mathewhe/aqua_rat huggingface dataset:
Question: Every year Taylor goes to the same carnival, and he attempts to shoot a basketball into a small hoop, hoping that he will win a ten-foot tall teddy bear. If the probability that Taylor does not make a basket is 1/3, what is the probability that Taylor makes exactly one basket in three tries?
(A) 1/9
(B) 2/9
(C) 2/5
(D) 3/5
(E) 3/7
Rationale: Probability of basket = 2/3
Probability of no basket = 1/3
Required probability=3* 2/3*1/3*1/3
= 2/9
B is the answer .
Answer: (B) 2/9
Question: 100 people are standing in a circle. The person standing at number 1 is having a sword. He kills the person next to him with the sword and then gives the sword to the third person. This process is carried out till there is just one person left.
Can you find out who survives?
(A) 93
(B) 73
(C) 90
(D) 75
(E) 87
Rationale: B
The person on 73rd number will survive.
Till the number is the power of 2, the last person to survive will be the one who started it. But since the number here is not the power of 2, we will take the greatest power of 2 that is less than the number which is 64.
100 - 64 = 36
36 people are killed as 2, 4, 6, ..., 72. Thus the sword will now be given to the 73rd person. Now he is the first person to start in the remaining 64 people. Thus he will be the one to survive.
Answer: (B) 73
Question: Anmol can eat 27 pastries in a hour.
Aakriti can eat 2 pastries in 10 minutes.
Divya can eat 7 pastries in 20 minutes.
How long will it take them to eat a 420 pastries ?
(A) 2 hours.
(B) 1 hours.
(C) 5 hours.
(D) 4 hours.
(E) 7 hours.
Rationale: In one hour, Anmol eats 27 pastries, Aakriti eats 12, and Divya eats 21. A total of 60 pastries. Therefore 420 pastries would take 420 ÷ 60 = 7 hours.
ANSWER E
Answer: (E) 7 hours.
Question: Total Rs.700 are divided among 3 persons (A, B, and C). A gets 1/2 of B and B gets 1/2 of C. How much C have?
(A) 300
(B) 400
(C) 500
(D) 600
(E) 700
Rationale: A gets 100 Rs.
B gets 200 Rs.
C gets 400 Rs.
A=B/2
B=c/2
A+B+C=700
(B/2)+B+(2B)=700
B=200
A=B/2=200/2=100
C=2B=2*200=400
ANSWER:B
Answer: (B) 400
Question: The sum of the digits of a two-digit number is 15 and the difference between the digits is 3. What is the two-digit number?
(A) 69
(B) 78
(C) 96
(D) Cannot be determined
(E) None of these
Rationale: Let the ten's digit be x and unit's digit by y
Then, x + y = 15 and x - y = 3 or y - x = 3
Solving x + y = 15 and x - y = 3, we get: x = 9, y = 6
Solving x + y = 15 and y - x = 3, we get: x = 6, y = 9
So, the number is either 96 or 69.
Hence, the number cannot be determined.
ANSWER:D
Answer: (D) Cannot be determined
Question: If selling price is doubled, the profit triples. Find the profit percent.
(A) 100 %
(B) 50 %
(C) 25 %
(D) 18 %
(E) 12 %
Rationale: Explanation:
Let C.P. be Rs. x and S.P. be Rs. y.
Then, 3(y - x) = (2y - x) y = 2x.
Profit = Rs. (y - x) = Rs. (2x - x) = Rs. x.
Profit % =(x/x*100)%=100%
Answer:A
Answer: (A) 100 %
Question: How much water must be added to 60 litres of milk at 1 1⁄2 litres for 20 so as to have a mixture worth 10 2⁄3 a litre?
(A) 10 litres
(B) 12 litres
(C) 15 litres
(D) 18 litres
(E) None of these
Rationale: C.P. of 1 litre of milk = (20 × 2⁄3) = 40⁄3
∴ Ratio of water and milk = 8⁄3 : 32⁄3 = 8 : 32 = 1 : 4
∴ Quantity of water to be added to 60 litres of milk
= (1⁄4 × 60) litres = 15 litres.
Answer C
Answer: (C) 15 litres
Question: What is the least value of k. So that 123k578 is divisible by 11.
