mathewhe/aqua_rat huggingface dataset:
Question: The average of 60 results is 40 and the average of other 40 results is 60 . what is the average of all the results?
(A) 24
(B) 25
(C) 48
(D) 50
(E) None
Rationale: Answer
Sum of 100 result = sum of 60 result + sum of 40 result.
= 60 x 40 + 40 x 60
= 4800/100
Correct Option: C
Answer: (C) 48
Question: A question paper has 5 multiple choice questions. Each question has 2 choices with only one choice as the correct answer. What is the total number of ways in which a candidate will not get all the 10 answers correct?
(A) 19
(B) 85
(C) 120
(D) 624
(E) 1024
Rationale: A candidate can answer the test in 2^5 number of ways (each question has 2 choices and we have total of 5 questions). Now, out of these cases there will be only one case when the candidate answered all the 5 questions correct. Therefore the total number of ways in which a candidate will NOT get all the four answers correct is 5^4-1=624.
Answer: D.
Answer: (E) 1024
Question: The list price of an article is Rs.65. A customer pays Rs.56.16 for it. He was given two successive discounts, one of them being 10%. The other discount is?
(A) 8%
(B) 4%
(C) 6%
(D) 3%
(E) 1%
Rationale: 65*(90/100)*((100-x)/100) = 56.16
x = 4%
Answer: B
Answer: (B) 4%
Question: Tough and Tricky questions: Word Problems.
A salesman's income consists of commission and base salary. His weekly income totals over the past 5 weeks have been $406, $413, $420, $436 and $395. What must his average (arithmetic mean) income over the next two weeks be to decrease his average weekly income to $400 over the 7-week period?
(A) $350
(B) $400
(C) $365
(D) $385
(E) $375
Rationale: OFFICIAL SOLUTION:
(C) First, we need to add up the wages over the past 5 weeks: $406 + $413 + $420 + $436 + $395 = $2070.
To average $400 over 7 weeks, the salesman would need to earn: $400 × 7 = $2800.
Subtract $2070 from $2800 to determine how much he would need to earn, in total, over the next 2 weeks to average $400 for the 7 weeks: $2800 – $2070 = $730.
Dividing $730 by 2 will give us the amount he needs to earn on average over the next 2 weeks: $730/2 = $365.
The correct answer is choice (C).
Answer: (C) $365
Question: The probability of a lottery ticket being a prized ticket is 0.2. When 4 tickets are purchased, the probability of winning a prize on atleast one ticket is?
(A) 0.5904
(B) 0.5914
(C) 0.5912
(D) 0.5916
(E) 1
Rationale: Explanation:
P(winning prize atleast on one ticket)
= 1 - P("Losing on all tickets")
= 1 - (0.8)4 = (1 + (0.8)2)(1 - (0.8)2)
= (1.64)(0.36) = 0.5904
A)
Answer: (A) 0.5904
Question: Country C imposes a two-tiered tax on imported cars: the first tier imposes a tax of 12% of the car's price up to a certain price level. If the car's price is higher than the first tier's level, the tax on the portion of the price that exceeds this value is 8%. If Ron imported a $12,000 imported car and ended up paying $1440 in taxes, what is the first tier's price level?
(A) $1600
(B) $6000
(C) $6050
(D) $1200
(E) $8000
Rationale: Let T be the tier price, P be total price = 12000
Per the given conditions:
0.12T + 0.08(P-T) = 1440 ----> T= 12000. D is the correct answer.
Answer: (D) $1200
Question: If x : y = 3 : 4, find (4x + 5y) : (5x - 2y).
(A) 32/7
(B) 13/7
(C) 2/7
(D) 32/17
(E) 2/17
Rationale: . X/Y=3/4  (4x+5y)/(5x+2y)= (4( x/y)+5)/(5 (x/y)-2) =(4(3/4)+5)/(5(3/4)-2)
=(3+5)/(7/4)=32/7
ANSWER A 32/7
Answer: (A) 32/7
Question: In how many ways can 10 people, A, B, C, D, E, F, G, H, I, J be seated in a row such that C and D are not seated next to each other as well as A and B are not seated next to each other?
