subject stringclasses 1
value | question stringlengths 3 1.14k | options listlengths 5 5 | solution stringlengths 18 3.7k | answer stringclasses 5
values |
|---|---|---|---|---|
mathematics | A box contains nine bulbs out of which 4 are defective. If four bulbs are chosen at random, find the probability that atleast one bulb is good. | [
"125/129",
"125/121",
"125/126",
"125/122",
"125/124"
] | Explanation:
Required probability = 1 - 1/126 = 125/126
Answer: C
The answer is: C | C |
mathematics | There are two examinations rooms A and B. If 10 students are sent from A to B, then the number of students in each room is the same. If 20 candidates are sent from B to A, then the number of students in A is double the number of students in B. The number of students in room A is? | [
"128",
"276",
"100",
"277",
"110"
] | Let the number of students in rooms A and B be x and y respectively.
Then, x - 10 = y + 10 ⇒ x - y = 20 .... (i)
and x + 20 = 2(y - 20) ⇒ x - 2y = -60 .... (ii)
Solving (i) and (ii) we get: x = 100 , y = 80.
∴ The required answer A = 100.
Answer: C
The answer is: C | C |
mathematics | The sum of three consecutive even numbers is 42. Find the middle number of the three? | [
"14",
"15",
"52",
"25",
"32"
] | Answer: Option A
Three consecutive even numbers (2P - 2), 2P, (2P + 2).
(2P - 2) + 2P + (2P + 2) = 42
6P = 42 => P = 7.
The middle number is: 2P = 14.
The answer is: A | A |
mathematics | In an exam, Amar scored 64 percent, Bhavan scored 36 percent and Chetan 44 percent. The maximum score awarded in the exam is 800. Find the average mark scored by all the three boys? | [
"384",
"656",
"443",
"324",
"534"
] | Average mark scored by all the three boys =
[64/100 (800) + 36/100 (800) + 44/100 (800)] / 3 = 384
Answer:A
The answer is: A | A |
mathematics | In a box, there are 3 grey, 5 brown and 2 yellow pencils. One pen is picked up randomly. What is the probability that it is neither brown nor yellow? | [
"2/5",
"3/5",
"3/10",
"3/4",
"3/11"
] | Explanation :
Neither brown nor yellow means the pencils drawn is grey.
Total number of outcomes = (3+5+2) = 10.
Number of Favourable outcomes = 3 = Number of grey pencils.
Hence, Probability of the event = 3/10 = 3/10.
Answer : C
The answer is: C | C |
mathematics | A sum was put at simple interest at certain rate for 3 years. Had it been put at 1% higher rate it would have fetched Rs. 66 more. The sum is: A. Rs. 2,400 B. Rs. 2,100 C. Rs. 2,200 D.Rs. 2,480 | [
"2000",
"2100",
"2200",
"2300",
"2400"
] | 1 percent for 3 years= 66
1 percent for 1 year = 22
=> 100 percent = 2200
ANSWER:C
The answer is: C | C |
mathematics | Of the three-digit integers greater than 800, how many have two digits that are equal to each other and the remaining digit different from the other two? | [
"90",
"82",
"80",
"45",
"36"
] | Let the three digit number be represented as X Y Z.
There are 3 cases:
Case I.[ X=Y ]Z is not equal to XY :XXZorYYZ
X can be either 7, 8 or 9, so digit at X can be chosen in 3 ways
After X is chosen, Y can be chosen in 1 way
After XY are chosen, Z can be chosen in 9 ways
Thus, possible No of digits = (3 ways) * (1 way)... | B |
mathematics | Roberto has three children: two girls and a boy. All were born on the same date in different years. The sum of the ages of the two girls today is smaller than the age of the boy today, but a year from now the sum of the ages of the girls will equal the age of the boy. Three years from today, the difference between the ... | [
"1",
"2",
"3",
"–2",
"–1"
] | girl1: g1, girl2: g2, boy:b, these are the symbols for their ages today.
g1+g2<b
(1 year from now): (g1+1)+(g2+1) = b+1 ; g1+g2 = b-1
The difference between the girls's age and the boy's age is one today:
Assume ages, g1:20, g2:25, b:46 (notice the difference is currently 1); in 3 years the ages will be g1:23, g2:28, b... | D |
mathematics | If a light flashes every 6 seconds, how many times will it flash in 2/5 of an hour? | [
"181",
"211",
"241",
"271",
"301"
] | In 2/5 of an hour there are 24*60 = 1440 seconds
The number of 6-second intervals = 1440/6 = 240
After the first flash, there will be 240 more flashes for a total of 241.
The answer is C.
The answer is: C | C |
mathematics | John walking at 4 Kmph reaches his office 8 minutes late. If he walks at 6 Kmph, he reaches there 10 minutes earlier. How far is the office from his house? | [
"3 2/5 Km",
"3 3/5 Km",
"4 1/5 Km",
"5 1/5 Km",
"None"
] | Formula = S1*S2/S2-S1 * T1+T2/60
= 4*6/2 * 18/6
= 24/2 * 18/60
= 18/5 = 3 3/5 Km
B
The answer is: B | B |
mathematics | In an election, candidate X got 75% of the total valid votes. If 15% of the total votes were declared invalid and the total numbers of votes is 560000, find the number of valid vote polled in favour of candidate? | [
"280000",
"300000",
"355000",
"356000",
"357000"
] | Total number of invalid votes = 15 % of 560000
= 15/100 × 560000
= 8400000/100
= 84000
Total number of valid votes 560000 – 84000 = 476000
Percentage of votes polled in favour of candidate X = 75 %
Therefore, the number of valid votes polled in favour of candidate X = 75 % of 476000
= 75/100 × 476000
= 35700000/100
= 3... | E |
mathematics | This is how Edward’s Lotteries work. First, 9 different numbers are selected. Tickets with exactly 7 of the 9 numbers randomly selected are printed such that no two tickets have the same set of numbers. Finally, the winning ticket is the one containing the 7 numbers drawn from the 9 randomly. There is exactly one winni... | [
"9C7",
"9P3",
"9C9",
"9C6",
"69"
] | since we have to select random 7 numbers from 9 and they all are distinct. i think it should be 9C7 or A
The answer is: A | A |
mathematics | There are seven thieves. They stole diamonds from a diamond merchant and ran away. While running, night sets in and they decide to rest in the jungle.