(A) 8
(B) 7
(C) 5
(D) 6
(E) 4
Rationale: Explanation:
The Difference of the sum of the digits at odd place and the sum of the digits at even place of the number, is either 0 or a number divisible by 11.
(1 + 3 + 5 + 8) - (2 + k + 7) = 17 - 9 - k = 8 - k
Therefore if k = 8, then the value become zero.
k = 8 is the least value
so that 123k578 is divisible by 11.
Answer: Option A
Answer: (A) 8
Question: What is the greatest positive integer x such that 6^x is a factor of 216^10?
(A) 5
(B) 9
(C) 10
(D) 20
(E) 30
Rationale: 216^10 = (6^3)^10 = 6^30
ANSWER:E
Answer: (E) 30
Question: Brindavan Express leave Chennai Central Station every day at 07.50 am and goes to Bangalore City Railway station. This train is very popular among the travelers. On 25th July 2012 number of passengers traveling by I class and II class was in the ratio 1:4. The fare for this travel is in the ratio 3:1. The total fare collected was Rs. 224000/. (Rs. Two lakhs twenty four thousand only). What was the fare collected from I class passengers on that day?
(A) Rs.32000
(B) Rs. 96000
(C) Rs.128000
(D) Rs. 5,00,000
(E) None of these
Rationale: Solution: Let the number of passenger traveling by first class be x.
Then, number of passenger traveling by second class will be 4x.
But the fare is in the ratio 3:1
In other words, if 3y fare is collected per I class passenger, y would be collected per II class passenger.
Fares of I class passengers : Fares of II class passengers
= x*3y : 4x*y
= 3:4 The above ratio can be interpreted as follows.
If total fare is 3+4 = 7, then I class passengers should pay Rs. 3
Similarly, we can calculate the fare of I class passengers when total was 224000
Total Fare I Class Fare
7 3
224000 ?
= 224000*(3/7) = Rs. 96000.
Answer: Option B
Answer: (B) Rs. 96000
Question: There is a square with sides of 13. What is the area of the biggest circle that can be cut out of this square?
(A) 132.73
(B) 231.92
(C) 530.93
(D) 113.1
(E) 204.33
Rationale: Area of a circle = A=Ï€r^2
Square is 13 wide, so circle's diameter would be 13, and radius would be 6.5
A=Ï€6.5^2 which is approximately 132.73
Answer is A
Answer: (A) 132.73
Question: A cycle is bought for Rs.600 and sold for Rs.1080, find the gain percent?
(A) 22
(B) 20
(C) 90
(D) 80
(E) 11
Rationale: 600 ---- 180
100 ---- ? => 80%
Answer:D
Answer: (D) 80
Question: Ratio between Rahul and Deepak is 4:3, After 10 Years Rahul age will be 26 years. What is Deepak present age.
(A) 12
(B) 15
(C) 20
(D) 22
(E) 24
Rationale: Explanation:
Present age is 4x and 3x,
=> 4x + 10 = 26 => x = 16
So Deepak age is = 3(4) = 12
Option A
Answer: (A) 12
Question: Running at their respective constant rate, machine X takes 2 days longer to produce w widgets than machines Y. AT these rates, if the two machines together produce 5w/4 widgets in 3 days, how many days would it take machine X alone to produce 4w widgets.
(A) 4
(B) 6
(C) 8
(D) 10
(E) 24
Rationale: I am getting 12. E. Hope havent done any calculation errors..
approach..
let y=no. of days taken by Y to do w widgets. Then X will take y+2 days.
1/(y+2) +1/y = 5/12(5/12 is because (5/4)w widgets are done in 3 days. So, x widgets will be done in 12/5 days or 5/12 th of a widget in a day)
Solving, we have y = 4
=>X takes 6 days to doing x widgets. So, he will take 24 days to doing 4w widgets.
Answer : E
Answer: (E) 24
Question: Bill’s compact disc player randomly plays a song, so that no song is repeated before the entire album is played. If Bill plays a disc with 15 songs, what are the chances that the third song he hears will be his favorite?
(A) 1/15
(B) 1/12
(C) 1/11
(D) 3/14
(E) 1/3
Rationale: The player plays the songs on the album at random, so there are 15 songs that can be the third one played. Only 1 of these ways will result in Bill's favorite song being the third one played.
