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	When n is divided by 13, the remainder is 6. When n is divided by 11, the quotient is equal to Z, and the remainder is equal to 6. Z must be divisible by which of the following numbers?	[ "13", "14", "15", "16", "17" ]	N = 139 q + 6 N = 11 z + 6 Equating 13Q + 6= 11z+6 11z=193 11z/13 = q since q is an integer Z must be divisible by 19. Hence A The answer is: A	A
mathematics	Six years ago, the ratio of the ages of Kunal and Sagar was 6:5, Four years hence, the ratio of their ages will be 11:10. What is Sagar age at present	[ "22", "17", "15", "16", "12" ]	Let six years ago the age of Kunal and Sagar are 6x and 5x resp. then, =>(6x+6)+4(5x+6)+4=1110 =>(6x+6)+4(5x+6)+4=1110 <=>10(6x+10)=11(5x+10) <=>10(6x+10)=11(5x+10) <=>5x=10=>x=2 <=>5x=10=>x=2 So Sagar age is (5x+6) = 16 Answer: D The answer is: D	D
mathematics	Can you get total of 720 by using six zeros 0,0,0,0,0,0 and any maths operators.	[ "650", "550", "700", "720", "500" ]	D 720 (0!+0!+0!+0!+0!+0!)! =(1+1+1+1+1+1)! =(5)! =6! is 65432*1=720 The answer is: D	D
mathematics	The combined area of the two black squares is equal to 1000 square units. A side of the larger black square is 8 units longer than a side of the smaller black square. What is the combined area of the two white rectangles in square units?	[ "928", "936", "948", "968", "972" ]	The length of a smaller square - x; The length of a larger square - x+8; The area of entire square - x^2+(x+8)^2=1000 --> 2x^2+16x=936; The combined area of the two white rectangles - x(x+8)+x(x+8)=2x^2+16x --> look up: 2x^2+16x=936. Answer: B. The answer is: B	B
mathematics	Find the invalid no.from the following series 3, 7, 15, 31, 63, 123, 255	[ "3", "7", "27", "63", "123" ]	Go on multiplying the number by 2 and adding 1 to it to get the next number.So, 123 is wrong. E The answer is: E	E
mathematics	The greatest number which on dividing 1657 and 2037 leaves remainders 6 and 5 respectively, is:	[ "123", "127", "235", "305", "505" ]	Explanation: Required number = H.C.F. of (1657 - 6) and (2037 - 5) = H.C.F. of 1651 and 2032 = 127. Answer: B The answer is: B	B
mathematics	The function f is defined for all positive integers m by the following rule. f(m) is the number of positive integers each of which is less than m and has no positive factor in common with m other than 1. If p is any prime, number then f(p)=	[ "p-1", "p-2", "(p+1)/2", "(p-1)/2", "2" ]	If not the wording the question wouldn't be as tough as it is now. The GMAT often hides some simple concept in complicated way of delivering it. This question for instance basically asks: how many positive integers are less than given prime number p which have no common factor with p except 1. Well as p is a prime, all positive numbers less than p have no common factors with p (except common factor 1). So there would be p-1 such numbers (as we are looking number of integers less than p). For example: if p=8 how many numbers are less than 8 having no common factors with 8: 1, 2, 3, 4, 5, 6, 7 --> 8-1=7. Answer: A. The answer is: A	A
mathematics	The difference between the place values of 6 and 5 in the number 826533 is	[ "5500", "4500", "2500", "6970", "None" ]	Sol. = (Place value of 6) – (place Value of 5) = (6000 - 500) = 5500 Answer A The answer is: A	A
mathematics	If Rs. 782 be divided into three parts, proportional to 1/2:2/3:3/4, then the second part is?	[ "A)426", "B)526", "C)207", "D)204", "E)272" ]	Given ratio = 1/2:2/3:3/4 = 6:8:9 1st part = 782 * 8/23 = Rs. 272 Answer:E The answer is: E	E
mathematics	A survey of n people in the town of Eros found that 50% of them preferred Brand A. Another survey of 120 people in the town of Angie found that 60% preferred Brand A. In total, 55% of all the people surveyed together preferred Brand A. What is the total number of people surveyed?	[ "50", "100", "150", "200", "240" ]	It is simply a weighted average question. Since the given average of 50% and 60% is 55% (right in the middle), it means the number of people surveyed in Eros (n) is same as the number of people surveyed in Angie. So n = 120 Total = 120 + 120 = 240 Answer (E) The answer is: E	E
mathematics	What should come in place of the question mark (?) in the following number series? 11 21 33 47 63 ?	[ "80", "81", "82", "83", "84" ]	The numbers increase by 10, 12, 14, 16,... The next number should be 63+18 = 81 The answer is B. The answer is: B	B
mathematics	trees of heights 30 and 40 sepatated by a river. fish in the river is at equal dis from top of the trees where two birds are there.ratio of the distances from fish to the root of the trees?	[ "4:3", "1:2", "2:1", "3:4", "1:3" ]	40/30 is the ratio of distance from fish to root of trees 4:3 ANSWER:A The answer is: A	A
mathematics	In an election between two candidates, 75 % of the voters cast their votes, out of which 2% of the votes were declared invalid. A candidate got 9261 votes which were 75% of the total valid votes. Find the total number of votes	[ "16800", "15800", "16700", "15700", "None of these" ]	Explanation: Let the total number of votes enrolled are x. Number of votes cast = 75% of x Valid votes = 98% of 75% of x Now, as 9261 is the 75% of valid casted votes so, 75% of 98% of 75% of x = 9261 [imporant] =>75×98×75×x100×100×100=9261=>x=16800 Answer: Option A The answer is: A	A
mathematics	For four days of work, a clerk had daily earnings of $160, $150, $160, and $160 respectively. In which of the following intervals does the standard deviation of the daily earnings lie?	[ "Between $10 and $50", "Between $0 and $10", "Between $20 and $25", "Between $50 and $100", "Between $50 and $65" ]	The standard deviation is between 0 and 10. The reason is that none of the numbers in the set is further away from the mean than 10(or rather Abs(150-(160*3+150)/4)). I am not fully sure how to calculate the standard deviation(I simply remember that there were some formula for calculating the average of the squared distances from the mean for all items in the set from statistics classes - variation), but I believe this will suffice for any GMAT question related to standard deviation. Answer : B The answer is: B	B
mathematics	A bag contains 7 red balls, 5 green balls and 6 white balls. A ball is drawn at random from the box. What is the probability that the ball drawn is either red or green?	[ "2/3", "3/5", "1/5", "7/15", "8/15" ]	Total number of balls = (7 + 5 + 6) = 18. Therefore, n(S) = 18. Let E1 = event of drawing a red ball. and E2 = event of drawing a green ball. Then, E1 n E2 = f. P (E1 n E2) = P(E1) + P(E2) = (7/18 + 5/18) = 2/3. ANSWER:A The answer is: A	A
mathematics	6, 11, 21, 36, 56, ?	[ "65", "78", "81", "97", "98" ]	The pattern is + 5, + 10, + 15, + 20,... Answer : C. The answer is: C	C
mathematics	A team of 6 cooks is chosen from 7 men and 5 women. The team must have at least 2 men and at least 3 women. How many ways can this team be created?	[ "140", "320", "560", "455", "840" ]	Only possible combinations are a team of 2M, 4 W or 3M,3W. Possible ways to make a team of 2M,4W = 7C2 * 5C4 =215 =105 Possible ways to make a team of 3M,3W = 7C3 5C3 = 35*10 = 350 Total possible ways = 105+350 = 455 Ans D it is. The answer is: D	D
mathematics	A person started from point A to point B and returned back to A with a speed of 60 kmh. If the distance between A and B is 120km, calculate the time he travelled	[ "4 hours", "2 hours", "3 hours", "6 hours", "5 hours" ]	Time = Distance/Speed Total distance = (from A->B and from B->A) = 120+120=240 km Speed = 60 kmh 240/60 = 4 Answer: A The answer is: A	A
mathematics	Jack and Paul are running 1000m. Jack runs 1.5Km/hr faster than Paul but also finishes the race 1.5 sec earlier. What is the speed of Jack??	[ "20.61", "21.61", "22.61", "23.61", "24.61" ]	distance(given) 1000m paul speed(let)= x m/s time(paul take)= 1000/x sec jack speed= x + 1.5*(5/18) m/s tym (jack)= 1000/(x+7.5/18) s tym(paul) - tym (jack) = 1.5 solving for x we get 20.20 speed of jack is 20.20+ 7.5/18=20.61 ANSWER:A The answer is: A	A
mathematics	12 + 13 + 14 + ... 61 + 62 + 63 = ?	[ "1361", "1362", "1950", "1364", "1365" ]	Sum = 12 + 13 + 14 + ... 61 + 62 + 63 Sum of n consecutive positive integers starting from 1 is given as n(n+1)/2 Sum of first 63 positive integers = 6364/2 Sum of first 11 positive integers = 1112/2 Sum = 12 + 13 + 14 + ... 61 + 62 + 63 = 6364/2 - 1112/2 = 1950 Answer : C The answer is: C	C
mathematics	Rs.2500 is divided into two parts such that if one part be put out at 5% simple interest and the other at 6%, the yearly annual income may be Rs.140. How much was lent at 5%?	[ "2288", "27669", "1766", "1000", "2871" ]	(x51)/100 + [(2500 - x)61]/100 = 140 X = 1000 Answer: D The answer is: D	D
mathematics	The triplicate ratio of 1:6 is?	[ "1:7", "1:8", "1:3", "1:1", "1:216" ]	1^3: 6^3 = 1:216 Answer: E The answer is: E	E
mathematics	A 8000 liter tank, half-full of water is being filled from a pipe with a flow rate of 1 kiloliter every 2 minutes. At the same time, the tank is losing water from two drains at a rate of 1 kiloliter every 4 minutes and every 6 minutes. How many minutes does it take to fill the tank completely?	[ "8", "12", "18", "24", "48" ]	In: we have: 1,000/2min = 500 litres per minute Out: we have: 1,000/4 + 1,000/6 Then do: IN - OUT to figure out the net inflow per minute (you get 83.3). Then divide the total number of litres you need (4,000 by that net inflow to get the minutes) - 48 min. Answer E. The answer is: E	E
mathematics	Find the value of x from this equation? 7(x - 1) = 21	[ "2", "4", "6", "8", "10" ]	1. Divide both sides by 7: 2. Simplify both sides: x - 1 = 3 3. Add 1 to both sides: x - 1 + 1 = 3 + 1 4. Simplify both sides: x = 4 B The answer is: B	B
mathematics	Baseball's World Series matches 2 teams against each other in a best-of-seven series. The first team to win four games wins the series and no subsequent games are played. If you have no special information about either of the teams, what is the probability w that the World Series will consist of fewer than 7 games?	[ "12.5%", "25%", "31.25%", "68.75%", "75%" ]	In order to determine the probability that the World Series will last less than 7 games, we can first determine the probability w that the World Series WILL last exactly 7 games and then subtract this value from 1. In order for the World Series to last exactly 7 games, the first 6 games of the series must results in 3 wins and 3 losses for each team. Let's analyze one way this could happen for Team 1: Game 1 Game 2 Game 3 Game 4 Game 5 Game 6 T1 Wins T1 Wins T1 Wins T1 Loses T1 Loses T1 Loses There are many other ways this could happen for Team 1. Using the permutation formula, there are 6!/(3!)(3!) = 20 ways for Team 1 to win 3 games and lose 3 games in the first 6 games. Logically, there are also 20 ways for Team 2 to win 3 games and lose 3 games in the first 6 games. Thus, there are a total of 40 ways for the World Series to last the full 7 games. The probability that any one of these 40 ways occurs can be calculated from the fact that the probability of a team winning a game equals the probability of a team losing a game = 1/2. Given that 7 distinct events must happen in any 7 game series, and that each of these events has a probability of 1/2, the probability that any one particular 7 game series occurs is. Since there are 40 possible different 7 game series, the probability that the World Series will last exactly 7 games is: Thus the probability that the World Series will last less than 7 games is 100% - 31.25% = 68.75%. The correct answer is D. The answer is: D	D