When everybody was sleeping, two of them woke up and decided to divide the diamonds equally among themselves. But when they divided the diamonds equally, one diamond is ... | [
"700",
"721",
"702",
"703",
"None of the above"
] | We need a number that is a multiple of 7 that will give a remainder of 1 when divided by 2, 3, 4, 5, and 6. The least common multiple of these numbers is 60. So, we need a multiple of 7 that is 1 greater than a multiple of 60.
Answer B
The answer is: B | B |
mathematics | If r = 2^4 * 5^2 * 7 and s = 2^3 * 3^2 * 5, which of the following is equal to the greatest common divisor of r and s? | [
"2 * 5",
"2^2 * 5",
"2^3 * 5^2",
"2*3*5*7",
"2^3 * 3^2 * 5^2 * 7"
] | GCD = product of prime factors raised to the least power = 2^3 * 5
The answer is B.
The answer is: B | B |
mathematics | If x is negative and y is positive, which of the following cannot be positive? | [
"-xy",
"x^2/y",
"x^4/y",
"-x^3*y",
"-x/-y"
] | - * - = +
+ / - = -
-x/-y is negative.
Answer : E
The answer is: E | E |
mathematics | A window 2 inches wide is placed on the back of a rectangular painted area with dimensions 8 inches by 12 inches. What is the area of the window, in square inches? | [
"44",
"96",
"128",
"144",
"168"
] | This question is an example of a 'punch out' question - we have to find the area of EVERYTHING, then 'punch out' the part that we don't want.
We're told that a window 2 inches wide is placed around a rectangular painted area with dimensions 8 inches by 12 inches. We're asked for the area of the window, in square inches... | B |
mathematics | Find compound interest on Rs. 8000 at 15% per annum for 2 years 4 months, compounded annually. | [
"Rs 309",
"Rs 319",
"Rs 3109",
"Rs 109",
"Rs 209"
] | Time = 2 years 4 months = 2(4/12) years = 2(1/3) years.
Amount = Rs'. [8000 X (1+¬(15/100))2 X (1+((1/3)*15)/100)]
=Rs. [8000 * (23/20) * (23/20) * (21/20)]
= Rs. 11109. .
:. C.I. = Rs. (11109 - 8000) = Rs. 3109.
ANSWER C 3109
The answer is: C | C |
mathematics | Two men starting from the same place walk at the rate of 5 kmph and 5.5 kmph respectively. What time will they take to be 5.5 km apart, if they walk in the same direction? | [
"11 hrs",
"14 hrs",
"15 hrs",
"17 hrs",
"None"
] | Sol.
to be 0.5 km apart, they take 1 hour.
To be 5.5 km apart, they take [1/0.5 * 5.5] hrs = 11 hrs.
Answer A
The answer is: A | A |
mathematics | A certain company assigns employees to offices in such a way that some of the offices can be empty and more than one employee can be assigned to an office. In how many ways can the company assign 4 employees to 2 different offices? | [
"5",
"16",
"7",
"8",
"9"
] | Ans. Each employee can go into any of the two offices. Thus we have
=> 2 * 2 * 2 * 2= 16
Answer : B
The answer is: B | B |
mathematics | There are 1500 jelly beans divided between two jars, Jar X and Jar Y. If there are 200 fewer jelly beans in jar X than three times the number of beans in jar Y, how many beans are in jar X? | [
"1050",
"1075",
"1100",
"1125",
"1150"
] | X+Y=1500 so Y=1500-X
X=3Y-200
X=3(1500-X)-200
4X=4300
X=1075
The answer is B.
The answer is: B | B |
mathematics | A mixture of 150 liters of wine and water contains 20% water. How much more water should be added so that water becomes 25% of the new mixture? | [
"87 liters",
"17 liters",
"10 liters",
"17 liters",
"16 liters"
] | Number of liters of water in150 liters of the mixture = 20% of 150 = 20/100 * 150 = 30 liters.
P liters of water added to the mixture to make water 25% of the new mixture.
Total amount of water becomes (30 + P) and total volume of mixture is (150 + P).
(30 + P) = 25/100 * (150 + P)
120 + 4P = 150 + P => P = 10 liters.
... | C |
mathematics | 16 people can write 52 book in 12 days working 8 hour a day.then in how many day 206 can be written by 64 people? | [
"309/26",
"309/28",
"309/22",
"319/26",
"339/26"
] | work per day epr hour per person= 52/(12*8*16) // eq-1
people= 64; let suppose day=p; per day work for 8 hours
acc. to condition
work per day epr hour per person= 206/(p*8*64) // eq-2
eq-1==eq-2;
p= 309/26
ANSWER:A
The answer is: A | A |
mathematics | If the number 52,1n9, where n represents the tens digit, is a multiple of 3, then the value of n could be which of the following? | [
"6",
"5",
"3",
"1",
"0"
] | Maybe you are misreading the question but it is saying that 52,1n9 is a multiple of 3 and not necessarily n is a multiple of 3.
The sum of the digits 5 + 2 + 1 + n + 9 must be a multiple of 3
17 + n must be a multiple of 3
substituting the numbers n must = 1
ANSWER:D
The answer is: D | D |
mathematics | A car averages 65 mph for the first 5 hours of a trip and averages 75 mph for each additional hour. The average speed for the entire trip was 60 mph. How many hours long is the trip? | [
"9",
"8",
"7",
"6",
"5"
] | Let the time for which car averages 75 mph = t
60*(t+5)= 65*4 + 70 t
=>10t= 40
=> t = 4
Total duration of the trip = 5+4=9
Answer A
The answer is: A | A |
mathematics | A cube has a volume of 343 cubic feet. If a similar cube is twice as long, twice as wide, and twice as high, then the volume, in cubic feet of such cube is? | [
"24",
"48",
"64",
"2744",
"100"
] | Volume = 343 = side^3
i.e. Side of Cube = 7
New Cube has dimensions 14, 14, and 14 as all sides are twice of teh side of first cube
Volume = 14*14*14 = 2744 square feet
Answer: option D
The answer is: D | D |
mathematics | If two dice are thrown together, the probability of getting an even number on one die and an odd number on the other is? | [
"1/8",
"1/2",
"1/6",
"1/1",
"1/5"
] | The number of exhaustive outcomes is 36.