Total outcomes ==> 15
Total positive outcomes ==> 1
Correct answer is A) 1/15
Answer: (A) 1/15
Question: Out of three numbers, the first is twice the second and is half of the third. If the average of the three numbers is 84, the three numbers in order are?
(A) 36, 72, and 144
(B) 36, 144, and 72
(C) 72, 36, and 144
(D) 72, 144, and 36
(E) 144, 36, and 72
Rationale: Let the numbers be 2x, x and 4x
(2x + x + 4x)/3 = 84
7x/3 = 84
x = 36
The numbers in order are 72, 36, and 144
The answer is C.
Answer: (C) 72, 36, and 144
Question: 8 men can dig a pit in 20 days. If a work half as much again as a boy, then 4 men and 9 boys can dig a similiar pit. Find the days for 15 days can dig?
(A) 20
(B) 14
(C) 16
(D) 10
(E) 21
Rationale: 1 man=3/2 boys.
(4 men +9 boys)=15 boys.
8men=(3/2)*8=12 boys.
now, 12 boys can dig the bit in 20 days.
15 boys can dig=20*12/15=16 days.
The option C is answer
Answer: (C) 16
Question: If the letters of the word PLACE are arranged taken all at a time, find how many do not start with AE?
(A) 114
(B) 124
(C) 130
(D) 134
(E) 135
Rationale: Total no'of arrangements 5P5 = 5! = 120
no'of arrangements start with AE = 1 × 6 = 6
no'of arrangements which do not start with AE = 120 - 6 = 114
A)
Answer: (A) 114
Question: The side of a square is increased by 30% then how much % does its area increases?
(A) 30.00 %
(B) 36.25 %
(C) 69.00 %
(D) 52.25 %
(E) 56.55 %
Rationale: a = 100 a2 = 10000
a = 130 a2 = 16900
----------------
10000 --------- 6900
100 -------? => 69.00 %
Answer:C
Answer: (C) 69.00 %
Question: In a bag, there are 4 white, 1 brown and 5 red pens. One pen is picked up randomly. What is the probability that it is neither white nor red?
(A) 1/5
(B) 1/10
(C) 1/2
(D) 1/3
(E) 1/4
Rationale: Explanation :
Neither white nor red means the pen drawn is brown.
Total number of outcomes = (4+1+5) = 10.
Number of Favourable outcomes = 1 = Number of brown pens.
Hence, Probability of the event = 1/10.
Answer : B
Answer: (B) 1/10
Question: A bag contains 6 red, 5 blue and 2 green balls. If 2 ballsare picked at random, what is the probability that both are red?
(A) 3/13
(B) 4/31
(C) 5/26
(D) 6/31
(E) 2/51
Rationale: P(Both are red),
=6C213C2=6C213C2
=5/26
C
Answer: (C) 5/26
Question: In how many different ways can the letters of the word ‘ARMOUM’ be arranged?
(A) 200
(B) 234
(C) 250
(D) 270
(E) 360
Rationale: ARMOUR = 6 letter whereas R repeated twice 6! 6xSx4x3x2x1 => 360
E
Answer: (E) 360
Question: If 12 men and 16 boys can do a piece of work in 5 days and 13 men together will 24 boys can do it in 4 days. Compare the daily work done by a man with that of a boy?
(A) 2:5
(B) 2:9
(C) 2:4
(D) 2:1
(E) 2:2
Rationale: 12M + 16B ----- 5 days
13M + 24B ------- 4 days
60M + 80B = 52M + 96B
8M = 16B => 1M = 2B
M: B = 2:1
Answer:D
Answer: (D) 2:1
Question: In a room with 7 people, 4 people have exactly 1 friend in the room and 3 people have exactly 2 friends in the room (Assuming that friendship is a mutual relationship, i.e. if Jane is Paul's friend, Paul is Jane's friend). If two individuals are selected from the room at random, what is the probability that those two individuals are NOT friends?
(A) 5/21
(B) 3/7
(C) 4/7
(D) 5/7
(E) 16/21
Rationale: (4/7)(5/6) + (3/7)(4/6) if you choose one of the 4 with one other friend, then you have a 5/6 chance of not picking their friend 2nd. If you choose one of the 3 with 2 friends, you have a 4/6 chance of not picking one of their friends second. Add them up.
