mathewhe/aqua_rat huggingface dataset:
Question: Mr. Wayne bungee jumps from the top of a building straight to the ground at a constant speed. 3 seconds after he starts plummeting he passes the 20th floor. 15 seconds after he starts plummeting he passes the 5th floor. Each floor is 3.6 meters high. What is Mr. Wayne's speed in meters per second?
(A) 3
(B) 3.75
(C) 4.5
(D) 4.25
(E) 5
Rationale: IMO: C
15 Floors * 3.6 Meter/Floor = 54 Meters
Time= 12 sec
Rate * 12 = 54
Rate= 54/12
=4.5
Answer C
Answer: (C) 4.5
Question: The speed of a boat in still water is 50kmph and the speed of the current is 20kmph. Find the speed downstream and upstream?
(A) 40, 68 kmph
(B) 40, 30 kmph
(C) 70, 30 kmph
(D) 40, 60 kmph
(E) 20, 60 kmph
Rationale: Speed downstream = 50 + 20 = 70 kmph
Speed upstream = 50 - 20 = 30 kmph
Answer: C
Answer: (C) 70, 30 kmph
Question: A man rows his boat 85 km downstream and 45 km upstream, taking 2 1/2 hours each time. Find the speed of the stream?
(A) 76 kmph
(B) 6 kmph
(C) 14 kmph
(D) 8 kmph
(E) 4 kmph
Rationale: Speed downstream = d/t = 85/(2 1/2)
= 34 kmph
Speed upstream = d/t = 45/(2 1/2)
= 18 kmph
The speed of the stream = (34 - 18)/2
= 8 kmph
Answer:D
Answer: (D) 8 kmph
Question: A 300 m long train crosses a platform in 39 sec while it crosses a signal pole in 18 sec. What is the length of the platform?
(A) 389 m
(B) 350 m
(C) 289 m
(D) 299 m
(E) 219 m
Rationale: Speed = 300/18 = 50/3 m/sec.
Let the length of the platform be x meters.
Then, (x + 300)/39 = 50/3
3x + 900 = 1950 => x = 350 m.
Answer:B
Answer: (B) 350 m
Question: A, B and C enter into a partnership. They invest Rs. 40,000, Rs. 80,000 and Rs. 1,20,000 respectively. At the end of the first year, B withdraws Rs. 40,000, while at the end of the second year, C withdraws Rs. 80,000. In what ratio will the profit be shared at the end of 3 years ?
(A) 8:7:4
(B) 1:3:5
(C) 3:4:7
(D) 4:5:9
(E) 5:7:10
Rationale: Explanation:
A:B:C =(40000Ã—36) :(80000Ã—12+40000Ã—24) :(120000Ã—24+40000Ã—12)
=144:192:336=144:192:336 =3:4:7.
ANSWER IS C
Answer: (C) 3:4:7
Question: If a committee of 3 people is to be selected from among 5 married couples so that the committee does not include two people who are married to each other, how many such committees are possible?
A.
B.
C.
D.
E.
(A) 20
(B) 40
(C) 50
(D) 80
(E) 120
Rationale: Each couple can send only one "representative" to the committee. Let's see in how many ways we can choose 3 couples (as there should be 3 members) each to send one "representative" to the committee: 5C3=10.
But these 3 chosen couples can send two persons (either husband or wife): 2*2*2=2^3=8.
Total # of ways: 5C3*2^3=80.
Answer: D.
Answer: (D) 80
Question: Ratio between Rahul and Deepak is 4:3, After 6 Years Rahul age will be 26 years. What is Deepak present age.
(A) 14
(B) 15
(C) 20
(D) 22
(E) 23
Rationale: Explanation:
Present age is 4x and 3x,
=> 4x + 6 = 26 => x = 5
So Deepak age is = 3(5) = 15
Answer: Option B
Answer: (B) 15
Question: The average weight of four boys A, B, C, and D is 75 kg. The fifth boy E is included and the average weight decreases by 4 kg. A is replaced by F. The weight of F is 6 kg more than E. Average weight decreases because of the replacement of A and now the average weight is 72 kg. Find the weight of A.
