743", "154", "852", "741", "785" ]

Divisor *quotient+remainder=dividend divisor=(dividend)-(remainder)/quotient (13698-14)/89=154 Answer(B) The answer is: B

B

mathematics

If A, B and C together can finish a piece of work in 4 days. A alone in 36 days and B in 18 days, then C alone can do it in?

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

C = 1/4 - 1/36 – 1/18 = 1/6 => 6 days' Answer: E The answer is: E

E

mathematics

If -1<= x <= 2 and 3 <= y <= 8, which of the following represents the range of all possible values of y-x?

[ "5 <= y-x <= 6", "1 <= y-x <= 5", "1 <= y-x <= 6", "1 <= y-x <= 9", "1 <= y-x <= 10" ]

Maximum value of y-x= 8 - (-1)= 9 Minimum value of y-x= 3-2= 1 D mentions the correct range The answer is: D

D

mathematics

Find the odd man out. 187, 264, 336, 473, 682, 781

[ "187", "336", "781", "682", "473" ]

In all numbers except 336, the middle digit is the sum of other two digits. Answer is B The answer is: B

B

mathematics

in how many ways u can form a group of 11 members from 5 men and 11 women if the men member not more than 3?

[ "2256 ways", "2356", "3456", "4456", "1554" ]

we need team members=11 such that there should not be more than 3 men so the conditions are (3M,8W),(2M,9W),(1M,10W) Now, no. of ways=11c11+5c3*11c8+5c2*11c9+5c1*11c10=2256 ANSWER:A The answer is: A

A

mathematics

40% of all students in a class commute by public transportation. If 25% of the students aspire to be scientists, which of the following can be the percentage of students who do not commute by public transportation and do not aspire to be scientists? I. 7% II. 20% III. 45%

[ "I ONLY", "II ONLY", "III ONLY", "I AND II", "I AND III" ]

40% Students use public transportation. This means 60% students do not use public transportation. 25% students aspire to be scientists means even if all these students use public transportation, minimum 60% - 25% = 35% students do not use public transportation and do not aspire to be scientists.This means correct answer is between 35% and 60% Answer :C. The answer is: C

C

mathematics

One hour after Adrienne started walking the 60 miles from X to Y, Harold started walking from X to Y as well. Adrienne walks 3 miles per hour and Harold walks 1 mile per hour faster than Adrienne. How far from X will Harold be when he catches up to Adrienne?

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

First, determine how far Adrienne has walked in the one hour. She has walked three miles which means she is three miles ahead of Harold when he sets off. Harold walks at four miles/hour which means that every hour, Harold will get one mile closer to Adrienne. If he gets one mile closer every hour, it will take him three hours to catch up to her which means he travels 3hours * 4 miles/hour = 12 miles and she travels 4 hours * 3 miles/hour = 12 miles. He will be 12 miles from X when he catches up to her. A slightly different way to solve... We don't know how long they will walk before they catch up to one another but we do know that A walks for one hour more than J. J = T and A = T+1. We are looking for the distance at which they meet up which means the distance will be the same. D=r*t so, r*t (Harold ) = r*t (adrienne) r*(t) = r*(t+1) 4t = 3t+3 t=3 d=r*t d=4*3 d=12 B) 12 miles The answer is: B

B

mathematics

A train moves with a speed of 108 kmph. Its speed in metres per second is

[ "10.8", "18", "30", "38.8", "None" ]

Solution Speed = 108 Kmph = (108 x 5/18)m/sec = 30 m/sec. Answer C The answer is: C

C

mathematics

A company pays 15.5% dividend to its investors. If an investor buys Rs.50 shares and gets 25% on investment, at what price did the investor buy the shares?

[ "25", "31", "18", "19", "01" ]

Explanation: Dividend on 1 share = (15.5 * 50)/100 = Rs.7.75 Rs.25 is income on an investment of Rs.100 Rs.7.75is income on an investment of Rs. (7.75 * 100)/25 = Rs.31 ANSWER: B The answer is: B

B

mathematics

If the annual interest on a principal is 8%, how many years before the amount is double?

[ "11.3", "12", "12.5", "10.2", "11.2" ]

P = (P*8*R)/100 R = 12.5 Answer: C The answer is: C

C

mathematics

How many 3-digit even numbers are possible such that if one of the digits is 5, the next/succeeding digit to it should be 1?