20/42 + 12/42
32/42 = 16/21
E. 16/21
Answer: (E) 16/21
Question: How much is 75% of 40 is greater than 4/5 of 25?
(A) 22
(B) 67
(C) 10
(D) 12
(E) 66
Rationale: (75/100) * 40 – (4/5) * 25
= 10
Answer: C
Answer: (C) 10
Question: If f(a)=3a+6, what is the value of (f(2a)+f(a)) ?
(A) 2a-4
(B) 8a-7
(C) 9a+5
(D) 8a+12
(E) 3a+5
Rationale: f(a)=3a+6
f(2a)= 5a+6
(f(2a)+f(a)) = 5a+6+3a+6 = 8a+12
Answer is D
Answer: (D) 8a+12
Question: Sum of 53 odd numbers is?
(A) 2709
(B) 2809
(C) 2909
(D) 3009
(E) 3109
Rationale: sum of 1st n odd no.s = 1+3+5+7+... = n^2
so, Sum of 1st 53 odd numbers = 53^2 = 2809
ANSWER:B
Answer: (B) 2809
Question: Given that 2x + 11 > 5 and 5x - 13 < 7, all values of x must be between which of the following pairs of integers?
(A) -4 and -1
(B) -1 and 4
(C) -4 and 1
(D) -3 and 4
(E) 2 and 5
Rationale: 2x + 11 > 5
i.e 2x >5-11
i.e. 2x > -6
i.e. x > -3
Also, 5x - 13 < 7
i.e. 5x <7+13
i.e 5x < 20
i.e x < 4
i.e. -3 < x < 4
Answer: Option D
Answer: (D) -3 and 4
Question: On dividing 136 by a number, the quotient is 9 and the remainder is 1. Find the divisor?
(A) A)12
(B) B)15
(C) C)16
(D) D)17
(E) E)18
Rationale: d = (D-R)/Q
= (136 - 1)/9
= 135/9 = 15
B)
Answer: (B) B)15
Question: The ratio of number of boys and girls in a school is 3:2. If there are 100 students in the school, find the number of girls in the school?
(A) 25
(B) 30
(C) 35
(D) 40
(E) 50
Rationale: Let the number of boys and girls be 3x and 2x
Total students = 100
Number of girls in the school = 2*100/5 = 40
Answer is D
Answer: (D) 40
Question: A train speeds past a pole in 15 seconds and a platform 150 meters long in 25 seconds. What is the length of the train (in meters)?
(A) 205
(B) 215
(C) 225
(D) 235
(E) 245
Rationale: Let the length of the train be x meters.
The speed of the train is x / 15.
Then, x + 150 = 25*(x / 15)
10x = 2250
x = 225 meters
The answer is C.
Answer: (C) 225
Question: -64x29+165=?
(A) 2436
(B) 2801
(C) -2801
(D) -1601
(E) None of them
Rationale: Given exp.=-64x(30-1)+165
=-(64x30)+64+165
=-1830+229
=-1601
Answer is D
Answer: (D) -1601
Question: Which of the following CANNOT be a product of two distinct positive integers r and s?
(A) r
(B) s
(C) 3s + 2r
(D) s - r
(E) sr
Rationale: In these questions it is best to take an example as if something is true for all positive integers than it as to be true for the smallest and the easiest integers to work with
take r = 1 and s = 2 and work with the options
rs = 2
A) r take r =2, s = 1
B) s take r = 1 s = 2
C) 3s + 2r Seems tricky, lets see other options and then come back to it.
D) s - r take s = 1 and r = 2 --> s - r = -1 .. How the hell can product of two positive integers be negative ?? or less than each of them?
E) sr Always true
You don't even have to worry what C is !
ans D
Answer: (D) s - r
Question: Three friends are buying a gift for a friend. Declan contributes 4 dollars more than 1/4 the cost of the gift, Ed contributes 6 dollar less than 1/3 the cost of the gift, and Frank contributes the remaining 22 dollars. What is the cost of the gift?
(A) 48
(B) 54
(C) 60
(D) 66
(E) 72
Rationale: Declan = D, Ed = E, Frank = F
t = total
D + E + F = t
(t/4 + 4) + (t/3 - 6) + 22 = t
t = 20 + (7t/12)
12t = 20(12) + 7t
5t = 5*4(12)
t = 48
The correct answer is A.