mathematics	A and B can do a work in 4 hours and 12 hours respectively. A starts the work at 6AM and they work alternately for one hour each. When will the work be completed?	[ "7 days", "9 days", "4 days", "6 days", "2 days" ]	Work done by A and B in the first two hours, working alternately = First hour A + Second hour B = 1/4 + 1/12 = 1/3. Total time required to complete the work = 2 * 3 = 6 days. Answer: D The answer is: D	D
mathematics	In a country named "gpuzzles" 1/2 of 5 = 3. If the same proportion holds, what is the value of 1/3 of 10 ?	[ "2", "5", "6", "9", "4" ]	E 4 5/2 = 3 and 10/3 = x (10/3)/(5/2) = 20/15 = 4/3 So x/3 = 4/3 x=4 The answer is: E	E
mathematics	An amount of money is to be divided between P, Q and R in the ratio of 3:7:12. If the difference between the shares of P and Q is Rs.4000, what will be the difference between Q and R's share?	[ "2788", "5000", "7282", "2782", "2729" ]	4 --- 4000 5 --- ? => 5000 Answer:B The answer is: B	B
mathematics	A 25% stock yielding 20% is quoted at:	[ "s. 83.33", "s. 110", "s. 112", "s. 125", "s. 140" ]	Income of Rs 20 on investment of Rs 100 Income of Rs 25 on investment of ? = (25*100)/20=125 ANSWER:D The answer is: D	D
mathematics	A certain team has 8 members, including Joey. A three-member relay team will be selected as follows: one of the 8 members is to be chosen at random to run first, one of the remaining 7 members is to be chosen at random to run second, and one of the remaining 6 members is to be chosen at random to run third. What is the probability that Joey will be chosen to run second or third?	[ "2/3", "1/4", "2/5", "3/8", "3/10" ]	Each member has an equal probability to run second (1/8) or third (1/8). The probability that Joey runs second or third is 1/8 + 1/8 = 1/4 The answer is B. The answer is: B	B
mathematics	There is a 50% chance Jen will visit Chile this year, while there is a 25% chance that she will visit Madagascar this year. What is the probability that Jen will visit either Chile or Madagascar this year, but NOT both?[/b]	[ "25%", "50%", "62.5%", "63.5%", "75%" ]	The thing to note in the question is she would not be visiting both. Thus p(Chile)(1-p(Madagascar))+p(Madagascar)(1-p(Chile)) which is (1/23/4) + (1/41/2), 3/8*1/8=1/2 =50% Answer: B The answer is: B	B
mathematics	The average weight of 7 person's increases by 6.2 kg when a new person comes in place of one of them weighing 76 kg. What might be the weight of the new person?	[ "160 kg", "175 kg", "180.7 kg", "119.4 kg", "190.8 kg" ]	Total weight increased = (7 x 6.2) kg = 43.4 kg. Weight of new person = (76 + 43.4) kg = 119.4 kg Option D The answer is: D	D
mathematics	The width of a rectangle is 10mtr and its area is 150 square meter. If length of the rectangle is increased, then its new area is 1(1/3) times of the original area. What is the new perimeter of the rectangle?	[ "45", "54", "67", "60", "69" ]	Ans.(D) Sol. Length of original rectangle = 150/10 = 15 (10(15+x))/(1015) = 4/3 x = 5 Perimeter of new rectangle = 2(10+20) = 60 The answer is: D	D
mathematics	A rectangular field is to be fenced on three sides leaving a side of 8 feet uncovered.If the area of the field is 680 sq.ft, how many feet of fencing will be required?	[ "244ft", "88ft", "122ft", "178ft", "66ft" ]	Given that length and area, so we can find the breadth. Length x Breadth = Area 8 x Breadth = 680 Breadth = 85 feet Area to be fenced = 2B + L = 2 (85) + 8 = 178 feet Answer: D) 178ft The answer is: D	D
mathematics	Stacy and Heather are 5 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?.	[ "2.5mile", "1.9mile", "1.7mile", "1.5mile", "1.18mile" ]	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 5 -2.4 = 2.6 Time taken = Distance/ Speed = 2.6/11 = 0.23 hrs Heather will cover = 50.23 = 1.18miles. Answer E The answer is: E	E
mathematics	John is traveling to a meeting that is 22 miles away. He needs to be there in 30 minutes. How fast does he need to go to make it to the meeting on time?	[ "25 mph", "44 mph", "41 mph", "49 mph", "56 mph" ]	Well 44mph. B. Timerate=distance --> 0.5rate=22 --> rate=44 The answer is: B	B
mathematics	The average age of a group of persons going for picnic is 16 years. Twenty new persons with an average age of 15 years join the group on the spot due to which their average age becomes 15.5 years. The number of persons initially going for picnic is?	[ "10", "20", "37", "26", "22" ]	Let the initial number of persons be x. Then, 16x + 20 * 15 = 15.5 (x + 20) <=> 0.5x = 10 <=> x = 20. Answer: B The answer is: B	B
mathematics	If x^2 − 2x − 15 = (x + r)( x + s) for all values of x, and if r and s are constants, then which of the following is a possible value of 2(r − s)?	[ "8", "16", "− 2", "− 3", "− 5" ]	We know that given ax^2 + bx + c = 0, Sum of the roots = -b/a and product of the roots = c/a. The roots here are -r and -s. -r - s = -(-2)/1 = r + s = -2 (-r)*(-s) = -15/1 = rs So one of r and s is -5 and the other is 3. So 2(r - s) could be 16 or -16. Answer (B) The answer is: B	B
mathematics	The profit earned by selling an article for Rs 900 is double the loss incurred when the same article is sold for Rs.490. At what price should the article be sold to make 25% profit?	[ "715", "469", "400", "750", "850" ]	Explanation: Let C.P be Rs. x 900 - x = 2(x - 450) => x = Rs.600 C.P = 600 gain required is 25% S.P = [(100 + 25) × 600]/100 = Rs.750 Answer: D The answer is: D	D
mathematics	Marcella has 26 pairs of shoes. If she loses 9 individual shoes, what is the greatest number of matching pairs she could have left?	[ "21", "20", "19", "16", "15" ]	Marcella has 26 pairs of shoes and loses 9 shoes. To minimize the loss of identical pairs of shoes we want Marcella to lose as many identical pairs as possible. This would yield 4 identical pairs and 1 additional shoe (destroying 5 pairs of shoes). The 26 pairs of shoes minus the 5 'destroyed' pairs yields 21 pairs that still fulfill the requirements. Answer: A The answer is: A	A
mathematics	Tickets numbered 1 to 20 are mixed up and then a ticket is drawn at random. What is the probability that the ticket drawn has a number which is a multiple of 3 or 5?	[ "2/5", "9", "9/5", "1/5", "9/20" ]	Here, S = {1, 2, 3, 4, ...., 19, 20}. Let E = event of getting a multiple of 3 or 5 = {3, 6 , 9, 12, 15, 18, 5, 10, 20}. P(E) = n(E)/n(S) = 9 /20 The answer is: E	E
mathematics	Each of seven different locks has a matching key. The keys are randomly reassigned to the locks. What is the probability that exactly two of the keys fit the locks to which they are reassigned?	[ "1/8", "1/6", "1/49", "3/8", "1/2" ]	I was just going over probability questions. can some one explain me what's wrong in my approach here. Probability of choosing one right key out of 7 is 1/7. Probability of choosing another right key is 1/7. since the question is asking for 2 right keys , probability is multiplication of both = 1/7 * 1/7 = 1/49. Ans C The answer is: C	C
mathematics	In what time will a cart 50 m long cross, if its speed be 36 km/hr?	[ "25", "5", "15", "20", "30" ]	Speed = 36 * 5/18 = 10 m/sec Time taken = 50/10 = 5 sec. Answer:B The answer is: B	B
mathematics	The difference between a number and its two-fifth is 510. What is 12% of that number?	[ "58", "110", "76", "102", "86" ]	Let the number be x. Then, x - 2/5 x = 510 x = (510 * 5)/3 = 850 12% of 850 = 102. Answer:D The answer is: D	D
mathematics	Find the odd man out. 2, 3, 5, 9, 12, 17, 23	[ "12", "9", "23", "2", "1" ]	Explanation : 2 2 + 1 = 3 3 + 2 = 5 5 + 3 = 8 8 + 4 = 12 12 + 5 = 17 17 + 6 = 23 ie, 8 should have come in place of 9. Answer : Option B The answer is: B	B
mathematics	The Delhi Express runs @ 144 kilometers per hours and it reaches destination 20 minute ahead of schedule. If it averages 100 km/hour, it reaches 24 minute behind schedule. What is the average speed it should maintain in order to reach the destination on schedule?	[ "250", "240", "230", "245", "235" ]	If the destination is D kilometer and the speed in order to reach on schedule is S km/hour, the time taken to reach on schedule is D/S hours Thus we get two equations: D/144 = D/S - 1/3 and D/100 = D/S + 2/5 and Subtracting the first equation from the second we get : 44D/14400 = 11/15 Thus D = 14400 x 11/ 44 x 15 = 240 ANSWER:B The answer is: B	B
mathematics	A train crosses a platform of 120 m in 15 sec, same train crosses another platform of length 180 m in 18 sec. then find the length of the train?	[ "298", "180", "289", "177", "123" ]	Length of the train be ‘X’ X + 120/15 = X + 180/18 6X + 720 = 5X + 900 X = 180m Answer: B The answer is: B	B
mathematics	What is the equation of a circle of radius 6 units centered at (3, 2)?	[ "x2 + y2 + 6x - 4y = 23", "x2 + y2 - 6x + 4y = 23", "x2 + y2 + 6x + 4y = 23", "x2 + y2 - 6x - 4y = -23", "x2 + y2 - 6x - 4y = 23" ]	Explanatory Answer Equation of a circle with center (a, b) and radius 'r' units is (x - a)2 + (y - b)2 = r2 Therefore, the equation of this circle = (x - 3)2 + (y - 2)2 = 62 i.e., x2 - 6x + 9 + y2 - 4y + 4 = 36 or x2 + y2 - 6x - 4y = 23 The correct choice is (E) The answer is: E	E
mathematics	In a nationwide poll, P people were asked 2 questions. If 2/5 answered “yes” to question 1, and of those 1/3 also answered “yes” to question 2, which of the following represents the number of people polled who did not answer “yes” to both questions?	[ "2/15P", "3/5P", "3/4P", "5/6P", "13/15*P" ]	no of people polled who did not answer “yes” to both questions = P - no of people polled who answered “yes” to both questions no of people who answered yes for the 2nd question = 1/3 * 2/5 * P = 2/15P no of people polled who did not answer “yes” to both questions = P - 2/15P = 13/15*P Hence, E will be the answer. The answer is: E	E
mathematics	A train moves fast a telegraph post and a bridge 264 m long in 8 sec and 20 sec respectively. What is the speed of the train?	[ "27.8 km/hr", "22.9 km/hr", "26.6 km/hr", "79.2 km/hr", "12.9 km/hr" ]	Let the length of the train be x m and its speed be y m/sec. Then, x/y = 8 => x = 8y (x + 264)/20 = y y = 22 Speed = 22 m/sec = 22 * 18/5 = 79.2 km/hr. Answer: D The answer is: D	D
mathematics	What is the next number in the sequence. 15 29 56 108 208 ?	[ "450", "400", "300", "500", "580" ]	B 400 Explanation: Begins with 15 215-1 => 29 229-2 => 56 256-4 => 108 2108-8 => 208 2*208-16 => 400 The answer is: B	B
mathematics	To asphalt 1km road, 30 men spent 12 days working 8 hours per day. How many days, 20 men will spend to asphalt a road of 2km working 15 hours a day?	[ "23", "22", "21", "20", "19.2" ]	Man-hours required to asphalt 1 km road=30128=2880 Man-hours required to asphalt 2 km road=28802=5760 Man-hours available per day=2015=300 Therefore number of days=5760/300=19.2 days Ans=E The answer is: E	E
