mathewhe/aqua_rat huggingface dataset:
Question: On a certain farm the ratio of horses to cows is 5:1. If the farm were to sell 15 horses and buy 15 cows, the ratio of horses to cows would then be 17:7. After the transaction, how many more horses than cows would the farm own?
(A) 30
(B) 40
(C) 50
(D) 60
(E) 70
Rationale: Originally, there were 5k horses and k cows.
7(5k-15) = 17(k+15)
35k-17k = 255+105
18k = 360
k = 20
The difference between horses and cows is (5k-15)-(k+15) = 4k-30 = 50
The answer is C.
Answer: (C) 50
Question: If a number is formed by writing integers 1 to 150 one after another, like 12345...150. How many W digits does this integer consists of?
(A) 150
(B) 339
(C) 342
(D) 359
(E) 362
Rationale: Number of single digit integers = 9
Number of 2 digit integers = 99 - 10 + 1 = 90
Number of 3 digit integers = 150 - 100 + 1 = 51
Number of digits in the integer W= 1*9 + 2*90 + 3*51 = 9 + 180 + 153 = 342
Answer: C
Answer: (C) 342
Question: Ashok secured average of 70 marks in 6 subjects. If the average of marks in 5 subjects is 74, how many marks did he secure in the 6th subject?
(A) 50
(B) 74
(C) 78
(D) 80
(E) None of these
Rationale: Explanation:
Number of subjects = 6
Average of marks in 6 subjects = 70
Therefore total marks in 6 subjects = 70 * 6 = 420
Now, No. of subjects = 5
Total marks in 5 subjects = 74 * 5 = 370
Therefore marks in 6th subject = 420 – 370 = 50
ANSWER A
Answer: (A) 50
Question: If the sides of a triangle are 28 cm, 26 cm and 10 cm, what is its area?
(A) 120
(B) 130
(C) 288
(D) 266
(E) 2848
Rationale: The triangle with sides 28 cm, 26 cm and 10 cm is right angled, where the hypotenuse is 28 cm.
Area of the triangle = 1/2 * 26 * 10 = 130 cm2
Answer: B
Answer: (B) 130
Question: How many four digit numbers have no repeat digits, do not contain zero, and have a sum of digits D equal to 28?
(A) 14
(B) 24
(C) 28
(D) 48
(E) 96
Rationale: First, look for all 4 digits without repeat that add up to 28. To avoid repetition, start with the highest numbers first.
Start from the largest number possible 9874.
Then the next largest number possible is 9865.
After this, you'll realize no other solution. Clearly the solution needs to start with a 9 (cuz otherwise 8765 is the largest possible, but only equals 26). With a 9, you also need an 8 (cuz otherwise 9765 is the largest possible, but only equals 27). With 98__ only 74 and 65 work.
So you have two solutions. Each can be rearranged in 4!=24 ways. So D=24+24=48.D
Answer: (D) 48
Question: A watch was sold at a loss of 10%. If it was sold for Rs.140 more, there would have been a gain of 4%. What is the cost price?
(A) Rs.1000
(B) Rs.1087
(C) Rs.1028
(D) Rs.1029
(E) Rs.1023
Rationale: 90%
104%
--------
14% ---- 140
100% ---- ? => Rs.1000
Answer: A
Answer: (A) Rs.1000
Question: A lady has fine gloves and hats in her closet - 18 blue, 32 red, and 25 yellow. The lights are out and it is totally dark. In spite of darkness, she can make out the difference between a hat and a glove. She takes out an item out of the closet only if she is sure that it is a glove. How many gloves must she take out to make sure she has a pair of each color?
(A) 60
(B) 65
(C) 70
(D) 75
(E) 80
Rationale: 32r+24y+1y+1b+2b=60
ANSWER:A
Answer: (A) 60
Question: A tourist does not have to pay tax on the first $600 of goods he purchases in Country B, but does have to pay a 8 percent tax on the portion of the total value that is in excess of $600. What tax must be paid by a tourist if he buys goods with a total value of $1720?
(A) $54.00
(B) $89.60
(C) $90.00
(D) $100.80
(E) $154.80
Rationale: Correct Answer: B
The tourist must pay tax on $1720 - $600 = $1120. Thus, the amount of tax he has to pay is 0.08 ($1120) = $89.60. The correct answer is B.