(A) 384
(B) 396
(C) 576
(D) 3628704
(E) 6960087
Rationale: Number of total arrangements = 10!
Restriction 1= ABCD not next to each other --> let say AB and CD are considered as one unit, respectively
Restriction 2= AB is not the same as BA + CD is not the same as DC --> the number will increase by 2*2
Total number of arrangements - Number out of restrictions = Result
10! - (4!*2*2) = 3628800 - (24*2*2) = 3628704
Answer D
Answer: (D) 3628704
Question: The area of one square is x^2 + 10x + 25 and the area of another square is 4x^2 − 20x + 25. If the sum of the perimeters of both squares is 36, what is the value of x?
(A) 3
(B) 5
(C) 7
(D) 9
(E) 11
Rationale: The areas are (x+5)^2 and (2x-5)^2.
The lengths of the sides are x+5 and 2x-5.
If we add the two perimeters:
4(x+5) + 4(2x-5) = 36
12x = 36
x = 3
The answer is A.
Answer: (A) 3
Question: What is the rate percent when the simple interest on Rs.810 amount to Rs.155 in 4 Years?
(A) 4.78
(B) 4.68
(C) 4.58
(D) 4.48
(E) 4.38
Rationale: 155 = (810*4*R)/100
R = 4.78%
Answer: A
Answer: (A) 4.78
Question: In the standard formulation of a flavored drink the ratio by volume of flavoring to corn syrup to water is 1 : 12 : 30. In the sport formulation, the ratio of flavoring to corn syrup is three times as great as in the standard formulation, and the ratio of flavoring to water is half that of the standard formulation. If a large bottle of the sport formulation contains 5 ounces of corn syrup, how many ounces of water does it contain?
(A) 45
(B) 50
(C) 55
(D) 60
(E) 75
Rationale: F:C:W
1:12:30
Sport version:
F:C
3:12
F:W
1:60
OR 3:180
So C:F:W = 12:3:180
C/W = 12/180 = 3 ounces/x ounces
x = 5*180/12 = 75 ounces of water
E
Answer: (E) 75
Question: In how many ways 5 different balls can be arranged in to 3 different boxes so that no box remains empty?
(A) 125
(B) 150
(C) 175
(D) 200
(E) 225
Rationale: 1. The total number of possibilities including empty boxes: 35=24335=243
2. Two of the boxes are empty: C32=3C23=3
3. One but not two of the boxes is empty: 3∗(25−2)=903∗(25−2)=90
4. the total number of possibilities excluding empty boxes: 243 - 3 - 90 = 150
ANS:B
Answer: (B) 150
Question: The percentage profit earned by selling an article for $1920 is equal to the percentage loss incurred by selling the same article for $1280. At what price should the article be sold to make 25% profit?
(A) 1000
(B) 3000
(C) 2000
(D) 4000
(E) 5000
Rationale: B
2000
Let C.P. be $x.
Then, (1920 - x)/x * 100 = (x - 1280)/x * 100
1920 - x = x - 1280
2x = 3200 => x = 1600
Required S.P. = 125 % of $1600 = 125/100 * 1600 = $2000.
Answer: (C) 2000
Question: Mr. Smith calculated the average of 10three digit numbers. But due to a mistake he reversed the digits of a number and thus his average increased by 39.6. The difference between the unit digit and hundreds digit of that number is :
(A) a) 4
(B) b) 3
(C) c) 2
(D) d) 1
(E) e) 0
Rationale: Since the average increased by 39.6 and there were a total of 10 numbers, it means the incorrect number was 396 greater than the correct number.
Say, the correct number was abc (where a, b and c are the digits of the 3 digit number)
Then the incorrect number was cba.
100c + 10b + a - (100a + 10b + c) = 396
99c - 99a = 99(c - a) = 396
396 = 99*4 = 99(c - a)
So c - a = 4
Answer (A
Answer: (A) a) 4
Question: In a University the average age in an arts class is 21 and average age in technical class is 18. What is the age average of University if there are 8 arts classes and 5 technical classes?