Let E be the event of getting an even number on one die and an odd number on the other. Let the event of getting either both even or both odd then
= 18/36 = 1/2
P(E)
= 1 - 1/2 = 1/2.
Answer: B
The answer is: B | B |
mathematics | A pair of prime numbers that can be expressed in the form {p, (p + 6)} is defined as a pair of “sexy primes.” A “sexy triplet” is a group of three primes that can be expressed in the form {p, (p + 6), (p + 12)}. All of the following prime numbers are the middle term of a sexy triplet EXCEPT | [
"11",
"13",
"17",
"19",
"23"
] | {x-6, x, x+6} all must be primes. Substitute options for x to check whether this will hold true. If x=19, then x+6=25, which is not a prime.
Answer: D
The answer is: D | D |
mathematics | If p and q are positive integers, how many integers are larger than pq and smaller than p(q + 5)? | [
"3",
"P + 2",
"p – 2",
"2p – 1",
"5p - 1"
] | The number of integers between x and y, where x>y is (x-y)-1. For example, the number of integers between 1 and 5 is (5-1)-1=3: 2, 3, and 4.
Thus, the number of integers between pq and p(q+5)=pq+5p is (pq+5p-pq)-1=5p-1.
Answer: E.
The answer is: E | E |
mathematics | What will be the ans of that 126th term in the series abbcccdddd......??? | [
"m",
"n",
"o",
"q",
"p"
] | use formula n(n+1)/2=126
15*16=2*126
so 15 th letter is p
ANSWER:E
The answer is: E | E |
mathematics | Worker A takes 8 hours to do a job. Worker B takes 10 hours to do the same Job.How long should it take both A and B, working together but independently, to do the same job? | [
"40/9 days",
"9 days",
"40 days",
"94 days",
"7 days"
] | A’s 1 hour's work = 1/8
B's 1 hour's work = 1/10
(A + B)'s 1 hour's work = (1/8) +(1/10)=9/40
Both A and B will finish the work in 40/9 days.
Ans: A
The answer is: A | A |
mathematics | If annual decrease in the population of a town is 10% and the present number of people is 500 what will the population be in 1 year? | [
"450",
"310",
"250",
"410",
"390"
] | Population in 1 year = 500(1 - 10/100) = 500*90/100 = 450
Answer is A
The answer is: A | A |
mathematics | Kamal started a business with Rs.25000 and after 4 months, Kiran joined him with Rs.60000. Kamal received Rs.58000 including 10% of profit as commission for managing the business. What amount did Kiran receive? | [
"72000",
"720",
"82000",
"92000",
"7200"
] | Ratio of the profits = 25000*12 : 60000*8
= 25*12 : 60*8 = 5*3 : 12:2 = 5 : 4*2
= 5:8
Let the total profit = x.
Then Kamal received 10x/100 = x/10 as commission for managing the business
Remaining profit = x- x/10 = 9x/10 which is shared in the ration 5:8
Kamal's share = x/10 + (9x/10) * (5/13) = 58000
=> x + 9x(5/13) ... | A |
mathematics | 5+8 | [
"8",
"13",
"28",
"6",
"2"
] | B
The answer is: B | B |
mathematics | A shopkeeper labeled the price of his articles so as to earn a profit of 30% on the cost price. He then sold the articles by offering a discount of 10% on the labeled price. What is the actual percent profit earned in the deal? | [
"18%",
"20%",
"17%",
"18%",
"None of these"
] | Explanation:
Let the CP of the article = Rs.100.
Then labeled price = Rs.130.
SP = Rs.130- 10% of 130 = Rs.130-13 = Rs.117.
Gain = Rs.117 – Rs.100 = Rs.17
Therefore, gain/profit percent = 17%.
Answer: Option C
The answer is: C | C |
mathematics | A can do a work in 6 days. B can do the same work in 4 days. Both A&B together will finish the work and they got $2000 from that work. Find their shares? | [
"600,400",
"500,500",
"300,700",
"800,1200",
"550,1450"
] | Ratio of their works A:B = 6:4
Ratio of their wages A:B = 2:3
A's share = (2/5)2000 = 800
B's share = (3/5)2000 = 1200
correct option is D
The answer is: D | D |
mathematics | The average age of husband, wife and their child 3 years ago was 27 years and that of wife and the child 5 years ago was 20 years. The present age of the husband is: | [
"40",
"25",
"30",
"35",
"48"
] | Sum of the present ages of husband, wife and child = (27 * 3 + 3 * 3) = 90 years.
Sum of the present age of wife and child = (20 * 2 + 5 * 2) = 50 years.
Husband's present age = (90 - 50) = 40 years.
ANSWER A
The answer is: A | A |
mathematics | Which of the following has the most number of divisors? | [
"99",
"101",
"176",
"182",
"107"
] | 99 = 1 x 3 x 3 x 11
101 = 1 x 101
176 = 1 x 2 x 2 x 2 x 2 x 11
182 = 1 x 2 x 7 x 13
So, divisors of 99 are 1, 3, 9, 11, 33, .99
Divisors of 101 are 1 and 101
Divisors of 176 are 1, 2, 4, 8, 11, 16, 22, 44, 88 and 176
Divisors of 182 are 1, 2, 7, 13, 14, 26, 91 and 182.