Answer: (B) $89.60
Question: The sum of the digits of a two digit number is 10. When the digits are reversed, the number decreases by 54. Find the changed Number.
(A) 28
(B) 19
(C) 37
(D) 46
(E) 50
Rationale: a+b = 10
10a + b - 10b - a = 54
a-b = 6
a= 8, b = 2.
Reversed number is 28.
Ans A
Answer: (A) 28
Question: If n + 14 is a positive odd integer, which of the following must be true about the sum of the next four integers?
(A) It is a multiple of 3
(B) It is a multiple of 4
(C) It is a multiple of 2
(D) It is a multiple of 5
(E) It is a prime number
Rationale: n+14 is a positive odd integer. This means n will be an odd integer
The next 4 integers would be: n + 14, n + 15, n + 16, n + 17
Sum = 4n + 62
This sum will always be even.
Option C
Answer: (C) It is a multiple of 2
Question: 16 boys or 24 girls can construct the wall in 6 days. the number of days that 8 boys and 24 girls Will take to construct?
(A) 4 days
(B) 14 days
(C) 6 days
(D) 8 days
(E) 9 days
Rationale: Explanation:
16 boys =24 girls, 1 boy = 24/16 girls
1 boy = 6/4 girls
8 boys + 24 girls = 8 Ã— 6/4 + 12 = 12 + 24 = 36 girls
4 days to complete the work
Answer: Option A
Answer: (A) 4 days
Question: A dishonest dealer uses a scale of 92 cm instead of a metre scale and claims to sell at cost price. His profit is
(A) 9%
(B) 10%
(C) 12%
(D) None of these
(E) 8.7%
Rationale: Solution
Gain%	= (8 / 92 x 100)%
= 8.7%
Answer E
Answer: (E) 8.7%
Question: A man is 28 years older than his son. In four years, his age will be twice the age of his son. The present age of this son is
(A) 21 years
(B) 22 years
(C) 23 years
(D) 24 years
(E) 25 years
Rationale: Explanation:
Let's Son age is x, then Father age is x+28.
=> 2(x+4) = (x+28+4)
=> 2x+8 = x+32
=> x = 24 years
Answer: Option D
Answer: (D) 24 years
Question: Reduce
368/736
to the lowest terms
(A) 3/5
(B) 2/9
(C) 2/8
(D) 1/2
(E) None of these
Rationale: Explanation:
We can do it easily by in two steps
Step1: We get the HCF of 368 and 736 which is 368
Step2: Divide both by 368, we will get the answer 1/2
Answer: Option D
Answer: (D) 1/2
Question: From a group of 5 boys and 5 girls, 6 children are to be randomly selected. What is the probability that 3 boys and 3 girls will be selected?
(A) 4/15
(B) 6/17
(C) 8/19
(D) 10/21
(E) 12/23
Rationale: The total number of ways to choose 6 children from 10 is 10C6 = 210
The number of ways to choose 3 boys and 3 girls is 5C3*5C3 = 10*10 = 100
P(3 boys and 3 girls) = 100/210 = 10/21
The answer is D.
Answer: (D) 10/21
Question: If x and y are integers and x divided by y is 17.15, then which of the following integers is a possible value for the remainder when x is divided by y? I. 15 II. 5 III. 3
(A) II only
(B) I only
(C) II,III only
(D) III only
(E) I,III only
Rationale: x=17.15y from which x = 17y + 15y/100 or x = 17y + 3y/20.
Since x and y are integers, 3y/20 must also be an integer. 3 is not divisible by 20, then y must be divisible by 20, and therefore, y/20 is an integer and 3y/20 is an integer which is a multiple of 3. From the given answers, only 15 and 3 are divisible by 3.
Answer E
Answer: (E) I,III only
Question: If each side of a rectangle is increased by 50% with the length being double the width, find the percentage change in its area?
(A) 284%
(B) 276%
(C) 265.25%
(D) 284.5%
(E) 275%
Rationale: area = 2a x a
New length = 250a / 100 = 5a /2
New width = 150a / 100 = 3a /2
New area =(5a x 3a) / (2 x 2) = (15a²/4)
increased area== (15a²/4) - a²
Increase %= [(11a²/4 ) x (1/a² ) x 100]% = 275%
answer :E
Answer: (E) 275%
Question: Having received his weekly allowance, John spent 3/5 of his allowance at the arcade. The next day he spent one third of his remaining allowance at the toy store, and then spent his last $0.75 at the candy store. What is John’s weekly allowance?