(A) 57 kg
(B) 54 kg
(C) 56 kg
(D) 60 kg
(E) 58 kg
Rationale: Sum of the weight of A, B, C and D = 75 × 4 = 300 kg
and average weight of A, B, C, D and E = 71 kg
sum of the weight of A, B, C, D and E
= 71 × 5 = 355 kg
weight of E = 355 – 300 = 55 kg
weight of F = 55 + 6 = 61 kg
Now, average weight of F, B, C, D and E = 72 kg
Sum of the weight of F, B, C, D and E = 72 × 5 = 360 kg
B + C + D = 360 – 55 – 61 = 244 kg.
Weight of A = 300 – 244 = 56 kg.
ANSWER:C
Answer: (C) 56 kg
Question: A train leaves Mumabai at 9 am at a speed of 40 kmph. After one hour, another train leaves Mumbai in the same direction as that of the first train at a speed of 60 kmph. When and at what distance from Mumbai do the two trains meet?
(A) 187
(B) 279
(C) 120
(D) 278
(E) 379
Rationale: When the second train leaves Mumbai the first train covers 40 * 1 = 40 km
So, the distance between first train and second train is 40 km at 10.00am
Time taken by the trains to meet
= Distance / relative speed = 40 / (60 -40) = 2 hours
So, the two trains meet at 12 a.m. The two trains meet 2 * 60 = 120 km away from Mumbai.
Answer:C
Answer: (C) 120
Question: On a man's tombstone, it is said that one sixth of his life was spent in childhood and one twelfth as a teenager. One seventh of his life passed between the time he became an adult and the time he married; five years later, his son was born. Alas, the son died four years before he did. He lived to be twice as old as his son did. How old did the man live to be?
(A) 82
(B) 83
(C) 84
(D) 85
(E) 86
Rationale: Let the age of man is x so that of son = x/2 (given)
now according to the given condition
(x/6) + (x/12) + (x/7) + 5 + (x/2) + 4 = x
or x = 84
ANSWER:C
Answer: (C) 84
Question: If the annual interest on a principal is 16%, how many years before the amount is double?
(A) 6.25
(B) 20
(C) 17.2
(D) 15.2
(E) 15.2
Rationale: P = (P*16*R)/100
R = 6.25
Answer: A
Answer: (A) 6.25
Question: Josh spends a total of $7.50 buying N items in the convenience store. If each of the items is either a 5 cents single bubblegum, or a 50 cents bubblegum pack, then N may be which of the following?
(A) 99
(B) 100
(C) 101
(D) 109
(E) 141
Rationale: Let x be 0.05$ single bubblegum and y be the total 0.5$ packs ---> 0.05x+0.5y=7.5 ---> x+10y=150 ...(1)
Also, x+y=N ...(2)
Solving 1 and 2 , we get, N = 150-9y ---> only value satisfied is when y = 1---> N = 150-9=141. E is the correct answer. Other options are not equal to multiples of 9 removed from 150.
Answer: (E) 141
Question: The area of Circle O is added to its diameter. If twice the circumference of Circle O is then subtracted from this total, the result is 8. What is the diameter of Circle O?
(A) 4/π
(B) 4
(C) 8
(D) 10
(E) 6
Rationale: area+diameter-2*circumference=8
pi*r^2+2r=8+2*2pi*r
isolate r and get r(pi*r+2)=8+4pi*r
r=(8+4pi*r)/(pi*r+2) =>4(pi*r+2)/(pi*r+2)
r=4
Diameter = 2r = 8
C
Answer: (C) 8
Question: What is the dividend. divisor 18, the quotient is 9 and the remainder is 4
(A) A)166
(B) B)148
(C) C)150
(D) D)153
(E) E)158
Rationale: D = d * Q + R
D = 18 * 9 + 4
D = 166
Answer : A
Answer: (A) A)166
Question: A reduction of 20% in the price of oil enables a house wife to obtain 5kgs more for Rs.800, what is the reduced price for kg?
(A) 30
(B) 31
(C) 32
(D) 33
(E) 34
Rationale: 800*(20/100) = 160 ---- 5
? ---- 1 => Rs.32
Answer: C
Answer: (C) 32
Question: A can contains a mixture of two liquids A and B is the ratio 7 : 5. When 9 litres of mixture are drawn off and the can is filled with B, the ratio of A and B becomes 7 : 9. How many litres of liquid A was contained by the can initially?