Answer: Option C
Hence, 176 has the most number of... | C |
mathematics | The amount of an investment will double in approximately 70/ p years, where p is the percent interest, compounded annually. If Thelma invests $ 40,000 in a long-term CD that pays 5 percent interest, compounded annually, what will be the approximate total value of the investment when Thelma is ready to retire 42 years l... | [
"$ 280,000",
"$ 320,000",
"$ 360,000",
"$ 450,000",
"$ 540,000"
] | The amount of an investment will double in approximately 70/ p years, where p is the percent interest, compounded annually. If Thelma invests $ 40,000 in a long-term CD that pays 5 percent interest, compounded annually, what will be the approximate total value of the investment when Thelma is ready to retire 42 years l... | B |
mathematics | If A speaks the truth 30% of the times, B speaks the truth 40% of the times. What is the probability that at least one will tell the truth | [
"0.58",
"0.9",
"1.9",
"2.2",
"2.3"
] | probability of A speaks truth p(A)=3/10;false=7/10
probability of B speaks truth p(B)=4/10;false=6/10.For given qtn
Ans=1-(neither of them tell truth).Because A & B are independent events
=1-[(7/10)*(6/10)]=1-42/100=1-0.42=0.58
ANSWER:A
The answer is: A | A |
mathematics | A rectangular-shaped carpet that measures x feet by y feet is priced at $50. What is the cost of the carpet, in dollars per square yard? (1 square yard = 9 square feet) | [
"xy/360",
"9xy/40",
"40xy/9",
"450xy",
"450/(xy)"
] | The area of the carpet in feet is xy.
The area in square yards is xy / 9.
The price per square yard is 50 / (xy/9) = 450/(xy).
The answer is E.
The answer is: E | E |
mathematics | An office supply store stocks two sizes of notebooks, each in five colors: blue, green, yellow, red, or pink. The store packs the notebooks in packages that contain either 4 notebooks of the same size and the same color or 4 notebooks of the same size and of 4 different colors. If the order in which the colors are pack... | [
"10",
"12",
"20",
"24",
"28"
] | First let's consider the small notebooks.
There are 5 ways to choose notebooks of the same color.
The number of ways to choose four notebooks with different colors is 5C4=5.
There are 10 different packages we can make with the small notebooks.
We can use the same process to find 10 different packages with large noteboo... | C |
mathematics | A store sells chairs and tables. If the price of 2 chairs and 1 table is 60% of the price of 1 chair and 2 tables, and the price of 1 table and 1 chair is $60, what is the price, in dollars, of 1 table? (Assume that every chair has the same price and every table has the same price.) | [
"105/2",
"45",
"44",
"52",
"50"
] | LET C= CHAIR ; T =TABLE
2C+1T = 0.6 (1C + 2T) OR C( 2-0.6) = 1.2T -1T OR 1.4C = 0.2 T THEREFORE C= 0.2/1.4 T = 1/7 T
IC +1T =60 OR 1/7T + 1T =60 THEREFORE T= 60*7/8 = 105/2
A
The answer is: A | A |
mathematics | Two whales are moving in the same direction at 60 kmph and 42 kmph. The faster whale manages to cross the other whale in 14 seconds. Find the length of the faster whale in meters. | [
"110 m",
"45 m",
"70 m",
"120 m",
"113 m"
] | Relative speed = ( 60 - 42 ) * 5 / 18 = 5 mps.
Distance covered in 14 seconds = 14 * 5 = 70 m.
The length of the faster whale = 70m.
Answer: C
The answer is: C | C |
mathematics | The length of a rectangular plot is thrice its width. If the area of the rectangular plot is 588 sq meters, then what is the width (in meters) of the rectangular plot? | [
"14",
"16",
"18",
"20",
"22"
] | Area = L*W = 3W^2 = 588
W^2 = 196
W = 14
The answer is A.
The answer is: A | A |
mathematics | The average of a set of five distinct integers is 370. If each number is less than 2,000, and the median of the set is the greatest possible value, what is the sum of the two smallest numbers? | [
"-4,494",
"-3,997",
"-3,494",
"-4,144",
"The answer cannot be determined from the information given"
] | Sum of the set = 370*5=1850 Each number is less than 2000 and median of the set is the greatest possible value.
Therefore last 3 numbers can be 1999,1998 and 1997. Their sum=5994.
Therefore sum of two smallest numbers= 1850-5994= -4144
Answer=D
The answer is: D | D |
mathematics | Of the goose eggs laid at a certain pond, 1/4 hatched and 4/5 of the geese that hatched from those eggs survived the first month. Of the geese that survived the first month, 3/5 did not survive the first year. If 120 geese survived the first year and if no more than one goose hatched from each egg, how many goose eggs ... | [
"1200",
"1300",
"1400",
"1500",
"1600"
] | Let x be the number of eggs that were laid.
(2/5)(4/5)(1/4)x = 120
(8/100)x = 120
x = 1500
The answer is D.
The answer is: D | D |
mathematics | The probability of having a girl is identical to the probability of having a boy. In a family with five children, what is the probability that all the children are of the same gender? | [
"1/16",
"1/4",
"1/8",
"1/12",
"1/25"
] | There are two cases. All boys and all girls
case 1. all boys.
1/2*1/2*1/2*1/2*1/2= 1/32
case 2 .all girls.
1/2*1/2*1/2*1/2*1/2=1/32
We will add the cases to get 1/16
The answer is: A | A |
mathematics | A shopkeeper buys two articles for Rs.1000 each and then sells them, making 20% profit on the first article and 20% loss on second article. Find the net profit or loss percent? | [
"200",
"88",
"77",
"66",
"51"
] | Profit on first article = 20% of 1000 = 200.
This is equal to the loss he makes on the second article. That, is he makes neither profit nor loss.
Answer: A
The answer is: A | A |
mathematics | Working in a South Side studio at a constant rate, Kanye can drop a full-length platinum LP in 5 weeks. Working at his own constant rate, Common can drop a full-length platinum LP in x weeks. If the two emcees work together at their independent rates, they can drop a full-length platinum compilation LP in 2 weeks. Assu... | [
"3 and 1/3 weeks",
"3 weeks",
"2 and 1/2 weeks",
"2 and 1/3 weeks",
"2 weeks"
] | VERITAS PREPOFFICIAL SOLUTION:
Now, while your instinct may be to Go! and speed through your initial read of this rate problem, remember: slow motion (is) better than no motion. As you read each sentence, you should start jotting down variables and relationships so that by the time you get to the question mark you have... | A |
mathematics | In a convention where they distributes prizes. In how many ways can 3 prizes be distributed among 4 boys when a boy gets any number of prizes? | [
"58",
"60",
"64",
"68",
"90"
] | In this case, repetitions are allowed, so all the three prizes can be given in 4 ways, i.e. (4 x 4 x 4) ways = 4*3 ways = 64 ways
The answer is: C | C |
mathematics | A taxi company charges $1.25 for the first quarter of a mile and fifteen cents for each additional quarter of a mile. What is the maximum distance someone could travel with $4.90? | [
"4 miles",
"4 1/4 miles",
"4 3/4 miles",
"5 1/2 miles",
"6 1/3 miles"
] | If we start out with $4.90 and have to spend $1.25 for the first quarter-mile, we will have $3.65 left to spend on quarter-mile intervals.