(A) $2.40
(B) $2.80
(C) $3.20
(D) $3.60
(E) $4.80
Rationale: Total allowance=X
Amount spent at the arcade=3/5X
Amount Remaining=2/5X
Amount Spent at the toy store=2/5*1/3X=2/15X
Amount Remaining=2/5X-2/15X=4/15X
Now, 4/15X=$0.8
Therefore, X=$2.80. Answer B
Answer: (B) $2.80
Question: By approximately what percent is x greater than 2/5 if (3/5)(x) = 1?
(A) 723%
(B) 156%
(C) 316%
(D) 37%
(E) 29%
Rationale: what percent is x greater than 2/5 if (3/5)(x) = 1?
=> x = 5/3
% change =[(5/3 -2/5) /(2/5) ] * 100
= 316.5%
= 316% approx
Ans ,C
Answer: (C) 316%
Question: How many positive integer solutions does the equation 2x+3y = 100 have?
(A) 50
(B) 33
(C) 16
(D) 35
(E) 14
Rationale: formula: (constant)/(lcm of two nos)
=100/(2*3)=15.5
ANSWER:C
Answer: (C) 16
Question: A diner is having lunch at a salad bar. There are two types of lettuce to choose from, as well as three types of tomatoes, and five types of olives. If the diner picks one type of lettuce, one type of tomato, and one type of olive for the salad, how many total options does the diner have for the salad?
(A) 25
(B) 30
(C) 35
(D) 40
(E) 45
Rationale: 2*3*5 = 30
The answer is B.
Answer: (B) 30
Question: The ratio of two numbers is 3 : 4 and their H.C.F. is 4. Their L.C.M. is
(A) 48
(B) 22
(C) 56
(D) 27
(E) 67
Rationale: Explanation:
Let the numbers be 3x and 4x. Then, their H.C.F. = x. So, x = 4.
So, the numbers 12 and 16.
L.C.M. of 12 and 16 = 48.
Option A
Answer: (A) 48
Question: A, B, C subscribe Rs. 50,000 for a business. If A subscribes Rs. 4000 more than B and B Rs. 5000 more than C, out of a total profit of Rs. 35,000, what will be the amount A receives?
(A) 14700
(B) 14500
(C) 14000
(D) 15000
(E) 15200
Rationale: Total amount invested = 50000
Assume that investment of C =x.
Then investment of B =5000+x,
Investment of A =4000+5000+x=9000+x
x+5000+x+9000+x=50000
⇒3x+14000=50000
⇒3x=50000–14000=36000
⇒x=36000/3=12000
Investment of C =x=12000
Investment of B =5000+x=17000
Investment of A =9000+x=21000
Ratio of the investment of A, B and C
=21000:17000:12000=21:17:12
Share of A = Total profit ×21/50
=35000×2150=700×21=14700
Answer is A.
Answer: (A) 14700
Question: A box contains 3 blue marbles, 4 red, 6 green marbles and 2 yellow marbles. If two marbles are picked at random, what is the probability that they are either blue or yellow?
(A) 2/26
(B) 2/20
(C) 2/21
(D) 2/22
(E) 6/21
Rationale: Given that there are three blue marbles, four red marbles, six green marbles and two yellow marbles. Probability that both marbles are blue = = (3 * 2)/(15 * 14) = 1/35
Probability that both are yellow = = (2 * 1)/(15 * 14) = 1/105
Probability that one blue and other is yellow = = (2 * 3 * 2)/(15 * 14) = 2/35
Required probability = 1/35 + 1/105 + 2/35
= 3/35 + 1/105 = 1/35(3 + 1/3)
= 10/(3 * 35) = 2/21.Answer:C
Answer: (C) 2/21
Question: A, B and C invested Rs.6300, Rs.4200 and Rs.10500 respectively, in a partnership business. Find the share of A in profit of Rs.12100 after a year?