mathematics	A retailer bought a machine at a wholesale price of $99 and later on sold it after a 10% discount of the retail price. If the retailer made a profit equivalent to 20% of the whole price, what is the retail price of the machine?	[ "81", "100", "120", "132", "160" ]	My solution: Wholesale Price= 99 Retail Price, be = x He provides 10 % discount on Retail price= x-10 x/100 This Retail price = 20 % profit on Wholesale price x-10 x/100 = 99+ 1/5(99) x=132; ANSWER:D The answer is: D	D
mathematics	The true discount on a bill of Rs. 2460 is Rs. 360. What is the banker's discount?	[ "Rs. 432", "Rs. 422", "Rs. 412", "Rs. 442", "None of these" ]	Explanation : F = Rs. 2460 TD = Rs. 360 PW = F - TD = 2460 - 360 = Rs. 2100 True Discount is the Simple Interest on the present value for unexpired time =>Simple Interest on Rs. 2100 for unexpired time = Rs. 360 Banker's Discount is the Simple Interest on the face value of the bill for unexpired time = Simple Interest on Rs. 2460 for unexpired time =360/2100 × 2460 = 0.17 × 2460 = Rs. 422 Answer : Option B The answer is: B	B
mathematics	How many seconds will a 500 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?	[ "22", "30", "88", "266", "121" ]	Speed of train relative to man = 63 - 3 = 60 km/hr. = 60 * 5/18 = 50/3 m/sec. Time taken to pass the man = 500 * 3/50 = 30 sec. Answer:B: The answer is: B	B
mathematics	If 30% of 100 is greater than 50% of a number by 10, then the number is?	[ "40", "30", "60", "80", "50" ]	Let the number be x 30% of 100 - 50% of x = 10 50/100 x = (30/100 * 100)-10 x/2 = 20 x = 40 Answer is A The answer is: A	A
mathematics	A can do a piece of work in 10 days and B can do the same work in 12 days. A and B worked together for 2 days. How many more days are required to complete the remaining work if they work together?	[ "3 (5/18) days", "3 (7/11) days", "3 (5/11) days", "2 (5/11) days", "3 (2/11) days" ]	A can do 1/10 of the work in a day. B can do 1/12 of the work in a 1 day. Both of them together can do (1/10 + 1/12) part of work in 1 day = (6 + 5)/60 = 11/60 They take 60/11 days to complete the work together. Given that they already worked for 2 days. The number of days required to complete remaining work => 60/11 - 2 = 38/11 = 3 (5/11) days. Answer:C The answer is: C	C
mathematics	A man whose speed is 4.5 kmph in still water rows to a certain upstream point and back to the starting point in a river which flows at 1.5 kmph, find his average speed for the total journey?	[ "5", "4", "8", "9", "2" ]	M = 45 S = 1.5 DS = 6 US = 3 AS = (2 * 6 * 3) /9 = 4 Answer: B The answer is: B	B
mathematics	A can give B 100 meters start and C 200 meters start in a kilometer race. How much start can B give C in a kilometer race?	[ "111.12 m", "111.22 m", "111.19 m", "118.12 m", "311.12 m" ]	A runs 1000 m while B runs 900 m and C runs 800 m. The number of meters that C runs when B runs 1000 m, = (1000 * 800)/900 = 8000/9 = 888.88 m. B can give C = 1000 - 888.88 = 111.12 m.Answer:A The answer is: A	A
mathematics	If an item that originally sold for A dollars was marked up by x percent and then discounted by y percent, which of the following expressions represents the final price of the item?	[ "(A+ Ax/100) - Y/100 ( A +Ax/100)", "(10,000z + 100z(y – x) – xyz)/10,000", "(100z(x – y) – xyz)/10000", "(100z(y – x) – xyz)/10000", "10000 /(x – y)" ]	value of item =A ..marked up by x% = Ax/100 total value = A +ax/100 .discounted by Y% on Total Y/100 * ( A+Ax/100) Final price =(A+ Ax/100) - Y/100 ( A +Ax/100) A The answer is: A	A
mathematics	A shop sells two variants of chocolates - one that costs $3 and the other that costs $5. If the shop sold $131 chocolates on a given day, how many different combinations of (number of $3 sold, number of $5 sold) exist?	[ "3", "5", "7", "9", "11" ]	$131 = 25$5 + 2$3 We can find other combinations by reducing the $5 chocolates by 3 (which is -$15)and increasing the $3 chocolates by 5 (which is +$15). The number of $5 chocolates can be 25, 22, 19, 16,...,1 for a total of 9 combinations. The answer is D. The answer is: D	D
mathematics	A number is divided by 406 leaves remainder 115,what will be the remainder when it will be divided by 29?	[ "26", "30", "27", "28", "29" ]	Let the Number be N. So N=406x+115. Now divide this number by 29 As 406 is exactly divisible by 29,we have to divide 115 by 29 and find the remainder. So Remainder is 28 Option D is answer The answer is: D	D
mathematics	Using all the letters of the word "NOOKIASS", how many words can be formed, which begin with N and end with S?	[ "550", "160", "720", "620", "820" ]	There are five letters in the given word. Consider 8 blanks .... The first blank and last blank must be filled with N and S all the remaining three blanks can be filled with the remaining 6 letters in 6! ways. The number of words = 6! = 720. Answer: C The answer is: C	C
mathematics	Sonika deposited Rs.8000 which amounted to Rs.9200 after 3 years at simple interest. Had the interest been 0.5% more. She would get how much?	[ "9320", "96288", "26667", "1662", "2882" ]	(800030.5)/100 = 120 9200 -------- 9320 Answer:A The answer is: A	A
mathematics	Last year’s receipts from the sale of greeting cards during the week before Mother’s Day totaled $167 million, which represented 10 percent of total greeting card sales for the year. Total greeting card sales for the year totaled how many million dollars?	[ "1,650", "1,670", "1,890", "1,701", "3,210" ]	10% ---- 167 millions for 100% => ( 167 * 100% )/10% = 1670. Option B. The answer is: B	B
mathematics	If w/x = 1/3 and w/y = 3/4, then (x + y)/y =	[ "13/4", "6/5", "7/5", "8/5", "9/5" ]	W/X = 1/3=>x=3w and W/Y = 3/4=>y=(4/3)w (X+Y)/Y = (3w+4/3w)/(4/3w)=(13/3w)/(4/3w)=13/4 Correct Option: A The answer is: A	A
mathematics	A, B and C invest in the ratio of 3 : 4: 5. The percentage of return on their investments are in the ratio of 6 : 5 : 4. Find the total earnings, If B earns Rs. 250 more than A :	[ "2348", "7250", "2767", "1998", "2771" ]	Explanation: A B C investment 3x 4x 5x Rate of return 6y% 5y% 4y% Return \inline \frac{18xy}{100} \inline \frac{20xy}{100} \inline \frac{20xy}{100} Total = (18+20+20) = \inline \frac{58xy}{100} B's earnings - A's earnings = \inline \frac{2xy}{100} = 250 Total earning = \inline \frac{58xy}{100} = 7250 Answer: B) Rs.7250 The answer is: B	B
mathematics	Jim’s Taxi Service charges an initial fee of $2.05 at the beginning of a trip and an additional charge of $0.35 for each 2/5 of a mile traveled. What is the total charge for a trip of 3.6 miles?	[ "$5.20", "$4.45", "$4.80", "$5.05", "$5.40" ]	Let the fixed charge of Jim’s Taxi Service = 2.05 $ and charge per 2/5 mile(.4 mile) = .35$ Total charge for a trip of 3.6 miles = 2.05 + (3.6/.4) * .35 = 2.05 + 9*.35 = 5.2 $ Answer A The answer is: A	A
mathematics	If m=4p where p is a prime number greater than 2, how many different positive even divisors does m have, including m?	[ "two", "three", "four", "six", "eight" ]	m=2, 2, p (p is in the prime factorization since were told it is a prime number in the question) 2 4 (because of 22) 2p (because of 2 p) 4p (because of 2 * 2 * p)=C The answer is: C	C
mathematics	In a pair of fractions, fraction A is twice the fraction B and the product of two fractions is 2/25. What is the value of fraction A?	[ "2/9", "2/2", "2/5", "2/6", "2/4" ]	Explanation: A = 2B => B = 1/2 A, so, AB = 2/25 1/2 A2 = 2/25 A2 = 4/25 A = 2/5 Answer:C The answer is: C	C
mathematics	Ram and Shyam together can do a piece of work in 30 days. Ram having worked for 16 days, Shyam finishes the remaining work alone in 44 days. In how many days shall Shyam finish the whole work alone?	[ "30 days", "40 days", "60 days", "70 days", "80 days" ]	Let us assume the total work to be done is 120 units. According to the question, Ram and Shyam finish the work in 30 days which implies 4 units of work is done by them in a single day, i.e., R + S = 4. ------ (1) Also, Ram works for 16 days and the remaining work is finished by Shyam in 44 days, i.e., 16R + 44S = 120 ------ (2) Equating the equations (1) and (2), S = 2 units and R = 2 units. Shyam alone finishes 2 units of work in one day. Therefore, the number of days taken by Shyam alone to finish the whole work = 120/2 = 60 days. ANSWER:C The answer is: C	C
mathematics	In a group of 28 junior high school students, 7 take French, 10 take Spanish, and 2 take both languages. The students taking both French and Spanish are not counted with the 7 taking French or the 10 taking Spanish. How many students are not taking either French or Spanish?	[ "7", "6", "9", "4", "8" ]	C 9 Add 7 + 10 + 2 to get 19 Then subtract 21 from the total students ⇒ 28 – 19 = 9. Answer is C The answer is: C	C
mathematics	All the water in container A which was filled to its brim was poured into two containers B and C. The quantity of water in container B was 62.5% less than the capacity of container A. If 152 liters was now transferred from C to B, then both the containers would have equal quantities of water. What was the initial quantity of water in container A?	[ "1289", "1198", "281", "1216", "282" ]	Explanation: B has 62.5% or (5/8) of the water in A. Therefore, let the quantity of water in container A(initially) be 8k. Quantity of water in B = 8k - 5k = 3k. Quantity of water in container C = 8k - 3k = 5k Container: A B C Quantity of water: 8k 3k 5k It is given that if 152 liters was transferred from container C to container B, then both the containers would have equal quantities of water. 5k - 152 = 3k + 152 => 2k = 304 => k = 152 The initial quantity of water in A = 8k = 8 * 152 = 1216 liters. Answer: Option D The answer is: D	D
mathematics	A certain factory employed 600 men and 400 women and the average wager was Rs. 25.50 per day, If a woman got Rs. 5 less than a man, then what are their daily wages ?	[ "27.50,22.59", "27.50,22.50", "27.50,32.50", "27.70,22.59", "27.50,22.51" ]	Explanation: Let the daily wage of a man be Rs. x. Then, daily wage of a woman = Rs. (x - 5). Now, 600x + 400 (x - 5) = 25.50 * (600 + 400) <=> 1000x = 27500 <=> x = 27.50. Man's daily wages = Rs. 27.50; Woman's daily wages = (x - 5) = Rs. 22.50. Answer: B) m:27.50 w:22.50 The answer is: B	B
mathematics	If x + (1/x) = 5, what is the value Q of x^2 + (1/x)^2?	[ "Q=21", "Q=22", "Q=23", "24", "27" ]	Squaring on both sides, x^2 + (1 /x)^2 + 2(x)(1/x) = 5^2 x^2 + (1 /x)^2 = 23 Answer: C The answer is: C	C
mathematics	Arabica coffee costs $0.4 per ounce while Robusta coffee costs $0.3 per ounce. If the blend of Arabica and Robusta costs $0.37 per ounce, what is the share of Arabica in this blend?	[ "20%", "24%", "70%", "33%", "40%" ]	a= amount of arabica coffee 1-a = amount of robusta coffee. because if you subtract a from the 1 ounce, the remaining amount is robusta therefore: .4a + .3(1-a) = .37 .4a + .3 - .3a = .37 a= .7 therefore: .7/1 ounce = 70%. Therefore, the answer should be C The answer is: C	C