[ "5", "305", "365", "405", "495" ]

510, 512, 514, 516, and 518, so total 5. Hence Option A. The answer is: A

A

mathematics

If a function f is defined by f(x)= (2x-1)/3 for all non zero numbers x. If f(a) = 1 and f(ab) = 1/9 then b= ?

[ "3", "1/3", "-1/3", "-3", "-12" ]

Given that f(x)= (2x-1)/3 and f(a) = 1, then f(a) =(2a-1)/3=1 ===> a=2, then backsolve using the answer choices: f(ab) = f(2b) = 1/6 A) 3 ===> f(2*3) = f(6) = (12-1)/3 = 11/3 B) 1/3 ===> f((2*1/3) = f(2/3) = (4/3-1)/3 = 1/9 WINS C) -1/3 ===> f(2*-1/3) = f(-2/3) = (-4/3-1)/3 = -7/9 D) -3 ===> f(2*-3) = f(-6) = (-12-1)/3 = -13/3 E) -12 ===> f(2*-12) = f(-24) = (-24-1)/3 = -25/3 Answer: B The answer is: B

B

mathematics

A train passes a station platform in 36 seconds and a man standing on the platform in 20 seconds. If the speed of the train is 54 km/hr, what is the length of the platform?

[ "299", "200", "240", "111", "161" ]

Speed = [54 * 5/18] m/sec = 15 m/sec. Length of the train = (15 * 20) m = 300 m. Let the length of the platform be x meters. Then, x + 300 / 36 = 15 x + 300 = 540 x = 240 m. Answer:C The answer is: C

C

mathematics

Reena took a loan of Rs. 1200 with simple interest for as many years as the rate of interest. If she paid Rs. 432 as interest at the end of the loan period, what was the rate of interest?

[ "2", "6", "5", "4", "8" ]

Explanation: Explanation: Let rate = R% and time = R years. Then, Answer: B) 6 The answer is: B

B

mathematics

If y = x^2 + cx + d, y is minimum when x is:

[ "c/d", "-c/d", "-c/2", "-d/2", "d/c" ]

We're given the equation Y = X^2 + cX + d. IF.. we use a simple Classic Quadratic.... c = 2 d = 1 Y = X^2 + 2X + 1 We can then go about finding the answer that yields the MINIMUM result when X = ... Answer A: c/d = 2/1 = 2 --> 4+4+1 = +9 Answer B: -c/d = -2/1 = -2 --> 4-4+1 = +1 Answer C: -c/2 = -2/2 = -1 --> 1-2+1 = 0 Answer D: -d/2 = -1/2 -->(1/4)-1+1 = +1/4 Answer E: d/c = 1/2 --> (1/4)+1+1 = +2 1/4 From these results, we can see the minimum result: C The answer is: C

C

mathematics

To furnish a kitchen in a model home an interior decorator is to select 2 chairs and 2 tables from the collection of chairs and tables in a warehouse that are all different from each other. If there are 5 chairs in the warehouse and if 120 different combinations are possible, how many tables are there in the warehouse?

[ "A)5", "B)8", "C)10", "D)15", "E)30" ]

Total number of ways to choose 2 chairs from 5= 5C2=10 Total number of combination=100 That means we need get 10 combinations from the selection of tables.... Screening through the answers.... 5C2=10..... 10*10=100 Answer is 6... A The answer is: A

A

mathematics

The cost price of an article is 25% of the marked price. Calculate the gain percent after allowing a discount of 50%.

[ "25%", "50%", "100%", "150%", "none" ]

Sol. Let marked price = Rs. 100. Then, C.P. = Rs. 25. S.P = Rs. 50. âˆ´ Gain % = [25/25 * 100]% = 100.0%. Answer C The answer is: C

C

mathematics

On a partly cloudy day, Derek decides to walk back from work. When it is sunny, he walks at a speed of s miles/hr (s is an integer) and when it gets cloudy, he increases his speed to (s + 1) miles/hr. If his average speed for the entire distance is 2.8 miles/hr, what fraction T of the total distance did he cover while the sun was shining on him?