Since $3.65/$0.15 = 24.33 we can buy 24.33 more quarter-miles, and will travel 25.33 quarter miles in all:
25.33 × 1/4 =6 1/3 miles.
The correct answer is choice (E).
The answer is:... | E |
mathematics | Two trains each 250 m in length are running on the same parallel lines in opposite directions with the speed of 90 kmph and 70 kmph respectively. In what time will they cross each other completely? | [
"15 sec",
"19 sec",
"12 sec",
"10 sec",
"11.25 sec"
] | Explanation:
D = 250 m + 250 m = 500 m
RS = 90 + 70 = 160 * 5/18 = 400/9
T = 500 * 9/400 = 11.25 sec
Answer: Option E
The answer is: E | E |
mathematics | Find the ratio in which rice at Rs. 7.20 a kg be mixed with rice at Rs. 5.70 a kg to produce a mixture worth Rs. 6.30 a kg. | [
"2:7",
"2:3",
"2:0",
"2:1",
"2:2"
] | Explanation:
By the rule of alligation:
Cost of 1 kg rice of 1st kind Cost of 1 kg rice of 2nd kind
{\color{Blue} \therefore } Required ratio = 60 : 90 = 2 : 3
Answer: B) 2:3
The answer is: B | B |
mathematics | Jadeja rented a power tool from a rental shop. The rent for the tool was $13 for the first hour and $8 for each additional hour. If Jadeja paid a total of $133, excluding sales tax, to rent the tool, for how many hours did she rent it? | [
"14",
"19",
"16",
"13",
"12"
] | 13 + 8n = 133
n = 15
Total time = n+1 hrs = 15+1 hrs = 16 hrs
Answer : C
The answer is: C | C |
mathematics | Exactly 3/7 of the people in the room are under the age of 21, and exactly 5/10 of the people in the room are over the age of 65. If the total number of the people in the room is greater than 50 and less than 100, how many people in the room are under the age of 21? | [
"21",
"35",
"39",
"30",
"65"
] | The total number of the people in the room must be a multiple of both 7 and 10 (in order 3/7 and 5/10 of the number to be an integer), thus the total number of the people must be a multiple of LCM of 7 and 10, which is 70.
Since, the total number of the people in the room is greater than 50 and less than 100, then ther... | D |
mathematics | In year Y imported machine tools accounted for 60 percent of total machine-tools sales in the United States, and Japanese imports accounted for 30 percent of the sales of imported machine tools. If the total sales of machine tools imported from Japan that year was x billion dollars, then the total sales of all machine ... | [
"55x/9",
"50x/9",
"60x/9",
"65x/9",
"75x/9"
] | Sales of imported tools = 60% of the total sales = 0.60*{total} = 3{total}/5;
Sales of Japanese tools = 30% of the sales of imported tools = 3/10*3{total}/5 = 9{total}/50.
Since the sales of of Japanese tools was x, then 9{total}/50 = x -->9 {total} = 50x
{total} = 50x/9
Answer: B
The answer is: B | B |
mathematics | At what rate percent on simple interest will Rs.1750 amount to Rs.2000 in 4 years? | [
"4 %",
"3.57 %",
"2 6/7 %",
"5 %",
"6 %"
] | Explanation:
250 = (1750x4xR)/100
R = 3.57 %
Answer: Option B
The answer is: B | B |
mathematics | If (5^5)(9^3)=3(15^x), what is the value of x? | [
"5",
"9",
"11",
"13",
"15"
] | (5^5)(9^3)=3(15^x)
=> 5^5 * 3^6 = 3 * 3^x * 5^x
=> 5^5 * 3^6 = 3^(x+1) * 5^x
Value of x = 5
Answer A
The answer is: A | A |
mathematics | City A to city B, Andrew drove for 1hr at 46 mph and for 3 hours at 60 mph. What was the average speed for the whole trip? | [
"56.5",
"57.5",
"61",
"61.5",
"62.5"
] | The total distance is 1×46+3×60=226
And the total time is 4 hours. Hence,
Average Speed=(Total Distance/Total Time)
=226/4=56.5
A
The answer is: A | A |
mathematics | Given that x = 2^b – (8^35 + 16^5), which of the following values for b yields the lowest value for |x|? | [
"104",
"105",
"106",
"107",
"125"
] | 8^35 + 16^5 = 2^105 + 2^20
Compared to 2^105, the value of 2^20 is negligible.
2^105 - (2^105 +2^20) will minimize the value of |x|.
The answer is B.