(A) Rs.500
(B) Rs.1000
(C) Rs. 3630
(D) Rs.2500
(E) Rs.6000
Rationale: Explanation:
6300:4200:10500
3:2:5
3/10 * 12100 =Rs. 3630
ANSWER:C
Answer: (C) Rs. 3630
Question: When 5 + 6 = 305, 6 + 7 = 425, 7 + 8 = 565, then 8 + 9 = ?
(A) 705
(B) 735
(C) 685
(D) 665
(E) 725
Rationale: 5 + 6 => 5 Ã— 6 = 30 => 30 Ã— 10 + 5 = 305
6 + 7 => 6 Ã— 7 = 42 => 42 Ã— 10 + 5 = 425
7 + 8 => 7 Ã— 8 = 56 => 56 Ã— 10 + 5 = 565
Then 8 + 9 => 8 Ã— 9 = 72 => 72 Ã— 10 + 5 = 725
Answer : E
Answer: (E) 725
Question: How long does a train 120 m long traveling at 60 kmph takes to cross a bridge of 170 m in length?
(A) sec
(B) sec
(C) sec
(D) sec
(E) sec
Rationale: D = 120+ 170 = 290 m
S = 60 * 5/18 = 50/3
T = 290 * 3/50 = 17.4 sec
Answer: D
Answer: (D) sec
Question: |x+3| – |4-x| = |8+x| How many solutions Zwill this equation have?
(A) 0
(B) 1
(C) 2
(D) 3
(E) 4
Rationale: Z=|x| = x when x >= 0 (x is either positive or 0)
|x| = -x when x < 0 (note here that you can put the equal to sign here as well x <= 0 because if x = 0,
|0| = 0 = -0 (all are the same)
So the '=' sign can be put with x > 0 or with x < 0. We usually put it with 'x > 0' for consistency.A
Answer: (A) 0
Question: A does a work in 30 days and B does the same work in 15 days. In how many days they together will do the same work ?
(A) 7 days
(B) 8 days
(C) 9 days
(D) 10 days
(E) None of these
Rationale: Explanation:
Firstly we will find 1 day work of both A and B, then by adding we can get collective days for them,
So,
A's 1 day work = 1/30
B's 1 day work = 1/15
(A+B)'s 1 day work =
(1/30+1/15)=1/10
So together they can complete work in 10 days.
Answer: D
Answer: (D) 10 days
Question: A man cycling along the road noticed that every 6 minutes a bus overtakes him and every 2 minutes he meets an oncoming bus. If all buses and the cyclist move at a constant speed, what is the time interval between consecutive buses?
(A) 3 minutes
(B) 6 minutes
(C) 8 minutes
(D) 9 minutes
(E) 10 minutes
Rationale: Let's say the distance between the buses is d. We want to determine Interval=\frac{d}{b}, where b is the speed of bus.
Let the speed of cyclist be c.
Every 6 minutes a bus overtakes cyclist: \frac{d}{b-c}=6, d=6b-6c;
Every 2 minutes cyclist meets an oncoming bus: \frac{d}{b+c}=2, d=2b+2c;
d=6b-6c=2b+2c, --> b=2c, --> d=6b-3b=3b.
Interval=\frac{d}{b}=\frac{3b}{b}=3
Answer: A (3 minutes).
Answer: (A) 3 minutes
Question: A certain Maroon paint contains 50 percent blue pigment and 50 percent red pigment by weight. A certain green paint contains 30 percent blue pigment and 70 percent yellow pigment. When these paints are mixed to produce a brown paint, the brown paint contains 40 percent blue pigment. If the brown paint weighs 10 grams, then the red pigment contributes how many grams of that weight?
(A) 3
(B) 3.5
(C) 2.5
(D) 4
(E) 4.5
Rationale: 10 Grams of combined mixture and 40% blue pigment means that the mixtures were mixed 50% each. Thus 5 grams a piece. Out of the 5 grams of the Dark Blue paint, 60% is red. Therefore, 5*.5 = 2.5 Grams of red pigment
Answer: (C) 2.5
Question: A sum of money is to be distributed among A, B, C, D in the proportion of 5 : 2 : 4 : 3. If C gets $500 more than D, what is B's share?
(A) $500
(B) $1000
(C) $1500
(D) $2000
(E) $2500
Rationale: Let the shares of A, B, C and D be 5x, 2x, 4x and 3x respectively.