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

If s is an integer and we know that the average speed is 2.8, s must be = 2. That meanss+1= 3. This implies that the ratio of time for s=2 is 1/4 of the total time. The formula for distance/rate is D=Rt...so the distance travelled when s=2 is 2t. The distance travelled for s+1=3 is 3*4t or 12t. Therefore, total distance covered while the sun was shining over him is T=2/14 = 1/7. Answer: E The answer is: E

E

mathematics

A trained covered x km at 40 kmph and another 2x km at 20 kmph. Find the average speed of the train in covering the entire 3x km?

[ "43 kmph", "65 kmph", "24 kmph", "14 kmph", "61 kmph" ]

Total time taken = x/40 + 2x/20 hours = 5x/40 = x/8 hours Average speed = 3x/(x/8) = 24 kmph Answer:C The answer is: C

C

mathematics

A herd of goats consists of A males and B females. In that herd, half of the goats that have horns are females. If C goats of the herd do not have horns, then the total number of male goats in the herd that do NOT have horns, in terms of A, B and C is -

[ "(A−B+C)/2", "(A−B−C)/2", "(A+B+C)/2", "(A+B−C)/2", "(2A−B+C)/2" ]

Male Goats = A Female Goats = B 1/2 of Horn Goats = Females = x (say) Therefore, other half will be Male = x Now, Male Goats without horn = A -x -- (1) Also, Total Goats without horn = C = (A -x) + (B-x) or x = (A+B - C)/2 Substituting the value of x in equation (1) We will have A - x =(A−B+C)/2. Answer A. The answer is: A

A

mathematics

There are 3 department available in XYZ company,namely Finance, Marketing, HR.The total expenditure of the company $69700.the ratio of department expenditure are 11:14:16.Then find out the total expenditure of marketing department?

[ "$27560", "$28900", "$27250", "$15600", "$23800" ]

Finance:Marketing:HR ratio of expenditure = 11+14+16=41; Expenditure of marketing department = 14/41 * $69700 = $23800. Answer =E The answer is: E

E

mathematics

The average of five numbers is 27. If one number is excluded, the average becomes 25. The excluded number is?

[ "25", "35", "38", "29", "22" ]

excluded number = (27 x 5) - (25 x 4) = 135 - 100 = 35. Answer: B The answer is: B

B

mathematics

A 260 m long train running at the speed of 120 km/hr crosses another train running in opposite direction at the speed of 80 km/hr in 9 sec. What is the length of the other train ?

[ "240 mts", "270 mts", "260 mts", "250 mts", "230 mts" ]

Explanation: Relative speed = 120 + 80 = 200 km/hr. = 200 x 5/18 = 500/9 m/sec. Let the length of the other train be L mts. Then, (L + 260)/9 = 500/9 => L = 240 mts. ANSWER IS A The answer is: A

A

mathematics

An IT company wants to hire 500 candidate, and each candidate is either engineer, manager, or peon . If it wants to hire 300 more engineers than managers, and twice as many peons as managers. how many engineers does The company want to hire ?

[ "310", "320", "330", "340", "350" ]

x = the number of engineers y = the number of managers z = the number of peons From the first sentence we have Equation #1: x + y + z = 500 ...It wants to hire 300 more engineers than managers... Equation #2: x = 300 + y ...twice as many peons as managers... Equation #3: z = 2y by reshuffling of equation #2 : x - y = 300 Now, we can replace z with y in Equation #1 equation #4 : x + y + 2y= 500 x+3y = 500 by adding equation #4 and equation #5 we get y = 50 There are 50 managers.This is 300 less than the number of engineers, so x = 350. That's the answer. Just as a check, z = 100, and 350 + 50 + 100 = 500. Answer = 350,(E) The answer is: E

E

mathematics

Working alone, pump A can empty a pool in 4 hours. Working alone, pump B can empty the same pool in 2 hours. Working together, how many minutes will it take pump A and pump B to empty the pool?

[ "65", "70", "75", "80", "85" ]

Pump A can empty (1/4) of the pool per hour. Pump B can empty (1/2) of the pool per hour. Together the pumps can empty 1/4+1/2=3/4 of the pool per hour. 1 pool / (3/4) pool per hour = 4/3 hours = 80 minutes. The answer is D. The answer is: D

D

mathematics

From the sale of sleeping bags, a retailer made a gross profit of 17% of the wholesale cost. If each sleeping bag was sold for $28, what was the wholesale cost per bag?