mathematics	90 students represent x percent of the boys at Jones Elementary School. If the boys at Jones Elementary make up 20% of the total school population of x students, what is x?	[ "125", "150", "212", "250", "500" ]	90=x/10020/100x=>x^2 = 9*10000/2 = > x =212 C The answer is: C	C
mathematics	A shirt goes on sale for 60% of its original price. One week later, the sale price is marked down 10%. The final price is what percent of the original price?	[ "72%", "70%", "52%", "50%", "28%" ]	Just assume original price is 100. Sale price = 60 Then it is marked down by 10% = 60-6=52. Hence it is 52% od the original price. Hence answer is C. The answer is: C	C
mathematics	Two numbers are in the ratio of 6 : 8. If 10 is subtracted from each, the new numbers are in the ratio 16 : 32. Find the smaller number.	[ "22", "12", "38", "15", "17" ]	Explanation: Let the number be 6x and 8x. Then, (6x – 10) / (8x – 10) = 1 / 2 2 (6x – 10) = (8x – 10) 12x – 20 = 8x – 10 4x = 10 x = 2.5 The smaller number = (6 x 2.5) = 15 ANSWER D The answer is: D	D
mathematics	If s and t are positive integers such that s/t = 43.18, which of the following could be the remainder when s is divided by t ?	[ "44", "17", "54", "20", "47" ]	s/t= 43.18 s = 43.18t s = (43 + 0.18)t s = 43t + (18/100)t s = 43t + (9/50)t So remainder will be multiple of 9. The only multiple of 9 is 54. Ans. C The answer is: C	C
mathematics	Mr. Jones sold two pipes at $1.20 each. Based on the cost, his profit one was 20% and his loss on the other was 20%. On the sale of the pipes, he:	[ "lost 4 cents", "broke even", "gained 4 cents", "lost 10 cents", "gained 10 cents" ]	B broke even 20 % profit on $ 1.20 = $ 20/100 × 1.20 = $ 0.20 × 1.20 = $ 0.24 Similarly, 20 % loss on $ 1.20 = $ 20/100 × 1.20 = $ 0.20 × 1.20 = $ 0.24 Therefore, in one pipe his profit is $ 0.24 and in the other pipe his loss is $ 0.24. Since both profit and loss amount is same so, it’s broke even. The answer is: B	B
mathematics	A and B invests Rs.10000 each, A investing for 8 months and B investing for all the 12 months in the year. If the total profit at the end of the year is Rs.35000, find their shares?	[ "s.14000, Rs.15020", "s.14000, Rs.15700", "s.10000, Rs.21090", "s.10000, Rs.21000", "s.14000, Rs.21000" ]	The ratio of their profits A:B = 8:12 = 2:3 Share of A in the total profit = 2/5 * 35000 = Rs.14000 Share of A in the total profit = 3/5 * 35000 = Rs.21000 Answer: E The answer is: E	E
mathematics	Buses A and B start from a common bus stop X. Bus A begins to travel in a straight line away from bus B at a constant rate of 40 miles per hour. One hour later, bus B begins to travel in a straight line in the exact opposite direction at a constant rate of 80 miles per hour. If both buses travel indefinitely, what is the positive difference, in minutes, between the amount of time it takes bus B to cover the exact distance that bus A has covered and the amount of time it takes bus B to cover twice the distance that bus A has covered?	[ "36", "72", "132", "144", "180" ]	1st part: - In 1hr, Bus A covers 30 miles. Relative speed of bus ABus B is (80-30) = 50mph. So time required for Bus B to cover the exact distance as A is 50t = 30 t=3/5 = 36min 2nd part 80t=2d - B has to cover twice the distance 30*(t+1) = d - A traveled 1hr more and has to travel only only d so d/30 - 2d/80 = 1 D=120 T= 3hrs = 180 min Question asks for +ve difference between part 1 and part 2 in minutes = 180-36 = 72min B The answer is: B	B
mathematics	Shanmukham buys good worth Rs. 6650. He gets a rebate of 6% on it. After getting the rebate, he pays sales tax @ 10%. Find the amount he will have to pay for the goods	[ "6999.2", "6876.1", "6654", "7000", "None of these" ]	Explanation : Rebate = 6% of Rs. 6650 = Rs. 6/100 x 6650 = Rs. 399. Sales tax = 10% of Rs. (6650 399) = Rs. 10/100 x 6251 = Rs. 625.10 Final amount = Rs. (6251 + 625.10) = Rs. 6876.10 Answer : B The answer is: B	B
mathematics	A man can row downstream at 16 kmph and upstream at 12 kmph. Find the speed of the man in still water .	[ "14", "13", "12", "16", "15" ]	Let the speed of the man in still water and speed of stream be x kmph and y kmph respectively. Given x + y = 16 --- (1) and x - y = 12 --- (2) From (1) & (2) 2x = 28 => x = 14, y = 2. Answer:A The answer is: A	A
mathematics	Working alone, Printers X, Y, and Z can do a certain printing job, consisting of a large number of pages, in 12, 20, and 20 hours, respectively. What is the ratio of the time it takes Printer X to do the job, working alone at its rate, to the time it takes Printers Y and Z to do the job, working together at their individual rates?	[ "4/11", "1/2", "15/22", "10/1", "11/4" ]	P1 takes 12 hrs Rate for P2P3 together = 1/20 + 1/20 = 1/10 Therefore they take 10 Ratio = 10/1 = D The answer is: D	D
mathematics	Three numbers are in the ratio 3:5:8. The largest number value is 152. Find difference between Smallest & largest number is?	[ "16", "90", "38", "95", "78" ]	Explanation: == 3:5:8 Total parts = 16 = The largest number value is 152 = The largest number is = 8 = Then 8 parts -----> 152 ( 8 * 19 = 152 ) = smallest number = 3 & Largest number = 8 = Difference between smallest number & largest number is = 8 - 3 = 5 = Then 5 parts -----> 95 (5 * 19 = 95) Answer: Option D The answer is: D	D
mathematics	A waiter's salary consists of his salary and tips. During one week his tips were 7/4 of his salary. What fraction of his income came from tips ?	[ "4/9", "5/4", "5/8", "5/9", "7/11" ]	Income = salary (s) +tips = s + s7/4 = s11/4 Tips = s7/4 fraction of his income came from tips = (s7/4)/(s*11/4)= 7/11 ANSWER:E The answer is: E	E
mathematics	Solve the given two equations and find the inequality of X and Y. (a) x^2 = 729 and (b) Y= (729)^(1/2)	[ "If x>y", "If x>=y", "If x < y", "If x<=y", "x=y or relationship cannot be established" ]	Solution:- X=+27, -27 and Y= +27 Comparing we get X<=Y D The answer is: D	D
mathematics	In an election between two candidates, 70% of the voters cast their votes, out of which 4% of the votes were declared invalid. A candidate got 655200 votes which were 75% of the total valid votes. Find the total number of votes enrolled in that election.	[ "1300000", "12500", "14000", "12000", "None of these" ]	Explanation : Solution: let the total number of votes enrolled be x. then, number of votes cast = 70% of x. valid votes = 96% of(70% of x). .'. 75% of(96% of (70% of of x)) = 655200. (75/100 * 96/100 * 70/100 * x) = 655200. => x = (655200100100100)/(7596*70) = 1300000 Answer : A The answer is: A	A
mathematics	The sum of five numbers is 655. The average of the first two numbers is 85 and the third number is 125. Find the average of the two numbers?	[ "150", "180", "190", "200", "250" ]	Let the five numbers be P, Q, R, S and T. => P + Q + R + S + T = 655. (P + Q)/2 = 85 and R = 125 P + Q = 170 and R = 125 P + Q + R = 295 S + T = 655 - (P + Q + R) = 360 Average of the last two numbers = (S + T)/2 = 180. ANSWER B The answer is: B	B
mathematics	The ratio of the present age of two brothers is 1:2 and 5 years back, the ratio was 1:3. What will be the ratio of their ages after 5 years?	[ "3:9", "3:0", "ratio 3:5", "3:2", "3:1" ]	Let the present ages of the two brothers be x and 2x years respectively. Then, (x - 5)/(2x - 5) = 1/3 3(x - 5) = (2x - 5) => x = 10 Required ratio = (x + 5) : (2x + 5) = 15 : 25 = 3:5 Answer: C The answer is: C	C
mathematics	A room is 6 meters 24 centimeters in length and 4 meters 32 centimeters in width. Find the least number of square tiles of equal size required to cover the entire floor of the room?	[ "110", "124", "96", "117", "127" ]	Length = 6 m 24 cm = 624 cm Width = 4 m 32 cm = 432 cm HCF of 624 and 432 = 48 Number of square tiles required = (624 * 432)/(48 * 48) = 13 * 9 = 117 ANSWER:D The answer is: D	D
mathematics	The average weight of a group of boys is 30 kg. After a boy of weight 33 kg joins the group, the average weight of the group goes up by 1 kg. Find the number of boys in the group originally ?	[ "4", "8", "5", "2", "9" ]	Let the number off boys in the group originally be x. Total weight of the boys = 30x After the boy weighing 33 kg joins the group, total weight of boys = 30x + 33 So 30x + 33 + 31(x + 1) = > x = 2. Answer: D The answer is: D	D
mathematics	The volume of water in a certain tank is x percent greater than it was one week ago. If r percent of the current volume of water in the tank is removed, the resulting volume will be 90 percent of the volume it was one week ago. What is the value of r in terms of x?	[ "x+10", "10x+1", "100(x+10)", "100( x+10/x+100)", "100 ( 10x+1/10x+10)" ]	Given that, the water was increased by x percent -> then reduced by r percent -> to 90 percent of what it was one week ago. Consider, the 100 units of water was increased by 20% to 120 units -> then reduced by 25% of 120 (i.e. by 30 units) -> to 90 units. i.e. Pick numbers as x = 20% and r = 25% Substitute x=20 and identify the answer that gives r=25 A) x+10 --20+1=30 b) 10x+1 --200+1=201 c) 100(x+10) --100(20+10)=3000 d) 100( x+10/x+100) --100(20+10/20+100) = 100(30/120)=25 e) 100 ( 10x+1/10x+10) -- 100(200+1/200+10)= 100(201/210) Hence choice(D) is the answer. The answer is: D	D
mathematics	The combined salaries of three brothers is $135,000. Mr. Big earns twice what Mr. Small earns, and Mr. Middle earns 1 1/2 times what Mr. Small earns. What is the smallest salary of the three brothers?	[ "20,000", "22,000", "25,000", "30,000", "40,000" ]	Mr. Small = x; Mr. Middle = 3/2x; Mr. Big = 2x. x + 3/2x + 2x = 135 --> x=30 Answer: D The answer is: D	D
mathematics	Two trains are running at 40 km/hr and 20 km/hr respectively in the same direction. Fast train completely passes a man sitting in the slower train in 5 sec. What is the length of the fast train?	[ "27 7/8", "27 9/9", "28 7/9", "27 7/9", "21 7/9" ]	Relative speed = (40 - 20) = 20 km/hr. = 20 * 5/ 18 = 50/9 m/sec. Length of faster train = 50/9 * 5 = 250/9 = 27 7/9 m. Answer: D The answer is: D	D
mathematics	If 2*f(x) - f(1/x) = x2x2 , then f(x) is?	[ "f(x) = 3{2x2x2 + (1x)2(1x)9 }", "f(x) = 3{2x2x2 + (1x)2(1x)2 }", "f(x) = 3{2x2x2 + (1x)2(1x)3 }", "f(x) = 3{2x2x2 + (1x)2(1x)4 }", "f(x) = 3{2*x2x2 + (1x)2(1x)1 }" ]	2f(x) - f(1/x) = x2x2 ..............(1) Take x = (1/x), 2(1/x) - f(x) = (1x)2(1x)2 ...............(2) Add: 2 (equation 1) + equation 2 3f(x) = 2x2x2+ (1x)2(1x)2 f(x) = {2*x2x2 + (1x)2(1x)2}/3 Answer:B The answer is: B	B
mathematics	If 7^q is a factor of the product of the integers from 1 to 100, inclusive, what is the largest value of q?	[ "12", "13", "14", "15", "16" ]	So the question just means that we have to find all the multiples q of 7 between 1 to 100 So there are 14 multiples of 7 ( 7 - 98) But 49 and 98 contain two 7's as factors so we have to add 14 + 2 = 16 E The answer is: E	E
mathematics	In how many different ways can the letters of the word ATRIUMS be arranged in such a way that the vowels occupy only the even positions?	[ "72", "96", "120", "144", "180" ]	The 3 vowels can be arranged in 3 even places in 3! ways. The 4 consonants can be arranged in 4 odd places in 4! ways. The number of arrangements with vowels in even positions = 3! Ã— 4! = 6 Ã— 24 = 144 The answer is D. The answer is: D	D