Then, 4x - 3x = 500
x = $500
B's share = 2x = 2*$500 = $1000
The answer is B.
Answer: (B) $1000
Question: In what time a sum of money double itself at 4% per annum simple interest?
(A) 33 1/8%
(B) 33 1/3%
(C) 33 7/3%
(D) 32 1/3%
(E) 25 %
Rationale: P = (P*4*R)/100
R = 25%
Answer: E
Answer: (E) 25 %
Question: In a throw of a coin find the probability of getting a head?
(A) 1/2
(B) 1/3
(C) 1/4
(D) 2/3
(E) 2/5
Rationale: S = {H,T}
E = {H}
P(E) = 1/2
Answer is A
Answer: (A) 1/2
Question: A and B can do a piece of work in 12 days and 16 days respectively. Both work for 3 days and then A goes away. Find how long will B take to complete the remaining work?
(A) 2 days
(B) 6 days
(C) 8 days
(D) 9 days
(E) 5 days
Rationale: Explanation:
3/12 + (3 + x)/16 = 1
x = 9 days
Answer:D
Answer: (D) 9 days
Question: 23, 18, 16, 11, 9, 4 ?
(A) 3
(B) 2
(C) 7
(D) 5
(E) 1
Rationale: This is a simple alternating subtraction series, with a pattern -2, -5, -2, -5 ....
Answer : B.
Answer: (B) 2
Question: What should come in place of the question mark (?) in the following number series?
5690 5121 4552 3983 3414 2845 ?
(A) 2276
(B) 2516
(C) 2746
(D) 2356
(E) None of these
Rationale: Explanation:
By Subtracting 569,We Get the Next Term,
5690-569=5121
5121-569=4552
4552-569=3983
3983-569=3414
3414-569=2845
2845-569=2276
Answer: A
Answer: (A) 2276
Question: is two years older than B who is twice as old as C. If the total of the ages of A, B and C be 22, then how old is B?
(A) 7
(B) 8
(C) 9
(D) 10
(E) 11
Rationale: Let C's age be x years.
Then, B's age = 2x years.
A's age = (2x + 2) years.
(2x + 2) + 2x + x = 22
5x = 20 => x = 4
Hence, B's age = 2x = 8 years.
ANSWER:B
Answer: (B) 8
Question: 16 men can complete a piece of work in 25 days. In how many days can 15 men complete that piece of work?
(A) 26.7 days
(B) 77 days
(C) 20 days
(D) 88 days
(E) 44 days
Rationale: 16 * 25 = 15 * x => x
= 26.7 days
Answer: A
Answer: (A) 26.7 days
Question: Out of 7 consonants and 4 vowels, how many words of 3 consonants and 2 vowels can be formed?
(A) 25200
(B) 33232
(C) 23228
(D) 29982
(E) 20822
Rationale: Number of ways of selecting (3 consonants out of 7) and (2 vowels out of 4)
=7C3X4C2
= 210.
Number of groups, each having 3 consonants and 2 vowels = 210.
Each group contains 5 letters.
Number of ways of arranging 5 letters among themselves
= 5!
= 120
Required number of ways = (210 x 120) = 25200.
Answer: A
Answer: (A) 25200
Question: If 12 men or 20 women can do a piece of work in 54 days, then in how many days can 9 men and 12 women together do the work?
(A) 22 days
(B) 88 days
(C) 40 days
(D) 55 days
(E) 44 days
Rationale: Given that 12m = 20w => 3m = 5w
9 men + 12 women = 15 women + 12 women = 27 women
20 women can do the work in 54 days. So, 27 women can do it in (20 * 54) /27
= 40 days.
Answer: C:
Answer: (C) 40 days
Question: On tuesday Morning, Chris receives tickets to a baseball game that will be played at 8pm on the next evening that it does not rain. However, Chris is only in town until Thursday morning, at which point he must fly to another city. If there is a 30% chance of rain each of the next two evenings, what is the probability that Chris will be able to attend the game?
(A)  36%
(B)  91%
(C)  66%
(D)  80%
(E)  84%
Rationale: Chris won't be able to attend the game if it be raining on Monday eveningandTuesday evening. The probability of that is 0.3*0.3 = 0.09. So, the probability that he will be able to attend is 1 - 0.09 = 0.91.