[ "3.0", "3.36", "23.93", "25.0", "31.36" ]

Cost price * 1.17 = Selling price --> Cost price * 1.17= $28 --> Cost price = $23.93. Answer: C. The answer is: C

C

mathematics

How many positive integers less than 5,000 are evenly divisible by neither 16 nor 21?

[ "4,514", "4,475", "4,521", "4,428", "4,349" ]

integers less than 5000 divisible by 16 5000/16 =333.something , so 333 integers less than 5000 divisible by 21 5000/21 = 238.## , so 238 we have double counted some, so take LCM of 16 and 21 =105 and divide by 5000, we get 47. so all numbers divisible by 16 and 21 = 333 +238 -47 =524 now subtract that from 4999. 4999- 524 = 4514 answer A. The answer is: A

A

mathematics

A pupil's marks were wrongly entered as 83 instead of 63. Due to the average marks for the class got increased by half. The number of pupils in the class is?

[ "13", "18", "40", "82", "43" ]

Let there be x pupils in the class. Total increase in marks = (x * 1/2) = x/2 x/2 = (83 - 63) => x/2 = 20 => x = 40 Answer:C The answer is: C

C

mathematics

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

[ "32", "20", "36", "88", "34" ]

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

A

mathematics

If x and y are multiples of 2 then which are all the multiples of 2 1) x*y 2) x^y 3) x+y 4) x-y 5) x/y

[ "1,3", "1,2,4,5", "1,2,5", "1,2,3,4", "all of these" ]

x*y,x^y,x+y, x-Y are even numbers ANSWER:D The answer is: D

D

mathematics

Julie put half of her savings in a savings account that pays an annual simple interest and half in a savings account that pays an annual compound interest. After two years she earned $112 and $120 from the simple interest account and the compound interest account respectively. If the interest rates for both accounts were the same, what was the amount of Julie's initial savings?

[ "600", "784", "1080", "1200", "1440" ]

$112 for 2 years = $56 per year. Extra $8 yearned with the compound interest is the percent yearned on percent. So, $8 is yearned on $56, which means that the interest = 7%. This on the other hand means that half of the savings = 56*7 = $392. Twice of that = $784. Answer: B. The answer is: B

B

mathematics

What is the greatest positive integer n such that 3^n is a factor of 36^50?

[ "100", "200", "300", "600", "900" ]

36 = 3^2 * 2^2. 36^50 = 3^100 * 2^100 The answer is A. The answer is: A

A

mathematics

Let us say that a table tennis tournament was going on with knock out terms which means the one who loses the match is out of the tournament. 101 players took part in that tournament. How many matches were played?

[ "90 matches", "95 matches", "99 matches", "100 matches", "87 matches" ]

D 100 matches. The number of matches will always sum up to one less than the number of players in a knock out tournament. You may calculate it in any manner. Thus 100 matches were played. The answer is: D

D

mathematics

The denominator of a fraction is 8 greater than the numerator. If the numerator and the denominator are increased by 5, the resulting fraction is equal to 6â„7. What is the value of the original fraction?

[ "25/33", "31/39", "37/45", "43/51", "53/61" ]

Let the numerator be x. Then the denominator is x+8. x+5 / x+13 = 6/7. 7x+35=6x+78. x=43. The original fraction is 43/51. The answer is D. The answer is: D

D

mathematics

Two pipes can separately fill a tank in 20 and 30 hours respectively. Both the pipes are opened to fill the tank but when the tank is full, a leak develops in the tank through which one-third of water supplied by both the pipes goes out. What is the total time taken to fill the tank?

[ "17 hrs", "16 hrs", "15 hrs", "13 hrs", "12 hrs" ]

1/20 + 1/30 = 1/12 1 + 1/3 = 4/3 1 --- 12 4/3 --- ? 4/3 * 12 = 16 hrs Answer:B The answer is: B

B

mathematics

You and your friend spent a total of $15 for lunch. Your friend spent $5 more than you. How much did your friend spend on their lunch?