(A) 18
(B) 19
(C) 21
(D) 26
(E) 28
Rationale: Suppose the can initially contains 7x and 5x of mixtures A and B respectively.
Quantity of A in mixture left = 7x -	7	x 9 litres = 7x -	21 litres.
12	4
Quantity of B in mixture left = 5x -	5	x 9 litres = 5x -	15 litres.
12	4
7x -	21
4
=	7
5x -	15 + 9
4
9
28x - 21	=	7
20x + 21	9
252x - 189 = 140x + 147
112x = 336
x = 3.
So, the can contained 21 litres of A.
Option C
Answer: (C) 21
Question: The angle between the minute hand and the hour hand of a clock when the time is 4.20, is:
(A) 0
(B) 5
(C) 12
(D) 8
(E) 10
Rationale: angle 13/3 hrs = 360/12 * 13/3 = 130deg
angle hand in 20 min 360/60*20 = 120 deg
req = 130-120 = 10deg
ANSWER E
Answer: (E) 10
Question: In a mixture of 45 litres the ratio of milk to water is 4:1. Additional 18 litres of water is added to the mixture. Find the ratio of milk to water in the resulting mixture.
(A) 2/1
(B) 4/3
(C) 2/3
(D) 3/4
(E) 3/2
Rationale: Given that Milk/Water=4x/x and 4x+x=45 --> x=9.
Thus Milk=4x=36 liters and Water=x=9 liters.
New ratio = 36/(9+18) = 36/27 = 4/3.
Answer: B.
Answer: (B) 4/3
Question: Without any stoppages a person travels a certain distance at an average speed of 40 km/hr and with stoppages he covers the same distance at an average of 20 km/hr. How many minutes per hour does he stop?
(A) 15 minute
(B) 20 minutes
(C) 30 minutes
(D) 45 minutes
(E) None of these
Rationale: Explanation :
In one hour the distance covered at actual speed = 40km and with stoppages it covers only 20 km
so to travel 20 km at original speed i.e. 20 = 40*t, so t = 1/2 hour = 30
minutes
Answer – C
Answer: (C) 30 minutes
Question: Divide Rs. 720 among A, B and C so that A receives 1/3 as much as B and C together and B receives 2/3 as A and C together. A's share is?
(A) s.800
(B) s.400
(C) s.600
(D) s.180
(E) s.900
Rationale: A+B+C = 720
A = 1/3(B+C); B = 2/3(A+C)
A/(B+C) = 1/3
A = 1/4 * 720 => 180
ANSWER:D
Answer: (D) s.180
Question: The average mark of a class of thirty two students is 75. If three students whose marks are 28 and 34 are removed , then find the approximate average mark of the remaining students of the class.
(A) 71
(B) 74
(C) 78
(D) 70
(E) 80
Rationale: Exp. Total mark of 32 students = 75*32 = 2400,
Total mark after the removal of 2 students = 2400 –(28+34)
= 2400 – 62 = 2338
Approximate average mark = 2338/(32-2) = 2338/30 = 78
Answer: C
Answer: (C) 78
Question: The function f(x) = x + 4 is given. Solve the equation:
[3.f(x - 2)]/f(0) + 4 = f(2x + 1)
(A) 0.2
(B) 0.3
(C) 0.4
(D) 0.5
(E) None of these
Rationale: Solution:
We calculate f(0), f(x -2), f(2x +1), namely f(0) = 0 + 4 = 4;
f(x - 2) = x - 2 + 4 = x + 2;
f(2x + 1) = 2x + 1 + 4 = 2x + 5 The equation gets this look
[3(x + 2)]/4 + 4 = 2x + 5 <=>
3(x + 2) +16 = 4(2x + 5) <=>
3x + 6 +16 = 8x + 20 <=>
22 - 20 = 8x - 3x <=>
2 = 5x <=> x = 0.4
Answer C
Answer: (C) 0.4
Question: If a quality control check is made inspecting a sample of 2 light bulbs from a box of 13 lighbulbs, how many different samples can be chosen?
(A) 6
(B) 24
(C) 36
(D) 66
(E) 78
Rationale: Try using the formula for combinations:
n!/r!(n-r)!
13!/2!(13-2)!
13!/2!*11!