(A) 18.75
(B) 19.85
(C) 20.32
(D) 20.9
(E) 21.0
Rationale: Average age of University= ((8x21)+(5x18))/13
=19.85
Answer: B
Answer: (B) 19.85
Question: In a certain deck of cards, each card has a positive integer written on it, in a multiplication game a child draws a card and multiplies the integer on the card with the next large integer. If the each possible product is between 11 and 200, then the least and greatest integer on the card would be
(A) 3 and 15
(B) 3 and 20
(C) 4 and 13
(D) 4 and 14
(E) 5 and 14
Rationale: Given: 11<x(x+1)<200.
Now, it's better to test the answer choices here rather than to solve:
If x=3 then x(x+1)=12>11 --> so, the least value is 4. Test for the largest value: if x=15 then
x(x+1)=15*16=240>200 --> discard B.
Answer: A.
Answer: (A) 3 and 15
Question: In an electric circuit, two resistors with resistances x and y are connected in parallel. If R is the combined resistance of these two resistors, then the reciprocal of R is equal to the sum of the reciprocals of x and y. What is R if x is 5 Ohms and y is 7 Ohms?
(A) 3/5
(B) 1/7
(C) 12/35
(D) 31/12
(E) 35/12
Rationale: 1/R = 1/x + 1/y
1/R = 1/5+1/7 = 12/35
R = 35/12
The answer is E.
Answer: (E) 35/12
Question: How many real roots does the equation x^2y+15xy+64y=0 have if y < 0?
(A) 0
(B) 1
(C) 2
(D) 3
(E) Infinite
Rationale: x^2y+15xy+64y=0
=> y ( x^2 + 15x + 64) = 0
=> y (x+8)^2 = 0
if y<0 , then x=-7
So although there are 2 factors , they are the same x=-7 .
The equations has 2 distinct real root .
Answer C
Answer: (C) 2
Question: A fruit-salad mixture consists of apples, peaches, and grapes in the ratio 6:5:4, respectively, by weight. If 60 pounds of the mixture is prepared, the mixture includes how many more pounds of apples than grapes?
(A) 15
(B) 12
(C) 8
(D) 6
(E) 4
Rationale: We can first set up our ratio using variable multipliers. We are given that a fruit-salad mixture consists of apples, peaches, and grapes, in the ratio of 6:5:4, respectively, by weight. Thus, we can say:
apples : peaches : grapes = 6x : 5x : 4x
We are given that 60 pounds of the mixture is prepared so we can set up the following question and determine a value for x:
6x + 5x + 4x = 60
15x = 60
x = 4
Now we can determine the number of pounds of apples and of grapes.
pounds of grapes = (4)(4) = 16
pounds of apples = (6)(4) = 24
Thus we know that there are 24 - 16 = 8 more pounds of apples than grapes.
Answer is C.
Answer: (C) 8
Question: If the personal income tax rate is lowered from 40% to 33%, what is the differential savings for a tax payer having an annual income before tax to the tune of $45000?
(A) $3500
(B) $5000
(C) $3150
(D) $7000
(E) $10000
Rationale: Saving = (40-33)% of 45000 = 3150.
Answer:C
Answer: (C) $3150
Question: E is the set of all positive integers x such that x^2 is a multiple of both 27 and 375. Which of the following integers must be a divisor of every integer x in E?
I. 9
II. 15
III. 27
(A) I only
(B) II only
(C) I and II only
(D) I and III only
(E) I, II, and III
Rationale: Ans: C
E->{x} where x^2 is a multiple of both 27 and 375 means 3^3 and (5^3)*3
means x must contain 3^2 and 5^2
so with these conditions we know that 9=3^2 and 15=3*5 both have required factors for the divisibility of lowest int for x which is 9*25
but 27 is not a divisor because it can't divide 9*25 fully.
so Ans : C
Answer: (C) I and II only
Question: The first three terms of a proportion are 2, 10 and 20. The fourth term is?
(A) 105
(B) 102
(C) 190
(D) 100
(E) 134
Rationale: (10*20)/2 = 100
Answer:D
Answer: (D) 100
Question: A bag contains 6 black and 7 white balls. One ball is drawn at random. What is the probability that the ball drawn is white?