[ "$9", "$3", "$4", "$6", "$10" ]

My lunch = l, my friends lunch = l+5 (l)+(l+5)=15 l+l+5-5=15-5 2l=10 l=5 My friends lunch l+5 = 5+5=$10, the answer is E The answer is: E

E

mathematics

Tanks X and Y contain 500 and 200 gallons of water respectively. If water is being pumped out of tank X at a rate of K gallons per minute and water is being added to tank Y at a rate of M gallons per minute, how many hours will elapse before the two tanks contain equal amounts of water?

[ "5/M+K hours", "6(M+K) hours", "300/M+K hours", "300/M−K hours", "60/M−K hours" ]

Consider k=1,m=2 Then per the question, 500 - 1x = 200 + 2x x=100 Check answer options for No. of hours (x)=100 for k=1 and m=2 ANSWER:C The answer is: C

C

mathematics

Which of the following are divisible by both 2 and 3? I. 234,124,422 II. 88,865,544,264 III. 5,555,554,674

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

I. is divisible by 3 since sum of the digits is 24 , which is divisible by 3 II. is divisible by 3 since sum of the digits is 60 , which is divisible by 3 III. is divisible by 3 since sum of the digits is divisible by 3 Thus among the given options only (B) holds true. The answer is: B

B

mathematics

Sarah made $45 more than Kara yesterday. Today, they each made the same amount of money as yesterday and it totaled $834. How much would Kara make in 5 days if she continues to make the same amount of money every day.

[ "$225", "$879", "$930", "$2,085", "None of the above" ]

S-K=45 2(S+K)=834 Solving the 2 equations, you get, S=$231 and K=$186 So $186x5=$930 Correct Answer: C The answer is: C

C

mathematics

How many positive integer solutions does the equation 4x+5y = 100 have?

[ "50", "33", "16", "5", "14" ]

formula: (constant)/(lcm of two nos) =100/(4*5)=5 ANSWER:D The answer is: D

D

mathematics

11 persons are sitting ina row. how many ways can 11persons be arranged in a row such that 3 persons should always be together?

[ "7!×3!", "7!×2!", "9!×3!", "7!×1!", "6!×2!" ]

Given that three particular persons should always be together. Hence, just group these three persons together and consider as a single person. Therefore we can take total number of persons as 9. These 9 persons can be arranged in 9! ways. We had grouped three persons together. These three persons can be arranged among themselves in 3! ways. Hence, required number of ways =9!×3! C The answer is: C

C

mathematics

A computer manufacturer produces a certain electronic component at a cost of $150 per component. Shipping costs for delivering the components are $1 per unit. Further, the manufacturer has costs of $19,500 a month related to the electronic component regardless of how many it produces. If the manufacturer produces and sells 250 components a month, what is the lowest price it can sell them for such that the costs don't exceed the revenues?

[ "199", "249", "233", "215", "229" ]

$19500 is a fixed cost Each component is $151 ($150 to produce, $1 to ship) Manufacturer will be producing and selling 250 components so therefore the equation to find price would be 250*p = 19500+(250*150)+(250*1) p = (19500+37500+250)/250 p = 229 Answer: E The answer is: E

E

mathematics

A train covers a distance of 10 km in 20 min. If it takes 6 sec to pass a telegraph post, then the length of the train is?

[ "50", "80", "120", "100", "40" ]

Speed = (10/20 * 60) km/hr = (30 * 5/18) m/sec = 8.333333 m/sec. Length of the train = 8.333333 * 6 = 50 m.Answer: A The answer is: A

A

mathematics

Pipes A and B can fill a cistern in 8 and 24 minutes respectively. They are opened an alternate minutes. Find how many minutes, the cistern shall be full?

[ "16", "12", "14", "61", "51" ]

1/8 + 1/24 = 1/6 6 * 2 = 12 Answer:B The answer is: B

B

mathematics

Of the three- digit integers greater than 700, how many have two digits Q that are equal to each other and the remaining digit different from the other two?