Answer: (A) 48
Question: In how many different number of ways 5 boys and 2 girls can sit on a shopa which can accommodate persons?
(A) 190
(B) 210
(C) 220
(D) 230
(E) 234
Rationale: Option 'B'
7p3 = 7 × 6 × 5 = 210
Answer: (B) 210
Question: Find the greatest number which leaves the same remainder when it divides 25, 57 and 105.
(A) 23
(B) 28
(C) 18
(D) 16
(E) 12
Rationale: Explanation:
105 - 57 = 48
57 - 25 = 32
105 - 25 = 80
The H.C.F of 32, 48 and 80 is 16.
Answer: D
Answer: (D) 16
Question: A small, rectangular park has a perimeter of 560 feet and a diagonal measurement of 600 feet. What is its area, in square feet?
(A) 172,800
(B) 19,600
(C) 20,000
(D) 20,400
(E) 20,800
Rationale: you can avoid a lot of work in this problem by recognizing that, with the info provided, the diagonal forms a triangle inside the rectangle with sides that have a 3:4:5 ratio.
diagonal = 200
2x + 2y = 560, or x + y = 280
a^2 + b^2 = c^2 for each the sides of the triangle
using the ratio 3:4:5 for sides, and knowing c = 600, you can deduce the following
a=360
b=480
360x480=172,800
A is the answer.
Answer: (A) 172,800
Question: If the remainder is 3 when positive integer n is divided by 18, what is the remainder when n is divided by 6?
(A) 3
(B) 1
(C) 2
(D) 3
(E) 4
Rationale: Assume x is quotient here,
n=18x+3 ----------(1)
and n=6x+ ?
We can also write first term as
n=(18x+6) = 6(3x+1) +3
ie 6(3x+1)+3 ie the first term is perfectly divisible by 6.
So,the remainder left is 3.
So,answer (A) is right choice.
Answer: (A) 3
Question: Health insurance Plan W requires the insured to pay $1000 or 50% of total cost, whichever is lower. Plan B requires the insured to pay the initial $300, but then pays 80% of the cost over $300. Which of the following is a cost level for which both insurance plans pay out the same amount?
(A) $600
(B) $1000
(C) $3800
(D) $5300
(E) $6200
Rationale: 0.5 * 600 = 300 where W = B.
Answer: (B) $1000
Question: We have boxes colored either red or blue. In each blue box there is a fixed number of blueberries. In each red box there is a fixed number of strawberries. If we dispose of one blue box for one additional red box, the total number of berries would increase by 30, and the difference between the total number of strawberries and the total number of blueberries would increase by 100. Each blue box contains how many blueberries?
(A) 35
(B) 40
(C) 45
(D) 50
(E) 55
Rationale: Let x be the number of blueberries in each blue box.
Then there are x+30 strawberries in each red box.
x+(x+30)=100
x = 35
The answer is A.
Answer: (A) 35
Question: If s and t are positive integers such that s/t = 56.18, which of the following could be the remainder when s is divided by t ?
(A) 2
(B) 4
(C) 8
(D) 20
(E) 90
Rationale: The remainder is 0.18 or 18/100. You can go one step further and say that X/Y=18/100, where X and Y are whole numbers. Plug in all the answer choices for X and see which one makes Y a whole number.
One thing that jumps out at me is that A, B, C, and D are all even. E on the other hand is odd. Why? Maybe I'll start plugging in here first.
90/Y=18/100
18Y=9000
Y=500
Answer: E.
Answer: (E) 90
Question: If three numbers in the ratio 3 : 2: 5 be such that the sum of their squares is 1862, the middle number will be
(A) 10
(B) 14
(C) 18
(D) 22
(E) 24
Rationale: Explanation:
Let the numbers be 3x, 2x and 5x.
Then,
9x + 4x + 25x =1862
⇒ 38x = 1862
⇒ x = 49 ⇒ x = 7.
middle number = 2x = 14
Option B
Answer: (B) 14
Question: Rahul went to a shop and bought things worth Rs. 24, out of which 30 Paise went on sales tax on taxable purchases. If the tax rate was 6%, then what was the cost of the tax free items?