13*12/2*1
=78
E
Answer: (E) 78
Question: In a game of billiards, A can give B 20 points in 60 and he can give C 40 points in 60. How many points can B give C in a game of 100?
(A) 18
(B) 27
(C) 50
(D) 21
(E) 17
Rationale: A scores 80 while B score 40 and C scores 20.
The number of points that C scores when B scores 100 = (100 * 20)/40 = 50.
In a game of 100 points, B gives (100 - 50) = 50 points to C.
Answer: C
Answer: (C) 50
Question: The perimeter of a triangle is 40 cm and the inradius of the triangle is 2.5 cm. What is the area of the triangle
(A) A)72
(B) B)828
(C) C)50
(D) D)34
(E) E)35
Rationale: Explanation:
Area of a triangle = r * s
Where r is the inradius and s is the semi perimeter of the triangle.
Area of triangle = 2.5 * 40/2 = 50 cm2
Answer: Option C
Answer: (C) C)50
Question: The length Q of a rectangle is decreased by 15% and its width is increased by 40%. Does the area of the rectangle decrease or increase and by what percent?
(A) Decreases by 19%
(B) Decreases by 25%
(C) Increases by 6%
(D) Increases by 19%
(E) Increases by 25%
Rationale: Let the length Q of the rectangle be 100x, and width be 100y. Area = 100x * 100y = 10000xy
Now after the change Length = 85x, and width = 140 y. Area = 11900xy
% Change = (11900xy - 10000xy)/(10000xy) = 19 % Increase. Hence D.
Answer: (D) Increases by 19%
Question: The largest natural number which exactly divides the product of any four consecutive natural numbers is
(A) 6
(B) 12
(C) 24
(D) 36
(E) 48
Rationale: Required numbers; 1×2×3×4 = 24, which is divisible by 24.
also checking 5 x 6 x 7 x 8 = 1680, which is also divisible by 24.
ANSWER:C
Answer: (C) 24
Question: The average weight of 25 boys sitting in a boat had some value. A new person added to them whose weight was 60 kg only. Due to his arrival, the average weight of all the boys decreased by 10 kg. Find the average weight of first 25 boys?
(A) 302
(B) 203
(C) 320
(D) 260
(E) 192
Rationale: 25x + 60 = 26(x - 10)
x = 320
C
Answer: (C) 320
Question: On one particular day, Beth's garden bloomed 1235 flowers. If Beth separates her flowers evenly across 9 different vases, how many flowers would remain with her.
(A) 1 Flowers
(B) 2 Flowers
(C) 3 Flowers
(D) 4 Flowers
(E) 5 Flowers
Rationale: This is equivalent to finding the first number that is divisible by 9 that occurs before 1235.
In order to divide the sum in 9 parts, the amount must be divisible by 9
Divisibility rule of 9: The sum of the digits must be divisible by 9
Sum of digits of 1235 = 11 and 9 is divisible by 9.
Therefor, we need to remove 2 to this number for it to be divisible by 9
Correct Option: B
Answer: (B) 2 Flowers
Question: A girl sold a book at a profit of 7%. Did she sold it for Rs.7.50 more, 22% would have been gained. Find the CP?
(A) 40%
(B) 45%
(C) 50%
(D) 60%
(E) 69%
Rationale: 50%
C
Answer: (C) 50%
Question: Which of the following number should be added to 11158 to make it exactly divisible by 77?
(A) 6
(B) 5
(C) 8
(D) 7
(E) 9
Rationale: Ondividing 11158 by 77, the remainder is 70
Thus, Number to be added = (77 - 70)=7
ANSWER:D
Answer: (D) 7
Question: If p is a positive integer and p^2 is divisible by 12, then the largest positive integer that must divide p ^3 is
(A) 2^3
(B) 2^6
(C) 3^3
(D) 6^3
(E) 12^2
Rationale: Since p is an integer so p cannot have a 2 and sqrt 3 (because squaring this will give us a 2^2 and 3 (making the product as 12, and making p^2 as a multiple of 12))
p^2 is divisible by 12 (12 = 2*2*3), So, p should have at least one 2 and one 3 so that p^2 has a 2^2 and two 3
So, p will have a 2 and a 3. Or p will be a multiple of 6
So, largest possible integer than should divide p^3 is 6^3
So, Answer will be D
Answer: (D) 6^3
Question: 40, 45, 50, 55, 65, 75, 75, 100, 100, 100.