(A) 3/4
(B) 7/13
(C) 1/7
(D) 1/8
(E) 4/3
Rationale: Let number of balls = (6 + 7) = 13.
Number of white balls = 7.
P (drawing a white ball) =7/13
Option B.
Answer: (B) 7/13
Question: Apple Street begins at Peach Street and runs directly east for 3.2 kilometers until it ends when it meets Cherry Street. Apple Street is intersected every 200 meters by a perpendicular street, and each of those streets other than Peach Street and Cherry Street is given a number beginning at 1st Street (one block east of Peach Street) and continuing consecutively (2nd Street, 3rd Street, etc...) until the highest-numbered street one block west of Cherry Street. What is the highest-numbered street that intersects Apple Street?
(A) 14th
(B) 15th
(C) 16th
(D) 17th
(E) 18th
Rationale: 3.2 km / 200 m = 16.
However, the street at the 3.2-km mark is not 16th Street; it is Cherry Street.
Therefore, the highest numbered street is 15th Street.
The answer is B.
Answer: (B) 15th
Question: When the integer n is divided by 17, the quotient is x and the remainder is 5. When n is divided by 23, the quotient is y and the remainder is 13. Which of the following is true?
(A)  23x + 17y =19
(B)  17x –23y = 8
(C)  17x +23y =19
(D)  14x + 5y = 6
(E)  5x – 14y = -6
Rationale: From the problem it follows:
n=17x+5
n=23y+13
So, 17x+5=23y+13
17x-23y=8
The answer is B
Answer: (B)  17x –23y = 8
Question: f(x) = x! g(x)=x^10 h(x)= 10^x for large values of x which is greater?
(A) f(x)
(B) g(x)
(C) h(x)
(D) both
(E) none
Rationale: let x=100
then g(x)=100^10=10^20
h(x)=10^100
so h(x) is greater
ANSWER:C
Answer: (C) h(x)
Question: If (2^x)(3^y) = 108, where x and y are positive integers, then (2^x-1)(3^y-2) equals:
(A) 6
(B) 24
(C) 48
(D) 96
(E) 144
Rationale: So I would start attacking this problem by quickly performing the prime factorization of 288. With that it is easy to count the 5 twos and the 2 threes that are the prime factors. So x=2, y=3. now quickly 2^1(3^1)=6. Than answer should be number 1.
A
Answer: (A) 6
Question: Mr. Shah decided to walk down the escalator of a tube station. He found Â that if he walks down 26 steps, he requires 30 seconds to reach the bottom. However, if he steps down 34 stairs he would only require 18 seconds to get to the bottom. If the time is measured from the moment the top step begins Â to descend to the time he steps off the last step at the bottom, find out the height of the stair way in steps?
(A) 44
(B) 45
(C) 46
(D) 47
(E) 48
Rationale: (s1*t2~s2*t1)/(t2~t1)=(26*18~34*30)/(18~30)=46
ANSWER:C
Answer: (C) 46
Question: If a certain sample of data has a mean of 35.0 and a standard deviation of 2.0, which of the following pairs contain two values that are each at least 2.5 standard deviations from the mean?
(A) (14.0; 16.5)
(B) (14.5; 21.0)
(C) (14.0; 26.5)
(D) (16.5; 26.0)
(E) (28.0; 46.5)
Rationale: 2.5 standard deviation equals to 2.5*2=5;
2.5 standard deviations from the mean, so5 points, from the mean is the range from {mean-5} to {mean+5}, so from 30 40.
The correct answer choice must cover all this range: only answer choice E does this.
Answer:E.
Answer: (E) (28.0; 46.5)
Question: Three people each took 3 tests. If the ranges of their scores in the 3 practice tests were 17, 28 and 35, what is the minimum possible range in scores of the three test-takers?
(A) a 17
(B) b) 28
(C) c) 35
(D) d) 45
(E) e) 80
Rationale: It is finding the minimum range between all their scores, if all test taker scores are between 0 and maximum range we will have:
A- 0 and 17
B- 0 and 28
therefore the minimum range is 35, it cant be any lower however you play with the numbers.