mathematics

When n is divided by 13, the remainder is 6. When n is divided by 11, the quotient is equal to Z, and the remainder is equal to 6. Z must be divisible by which of the following numbers?

[ "13", "14", "15", "16", "17" ]

N = 139 q + 6 N = 11 z + 6 Equating 13Q + 6= 11z+6 11z=193 11z/13 = q since q is an integer Z must be divisible by 19. Hence A The answer is: A

A

mathematics

Six years ago, the ratio of the ages of Kunal and Sagar was 6:5, Four years hence, the ratio of their ages will be 11:10. What is Sagar age at present

[ "22", "17", "15", "16", "12" ]

Let six years ago the age of Kunal and Sagar are 6x and 5x resp. then, =>(6x+6)+4(5x+6)+4=1110 =>(6x+6)+4(5x+6)+4=1110 <=>10(6x+10)=11(5x+10) <=>10(6x+10)=11(5x+10) <=>5x=10=>x=2 <=>5x=10=>x=2 So Sagar age is (5x+6) = 16 Answer: D The answer is: D

D

mathematics

Can you get total of 720 by using six zeros 0,0,0,0,0,0 and any maths operators.

[ "650", "550", "700", "720", "500" ]

D 720 (0!+0!+0!+0!+0!+0!)! =(1+1+1+1+1+1)! =(5)! =6! is 6*5*4*3*2*1=720 The answer is: D

D

mathematics

The combined area of the two black squares is equal to 1000 square units. A side of the larger black square is 8 units longer than a side of the smaller black square. What is the combined area of the two white rectangles in square units?

[ "928", "936", "948", "968", "972" ]

The length of a smaller square - x; The length of a larger square - x+8; The area of entire square - x^2+(x+8)^2=1000 --> 2x^2+16x=936; The combined area of the two white rectangles - x(x+8)+x(x+8)=2x^2+16x --> look up: 2x^2+16x=936. Answer: B. The answer is: B

B

mathematics

Find the invalid no.from the following series 3, 7, 15, 31, 63, 123, 255

[ "3", "7", "27", "63", "123" ]

Go on multiplying the number by 2 and adding 1 to it to get the next number.So, 123 is wrong. E The answer is: E

E

mathematics

The greatest number which on dividing 1657 and 2037 leaves remainders 6 and 5 respectively, is:

[ "123", "127", "235", "305", "505" ]

Explanation: Required number = H.C.F. of (1657 - 6) and (2037 - 5) = H.C.F. of 1651 and 2032 = 127. Answer: B The answer is: B

B

mathematics

The function f is defined for all positive integers m by the following rule. f(m) is the number of positive integers each of which is less than m and has no positive factor in common with m other than 1. If p is any prime, number then f(p)=

[ "p-1", "p-2", "(p+1)/2", "(p-1)/2", "2" ]

If not the wording the question wouldn't be as tough as it is now. The GMAT often hides some simple concept in complicated way of delivering it. This question for instance basically asks: how many positive integers are less than given prime number p which have no common factor with p except 1. Well as p is a prime, all positive numbers less than p have no common factors with p (except common factor 1). So there would be p-1 such numbers (as we are looking number of integers less than p). For example: if p=8 how many numbers are less than 8 having no common factors with 8: 1, 2, 3, 4, 5, 6, 7 --> 8-1=7. Answer: A. The answer is: A

A

mathematics

The difference between the place values of 6 and 5 in the number 826533 is

[ "5500", "4500", "2500", "6970", "None" ]

Sol. = (Place value of 6) – (place Value of 5) = (6000 - 500) = 5500 Answer A The answer is: A

A

mathematics

If Rs. 782 be divided into three parts, proportional to 1/2:2/3:3/4, then the second part is?

[ "A)426", "B)526", "C)207", "D)204", "E)272" ]

Given ratio = 1/2:2/3:3/4 = 6:8:9 1st part = 782 * 8/23 = Rs. 272 Answer:E The answer is: E

E

mathematics

A survey of n people in the town of Eros found that 50% of them preferred Brand A. Another survey of 120 people in the town of Angie found that 60% preferred Brand A. In total, 55% of all the people surveyed together preferred Brand A. What is the total number of people surveyed?

[ "50", "100", "150", "200", "240" ]

It is simply a weighted average question. Since the given average of 50% and 60% is 55% (right in the middle), it means the number of people surveyed in Eros (n) is same as the number of people surveyed in Angie. So n = 120 Total = 120 + 120 = 240 Answer (E) The answer is: E

E

mathematics

What should come in place of the question mark (?) in the following number series? 11 21 33 47 63 ?

[ "80", "81", "82", "83", "84" ]

The numbers increase by 10, 12, 14, 16,... The next number should be 63+18 = 81 The answer is B. The answer is: B

B

mathematics

trees of heights 30 and 40 sepatated by a river. fish in the river is at equal dis from top of the trees where two birds are there.ratio of the distances from fish to the root of the trees?

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

40/30 is the ratio of distance from fish to root of trees 4:3 ANSWER:A The answer is: A

A

mathematics

In an election between two candidates, 75 % of the voters cast their votes, out of which 2% of the votes were declared invalid. A candidate got 9261 votes which were 75% of the total valid votes. Find the total number of votes

[ "16800", "15800", "16700", "15700", "None of these" ]

Explanation: Let the total number of votes enrolled are x. Number of votes cast = 75% of x Valid votes = 98% of 75% of x Now, as 9261 is the 75% of valid casted votes so, 75% of 98% of 75% of x = 9261 [imporant] =>75×98×75×x100×100×100=9261=>x=16800 Answer: Option A The answer is: A

A

mathematics

For four days of work, a clerk had daily earnings of $160, $150, $160, and $160 respectively. In which of the following intervals does the standard deviation of the daily earnings lie?

[ "Between $10 and $50", "Between $0 and $10", "Between $20 and $25", "Between $50 and $100", "Between $50 and $65" ]

The standard deviation is between 0 and 10. The reason is that none of the numbers in the set is further away from the mean than 10(or rather Abs(150-(160*3+150)/4)). I am not fully sure how to calculate the standard deviation(I simply remember that there were some formula for calculating the average of the squared distances from the mean for all items in the set from statistics classes - variation), but I believe this will suffice for any GMAT question related to standard deviation. Answer : B The answer is: B

B

mathematics

A bag contains 7 red balls, 5 green balls and 6 white balls. A ball is drawn at random from the box. What is the probability that the ball drawn is either red or green?

[ "2/3", "3/5", "1/5", "7/15", "8/15" ]

Total number of balls = (7 + 5 + 6) = 18. Therefore, n(S) = 18. Let E1 = event of drawing a red ball. and E2 = event of drawing a green ball. Then, E1 n E2 = f. P (E1 n E2) = P(E1) + P(E2) = (7/18 + 5/18) = 2/3. ANSWER:A The answer is: A

A

mathematics

6, 11, 21, 36, 56, ?

[ "65", "78", "81", "97", "98" ]

The pattern is + 5, + 10, + 15, + 20,... Answer : C. The answer is: C

C

mathematics

A team of 6 cooks is chosen from 7 men and 5 women. The team must have at least 2 men and at least 3 women. How many ways can this team be created?

[ "140", "320", "560", "455", "840" ]

Only possible combinations are a team of 2M, 4 W or 3M,3W. Possible ways to make a team of 2M,4W = 7C2 * 5C4 =21*5 =105 Possible ways to make a team of 3M,3W = 7C3* 5C3 = 35*10 = 350 Total possible ways = 105+350 = 455 Ans D it is. The answer is: D

D

mathematics

A person started from point A to point B and returned back to A with a speed of 60 kmh. If the distance between A and B is 120km, calculate the time he travelled

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

Time = Distance/Speed Total distance = (from A->B and from B->A) = 120+120=240 km Speed = 60 kmh 240/60 = 4 Answer: A The answer is: A

A

mathematics

Jack and Paul are running 1000m. Jack runs 1.5Km/hr faster than Paul but also finishes the race 1.5 sec earlier. What is the speed of Jack??

[ "20.61", "21.61", "22.61", "23.61", "24.61" ]

distance(given) 1000m paul speed(let)= x m/s time(paul take)= 1000/x sec jack speed= x + 1.5*(5/18) m/s tym (jack)= 1000/(x+7.5/18) s tym(paul) - tym (jack) = 1.5 solving for x we get 20.20 speed of jack is 20.20+ 7.5/18=20.61 ANSWER:A The answer is: A

A

mathematics

12 + 13 + 14 + ... 61 + 62 + 63 = ?

[ "1361", "1362", "1950", "1364", "1365" ]

Sum = 12 + 13 + 14 + ... 61 + 62 + 63 Sum of n consecutive positive integers starting from 1 is given as n(n+1)/2 Sum of first 63 positive integers = 63*64/2 Sum of first 11 positive integers = 11*12/2 Sum = 12 + 13 + 14 + ... 61 + 62 + 63 = 63*64/2 - 11*12/2 = 1950 Answer : C The answer is: C

C

mathematics

Rs.2500 is divided into two parts such that if one part be put out at 5% simple interest and the other at 6%, the yearly annual income may be Rs.140. How much was lent at 5%?

[ "2288", "27669", "1766", "1000", "2871" ]

(x*5*1)/100 + [(2500 - x)*6*1]/100 = 140 X = 1000 Answer: D The answer is: D

D

mathematics

The triplicate ratio of 1:6 is?

[ "1:7", "1:8", "1:3", "1:1", "1:216" ]

1^3: 6^3 = 1:216 Answer: E The answer is: E

E

mathematics

A 8000 liter tank, half-full of water is being filled from a pipe with a flow rate of 1 kiloliter every 2 minutes. At the same time, the tank is losing water from two drains at a rate of 1 kiloliter every 4 minutes and every 6 minutes. How many minutes does it take to fill the tank completely?

[ "8", "12", "18", "24", "48" ]

In: we have: 1,000/2min = 500 litres per minute Out: we have: 1,000/4 + 1,000/6 Then do: IN - OUT to figure out the net inflow per minute (you get 83.3). Then divide the total number of litres you need (4,000 by that net inflow to get the minutes) - 48 min. Answer E. The answer is: E

E

mathematics

Find the value of x from this equation? 7(x - 1) = 21

[ "2", "4", "6", "8", "10" ]

1. Divide both sides by 7: 2. Simplify both sides: x - 1 = 3 3. Add 1 to both sides: x - 1 + 1 = 3 + 1 4. Simplify both sides: x = 4 B The answer is: B

B

mathematics

Baseball's World Series matches 2 teams against each other in a best-of-seven series. The first team to win four games wins the series and no subsequent games are played. If you have no special information about either of the teams, what is the probability w that the World Series will consist of fewer than 7 games?

[ "12.5%", "25%", "31.25%", "68.75%", "75%" ]

In order to determine the probability that the World Series will last less than 7 games, we can first determine the probability w that the World Series WILL last exactly 7 games and then subtract this value from 1. In order for the World Series to last exactly 7 games, the first 6 games of the series must results in 3 wins and 3 losses for each team. Let's analyze one way this could happen for Team 1: Game 1 Game 2 Game 3 Game 4 Game 5 Game 6 T1 Wins T1 Wins T1 Wins T1 Loses T1 Loses T1 Loses There are many other ways this could happen for Team 1. Using the permutation formula, there are 6!/(3!)(3!) = 20 ways for Team 1 to win 3 games and lose 3 games in the first 6 games. Logically, there are also 20 ways for Team 2 to win 3 games and lose 3 games in the first 6 games. Thus, there are a total of 40 ways for the World Series to last the full 7 games. The probability that any one of these 40 ways occurs can be calculated from the fact that the probability of a team winning a game equals the probability of a team losing a game = 1/2. Given that 7 distinct events must happen in any 7 game series, and that each of these events has a probability of 1/2, the probability that any one particular 7 game series occurs is. Since there are 40 possible different 7 game series, the probability that the World Series will last exactly 7 games is: Thus the probability that the World Series will last less than 7 games is 100% - 31.25% = 68.75%. The correct answer is D. The answer is: D

D

mathematics

A and B can do a work in 4 hours and 12 hours respectively. A starts the work at 6AM and they work alternately for one hour each. When will the work be completed?