The list above shows the scores of 10 schoolchildren on a certain test. If the standard deviation of the 10 scores is 22.2, rounded to the nearest tenth, how many of the scores are more than 1 standard deviation below the mean of the 10 scores?
(A) 1
(B) 2
(C) 3
(D) 4
(E) 5
Rationale: The average of {40, 45, 50, 55, 65, 75, 75, 100, 100, 100} is 70.5
1 standard deviation below the mean is 70.5 - 22.2 = 48.3. Hence there are two scores (40 and 45) more than 1 standard deviation below the mean.
Answer B.
Answer: (B) 2
Question: Each of the products produced yesterday was checked by worker x or worker y. 0.5% of the products checked by worker x are defective and 0.8% of the products checked by worker y are defective. If the total defective rate of all the products checked by worker x and worker y is 0.74%, what fraction of the products was checked by worker y?
(A) 1/2
(B) 2/3
(C) 3/5
(D) 3/4
(E) 4/5
Rationale: x: 0.5% is 0.24%-points from 0.74%.
y: 0.8% is 0.06%-points from 0.74%.
Therefore the ratio of products checked by y:x is 4:1.
Thus, worker y checked 4/5 of the products.
The answer is E.
Answer: (E) 4/5
Question: seven family members: 5 grandchildren (3 brothers and 2 sisters) and their 2 grandparents are to be seated around a circular table. How many different seating arrangements are possible so that 2 sisters are seated between any two of the three brothers?
(A) 72
(B) 480
(C) 1440
(D) 2880
(E) 8640
Rationale: Answer: A.
Answer: (A) 72
Question: A father said to his son, "I was as old as you are at present at the time of your birth." If the father's age is 42 years now, the son's age five years back was:
(A) 19 years
(B) 14 years
(C) 33 years
(D) 16 years
(E) 39 years
Rationale: Let the son's present age be x years.
Then, (42 - x) = x
2x = 42=> x = 21
Son's age 5 years back = (21 - 5) = 16 years.
ANSWER:D
Answer: (D) 16 years
Question: In the circular region shown above, sections A and B represent 3/8 and 5/11, respectively, of the area of the circular region. Section C represents what fractional part of the area of the circular region?
(A) 15/88
(B) 2/11
(C) 5/22
(D) 45/88
(E) 73/88
Rationale: A , B and C represent complete area of circle and c fraction be x.
3/8+5/11+x = 1.
=> x = 1- ( 3/8+5/11)
x = 15/88.
Answer:option A is correct answer..
Answer: (A) 15/88
Question: Which of the following is(are) false for a@b=b@a?
I. a@b=ab+ba
II. a@b=(a+b)(a-b)
III. a@b=(a/b)+(b/a)
(A) only Ⅰ
(B) only Ⅱ
(C) only Ⅲ
(D) only ⅠⅢ
(E) only ⅡⅢ
Rationale: -> If I. a@b=ab+ba, a@b=ab+ba=ba+ab=b@a (X).
If II. a@b=(a+b)(a-b), a@b=(a+b)(a-b)≠(b+a)/(b-a)=b@a (O).
If III.a@b=(a/b)+(b/a), a@b=(a/b)+(b/a)=(b/a)+(a/b)=b@a (O).
Thus, ⅠⅢ are the answers. Therefore, A is the answer.
Answer: (A) only Ⅰ
Question: You have 5 sticks of lengths 10, 30, 40, 50, and 60 centimeters. The number of non-congruent triangles that can be formed by choosing three of the sticks to make the sides is
(A) 3
(B) 4
(C) 7
(D) 10
(E) 12
Rationale: The length of any side of a triangle must be larger than the positive difference of the other two sides, but smaller than the sum of the other two sides.
Based on this there can be only 4 triangles formed:(30, 40, 50), (30, 40, 60), (30, 50, 60), (40, 50, 60).
Answer; B
Answer: (B) 4
Question: 10 men working 6 hrs per day manufacture 200 shoes in 18 days. How many hours a day must 15 men work to manufacture the same 200 shoes in 12 days?
(A) 6
(B) 10
(C) 12
(D) 15
(E) 18
Rationale: Let the required number of hours be x.