(A) 18.7
(B) 20
(C) 22
(D) 21.4
(E) 21.5
Rationale: Total cost of the items he purchased = Rs.24
Given that out of this Rs.24, 30 Paise is given as tax
=> Total tax incurred = 30 Paise = Rs.30/100
Let the cost of the tax free items = x
Given that tax rate = 6%
∴ (24−30/100−x)6/100 = 30/100
⇒ 6(24 −0.3 −x) = 30
⇒ (24 − 0.3 − x) = 5
⇒ x = 24 − 0.3 − 5 = 18.7
A
Answer: (A) 18.7
Question: In measuring the sides of a rectangle,one side is taken 5% in excess,and the other 4% in deficit.Find the error percent in the error percent in the area calculated from these measurements.
(A) 0.8%
(B) 0.2%
(C) 0.4%
(D) 0.9%
(E) 0.6%
Rationale: Let x and y be the sides of the rectangle.Then,correct area =xy.
calculated area =(105/100* x)*(96/100* y)=504/500*xy.
Error in measurement =504/500* xy)-xy=4/500*xy.
Error % =[4/500*xy*1/xy*100]%=4/5=0.8%.
Answer is A
Answer: (A) 0.8%
Question: there are five red shoe and 4 green. if one draw randomly a shoe then what is the probability of getting red
(A) 1/9
(B) 2/9
(C) 3/9
(D) 4/9
(E) 5/9
Rationale: prob of getting red shoe = 5/9
ANSWER:E
Answer: (E) 5/9
Question: There 3 kinds of books in the library physics, chemistry and biology. Ratio of physics to chemistry is 3 to 2; ratio of chemistry to biology is 4 to 3, and the total of the books is more than 3000. Which one of following can be the total E of the book?
(A) 3003
(B) 3027
(C) 3024
(D) 3021
(E) 3018
Rationale: First, you have to find the common ratio for all 3 books. You have:
P:C:B
3:2 --> multiply by 2 (gives you row 3)
4:6
6:4:3
Hence:
P:C:B:T(Total)
6:4:3:13 ----> This means, the Total Number E must be a multiple of 13.
Answer A is correct since 299 is divisible by 13, hence is 2990 and so is 3003 (2990+13).
Answer: (A) 3003
Question: From the given equation find the value of x: x² − 3x + 2
(A) 1
(B) 3
(C) 2
(D) 5
(E) 6
Rationale: (x − 1)(x − 2)
x = 1 or 2.
C
Answer: (C) 2
Question: Sam taken a loan Rs.15000/- from Co-operative Society with an interest @ 11.5% per month. At the same time he deposited Rs. 10000/- as Fixed Deposit with an interest @ 9.5% per month. After one week sam asked the manager to calculate the interest to be paid. What is the interest amount for 7 days?
(A) A)165
(B) B)220
(C) C)310
(D) D)185
(E) E)181
Rationale: Loan amount : Rs.15000/- @ 11.5%
Interest per month = 15000/- * 11.5% =Rs.1725
Interest for one day = 1725/30=57.50
Interest for 7 days is = 57.50*7 =403
FD amount is = Rs.10000/- @ 9.5%
Interest per month = 10000 * 9.5% = 950/-
Interest for 7 days = 950/30*7 = 222
Interest amount to be paid by Sam = 403-222 =181/- for 7 days
Answer is E
Answer: (E) E)181
Question: Calculate the time it will take for a train that is 200 meter long to pass a bridge of 180 meter length, if the speed of the train is 65 km/hour ?
(A) 20 seconds
(B) 4 seconds
(C) 31.04 seconds
(D) 11.04 seconds
(E) 21.04 seconds
Rationale: Speed = 65 Km/hr = 65*(5/18) m/sec = 18.06 m/sec
Total distance = 200+180 = 380 meter
Time = Distance/speed
= 380 * (100/1806) = 21.04 seconds
Answer: E
Answer: (E) 21.04 seconds
Question: Train E and F, 455 miles apart, are traveling toward each other at constant rates and in the same time zone. If train E left at 4 pm traveling at a speed of 60 miles per hour, and train F left at 5:45 pm and traveling at 45 miles per hour, then at what time would they pass each other?