The answer is: B | B |
mathematics | Find the odd pair of numbers
1) 55 - 42
2) 69 - 56
3) 48 - 34
4) 95 - 82
5) 45 - 32 | [
"55-42",
"69-56",
"48-34",
"95-82",
"45-32"
] | minus the numbers
55-42=13
69-56=13
48-34=14
95-82=13
45-32=13
here 48-34 = 14 which is not similar to the other, so 48 - 34 is the odd pair of numbers. correct answer (C)
The answer is: C | C |
mathematics | A company, Chauncy Co., has an annual travel budget of $53,000. The accounting department estimates that transportation expenses will increase 5 percent in the coming year, and nontransportation travel expenses will increase by 15 percent in the coming year. Last year, Chauncy Co. spent $19,500 on transportation-relate... | [
"Expenses will not go over the budget.",
"$500",
"$4,225",
"$7,725",
"$60,725"
] | annual travel budget of $53,000
Let, Transportation expenses = T = 19500
and Non-Transportation expenses = N=35000
i.e. Increased Transportation expenses = 1.05T = 20475
and Increased Non-Transportation expenses = 1.15N = 40250
Total Expense = 20475+40250 = 60725
Expense over Budget = Budget - expense = 53000-60725 = 7... | D |
mathematics | X can do a piece of work in 40days. He works at it for 8days and then Y finished it in 28 days. How long will Y take to complete the work? | [
"10",
"12",
"15",
"18",
"35"
] | Work done by X in 8days = 8*1/40 = 1/5
Remaining work = 1 - 1/5 = 4/5
4/5 work is done by Y in 28 days
Whole work will be done by Y in 28*5/4 = 35 days
Answer is E
The answer is: E | E |
mathematics | At Jefferson Elementary School, the number of teachers and students (kindergarten through sixth grade) totals 510. The ratio of students to teachers is 16 to 1. Kindergarten students make up 1/4 of the student population and fifth and sixth graders account for 1/3 of the remainder. Students in first and second grades a... | [
"12 greater",
"17 fewer",
"28 fewer",
"36 fewer",
"52 fewer"
] | Soln>> from the given ratio of 16:1 u can derive that ter are 480 students
KG= 1/4 * 480 =120
5th and 6th graders = 1/3 * 384= 128 (1/3 of remainder)
1st and 2nd grade = 1/4 * 480 =120 ( 1/4 of all students)
equal number of students in 3rd and 4th => 480 - 344= 136 and 136/2=68 each since equal number
(344 is the sum o... | E |
mathematics | If positive integer n is divisible by both 4 and 18, then n must be divisible by which of the following? | [
"8",
"13",
"18",
"24",
"48"
] | A number divisible by both 4,18 is 36 which s divisible by 18.
IMO : Answer C 18
The answer is: C | C |
mathematics | A train 575 m long crosses a tunnel of length 325 in 90 sec. What is the speed of the train in kmph. | [
"28",
"32",
"36",
"24",
"30"
] | Total distance traveled = Length of train + Length of tunnel = 575 + 325 = 900
Time taken to cross the tunnel = 90 sec.
Speed in kmph = distance/time *18/5 = 900/90 * 18/5
= 180/5 = 36 kmph
ANSWER:C
The answer is: C | C |
mathematics | Y and Z are in a relay race. Y runs the first leg of the course in 58 seconds. Z runs the second leg of the course in 26 seconds. What was the average time they took to run a leg of the course? | [
"39",
"40",
"41",
"42",
"43"
] | (58 seconds +26 seconds)/2= 42 seconds
Correct option is: D
The answer is: D | D |
mathematics | Train X crosses a stationary train Y in 60 seconds and a pole in 25 seconds with the same speed. The length of the train X is 300 m. What is the length of the stationary train Y? | [
"185 m",
"420 m",
"167 m",
"176 m",
"168 m"
] | Let the length of the stationary train Y be LY
Given that length of train X, LX = 300 m
Let the speed of Train X be V.
Since the train X crosses train Y and a pole in 60 seconds and 25 seconds respectively.
=> 300/V = 25 ---> ( 1 )
(300 + LY) / V = 60 ---> ( 2 )
From (1) V = 300/25 = 12 m/sec.
From (2) (300 + LY)/12 = ... | B |
mathematics | The events A and B are independent, the probability that event A occurs is greater than 0, and the probability that event A occurs is twice the probability that event B occurs. The probability that at least one of events A and B occurs is 5 times the probability that both events A and B occur. What is the probability t... | [
"1/45",
"1/2",
"1/8",
"2/3",
"2/11"
] | Let us say probability of A occuring is a.
Let us say probability of B occuring is b.
a = 2b
Probability (either A or B or both) = 5 times Probability (A and B)
a*(1-b) + b*(1-a) + ab = 5*ab
Substituting a=2b in the second equation:
2b*(1-b) + b*(1-2b) + 2b*b = 5*2b*b
3b-2b^2 = 110b^2
3b = 12b^2
b = 3/12 = 1/4
So, a = ... | B |
mathematics | lexus car agency has 135 cars.he sold some cars at 9% profit and rest at 36% profit thus he gains 17% on the sale of all his cars.the no. of cars sold at 36% profit is? | [
"36",
"37",
"38",
"39",
"40"
] | ratio of 36% profit cars to 9% profit cars = 8:19
so no. of cars sold at 36% profit = 135*8/27= 40 cars
ANSWER:E
The answer is: E | E |
mathematics | Two pipes can fill a tank in 8 minutes and 5 minutes. An outlet pipe can empty the tank in 12 minutes. If all the pipes are opened when the tank is empty, then how many minutes will it take to fill the tank? | [
"30 minutes",
"17 minutes",
"15 minutes",
"10 minutes",
"14 minutes"
] | Part of the filled by all the three pipes in one minute
= 1/8 + 1/5 - 1/12 = (15 + 24 - 10)/120 = 29/120
So, the tank becomes full in 14 minutes.
Answer: E
The answer is: E | E |
mathematics | 0.014×0.014= ? | [
"0.000196",
"0.00196",
"19.6",
"196",
"NONE"
] | Solution
Sum of decimals places= 6.
14×14 = 196.
= s0.014×0.014
= 0.000196
Answer A
The answer is: A | A |
mathematics | Twenty percent of the skiers that tried out for the ski patrol were selected. Of those that were not selected, 7 skiers were CPR certified and 17 were not. How many skiers tried out for the ski patrol? | [
"30",
"50",
"60",
"70",
"80"
] | Not Selected = 80%
If total is x.
Then 0.8x=7+17=24
x=30
Hence answer is A.
The answer is: A | A |
mathematics | 12, 14, x, 10
The median of the list of positive integers above is 11. Which of the following could be the average (arithmetic mean) of the list? | [
"3",
"5.5",
"11",
"7",
"7.5"
] | GivenThe median of the list of positive integers above is 11
So arranging the numbers from lowest to highest, avg of 2 middle terms needs to be 11
so the sequence will be x 10 12 14
Lets say x = 8, which gives us mean = sum/4 = 11
C is correct
The answer is: C | C |
mathematics | Find the compound interest on $ 56,000 at 20% per annum for 9 months, compounded quarterly | [
"2532",
"2552",
"6524",
"8827",
"9512"
] | Principal = $ 56000; Time = 9 months =3 quarters;
Rate = 20% per annum = 5% per quarter.