More men, less hours per day (Indirect proportion)
Less days, more working hours per day (Indirect proportion)
men 15 : 10
} : : 6 : x
days 12 : 18
.'. 15*12*x = 10*18*6
= x = 10*18*6/(15*12)
= x = 6 ANSWER : A
Answer: (A) 6
Question: Which of the following inequalities is equivalent to −1 < x < 5?
(A) |x - 1| < 7
(B) |x + 2| < 3
(C) |x + 3| < 5
(D) |x - 2| < 3
(E) None of the above
Rationale: We know that |x| < a means -a < x < a, where Sum of lower limit of x (i.e -a) and the upper limit of x (i.e a), is 0
Given is, -1 < x < 5, let's say by adding y to this inequality we will get into the above format
-1+y < x+y < 5+y
Now, to move this into the mod format, we need to have (-1+y) + (5+y) = 0 => y = -2
Thus, -3< x-2 < 3 => |x-2| < 3.
Hence, answer is D
Answer: (D) |x - 2| < 3
Question: P and Q started a business investing Rs. 85,000 and Rs. 15,000 respectively. In what ratio the profit earned after 2 years be divided between P and Q respectively?
(A) 17:6
(B) 17:4
(C) 17:8
(D) 17:1
(E) 17:3
Rationale: P:Q = 85000 : 15000 = 17:3.
Answer:E
Answer: (E) 17:3
Question: A part-time employee’s hourly wage was increased by 10%. She decided to decrease the number of hours worked per week so that her total income did not change. By approximately what percent should the number of hours worked be decreased?
(A) 9%
(B) 15%
(C) 25%
(D) 50%
(E) 100%
Rationale: Let's say the employee used to make $1/hour and worked 100 hours/week
So, the TOTAL weekly income was $100/week
After the 10% wage increase, the employee makes $1.10/hour
We want the employee's income to remain at $100/week.
So, we want ($1.10/hour)(new # of hours) = $100
Divide both sides by 1.10 to get:
new # of hours = 100/1.10
≈ 90 hours
So, the number of hours decreases from 100 hours to (approximately) 90 hours.
This represents a 10% decrease (approximately) .
Answer choice A is the closest answer.
Answer: (A) 9%
Question: The C.I. on a certain sum for 2 years Rs.41 and the simple interest is Rs.40. What is the rate percent?
(A) 8%
(B) 5%
(C) 6%
(D) 4%
(E) 2%
Rationale: SI = 20 + 20
CI = 20 + 21
20 ---- 1
100 ---- ? => 5%
Answer: B
Answer: (B) 5%
Question: In how many ways can four different rings be worn on four fingers of one hand?
(A) 10
(B) 1
(C) 15
(D) 16
(E) 18
Rationale: Required number of ways = ways of selecting 4 objects out of 4 given objects
= 4C4 = 4*3*2*1/24= 1
Answer B
Answer: (B) 1
Question: If six persons sit in a row, then the probability that three particular persons are always together is ?
(A) 1/5
(B) 1/7
(C) 1/2
(D) 1/1
(E) 1/9
Rationale: Six persons can be arranged in a row in 6! ways. Treat the three persons to sit together as one unit then there four persons and they can be arranged in 4! ways. Again three persons can be arranged among them selves in 3! ways. Favourable outcomes = 3!4! Required probability
= 3!4!/6! = 1/5
Answer:C
Answer: (C) 1/2
Question: Seven family members are seated around their circular dinner table. If only arrangements that are considered distinct are those where family members are seated in different locations relative to each other, and Michael and Bobby insist on sitting next to one another, then how many distinct arrangements around the table are possible?
(A) 120
(B) 240
(C) 360
(D) 480
(E) 720
Rationale: As I see it : 7 members, and Michael & Bobby sit together. So treat those two like a single person. Now you have to arrange 6 people around a table. This may be done in 5! or 120 ways
The number of ways to arrange Michael & Bobby is 2 (MB or BM).
So net there are 240 ways or B
Answer: (B) 240
Question: What is the sum of two consecutive even numbers, the difference of whose squares is 84?
(A) 34
(B) 38
(C) 42
(D) 46
(E) 48
Rationale: Solution
Let the numbers be x and x + 2.