[ "7 days", "9 days", "4 days", "6 days", "2 days" ]

Work done by A and B in the first two hours, working alternately = First hour A + Second hour B = 1/4 + 1/12 = 1/3. Total time required to complete the work = 2 * 3 = 6 days. Answer: D The answer is: D

D

mathematics

In a country named "gpuzzles" 1/2 of 5 = 3. If the same proportion holds, what is the value of 1/3 of 10 ?

[ "2", "5", "6", "9", "4" ]

E 4 5/2 = 3 and 10/3 = x (10/3)/(5/2) = 20/15 = 4/3 So x/3 = 4/3 x=4 The answer is: E

E

mathematics

An amount of money is to be divided between P, Q and R in the ratio of 3:7:12. If the difference between the shares of P and Q is Rs.4000, what will be the difference between Q and R's share?

[ "2788", "5000", "7282", "2782", "2729" ]

4 --- 4000 5 --- ? => 5000 Answer:B The answer is: B

B

mathematics

A 25% stock yielding 20% is quoted at:

[ "s. 83.33", "s. 110", "s. 112", "s. 125", "s. 140" ]

Income of Rs 20 on investment of Rs 100 Income of Rs 25 on investment of ? = (25*100)/20=125 ANSWER:D The answer is: D

D

mathematics

A certain team has 8 members, including Joey. A three-member relay team will be selected as follows: one of the 8 members is to be chosen at random to run first, one of the remaining 7 members is to be chosen at random to run second, and one of the remaining 6 members is to be chosen at random to run third. What is the probability that Joey will be chosen to run second or third?

[ "2/3", "1/4", "2/5", "3/8", "3/10" ]

Each member has an equal probability to run second (1/8) or third (1/8). The probability that Joey runs second or third is 1/8 + 1/8 = 1/4 The answer is B. The answer is: B

B

mathematics

There is a 50% chance Jen will visit Chile this year, while there is a 25% chance that she will visit Madagascar this year. What is the probability that Jen will visit either Chile or Madagascar this year, but NOT both?[/b]

[ "25%", "50%", "62.5%", "63.5%", "75%" ]

The thing to note in the question is she would not be visiting both. Thus p(Chile)*(1-p(Madagascar))+p(Madagascar)*(1-p(Chile)) which is (1/2*3/4) + (1/4*1/2), 3/8*1/8=1/2 =50% Answer: B The answer is: B

B

mathematics

The average weight of 7 person's increases by 6.2 kg when a new person comes in place of one of them weighing 76 kg. What might be the weight of the new person?

[ "160 kg", "175 kg", "180.7 kg", "119.4 kg", "190.8 kg" ]

Total weight increased = (7 x 6.2) kg = 43.4 kg. Weight of new person = (76 + 43.4) kg = 119.4 kg Option D The answer is: D

D

mathematics

The width of a rectangle is 10mtr and its area is 150 square meter. If length of the rectangle is increased, then its new area is 1(1/3) times of the original area. What is the new perimeter of the rectangle?

[ "45", "54", "67", "60", "69" ]

Ans.(D) Sol. Length of original rectangle = 150/10 = 15 (10*(15+x))/(10*15) = 4/3 x = 5 Perimeter of new rectangle = 2(10+20) = 60 The answer is: D

D

mathematics

A rectangular field is to be fenced on three sides leaving a side of 8 feet uncovered.If the area of the field is 680 sq.ft, how many feet of fencing will be required?

[ "244ft", "88ft", "122ft", "178ft", "66ft" ]

Given that length and area, so we can find the breadth. Length x Breadth = Area 8 x Breadth = 680 Breadth = 85 feet Area to be fenced = 2B + L = 2 (85) + 8 = 178 feet Answer: D) 178ft The answer is: D

D

mathematics

Stacy and Heather are 5 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?.

[ "2.5mile", "1.9mile", "1.7mile", "1.5mile", "1.18mile" ]

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 5 -2.4 = 2.6 Time taken = Distance/ Speed = 2.6/11 = 0.23 hrs Heather will cover = 5*0.23 = 1.18miles. Answer E The answer is: E

E

mathematics

John is traveling to a meeting that is 22 miles away. He needs to be there in 30 minutes. How fast does he need to go to make it to the meeting on time?

[ "25 mph", "44 mph", "41 mph", "49 mph", "56 mph" ]

Well 44mph. B. Time*rate=distance --> 0.5*rate=22 --> rate=44 The answer is: B

B

mathematics

The average age of a group of persons going for picnic is 16 years. Twenty new persons with an average age of 15 years join the group on the spot due to which their average age becomes 15.5 years. The number of persons initially going for picnic is?

[ "10", "20", "37", "26", "22" ]

Let the initial number of persons be x. Then, 16x + 20 * 15 = 15.5 (x + 20) <=> 0.5x = 10 <=> x = 20. Answer: B The answer is: B

B

mathematics

If x^2 − 2x − 15 = (x + r)( x + s) for all values of x, and if r and s are constants, then which of the following is a possible value of 2(r − s)?

[ "8", "16", "− 2", "− 3", "− 5" ]

We know that given ax^2 + bx + c = 0, Sum of the roots = -b/a and product of the roots = c/a. The roots here are -r and -s. -r - s = -(-2)/1 = r + s = -2 (-r)*(-s) = -15/1 = rs So one of r and s is -5 and the other is 3. So 2(r - s) could be 16 or -16. Answer (B) The answer is: B

B

mathematics

The profit earned by selling an article for Rs 900 is double the loss incurred when the same article is sold for Rs.490. At what price should the article be sold to make 25% profit?

[ "715", "469", "400", "750", "850" ]

Explanation: Let C.P be Rs. x 900 - x = 2(x - 450) => x = Rs.600 C.P = 600 gain required is 25% S.P = [(100 + 25) × 600]/100 = Rs.750 Answer: D The answer is: D

D

mathematics

Marcella has 26 pairs of shoes. If she loses 9 individual shoes, what is the greatest number of matching pairs she could have left?

[ "21", "20", "19", "16", "15" ]

Marcella has 26 pairs of shoes and loses 9 shoes. To minimize the loss of identical pairs of shoes we want Marcella to lose as many identical pairs as possible. This would yield 4 identical pairs and 1 additional shoe (destroying 5 pairs of shoes). The 26 pairs of shoes minus the 5 'destroyed' pairs yields 21 pairs that still fulfill the requirements. Answer: A The answer is: A

A

mathematics

Tickets numbered 1 to 20 are mixed up and then a ticket is drawn at random. What is the probability that the ticket drawn has a number which is a multiple of 3 or 5?

[ "2/5", "9", "9/5", "1/5", "9/20" ]

Here, S = {1, 2, 3, 4, ...., 19, 20}. Let E = event of getting a multiple of 3 or 5 = {3, 6 , 9, 12, 15, 18, 5, 10, 20}. P(E) = n(E)/n(S) = 9 /20 The answer is: E

E

mathematics

Each of seven different locks has a matching key. The keys are randomly reassigned to the locks. What is the probability that exactly two of the keys fit the locks to which they are reassigned?

[ "1/8", "1/6", "1/49", "3/8", "1/2" ]

I was just going over probability questions. can some one explain me what's wrong in my approach here. Probability of choosing one right key out of 7 is 1/7. Probability of choosing another right key is 1/7. since the question is asking for 2 right keys , probability is multiplication of both = 1/7 * 1/7 = 1/49. Ans C The answer is: C

C

mathematics

In what time will a cart 50 m long cross, if its speed be 36 km/hr?

[ "25", "5", "15", "20", "30" ]

Speed = 36 * 5/18 = 10 m/sec Time taken = 50/10 = 5 sec. Answer:B The answer is: B

B

mathematics

The difference between a number and its two-fifth is 510. What is 12% of that number?

[ "58", "110", "76", "102", "86" ]

Let the number be x. Then, x - 2/5 x = 510 x = (510 * 5)/3 = 850 12% of 850 = 102. Answer:D The answer is: D

D

mathematics

Find the odd man out. 2, 3, 5, 9, 12, 17, 23

[ "12", "9", "23", "2", "1" ]

Explanation : 2 2 + 1 = 3 3 + 2 = 5 5 + 3 = 8 8 + 4 = 12 12 + 5 = 17 17 + 6 = 23 ie, 8 should have come in place of 9. Answer : Option B The answer is: B

B

mathematics

The Delhi Express runs @ 144 kilometers per hours and it reaches destination 20 minute ahead of schedule. If it averages 100 km/hour, it reaches 24 minute behind schedule. What is the average speed it should maintain in order to reach the destination on schedule?

[ "250", "240", "230", "245", "235" ]

If the destination is D kilometer and the speed in order to reach on schedule is S km/hour, the time taken to reach on schedule is D/S hours Thus we get two equations: D/144 = D/S - 1/3 and D/100 = D/S + 2/5 and Subtracting the first equation from the second we get : 44D/14400 = 11/15 Thus D = 14400 x 11/ 44 x 15 = 240 ANSWER:B The answer is: B

B

mathematics

A train crosses a platform of 120 m in 15 sec, same train crosses another platform of length 180 m in 18 sec. then find the length of the train?

[ "298", "180", "289", "177", "123" ]

Length of the train be ‘X’ X + 120/15 = X + 180/18 6X + 720 = 5X + 900 X = 180m Answer: B The answer is: B

B

mathematics

What is the equation of a circle of radius 6 units centered at (3, 2)?

[ "x2 + y2 + 6x - 4y = 23", "x2 + y2 - 6x + 4y = 23", "x2 + y2 + 6x + 4y = 23", "x2 + y2 - 6x - 4y = -23", "x2 + y2 - 6x - 4y = 23" ]

Explanatory Answer Equation of a circle with center (a, b) and radius 'r' units is (x - a)2 + (y - b)2 = r2 Therefore, the equation of this circle = (x - 3)2 + (y - 2)2 = 62 i.e., x2 - 6x + 9 + y2 - 4y + 4 = 36 or x2 + y2 - 6x - 4y = 23 The correct choice is (E) The answer is: E

E

mathematics

In a nationwide poll, P people were asked 2 questions. If 2/5 answered “yes” to question 1, and of those 1/3 also answered “yes” to question 2, which of the following represents the number of people polled who did not answer “yes” to both questions?

[ "2/15*P", "3/5*P", "3/4*P", "5/6*P", "13/15*P" ]

no of people polled who did not answer “yes” to both questions = P - no of people polled who answered “yes” to both questions no of people who answered yes for the 2nd question = 1/3 * 2/5 * P = 2/15*P no of people polled who did not answer “yes” to both questions = P - 2/15*P = 13/15*P Hence, E will be the answer. The answer is: E

E

mathematics

A train moves fast a telegraph post and a bridge 264 m long in 8 sec and 20 sec respectively. What is the speed of the train?

[ "27.8 km/hr", "22.9 km/hr", "26.6 km/hr", "79.2 km/hr", "12.9 km/hr" ]

Let the length of the train be x m and its speed be y m/sec. Then, x/y = 8 => x = 8y (x + 264)/20 = y y = 22 Speed = 22 m/sec = 22 * 18/5 = 79.2 km/hr. Answer: D The answer is: D

D

mathematics

What is the next number in the sequence. 15 29 56 108 208 ?

[ "450", "400", "300", "500", "580" ]

B 400 Explanation: Begins with 15 2*15-1 => 29 2*29-2 => 56 2*56-4 => 108 2*108-8 => 208 2*208-16 => 400 The answer is: B

B

mathematics

To asphalt 1km road, 30 men spent 12 days working 8 hours per day. How many days, 20 men will spend to asphalt a road of 2km working 15 hours a day?

[ "23", "22", "21", "20", "19.2" ]

Man-hours required to asphalt 1 km road=30*12*8=2880 Man-hours required to asphalt 2 km road=2880*2=5760 Man-hours available per day=20*15=300 Therefore number of days=5760/300=19.2 days Ans=E The answer is: E

E

mathematics

A retailer bought a machine at a wholesale price of $99 and later on sold it after a 10% discount of the retail price. If the retailer made a profit equivalent to 20% of the whole price, what is the retail price of the machine?