Amount = $ [56000 x (1+(5/100))^3] = $ 64827.
CI. = $ (64827 - 56000) = $ 8827.
Answer D.
The answer is: D | D |
mathematics | 111 = O
222 = E
333 = T
444 = S
Reading and analyzing the above, can you find out the following ?
555 = ? | [
"J",
"A",
"M",
"K",
"O"
] | E
O
1 * 1 * 1 = One
2 * 2 * 2 = Eight
3 * 3 * 3 = Twenty seven
4 * 4 * 4 = Sixty Four
For all the above, you can see that the first letter of the sum is the code.
Thus 5 * 5 * 5 = One twenty five
Thus 555 = O.
The answer is: E | E |
mathematics | If x is the median of the set {8/2, 11/3, 27/9, 21/5, x}, x could be | [
"4",
"17/5",
"16/5",
"30/7",
"31/7"
] | The median is the middle number once all the numbers are arranged in increasing/decreasing order.
We see that
11/3 = 3.something,
28/9 = 3.something
21/5 = 4.something
9/2 = 4.something
So x should greater than the smallest two numbers and smaller than the greatest two numbers. We can see that x = 4 is possible. (First... | A |
mathematics | In a series of six consecutive even numbers, the sum of the second and sixth numbers is 24. What is the fourth number? | [
"8",
"12",
"6",
"14",
"None of these"
] | Let the numbers be x, x + 2, x + 4, x + 6, x + 8 and x + 10.
Given (x + 2) + (x + 10) = 24
=> 2x + 12 = 24 => x = 6
The fourth number = x + 6 = 6 + 6 = 12.
ANSWER:B
The answer is: B | B |
mathematics | Anne traveled from City A to City B in 4 hours, and her speed was between 35 miles per hour and 50 miles per hour. John traveled from City A to City B along the same route in 2 hours, and his speed was between 50 miles per hour and 90 miles per hour. Which of the following could be the distance, in miles, from City A t... | [
"95",
"115",
"125",
"135",
"170"
] | In four hours Anne must travel 4 times her speed
so Anne's possible distances =
4(35 -50) or 140-200 miles
in two hours John travels 2 times his speed or
2(50-90) or 100-180 miles
the statement is only true if both distances are possible,
so you can tell its between or equal to
140-180
E is the answer.
The answer is: E | E |
mathematics | 7 speakers gathered to deliver speeches on two topics. Even though 7 speeches were initially planned to be delivered, due to lack of time only 2 speeches were finally decided to be delivered. Topics are to be spoken in a specific order and the speeches differ with respect to speaker or topic. How many such two speeches... | [
"2",
"49",
"50",
"47",
"1024"
] | 1)there are 7 speeches in ONE topic and 7 in OTHER..
2)there is a specific order for topics, so
a) both the topics are to be spoken on- so ONE from each
b) the order does not matter since there is ONLY one specific order..
so 7C1∗7C1=7∗7=49
ANSWER:B
The answer is: B | B |
mathematics | In a certain city, 60% of the registered voters are democrats and the rest are republicans.In a mayoral race, if 75% of the registered voters who are democrats and 20% of the registered voters who are republicans are expected to vote for candidate A,What % of the registered voters are expected to vote for candidate A? | [
"50%",
"53%",
"54%",
"55%",
"57%"
] | Let total voters = 100
so D= 60, vote for the mayor 60*75%=45 (60*3/4)
R= 40, vote for the mayor 40*20%= (40*1/5)
45+8=53
53/100*100=53%
ANSWER:B
The answer is: B | B |
mathematics | Average of five numbers is 12, and the sum of three of the numbers is 39, what is the average of the other 2 numbers? | [
"9.5",
"8.5",
"7.5",
"11.5",
"10.5"
] | Let the five numbers be a, b, c, d, e. Then their average is (a+b+c+d+e)/5=12
a+b+c=39
(39+d+e)/5=12
39+d+e=60
d+e=21
average=21/2=10.5
Ans E
The answer is: E | E |
mathematics | A man rides at the rate of 20km/hr. But stops 20minutes to change horses at the end of every 30th kilometer. How long will he take to go a distance of 120 kilometers? | [
"5hr",
"6hr 30min",
"8hr 10min",
"7hr",
"9hr"
] | speed of man = 20km/hr
number of rests = (120/30)-1 = 3
time taken for the man = (120/20)+3*(20/60) = 7 hr
Answer is D
The answer is: D | D |
mathematics | Two trains are moving at 50 kmph and 70 kmph in opposite directions. Their lengths are 170 m and 100 m respectively. The time they will take to pass each other completely is? | [
"3 sec",
"8 sec",
"9 sec",
"5 sec",
"7 sec"
] | 70 + 50 = 120 * 5/18 = 100/3 mps
D = 170 + 100 = 270 m
T = 270 * 3/100 = 8 sec
ANSWER:B
The answer is: B | B |
mathematics | How many distinct four-digit numbers can be formed by the digits {1, 2, 3, 4, 5, 5, 6, 6}? | [
"280",
"360",
"486",
"560",
"606"
] | Option 1: each group of 4 different digits will produce 4!=24 four-digit numbers
- Option 2: each group of 4 digits that contains two 5's will produce 4!/2=12 four-digit numbers
- Option 3: same with option 2 -> 4!/2=12 four-digit numbers
- Option 4: 4!/4=6 four-digit numbers
In total, there are: 15*24 + 10*12 + 10*12 ... | E |
mathematics | A train sets off at 2 p.m. at the speed of 70 kmph. Another train starts at 4:00 p.m. in the same direction at the rate of 85 kmph. At what time the trains will meet? | [
"10.18 p.m",
"11.00 p.m",
"10.30 p.m",
"10.38 p.m",
"10.32 p.m"
] | D = 70 * 1 ½ = 105 km
RS = 85 – 70 = 15
T = 105/15 = 7 h
4.00 + 7 h = 11.00 p.m.