(A) 9.03pm
(B) 9.05pm
(C) 9.07pm
(D) 9.08pm
(E) 9.10pm
Rationale: First, since E has a headstart then in that 1hr45min or 1.75hrs he travels 105 miles
Then remaining distance to be traveled will be 455 - 105 = 350 miles
Now, using relative rates (105)(t) = 350
This gives 10/3 hours
Now 5.45pm + 10/3 hours gives us 9.05pm
Hence answer is B
Answer: (B) 9.05pm
Question: An athlete runs 200 metres race in 24 seconds. His speed is
(A) 20 km / hr
(B) 24 km /hr
(C) 28.5 km / hr
(D) 30 km / hr
(E) None
Rationale: Sol.
Speed = 200 / 24 m/sec = 25 / 3 m/sec
= (25/3 x 18 / 5) km / hr = 30 km / hr.
Answer D
Answer: (D) 30 km / hr
Question: While playing a certain dice game, Chris wins if the sum of the two dice is 10, at which point the game is over. If the game allows Chris three rolls in an attempt to win, what is the probability that Chris will win?
(A) 1/2
(B) 17/36
(C) 190/827
(D) 11/36
(E) 25/216
Rationale: Probability of winning game = 1- Probability of losing game
Probability of losing game = (Probability of not getting sum 7 in any of the three attempts)
Ways of getting sum 10 = (4,6)(5,5)(6,4)= 3 ways
Total ways of getting outcome on two dice =6*6=36
Probability of getting sum as 10 in any attempt =3/36=1/12
Probability of NOT getting sum as 10 in any attempt = 1-(1/12)= 11/12
Probability of losing game =(11/12)*(11/12)*(11/12)=637/827
I.e. Probability of wining game = 1-(637/827) = 190/827
Answer : Option C
Answer: (C) 190/827
Question: If the ratio of the change in the book's price to its new price is 1 : 5, What is the % price increase?
(A) 25%
(B) 50%
(C) 75%
(D) 90%
(E) 100%
Rationale: Solution:-
Given
ratio of change in book price/ new price = 1 /5
=>(new price−old price)/new price=1/5
=> old price/new price=4/5 ---- equation 1
% increase is always with respect in the initial or old price.
=> % increase = (( new price - old price)/old price)*100---equation 2
substituting 1 in 2 we have
% increase = ((new−(4/5)new)/((4/5)new))∗100
= 25%
ANSWER:A
Answer: (A) 25%
Question: If 4x+y=34, 2x-y=20, for integers of x and y, y^2=?
(A) 2
(B) 4
(C) 0
(D) 10
(E) 3
Rationale: 4x+y = 34
2x-y = 20
6x = 54
x = 9
y = -2
y^2 = 4
Answer is B
Answer: (B) 4
Question: A sum of $1162 is divided among A,B and C. Such that 4 times A's share share is equal to 5 times B's share and 7 times C's share . What is the share of C?
(A) $ 280
(B) $ 180
(C) $ 260
(D) $ 140
(E) $ 240
Rationale: 4 times of A's share =5 times of B's share=7 times of C's share=1
therefore , the ratio of their share =1/4:1/5:1/7
LCM of 4,5,7=140
therefore,A’s¼:1/5:1/7=35:28:20
the ratio now can be written as 35:28:20
therefore C's share=(20/83)*1162=20*14=$ 280
ANSWER : A 280
Answer: (A) $ 280
Question: The average of first 10 odd numbers is?
(A) 11
(B) average=10
(C) 18
(D) 12
(E) 19
Rationale: Explanation:
Sum of 10 odd no. = 100
Average = 100/10 = 10
Answer:B
Answer: (B) average=10
Question: The events A and B are independent. The probability that event A occurs is x and the probability that event B occurs is y. Which of the following is equal to the probability that exactly one of the events A and B occurs?
(A) x − 2xy
(B) y − xy
(C) x + y − 2xy
(D) x + y − xy
(E) x + y
Rationale: Probability of A occuring = x , Probability of A NOT occuring = 1-x
Probability of B occuring = y , Probability of B not occurring = 1-y
Probability of atleast of one of A and B occuring = 1-(1-x)(1-y) =x+y -xy
D
Answer: (D) x + y − xy