[ "81", "100", "120", "132", "160" ]

My solution: Wholesale Price= 99 Retail Price, be = x He provides 10 % discount on Retail price= x-10 x/100 This Retail price = 20 % profit on Wholesale price x-10 x/100 = 99+ 1/5(99) x=132; ANSWER:D The answer is: D

D

mathematics

The true discount on a bill of Rs. 2460 is Rs. 360. What is the banker's discount?

[ "Rs. 432", "Rs. 422", "Rs. 412", "Rs. 442", "None of these" ]

Explanation : F = Rs. 2460 TD = Rs. 360 PW = F - TD = 2460 - 360 = Rs. 2100 True Discount is the Simple Interest on the present value for unexpired time =>Simple Interest on Rs. 2100 for unexpired time = Rs. 360 Banker's Discount is the Simple Interest on the face value of the bill for unexpired time = Simple Interest on Rs. 2460 for unexpired time =360/2100 × 2460 = 0.17 × 2460 = Rs. 422 Answer : Option B The answer is: B

B

mathematics

How many seconds will a 500 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?

[ "22", "30", "88", "266", "121" ]

Speed of train relative to man = 63 - 3 = 60 km/hr. = 60 * 5/18 = 50/3 m/sec. Time taken to pass the man = 500 * 3/50 = 30 sec. Answer:B: The answer is: B

B

mathematics

If 30% of 100 is greater than 50% of a number by 10, then the number is?

[ "40", "30", "60", "80", "50" ]

Let the number be x 30% of 100 - 50% of x = 10 50/100 x = (30/100 * 100)-10 x/2 = 20 x = 40 Answer is A The answer is: A

A

mathematics

A can do a piece of work in 10 days and B can do the same work in 12 days. A and B worked together for 2 days. How many more days are required to complete the remaining work if they work together?

[ "3 (5/18) days", "3 (7/11) days", "3 (5/11) days", "2 (5/11) days", "3 (2/11) days" ]

A can do 1/10 of the work in a day. B can do 1/12 of the work in a 1 day. Both of them together can do (1/10 + 1/12) part of work in 1 day = (6 + 5)/60 = 11/60 They take 60/11 days to complete the work together. Given that they already worked for 2 days. The number of days required to complete remaining work => 60/11 - 2 = 38/11 = 3 (5/11) days. Answer:C The answer is: C

C

mathematics

A man whose speed is 4.5 kmph in still water rows to a certain upstream point and back to the starting point in a river which flows at 1.5 kmph, find his average speed for the total journey?

[ "5", "4", "8", "9", "2" ]

M = 45 S = 1.5 DS = 6 US = 3 AS = (2 * 6 * 3) /9 = 4 Answer: B The answer is: B

B

mathematics

A can give B 100 meters start and C 200 meters start in a kilometer race. How much start can B give C in a kilometer race?

[ "111.12 m", "111.22 m", "111.19 m", "118.12 m", "311.12 m" ]

A runs 1000 m while B runs 900 m and C runs 800 m. The number of meters that C runs when B runs 1000 m, = (1000 * 800)/900 = 8000/9 = 888.88 m. B can give C = 1000 - 888.88 = 111.12 m.Answer:A The answer is: A

A

mathematics

If an item that originally sold for A dollars was marked up by x percent and then discounted by y percent, which of the following expressions represents the final price of the item?

[ "(A+ Ax/100) - Y/100 ( A +Ax/100)", "(10,000z + 100z(y – x) – xyz)/10,000", "(100z(x – y) – xyz)/10000", "(100z(y – x) – xyz)/10000", "10000 /(x – y)" ]

value of item =A ..marked up by x% = Ax/100 total value = A +ax/100 .discounted by Y% on Total Y/100 * ( A+Ax/100) Final price =(A+ Ax/100) - Y/100 ( A +Ax/100) A The answer is: A

A

mathematics

A shop sells two variants of chocolates - one that costs $3 and the other that costs $5. If the shop sold $131 chocolates on a given day, how many different combinations of (number of $3 sold, number of $5 sold) exist?

[ "3", "5", "7", "9", "11" ]

$131 = 25*$5 + 2*$3 We can find other combinations by reducing the $5 chocolates by 3 (which is -$15)and increasing the $3 chocolates by 5 (which is +$15). The number of $5 chocolates can be 25, 22, 19, 16,...,1 for a total of 9 combinations. The answer is D. The answer is: D

D

mathematics

A number is divided by 406 leaves remainder 115,what will be the remainder when it will be divided by 29?

[ "26", "30", "27", "28", "29" ]

Let the Number be N. So N=406x+115. Now divide this number by 29 As 406 is exactly divisible by 29,we have to divide 115 by 29 and find the remainder. So Remainder is 28 Option D is answer The answer is: D

D

mathematics

Using all the letters of the word "NOOKIASS", how many words can be formed, which begin with N and end with S?

[ "550", "160", "720", "620", "820" ]

There are five letters in the given word. Consider 8 blanks .... The first blank and last blank must be filled with N and S all the remaining three blanks can be filled with the remaining 6 letters in 6! ways. The number of words = 6! = 720. Answer: C The answer is: C

C

mathematics

Sonika deposited Rs.8000 which amounted to Rs.9200 after 3 years at simple interest. Had the interest been 0.5% more. She would get how much?

[ "9320", "96288", "26667", "1662", "2882" ]

(8000*3*0.5)/100 = 120 9200 -------- 9320 Answer:A The answer is: A

A

mathematics

Last year’s receipts from the sale of greeting cards during the week before Mother’s Day totaled $167 million, which represented 10 percent of total greeting card sales for the year. Total greeting card sales for the year totaled how many million dollars?

[ "1,650", "1,670", "1,890", "1,701", "3,210" ]

10% ---- 167 millions for 100% => ( 167 * 100% )/10% = 1670. Option B. The answer is: B

B

mathematics

If w/x = 1/3 and w/y = 3/4, then (x + y)/y =

[ "13/4", "6/5", "7/5", "8/5", "9/5" ]

W/X = 1/3=>x=3w and W/Y = 3/4=>y=(4/3)w (X+Y)/Y = (3w+4/3w)/(4/3w)=(13/3w)/(4/3w)=13/4 Correct Option: A The answer is: A

A

mathematics

A, B and C invest in the ratio of 3 : 4: 5. The percentage of return on their investments are in the ratio of 6 : 5 : 4. Find the total earnings, If B earns Rs. 250 more than A :

[ "2348", "7250", "2767", "1998", "2771" ]

Explanation: A B C investment 3x 4x 5x Rate of return 6y% 5y% 4y% Return \inline \frac{18xy}{100} \inline \frac{20xy}{100} \inline \frac{20xy}{100} Total = (18+20+20) = \inline \frac{58xy}{100} B's earnings - A's earnings = \inline \frac{2xy}{100} = 250 Total earning = \inline \frac{58xy}{100} = 7250 Answer: B) Rs.7250 The answer is: B

B

mathematics

Jim’s Taxi Service charges an initial fee of $2.05 at the beginning of a trip and an additional charge of $0.35 for each 2/5 of a mile traveled. What is the total charge for a trip of 3.6 miles?

[ "$5.20", "$4.45", "$4.80", "$5.05", "$5.40" ]

Let the fixed charge of Jim’s Taxi Service = 2.05 $ and charge per 2/5 mile(.4 mile) = .35$ Total charge for a trip of 3.6 miles = 2.05 + (3.6/.4) * .35 = 2.05 + 9*.35 = 5.2 $ Answer A The answer is: A

A

mathematics

If m=4p where p is a prime number greater than 2, how many different positive even divisors does m have, including m?

[ "two", "three", "four", "six", "eight" ]

m=2, 2, p (p is in the prime factorization since were told it is a prime number in the question) 2 4 (because of 2*2) 2p (because of 2 * p) 4p (because of 2 * 2 * p)=C The answer is: C

C

mathematics

In a pair of fractions, fraction A is twice the fraction B and the product of two fractions is 2/25. What is the value of fraction A?

[ "2/9", "2/2", "2/5", "2/6", "2/4" ]

Explanation: A = 2B => B = 1/2 A, so, AB = 2/25 1/2 A2 = 2/25 A2 = 4/25 A = 2/5 Answer:C The answer is: C

C

mathematics

Ram and Shyam together can do a piece of work in 30 days. Ram having worked for 16 days, Shyam finishes the remaining work alone in 44 days. In how many days shall Shyam finish the whole work alone?

[ "30 days", "40 days", "60 days", "70 days", "80 days" ]

Let us assume the total work to be done is 120 units. According to the question, Ram and Shyam finish the work in 30 days which implies 4 units of work is done by them in a single day, i.e., R + S = 4. ------ (1) Also, Ram works for 16 days and the remaining work is finished by Shyam in 44 days, i.e., 16R + 44S = 120 ------ (2) Equating the equations (1) and (2), S = 2 units and R = 2 units. Shyam alone finishes 2 units of work in one day. Therefore, the number of days taken by Shyam alone to finish the whole work = 120/2 = 60 days. ANSWER:C The answer is: C

C

mathematics

In a group of 28 junior high school students, 7 take French, 10 take Spanish, and 2 take both languages. The students taking both French and Spanish are not counted with the 7 taking French or the 10 taking Spanish. How many students are not taking either French or Spanish?

[ "7", "6", "9", "4", "8" ]

C 9 Add 7 + 10 + 2 to get 19 Then subtract 21 from the total students ⇒ 28 – 19 = 9. Answer is C The answer is: C

C

mathematics

All the water in container A which was filled to its brim was poured into two containers B and C. The quantity of water in container B was 62.5% less than the capacity of container A. If 152 liters was now transferred from C to B, then both the containers would have equal quantities of water. What was the initial quantity of water in container A?

[ "1289", "1198", "281", "1216", "282" ]

Explanation: B has 62.5% or (5/8) of the water in A. Therefore, let the quantity of water in container A(initially) be 8k. Quantity of water in B = 8k - 5k = 3k. Quantity of water in container C = 8k - 3k = 5k Container: A B C Quantity of water: 8k 3k 5k It is given that if 152 liters was transferred from container C to container B, then both the containers would have equal quantities of water. 5k - 152 = 3k + 152 => 2k = 304 => k = 152 The initial quantity of water in A = 8k = 8 * 152 = 1216 liters. Answer: Option D The answer is: D

D

mathematics

A certain factory employed 600 men and 400 women and the average wager was Rs. 25.50 per day, If a woman got Rs. 5 less than a man, then what are their daily wages ?

[ "27.50,22.59", "27.50,22.50", "27.50,32.50", "27.70,22.59", "27.50,22.51" ]

Explanation: Let the daily wage of a man be Rs. x. Then, daily wage of a woman = Rs. (x - 5). Now, 600x + 400 (x - 5) = 25.50 * (600 + 400) <=> 1000x = 27500 <=> x = 27.50. Man's daily wages = Rs. 27.50; Woman's daily wages = (x - 5) = Rs. 22.50. Answer: B) m:27.50 w:22.50 The answer is: B

B

mathematics

If x + (1/x) = 5, what is the value Q of x^2 + (1/x)^2?

[ "Q=21", "Q=22", "Q=23", "24", "27" ]

Squaring on both sides, x^2 + (1 /x)^2 + 2(x)(1/x) = 5^2 x^2 + (1 /x)^2 = 23 Answer: C The answer is: C

C

mathematics

Arabica coffee costs $0.4 per ounce while Robusta coffee costs $0.3 per ounce. If the blend of Arabica and Robusta costs $0.37 per ounce, what is the share of Arabica in this blend?

[ "20%", "24%", "70%", "33%", "40%" ]

a= amount of arabica coffee 1-a = amount of robusta coffee. because if you subtract a from the 1 ounce, the remaining amount is robusta therefore: .4a + .3(1-a) = .37 .4a + .3 - .3a = .37 a= .7 therefore: .7/1 ounce = 70%. Therefore, the answer should be C The answer is: C

C

mathematics

90 students represent x percent of the boys at Jones Elementary School. If the boys at Jones Elementary make up 20% of the total school population of x students, what is x?

[ "125", "150", "212", "250", "500" ]

90=x/100*20/100*x=>x^2 = 9*10000/2 = > x =212 C The answer is: C

C

mathematics

A shirt goes on sale for 60% of its original price. One week later, the sale price is marked down 10%. The final price is what percent of the original price?