Answer: B.
Answer: (B)  91%
Question: How many of the following numbers are divisible by 132?
264, 396, 462, 792, 968, 2178, 5412, 6336
(A) 4
(B) 5
(C) 6
(D) 7
(E) 8
Rationale: A number is divisible by 132, if it is divisible by each one of 11, 3 and 4.
Clearly, 968 is not divisible by 3. None of 462 and 2178 is divisible by 4.
Each one of remaining 5 is divisible by each one of 11, 3 and 4 and therefore, by 132.
ANSWER:B
Answer: (B) 5
Question: Current age of Bruce and Tomy r in the ratio of 5:4 respectively. 3 years hence, the ratio of their ages will become 11:9 respectively. What is Tomy 's present age in years?
(A) 12 years
(B) 16 years
(C) 24 years
(D) 32 years
(E) 36 years
Rationale: Let the present ages of Bruce and Tomy be 5x years and 4x years respectively.
Then, 5x + 3 = 11
4x + 3 9
9(5x + 3) = 11(4x + 3)
45x + 27 = 44x + 33
45x - 44x = 33 - 27
x = 6.
Anand's present age = 4x = 24 years.
C
Answer: (C) 24 years
Question: In traveling from a dormitory to a certain city, a student went 1/3 of the way by foot, 1/4 of the way by bus, and the remaining 5 kilometers by car. What is the distance, in kilometers, from the dormitory to the city?
(A) 13
(B) 17
(C) 42
(D) 15
(E) 12
Rationale: Whole trip = distance by foot + distance by bus + distance by car
x = 1/2x + 3/5x + 5
x - 1/2x - 3/5x = 5
x = 12km
Option: E
Answer: (E) 12
Question: How many different arrangements are possible to place seven different books on a shelf if all three math books must be placed next to each other?
(A) 120
(B) 148
(C) 360
(D) 540
(E) 720
Rationale: Let the 3 math books be M1,M2,M3 while the rest be A,B,C,D for a total of 7 different books.
Consider 3 math books to be 1 collective item (=M1M2M3 = M , as they need to be together). Thus, number of arrangements of 3 different books (M1M2M3)= 3P3 = 3!
Total number of arrangements of M,A,B,C,D = 5P5= 5!
Thus, The total possible arrangements will be : M1M2M3 ABCD = 5!*3! = 720, E is the correct answer
Answer: (E) 720
Question: John bought 9.25m of cloth for $444. Find the cost price per metre.
(A) 48
(B) 47
(C) 58
(D) 56
(E) 54
Rationale: Cloth bought by John = 9.25 m
Cost of 9.25 m = $444
Cost per metre = 444 ÷ 9.25
The cost of the cloth per metre = $ 48
Answers: A
Answer: (A) 48
Question: A certain team has 15 members, including Joey. A three-member relay team will be selected as follows: one of the 15 members is to be chosen at random to run first, one of the remaining 14 members is to be chosen at random to run second, and one of the remaining 13 members is to be chosen at random to run third. What is the probability that Joey will be chosen to run second or third?
(A) 1/1320
(B) 1/132
(C) 1/110
(D) 1/12
(E) 2/15
Rationale: Total outcomes= 15*14*13
Favorable Outcomes= 14*1*13 and 14*13*1
P=2*14*13*1/15*14*13
P=2/15
Ans E
Answer: (E) 2/15
Question: Employee A work from 01:00 to 08:45 (24 hour clock) on each of the five days this week. Next week, he is scheduled to work the same total hours, but will work a compressed 4 day work schedule. If he starts work at 01:00 next week, what time will he finish each day?
(A) 09:04
(B) 10:41
(C) 10:45
(D) 11:56
(E) 16:19
Rationale: working hours between 01:00 - 08:45 for 5 days are 7:45*5 (5 days) = 38:45
same total hours are to be scheduled for 4 days,
so 38:45/4 = 10:41
ANSWER:B
Answer: (B) 10:41
Question: A certain restaurant offers 4 kinds of cheese and 2 kinds of fruit for its dessert platter. If each dessert platter contains an equal number of kinds of cheese and kinds of fruit, how many different dessert platters could the restaurant offer?