[ "90", "82", "80", "45", "36" ]

three-digit integers greater than 700: 701 to 999, inclusive. possible values for hundreds-digit--> 7,8,9 possible values for tens-digit and ones-digit --> 0, 1,2,3,4,5,6,7,8,9 when hundreds-digit and tens-digit are the same: (3x1x10)-3=27 ---> we minus three to exclude 777, 888 and 999 when hundreds-digit and ones-digit are the same: (3x10x1)-3=27 ---> we minus three to exclude 777, 888 and 999 when tens-digit and hundreds-digit are the same:[(3x10x1)-3]-1=26 ---> we minus three to exclude 777, 888 and 999; we minus one to exclude 700 Q=27+27+26 = 80 Answer: C The answer is: C

C

mathematics

I walk a certain distance and ride back taking a total time of 37 minutes. I could walk both ways in 55 minutes. How long would it take me to ride both ways?

[ "20mins", "19mins", "5mins", "4mins", "12mins" ]

Let the distance be x km. Then, ( Time taken to walk x km) + (time taken to ride x km) =37 min. ( Time taken to walk 2x km ) + ( time taken to ride 2x km )= 74 min. But, the time taken to walk 2x km = 55 min. Time taken to ride 2x km = (74-55)min =19 min. Ans: B The answer is: B

B

mathematics

A 340-liter solution of Kola is made from 64% water, 9% concentrated Kola and the rest is made from sugar. If 3.2 liters of sugar, 8 liter of water and 6.8 liters of concentrated Kola were added to the solution, what percent of the solution is made from sugar?

[ "6%.", "7.5%.", "9.2%.", "10.5%.", "26.5%." ]

Denominator: 340+8+3.2+6.8=358 Numerator: 340(1-.64-.09)+3.2 340(0.27)+3.2 91.8+3.2 95 Ratio: 95/358=0.265 Answer: E The answer is: E

E

mathematics

Marcus deposited $8,000 to open a new savings account that earned five percent annual interest, compounded semi-annually. If there were no other transactions in the account, what the amount of money in Marcuss account one year after the account was opened?

[ "$8,200", "$8,205", "$8,400", "$8,405", "$8,500" ]

Approach #1: 5 percent annual interest compounded semi-annually --> 2.5% in 6 moths. For the first 6 moths interest was 2.5% of $8,000, so $200; For the next 6 moths interest was 2.5% of $8,000, plus 2.5% earned on previous interest of $200, so $200+$5=$205; Total interest for one year was $200+$205=$405, hence balance after one year was $8,000+ $405=$8,405. Answer: D. The answer is: D

D

mathematics

10^25 - 760 is divisible by all of the following except:

[ "A.12", "B.8", "C.5", "D.4", "E.7" ]

The last three digits ( 1000 - 760 ) 240 240 is divisible by 12,4,8,5 240 is not evenly divisible by 7 so the answer is E) 7 The answer is: E

E

mathematics

The bacteria have the probability of split into 3 and probability to die is 1/3rd of the total bacteria. Let the probability is P. Some of them survived with probability 1/5.Then which among the following relation is true?

[ "P=1/3+1/5*3", "P=1/3+1/5*4", "P=1/3+1/5*2", "P=1/8*(1/8-3)", "P=1/5*(1/4-3)" ]

The bacteria have the probability of split into 3 and probability to die is 1/3rd of the total bacteria. Let the probability is P. Some of them survived with probability 1/5.Then which among the following relation is true? a)P=1/3+1/5*3 b)P=1/5*(1/8-3) P=1/3+1/5*3 is true. ANSWER:A The answer is: A

A

mathematics

If |5x-10| = 100, then find the sum of the values of x?

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

|5x-10| = 100 5x-10 = 100 or 5x-10 = -100 5x = 110 or 5x = -90 x = 22 or x = -18 sum = 21-18 = 3 Answer is C The answer is: C

C

mathematics

12 men can complete a piece of work in 4 days, while 15 women can complete the same work in 4 days. 6 men start working on the job and after working for 2 days, all of them stopped working. How many women should be put on the job to complete the remaining work, if it is to be completed in 3 days.

[ "15", "18", "22", "25", "26" ]

One man’s one day’s work = 1/48 One woman’s one day’s work = 1/60 6 men’s 2 day’s work = ((6/48) x 2) = 1/4 Remaining work = 3/4 Now, 1/60 work s done in 1 day by 1 woman. Thus, 3/4 work will be done in 3 days by (60 x (3/4) x (1/3)) = 15 women. ANSWER:A The answer is: A

A

mathematics

A walks with a speed of 6 km/hr and after 5 hr of his start, B starts running towards A at a speed of 8 km/hr. At what distance from start will B catch A.