B
Answer: (B) b) 28
Question: If (a-b) is 6 more than (c+d) and (a+b) is 3 less than (c-d), then (a-c)
(A) 0.5
(B) 1.5
(C) 2.5
(D) 1.0
(E) 2.0
Rationale: (a-b)-(c-d)=6 and (c-d)-(a+b)=3
(a-c)-(b+d)=6 and (c-a)-(b+d)=3
(b+d)= (a-c)-6 and (b+d)=3-(c-a)
2(a-c)=3
(a-c)=1.5
ANSWER B 1.5
Answer: (B) 1.5
Question: Two trains of length 100 m and 200 m are 100 m apart. They start moving towards each other on parallel tracks, at speeds 90 kmph and 72 kmph. After how much time will the trains meet?
(A) 27/7 sec
(B) 20/9 sec
(C) 33/7 sec
(D) 21/7 sec
(E) 32/7 sec
Rationale: They are moving in opposite directions, relative speed is equal to the sum of their speeds.
Relative speed = (90 + 72)*5/18 = 9*5 = 45 mps.
The time required = d/s = 100/45 = 20/9 sec.
Answer : B
Answer: (B) 20/9 sec
Question: What will be the compound interest on a sum of Rs. 26000 after 3 years at the rate of 12% p.a.?
(A) s.10123.22
(B) s.10823.20
(C) s.10123.20
(D) s.10123.29
(E) s.10528.13
Rationale: Explanation:
Amount = [26000 * (1 + 12/100)3]
= 26000 * 28/25 * 28/25 * 28/25 = Rs. 35123.20
C.I. = (36528.13 - 26000) = Rs.10528.13
Answer:E
Answer: (E) s.10528.13
Question: In 1970 there were 8,902 women stockbrokers in the United States. By 1978 the number had increased to 24,947. Approximately what was the percent increase?
(A)  45%
(B)  125%
(C)  145%
(D)  150%
(E)  180%
Rationale: The percent increase is (24947-8902)/8902=16045/8902=1.80
So the approximate answer is E
Answer: (E)  180%
Question: Find the invalid no.from the following series 13, 17, 22, 26, 31, 38
(A) 13
(B) 38
(C) 40
(D) 37
(E) 25
Rationale: The differences between two successive terms from the beginning are 4, 5, 4, 5, 4, 5. So, 38 is wrong.
Answer : B
Answer: (B) 38
Question: A man has Rs. 480 in the denominations of one-rupee notes, five-rupee notes and ten-rupee notes. The number of notes of each denomination is equal. What is the total number of notes that he has ?
(A) 45
(B) 60
(C) 75
(D) 80
(E) 90
Rationale: Let number of notes of each denomination be x.
Then x + 5x + 10x = 480
16x = 480
x = 30.
Hence, total number of notes = 3x = 90.
answer :E
Answer: (E) 90
Question: In some quantity of ghee, 60% is pure ghee and 40% is vanaspati. If 10kg of pure ghee is added, then the strength of vanaspati ghee becomes 20%. The original quantity was?
(A) 10
(B) 15
(C) 20
(D) 18
(E) 22
Rationale: Let the original quantity be x
then, vanaspati ghee in xkg = 40x/100 kg= 2x/5kg
(2x/5)/(x+10) = 20/100
2x/(5x+50) = 1/5
x = 10
Answer is A
Answer: (A) 10
Question: What will come in place of the x in the following Number series? 25, 100, x, 1600, 6400
(A) 2345
(B) 3579
(C) 6400
(D) 6799
(E) 8646
Rationale: (C)
25 x 4 = 100, 100 x 4 = 400, 400 x 4 = 1600, 1600 x 4 = 6400.
Answer: (C) 6400
Question: If 6x = 8y = 10z, then what is a possible sum of positive integers x, y, and z?