(A) 8
(B) 12
(C) 15
(D) 21
(E) 14
Rationale: As dessert platter should contain equal number of kinds of cheese and fruits, desert can contain:
A. 2 kinds of cheese and 2 kinds of fruits --> 4C2*2C2=6*1=6
B. 1 kind of cheese and 1 kind of fruit --> 4C1*2C1=4*2=8
A+B=6+8=14
Answer: E.
Answer: (E) 14
Question: If 5 machines can produce 20 units in 10 hours, how long would it take 10 machines to produce 100 units?
(A) 25
(B) 30
(C) 35
(D) 24
(E) 96
Rationale: 5 machines would produce 100 units in 50 hours. Increasing the amount of machines by 2 would mean dividing 50 hours by 2.
50/2 = 25
Answer : A
Answer: (A) 25
Question: A certain vehicle is undergoing performance adjustments during a set of three trials on an 8-mile track. The first time it travels around the track at a constant rate of p miles per minute, the second time at a constant rate of p^2 miles per minute, and the third time at a constant rate of p^3 miles per minute. If the vehicle takes the same time to travel the first 18 miles of these trials as it does to travel the last 8 miles, how many minutes does it take to complete all three trials (not counting any time between trials)?
(A) 18
(B) 36
(C) 60
(D) 96
(E) 112 minutes
Rationale: The first journey takes 18 miles whereas the last journey takes 8 miles.
r1= p
r2=p^2
and r3= p^3 so we set up a table like
r x t = d
p x t1 = 8
p^2 x t2= 8
p^3 x t3 = 2 (because 18-16)
so the time taken to complete each leg individually amounts to t1 + t2 + t3 = (8/p) + (8/p^2) + (2/p^3). ----> (equation 1)
On the other hand, the time taken to complete the last leg of miles is (8/p^3) ---> (equation 2) because p^3 is the speed on the last leg. Since both the times are equal, equate them to get:
(8/p) + (8/p^2) + (2/p^3) = (8/p^3)
Taking the LCM of the Left hand equation and solving both these equations gives us the value of p=1/2 and p= (-3/2) Since p can not be negative, we have p=1/2 as our value.
Now put this value in the time taken to finish each trial which is the sume of (8/p) + (8/p^2) + (8/p^3) and it will become 16+32+64 = 112 minutes.
Option E is the correct answer.
Answer: (E) 112 minutes
Question: Of the two square fields, the area of the one is 1 hectare, while anothe one is broader by 1%. There differences in area is:
(A) 201 m(power)2
(B) 220 m(power)2
(C) 211 m(power)2
(D) 219 m(power)2
(E) 205 m(power)2
Rationale: Area of one square field = 10000 m(power)2
10000 × 1 = 10000
Side of this field = √10000 m = 100 m
Side of another square = 101 m
Difference of areas = [ 101(power)2 - 100(power)2 ] m(power)2
[101+100][101-100] m(power)2
(201)(1) m2 = 201 m(power)2
Answer is A.
Answer: (A) 201 m(power)2
Question: Evaluate: 19 + sqrt(- 2 + 12Ã—6Ã·9) =?
(A) 51
(B) 53
(C) 55
(D) 57
(E) 59
Rationale: According to order of operations, inner brackets first where 12x6Ã·9 is first calculated since it has a multiplication and a division.
12x6Ã·9 = 72Ã·9 = 8
Hence
19 + sqrt(- 2 + 12Ã—6Ã·9) = 19+ sqrt(- 2 + 8)
= 19 + sqrt(6) = 19 + 36 = 55
correct answer C)55
Answer: (C) 55
Question: How many ways are there to arrange the letters in the word tenant ?
(A) 1
(B) 360
(C) 3780
(D) 7560
(E) 11340
Rationale: 6 total words, 2N
= 6! / 2! = 360. Answer B
Answer: (B) 360
Question: A, B and C are partners. A receives 2/3 of profits, B and C dividing the remainder equally. A's income is increased by Rs.300 when the rate to profit rises from 5 to 7 percent. Find the Capital of B?
(A) 3377
(B) 2899
(C) 3750
(D) 2778
(E) 1991
Rationale: A:B:C = 2/3:1/6:1/6 = 4:1:1
x * 2/100 * 2/3 = 300
B capital = 22500*1/6 = 3750
Answer: C
Answer: (C) 3750