Answer:B
The answer is: B | B |
mathematics | If 5 toys cost Rs, 234, what do 35 toys cost? | [
"1645",
"1564",
"1546",
"1638",
"None of them"
] | Let the required cost be Rs. x. Then,
More toys, More cost (Direct Proportion)
= x=(35 X 234)/5 =1638
Answer is D
The answer is: D | D |
mathematics | A certain characteristic in a large population has a distribution that is symmetric about the mean m. 60 percent of the distribution lies within one standard deviation d of the mean. If the shelf’s average life is 7.2 years and the standard deviation is 2.8 years, what percent of the distribution has more than 10.0 yea... | [
"10%",
"12%",
"14%",
"15%",
"17%"
] | Average = 7.2
SD = 2.8
7.2 - 2.8 < 60% of distribution < 7.2 + 2.8
4.4 < 60% of distribution < 10.0
30% is outside this range.
Given: Distribution is symmetric. So 15% of distribution is less than 7.5 and the other 15% of distribution is greater than 10.0.
Answer: D
The answer is: D | D |
mathematics | 81,162,49,98,25,50,64 | [
"126",
"127",
"129",
"128",
"131"
] | 81*2=162
49*2=98
25*2=50
64*2=128
ANSWER:D
The answer is: D | D |
mathematics | The average of first ten prime numbers which are odd is? | [
"15.5",
"15.7",
"15.2",
"15.8",
"15.1"
] | Sum of first 10 prime no. which are odd = 158
Average = 158/10 = 15.8
Answer:D
The answer is: D | D |
mathematics | If A : B= 1 : 2 and B : C = 3 : 4, then A : B : C is: | [
"9:6:4",
"1:2:3",
"3:6:9",
"12:25:87",
"3:5:7"
] | A:B=1:2, B:C=3:4, A:B:C=3×3:3×2:1×4
⇒ 9:6:4
Answer: A.
The answer is: A | A |
mathematics | The no. of girls in a class are seven times the no. of boys, which value cannever be the of total students? | [
"23",
"25",
"30",
"36",
"39"
] | Let the boys are X, then girls are 7X, total = X+7X = 8X
So it should be multiple of 8, 30 is not a multiple of 8.
C
The answer is: C | C |
mathematics | hree persons A, B and C divide a certain amount of money such that A's share is Rs. 4 less than half of the total amount, B's share is Rs. 8 more than half of what is left and finally C takes the rest which is Rs. 14. Find the total amount they initially had with them?
A. Rs. 61 B. Rs. 85 | [
"20",
"20",
"30",
"80",
"33"
] | Let the total amount be Rs. p.
Let shares of A and B be Rs. x and Rs. y respectively.
C's share was Rs. 14
we have, x + y + 14 = p ----- (1)
From the given data, x = (p/2) - 4 ----- (2)
Remaining amount = p - (p/2 - 4) => p/2 + 4.
y = 1/2(p/2 + 4) + 8 => p/4 + 10 ----- (3)
From (1), (2) and (3)
p/2 - 4 + p/4 + 10 + 14 ... | D |
mathematics | A man whose bowling average is 12.4, takes 8 wickets for 26 runs and there by decreases his average by 0.4. the number of wickets taken by him before his last match is? | [
"173",
"174",
"175",
"176",
"177"
] | 12.4*x+26=(8+x)12
solve equation x=175
ANSWER:C
The answer is: C | C |
mathematics | How many numbers are there between 20 and 60 which are divisible by 3 and the total of two digits is 9? | [
"2",
"3",
"4",
"5",
"6"
] | Since number are
27,36,45,54
ANSWER:C
The answer is: C | C |
mathematics | Find value of X: 5216 × 51 = X | [
"265016",
"343546",
"266016",
"353546",
"457632"
] | Normal way of multiplication may take time. Here is one alternative.
5216×51=(5216×50)+5216=(5216×1002)+5216=5216002+5216=260800+5216=266016
C
The answer is: C | C |
mathematics | How many numbers between 11 and 90 are divisible by 7 ? | [
"23",
"11",
"22",
"32",
"15"
] | The required numbers are 14, 21, 28, 35, .... 77, 84.
This is an A.P. with a = 14 and d = (21 - 14) = 7.
Let it contain n terms.
Then, Tn = 84 => a + (n - 1) d = 84
=> 14 + (n - 1) x 7 = 84 or n = 11.
Required number of terms = 11
ANSWER B 11
The answer is: B | B |
mathematics | A certain car averages 25 miles per gallon of gasoline when driven in the city and 35 miles per gallon when driving on the highway. According to these rates, which of the following is closest to the number of miles per gallon that the car averages when it is driven 10 miles in the city and then 50 miles on the highway? | [
"28",
"30",
"33",
"36",
"38"
] | 10*1/25 gpm+50*1/35 gpm=1.82 total gallons
60 total miles/1.82 total gallons=32.9 average mpg
C. 33
The answer is: C | C |
mathematics | What is the least number to be subtracted from 11, 15, 21 and 30 each so that the resultant numbers become proportional? | [
"7",
"6",
"3",
"4",
"9"
] | Let the least number to be subtracted be 'x', then 11 - x, 15 - x, 21 - x and 30 - x are in proportion.
<=> (11 - x):(15 - x) = (21 - x):(30 -x)(21 - x)
From the options, when x = 3
=> 8 * 27 = 12 * 18 => then x = 3. => (11 - x)(30 - x) = (15 - x)(21 - x)
Answer: C
The answer is: C | C |
mathematics | 5 men are equal to as many women as are equal to 8 boys. All of them earn Rs.90 only. Men’s wages are? | [
"Rs.6",
"Rs.6.5",
"Rs.8",
"Rs.5",
"Rs.2"
] | Answer: Option A
5M = xW = 8b
5M + xW + 8b ----- 90 Rs.
5M + 5M + 5M ----- 90 Rs.
15M ------ 90 Rs. => 1M = 6Rs.
The answer is: A | A |
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