[ "100 Km", "110 Km", "120 Km", "140 Km", "NONE" ]

Explanation : In 5hrs, A will cover 30 km. Now, at some distance ‘x’. So A will cover X distance and B will cover 30 + X. x/6 = (30+x)/8 x = 90. So distance from start after which B will catch A = 90+30 =120km Answer – C The answer is: C

C

mathematics

How many of the following numbers are divisible by 14 ? 264, 396, 462, 792, 968, 2178, 5184, 6336

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

By using your calculator you can calculate that the following numbers are divisible by 14 : 462. Required number of number = 1. E The answer is: E

E

mathematics

David used part of $100,000 to purchase a house. Of the remaining portion, he invested 1/3 of it at 4 percent simple annual interest and 2/3 of it at 6 percent simple annual interest. If after a year the income from the two investments totaled $320, what was the purchase price of the house?

[ "$96,000", "$94,000", "$88,000", "$75,000", "$40,000" ]

Of all the answer choices, (A) and (D) do not offer a number divisible by 3. (E) can be eliminated easily because when you invest 1/3 of $60,000 ($20,000) @ 4% interest rate, you earn $800 interest, which is definitely more than $320. But, if you calculate 2/3 of $60,000 ($40,000) @ 6% interest rate, you earn $2400 interest. Total interest when $60,000 is the remaining amount: $800 + $2400 = $3200. We need $320. It means the remaining amount should be $6000. Therefore, (B) is the answer. The answer is: B

B

mathematics

Of the five numbers in a sequence, the first term is 15,000, and each of the following terms is 20% of the previous term. What is the value range of the five numbers?

[ "9,375", "9,750", "9,975", "9,984", "14,976" ]

1st number= 15,000 2nd number = 20% of 15,000= 3000 3rd number= 20% of 3000= 600 4th number = 20% of 600= 120 5th number= 20% of 120= 24 Range = 15,000-24= 14976 E is the answer The answer is: E

E

mathematics

The area of a triangle is with base 10m and height 10m?

[ "11", "10", "50", "122", "12" ]

1/2 * 10 *10= 50 m2 Answer: C The answer is: C

C

mathematics

Kim purchased n items from a catalog for $8 each. Postage and handling charges consisted of $3 for the first item and $1 for each additional item. Which of the following gives the total dollar amount for Kim’s purchase, including postage and handling, in terms of n ?

[ "8n + 2", "8n + 4", "9n + 2", "9n + 3", "9n + 4" ]

n items for $8 each total price $8n postage and handling of $3 for 1st item and $1 for the rest total postage and handling = $ [3+ (n-1)] = $ n+2 total cost 8n+n+2 = 9n+2 ; ANSWER:C The answer is: C

C

mathematics

The area of a parallelogram is 72 sq m and its base is 12m . Then the length of the height is?

[ "6m", "7m", "60m", "13m", "none" ]

b*h=72. h*12=72 =>h=6m. Answer: (A) The answer is: A

A

mathematics

Find the least number must be subtracted from 427398 so that remaining no.is divisible by 15?

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

On dividing 427398 by 15 we get the remainder 3, so 3 should be subtracted A The answer is: A

A

mathematics

Two trains of length 160 m and 200 m are 100 m apart. They start moving towards each other on parallel tracks, at speeds 54 kmph and 72 kmph. In how much time will the trains cross each other?

[ "100/7 sec", "80/7 sec", "112/7 sec", "120/7 sec", "50/7 sec" ]

Relative speed = (54 + 72)* 5/18 = 7 * 5 = 35 mps. The time required = d/s = (160 + 100 + 300)/35 = 560/35 = 112/7 sec. ANSWER:C The answer is: C

C

mathematics

Find the odd man out. 742, 743, 633, 581, 871, 990, 532

[ "532", "990", "581", "743", "None of these" ]

Explanation : In all numbers except 581, the difference of third and first digit is the middle digit. Answer : Option C The answer is: C

C