[ "72%", "70%", "52%", "50%", "28%" ]

Just assume original price is 100. Sale price = 60 Then it is marked down by 10% = 60-6=52. Hence it is 52% od the original price. Hence answer is C. The answer is: C

C

mathematics

Two numbers are in the ratio of 6 : 8. If 10 is subtracted from each, the new numbers are in the ratio 16 : 32. Find the smaller number.

[ "22", "12", "38", "15", "17" ]

Explanation: Let the number be 6x and 8x. Then, (6x – 10) / (8x – 10) = 1 / 2 2 (6x – 10) = (8x – 10) 12x – 20 = 8x – 10 4x = 10 x = 2.5 The smaller number = (6 x 2.5) = 15 ANSWER D The answer is: D

D

mathematics

If s and t are positive integers such that s/t = 43.18, which of the following could be the remainder when s is divided by t ?

[ "44", "17", "54", "20", "47" ]

s/t= 43.18 s = 43.18t s = (43 + 0.18)t s = 43t + (18/100)t s = 43t + (9/50)t So remainder will be multiple of 9. The only multiple of 9 is 54. Ans. C The answer is: C

C

mathematics

Mr. Jones sold two pipes at $1.20 each. Based on the cost, his profit one was 20% and his loss on the other was 20%. On the sale of the pipes, he:

[ "lost 4 cents", "broke even", "gained 4 cents", "lost 10 cents", "gained 10 cents" ]

B broke even 20 % profit on $ 1.20 = $ 20/100 × 1.20 = $ 0.20 × 1.20 = $ 0.24 Similarly, 20 % loss on $ 1.20 = $ 20/100 × 1.20 = $ 0.20 × 1.20 = $ 0.24 Therefore, in one pipe his profit is $ 0.24 and in the other pipe his loss is $ 0.24. Since both profit and loss amount is same so, it’s broke even. The answer is: B

B

mathematics

A and B invests Rs.10000 each, A investing for 8 months and B investing for all the 12 months in the year. If the total profit at the end of the year is Rs.35000, find their shares?

[ "s.14000, Rs.15020", "s.14000, Rs.15700", "s.10000, Rs.21090", "s.10000, Rs.21000", "s.14000, Rs.21000" ]

The ratio of their profits A:B = 8:12 = 2:3 Share of A in the total profit = 2/5 * 35000 = Rs.14000 Share of A in the total profit = 3/5 * 35000 = Rs.21000 Answer: E The answer is: E

E

mathematics

Buses A and B start from a common bus stop X. Bus A begins to travel in a straight line away from bus B at a constant rate of 40 miles per hour. One hour later, bus B begins to travel in a straight line in the exact opposite direction at a constant rate of 80 miles per hour. If both buses travel indefinitely, what is the positive difference, in minutes, between the amount of time it takes bus B to cover the exact distance that bus A has covered and the amount of time it takes bus B to cover twice the distance that bus A has covered?

[ "36", "72", "132", "144", "180" ]

1st part: - In 1hr, Bus A covers 30 miles. Relative speed of bus ABus B is (80-30) = 50mph. So time required for Bus B to cover the exact distance as A is 50*t = 30 t=3/5 = 36min 2nd part 80*t=2d - B has to cover twice the distance 30*(t+1) = d - A traveled 1hr more and has to travel only only d so d/30 - 2d/80 = 1 D=120 T= 3hrs = 180 min Question asks for +ve difference between part 1 and part 2 in minutes = 180-36 = 72min B The answer is: B

B

mathematics

Shanmukham buys good worth Rs. 6650. He gets a rebate of 6% on it. After getting the rebate, he pays sales tax @ 10%. Find the amount he will have to pay for the goods

[ "6999.2", "6876.1", "6654", "7000", "None of these" ]

Explanation : Rebate = 6% of Rs. 6650 = Rs. 6/100 x 6650 = Rs. 399. Sales tax = 10% of Rs. (6650 399) = Rs. 10/100 x 6251 = Rs. 625.10 Final amount = Rs. (6251 + 625.10) = Rs. 6876.10 Answer : B The answer is: B

B

mathematics

A man can row downstream at 16 kmph and upstream at 12 kmph. Find the speed of the man in still water .

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

Let the speed of the man in still water and speed of stream be x kmph and y kmph respectively. Given x + y = 16 --- (1) and x - y = 12 --- (2) From (1) & (2) 2x = 28 => x = 14, y = 2. Answer:A The answer is: A

A

mathematics

Working alone, Printers X, Y, and Z can do a certain printing job, consisting of a large number of pages, in 12, 20, and 20 hours, respectively. What is the ratio of the time it takes Printer X to do the job, working alone at its rate, to the time it takes Printers Y and Z to do the job, working together at their individual rates?

[ "4/11", "1/2", "15/22", "10/1", "11/4" ]

P1 takes 12 hrs Rate for P2P3 together = 1/20 + 1/20 = 1/10 Therefore they take 10 Ratio = 10/1 = D The answer is: D

D

mathematics

Three numbers are in the ratio 3:5:8. The largest number value is 152. Find difference between Smallest & largest number is?

[ "16", "90", "38", "95", "78" ]

Explanation: == 3:5:8 Total parts = 16 = The largest number value is 152 = The largest number is = 8 = Then 8 parts -----> 152 ( 8 * 19 = 152 ) = smallest number = 3 & Largest number = 8 = Difference between smallest number & largest number is = 8 - 3 = 5 = Then 5 parts -----> 95 (5 * 19 = 95) Answer: Option D The answer is: D

D

mathematics

A waiter's salary consists of his salary and tips. During one week his tips were 7/4 of his salary. What fraction of his income came from tips ?

[ "4/9", "5/4", "5/8", "5/9", "7/11" ]

Income = salary (s) +tips = s + s*7/4 = s*11/4 Tips = s*7/4 fraction of his income came from tips = (s*7/4)/(s*11/4)= 7/11 ANSWER:E The answer is: E

E

mathematics

Solve the given two equations and find the inequality of X and Y. (a) x^2 = 729 and (b) Y= (729)^(1/2)

[ "If x>y", "If x>=y", "If x < y", "If x<=y", "x=y or relationship cannot be established" ]

Solution:- X=+27, -27 and Y= +27 Comparing we get X<=Y D The answer is: D

D

mathematics

In an election between two candidates, 70% of the voters cast their votes, out of which 4% of the votes were declared invalid. A candidate got 655200 votes which were 75% of the total valid votes. Find the total number of votes enrolled in that election.

[ "1300000", "12500", "14000", "12000", "None of these" ]

Explanation : Solution: let the total number of votes enrolled be x. then, number of votes cast = 70% of x. valid votes = 96% of(70% of x). .'. 75% of(96% of (70% of of x)) = 655200. (75/100 * 96/100 * 70/100 * x) = 655200. => x = (655200*100*100*100)/(75*96*70) = 1300000 Answer : A The answer is: A

A

mathematics

The sum of five numbers is 655. The average of the first two numbers is 85 and the third number is 125. Find the average of the two numbers?

[ "150", "180", "190", "200", "250" ]

Let the five numbers be P, Q, R, S and T. => P + Q + R + S + T = 655. (P + Q)/2 = 85 and R = 125 P + Q = 170 and R = 125 P + Q + R = 295 S + T = 655 - (P + Q + R) = 360 Average of the last two numbers = (S + T)/2 = 180. ANSWER B The answer is: B

B

mathematics

The ratio of the present age of two brothers is 1:2 and 5 years back, the ratio was 1:3. What will be the ratio of their ages after 5 years?

[ "3:9", "3:0", "ratio 3:5", "3:2", "3:1" ]

Let the present ages of the two brothers be x and 2x years respectively. Then, (x - 5)/(2x - 5) = 1/3 3(x - 5) = (2x - 5) => x = 10 Required ratio = (x + 5) : (2x + 5) = 15 : 25 = 3:5 Answer: C The answer is: C

C

mathematics

A room is 6 meters 24 centimeters in length and 4 meters 32 centimeters in width. Find the least number of square tiles of equal size required to cover the entire floor of the room?

[ "110", "124", "96", "117", "127" ]

Length = 6 m 24 cm = 624 cm Width = 4 m 32 cm = 432 cm HCF of 624 and 432 = 48 Number of square tiles required = (624 * 432)/(48 * 48) = 13 * 9 = 117 ANSWER:D The answer is: D

D

mathematics

The average weight of a group of boys is 30 kg. After a boy of weight 33 kg joins the group, the average weight of the group goes up by 1 kg. Find the number of boys in the group originally ?

[ "4", "8", "5", "2", "9" ]

Let the number off boys in the group originally be x. Total weight of the boys = 30x After the boy weighing 33 kg joins the group, total weight of boys = 30x + 33 So 30x + 33 + 31(x + 1) = > x = 2. Answer: D The answer is: D

D

mathematics

The volume of water in a certain tank is x percent greater than it was one week ago. If r percent of the current volume of water in the tank is removed, the resulting volume will be 90 percent of the volume it was one week ago. What is the value of r in terms of x?

[ "x+10", "10x+1", "100(x+10)", "100( x+10/x+100)", "100 ( 10x+1/10x+10)" ]

Given that, the water was increased by x percent -> then reduced by r percent -> to 90 percent of what it was one week ago. Consider, the 100 units of water was increased by 20% to 120 units -> then reduced by 25% of 120 (i.e. by 30 units) -> to 90 units. i.e. Pick numbers as x = 20% and r = 25% Substitute x=20 and identify the answer that gives r=25 A) x+10 --20+1=30 b) 10x+1 --200+1=201 c) 100(x+10) --100(20+10)=3000 d) 100( x+10/x+100) --100(20+10/20+100) = 100(30/120)=25 e) 100 ( 10x+1/10x+10) -- 100(200+1/200+10)= 100(201/210) Hence choice(D) is the answer. The answer is: D

D

mathematics

The combined salaries of three brothers is $135,000. Mr. Big earns twice what Mr. Small earns, and Mr. Middle earns 1 1/2 times what Mr. Small earns. What is the smallest salary of the three brothers?

[ "20,000", "22,000", "25,000", "30,000", "40,000" ]

Mr. Small = x; Mr. Middle = 3/2*x; Mr. Big = 2x. x + 3/2*x + 2x = 135 --> x=30 Answer: D The answer is: D

D

mathematics

Two trains are running at 40 km/hr and 20 km/hr respectively in the same direction. Fast train completely passes a man sitting in the slower train in 5 sec. What is the length of the fast train?

[ "27 7/8", "27 9/9", "28 7/9", "27 7/9", "21 7/9" ]

Relative speed = (40 - 20) = 20 km/hr. = 20 * 5/ 18 = 50/9 m/sec. Length of faster train = 50/9 * 5 = 250/9 = 27 7/9 m. Answer: D The answer is: D

D

mathematics

If 2*f(x) - f(1/x) = x2x2 , then f(x) is?

[ "f(x) = 3{2*x2x2 + (1x)2(1x)9 }", "f(x) = 3{2*x2x2 + (1x)2(1x)2 }", "f(x) = 3{2*x2x2 + (1x)2(1x)3 }", "f(x) = 3{2*x2x2 + (1x)2(1x)4 }", "f(x) = 3{2*x2x2 + (1x)2(1x)1 }" ]

2*f(x) - f(1/x) = x2x2 ..............(1) Take x = (1/x), 2*(1/x) - f(x) = (1x)2(1x)2 ...............(2) Add: 2 (equation 1) + equation 2 3*f(x) = 2*x2x2+ (1x)2(1x)2 f(x) = {2*x2x2 + (1x)2(1x)2}/3 Answer:B The answer is: B

B

mathematics

If 7^q is a factor of the product of the integers from 1 to 100, inclusive, what is the largest value of q?

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

So the question just means that we have to find all the multiples q of 7 between 1 to 100 So there are 14 multiples of 7 ( 7 - 98) But 49 and 98 contain two 7's as factors so we have to add 14 + 2 = 16 E The answer is: E

E

mathematics

In how many different ways can the letters of the word ATRIUMS be arranged in such a way that the vowels occupy only the even positions?

[ "72", "96", "120", "144", "180" ]

The 3 vowels can be arranged in 3 even places in 3! ways. The 4 consonants can be arranged in 4 odd places in 4! ways. The number of arrangements with vowels in even positions = 3! Ã— 4! = 6 Ã— 24 = 144 The answer is D. The answer is: D

D