(A) 52
(B) 58
(C) 84
(D) 94
(E) 168
Rationale: 6x = 8y = 10z
3x = 4y = 5z
3(4*5) = 4(3*5) = 5(3*4)
Addition = 20+15+12 = 47
Answer would be multiple of 47 which is 94
Answer :D
Answer: (D) 94
Question: 2^(24) + 2^(25) + 2^(26) + ... + 2^(43) + 2^(44) =
(A) 2^24(2^(21)-1)
(B) 2^24(2^(20)-1)
(C) 2^24(2^(23)-1)
(D) 2^21(2^(20)-1)
(E) 2^21(2^(21)-1)
Rationale: 2^(24) + 2^(25) + 2^(26) + ... + 2^(43) + 2^(44) =
2^(24)*(1+2+4+...+2^(20)) =
2^(24)*(2^(21) - 1)
The answer is A.
Answer: (A) 2^24(2^(21)-1)
Question: David pays the simple interest on an amount he borrowed from his boss, if interest rate is halved, then simple interest is multiplied by
(A) 2
(B) 1
(C) 1/4
(D) 1/2
(E) 4
Rationale: Formula for SI = (P*T*R)/100
SI = Simple Interest
P = Principle Amount
T = Time
R = Interest Rate
Say r=2 => SI1 = 2*SI
when r=1; SI2 = SI
SI2 = 1/2*SI1.
Answer : D
Answer: (D) 1/2
Question: Three people have $30, $72, and $98, respectively. If they pool their money then redistribute it among them, what is the maximum value for the median amount of money?
(A) $72
(B) $85
(C) $98
(D) $100
(E) $202
Rationale: Solution -
Total money distributed is $200. In order to maximize median, one person has to accept $0 and remaining two people share $100 each. Hence median is $100.
ANS D
Answer: (D) $100
Question: If the length of a rectangle is halved and its breadth is tripled, what is the percentage change in its area?
(A) 40%
(B) 30%
(C) 50%
(D) 70%
(E) 65%
Rationale: C
50%
Length is halved.
i.e., length is decreased by 50%
Breadth is tripled
i.e., breadth is increased by 200%
Change in area
=(−50+200−(50×200/100))%=50%
i.e., area is increased by 50%
Answer: (C) 50%
Question: What is value of ((2^5)*(9^2))/((8^2)*(3^5))=?
(A) 1/6
(B) 1/3
(C) 2/3
(D) 1/4
(E) 4
Rationale: =>((2^5)*((3^2)^2)/((2^3)^2)*(3^5))
=>((2^5)*(3^4))/((2^6)*(3^5))
=>1/(2*3)
=>1/6
Option A is answer
Answer: (A) 1/6
Question: A train running at the speed of 60 km/hr crosses a pole in 9 seconds. What is the length of the train?
(A) 120 metres
(B) 180 metres
(C) 324 metres
(D) 150 metres
(E) 175 metres
Rationale: Explanation:
Speed= 60 x	5/18	m/sec	= 50/3	m/sec.
Length of the train = (Speed x Time).
Length of the train = 50/3	x 9	m = 150 m.
ANSWER IS D
Answer: (D) 150 metres
Question: A can do a piece of work in 4 hours; B and C together can do it in 3 hours, which A and C together can do it in 2 hours. How long will B alone take to do it?
(A) 1/19
(B) 1/11
(C) 1/12
(D) 1/17
(E) 1/14
Rationale: A's 1 hour work = 1/4;
(B + C)'s 1 hour work = 1/3;
(A + C)'s 1 hour work = 1/2
(A + B + C)'s 1 hour work = (1/4 + 1/3) = 7/12
B's 1 hour work = (7/12 + 1/2) = 1/12
B alone will take 12 hours to do the work.
Answer: C
Answer: (C) 1/12
Question: Three 6 faced dice are thrown together. The probability that all the three show the same number on them is ?
(A) 1/37
(B) 1/36
(C) 1/31
(D) 1/33
(E) 1/32
Rationale: It all 3 numbers have to be same basically we want triplets. 111, 222, 333, 444, 555 and 666. Those are six in number. Further the three dice can fall in 6 * 6 * 6 = 216 ways.