Then, (x + 2)2–x2 = 84
‹=›4x + 4 = 84
‹=›4x = 80
‹=›x = 20.
Required sum = x+(x+2)= 2x+2 = 42.
Answer C
Answer: (C) 42
Question: In what time will a train 140 meters long cross an electric pole, if its speed is 210 km/hr
(A) 5 seconds
(B) 4.5 seconds
(C) 3 seconds
(D) 2.4 seconds
(E) None of these
Rationale: Explanation:
First convert speed into m/sec
Speed = 210*(5/18) = 58 m/sec
Time = Distance/speed
= 140/58 = 2.4 seconds
Option D
Answer: (D) 2.4 seconds
Question: Bell and Carol are partners in a business, they invested Rs. 25,800 and Rs. 32,000 respectively.If the business yielded a total profit of Rs. 21,500, what is Carol's share?
(A) 11903.11
(B) 12703.11
(C) 15103.11
(D) 11979.11
(E) 11990.11
Rationale: Explanation:
Ratio of their shares = 25,800 : 32,000 = 129 : 160.
Carol's share = Rs. (21,500 * 160/289) = Rs. 11903.11.
Answer: A) 11903.11
Answer: (A) 11903.11
Question: Two different primes may be said torhymearound an integer if they are the same distance from the integer on the number line. For instance, 3 and 7 rhyme around 5. What integer R between 1 and 20, inclusive, has the greatest number of distinct rhyming primes around it?
(A) 12
(B) 15
(C) 17
(D) R=18
(E) 20
Rationale: Since we are concerned with integers between 1 and 20, write down the primes till 40.
2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37
(you should be very comfortable with the first few primes... )
2, 3, 5, 7, 11,12, 13, 17, 19, 23, 29, 31, 37 - Three pairs (11,13), (7,17), (5, 19)
2, 3, 5, 7, 11, 13,15,17, 19, 23, 29, 31, 37 - Three pairs (13, 17), (11, 19), (7, 23)
2, 3, 5, 7, 11, 13,17, 19, 23, 29, 31, 37 - Three pairs (11, 23), (5, 29), (3, 31)
2, 3, 5, 7, 11, 13, 17,18,19, 23, 29, 31, 37 - Four pairs (17, 19), (13, 23), (7, 29), (5, 31)
2, 3, 5, 7, 11, 13, 17, 19,20,23, 29, 31, 37 - definitely cannot be more than 4 since there are only 4 primes more than 20. So must be less than 4 pairs. Ignore.
Answer (D).
Answer: (D) R=18
Question: There is a 100 pound watermelon laying out in the sun. 99 percent of the watermelon's weight is water. After laying out for a few hours 98 percent of the watermelon's weight is water.
How much water evaporated?
(A) A)20
(B) B)30
(C) C)40
(D) D)50
(E) E)10
Rationale: In the beginning it is 99 pounds water and 1 pound other stuff. At the end the 1 pound other stuff is 2 percent so the total weight is 50 pounds. 50 pounds - 1 pound other stuff = 49 pounds water. So 99 pounds - 49 pounds = 50 pounds water lost.answer is D
Answer: (D) D)50
Question: What is the dividend. divisor 19, the quotient is 9 and the remainder is 5?
(A) A)130
(B) B)134
(C) C)148
(D) D)176
(E) E)160
Rationale: D = d * Q + R
D = 19 * 9 + 5
D = 171 + 5
D = 176
Answer D
Answer: (D) D)176
Question: A person spends 1/3rd of the money with him on clothes, 1/5th of the remaining on food and 1/4th of the remaining on travel. Now, he is left with Rs 600. How much did he have with him in the beginning?
(A) s 200
(B) s 1500
(C) s 300
(D) s 450
(E) s 550
Rationale: Suppose the amount in the beginning was Rs ’x’
Money spent on clothes = Rs 1x/3 Balance = Rs 2x/3
Money spent on food = 1/5 of 2x/3 = Rs 2x/15
Balance = 2x/3 - 2x/15 = Rs 8x/15
Money spent on travel = 1/4 of 8x/15 = Rs 2x/15 = 8x/15 - 2x/15 = 6x/15 = Rs2x/5
Therefore 2x/5 = 100 = 1500
ANSWER:B
Answer: (B) s 1500