Hence the probability is 6/216 = 1/36.Answer: B
Answer: (B) 1/36
Question: There are three different hoses used to fill a pool: hose U, hose V, and hose W. Hose x can fill the pool in a days, hose y in b days, and hose z in c days, where a > b > c. When all three hoses are used together to fill a pool, it takes d days to fill the pool. Which of the following must be true?
I. d<c
II. d>b
III. c/3<d<a/3
(A) I
(B) III
(C) I and II only
(D) II & III
(E) II
Rationale: Name T = full pool
U fills a pool in a days ==> 1 day U fills: T/a
V fills a pool in b days ==> 1 day V fills: T/b
W fills a pool in c days ==> 1 day W fills: T/c
1 day (U+V+W) together fill: T(1/a + 1/b + 1/c)
d days (U+V+W) together fill: T
==> d = T1 / T(1/a+1/b+1/c) = abc/(ab+bc+ca)
==>d = abc/(ab+bc+ca)
d cannot be greater than c ; d is greater than b ; d is greater than c/3 but not less than a/3
E
Answer: (E) II
Question: A man’s speed with the current is 14 km/hr and the speed of the current is 2.5 km/hr. the man’s speed against the current is :
(A) 9 km/hr
(B) 8.5 km/hr
(C) 10 km/hr
(D) 12.5 km/hr
(E) None of these
Rationale: Solution
Man's rate in still water = (14-2.5) km/hr = 11.5 km/hr.
Man's rate against the current = (11.5-2.5) km/hr = 9 km/hr Answer A
Answer: (A) 9 km/hr
Question: Two motor cycles A & B are started from one point at 4 Kmph & 6 Kmph; After 45 min B starts returning, at what time they will meet ?
(A) 54 mins
(B) 55 mins
(C) 56 mins
(D) 57 mins
(E) 58 mins
Rationale: Distance covered by A in 45 mins= 3 kms.
Distance covered by B in 45 mins= 4.5 kms.
Distance between and B after 45 mins= 1.5 kms.
Relative speed when B is returning = 4+6=10 kmph
Distance between A and B is covered in 1.5/10 = 0.15 hrs = 9 mins
so they will meet again after 54 mins from starting time.
ANSWER:A
Answer: (A) 54 mins
Question: Set A consists of all the prime numbers between 2 and 13. What is the range of set A?
(A) 12
(B) 13
(C) 16.6
(D) 17
(E) 8
Rationale: The range of a set of data is the difference between the highest and lowest values in the set
In this set,
Highest number = 11
Lowest number = 3
Range = Highest - Lowest = 11 - 3 = 8
Option E
Answer: (E) 8
Question: How many shots of 1cm radius can be prepared from a sphere of 6cm radius?
(A) 33
(B) 88
(C) 216
(D) 288
(E) 299
Rationale: 4/3 Ï€ * 6 * 6 * 6 = 4/3 Ï€ * 1 * 1 * 1 * x
x = 216
Answer: C
Answer: (C) 216
Question: The numbers of pizza slices that are sold in Joey's Pizza are only in quantities of 3 and 5 slices per customer. How many slices cannot be bought?
(A) 19.
(B) 38.
(C) 33.
(D) 22.
(E) 21.
Rationale: Let X pizzas of 3 slices and Y pizzas of 5 slices.
3X + 5Y.
Lets check options wise.
A. 19 => 3(3) + 5(2)
B. 38 => 3(6) + 5(4)
C. 33 => 3(1) + 5(6)
D. 22 => 3(4) + 4(2)
E. 21 = we can't write anything with 3 and 5 series..Lets try 3(5) + 5(1) = 20 , 3(4) + 4(2) = 22 , nothing works out.
Answer: correct option is E
Answer: (E) 21.
Question: a=2, b=3, c=6 Find the value of c/(a+b)-(a+b)/c
(A) 8/30
(B) 9/30
(C) 10/30
(D) 11/30
(E) 12/30
Rationale: c/(a+b)-(a+b)/c
= (c/(a+b))-((a+b)/c)
= (6/(2+3))-((2+3)/6)
= (6/5)-(5/6)
= 11/30
ANSWER:D
Answer: (D) 11/30