mathewhe/aqua_rat huggingface dataset:
Question: A box contains 3 blue marbles, 4 red, 4 green marbles and 2 yellow marbles. If three marbles are picked at random, what is the probability that they are all blue?
(A) 1/286
(B) 2/455
(C) 1/91
(D) 4/455
(E) None of these
Rationale: Given that there are three blue marbles, four red marbles, four green marbles and one yellow marbles.
Probability that all the three marbles picked at random are blue = 3C₃/13C₃ = (1 * 3 * 2 * 1)/(13 * 12 * 11) = 1/286
ANSWER:A
Answer: (A) 1/286
Question: The length of a room is 5.5 m and width is 3.75 m. Find the cost of paying the floor by slabs at the rate of Rs. 1000 per sq.metre.
(A) Rs. 15,000
(B) Rs. 15,500
(C) Rs. 15,600
(D) Rs. 20,625
(E) None
Rationale: Solution
Area of the floor	= (5.5 x 3.75)m²
= 20.635m ²
Cost of paying	= Rs. (1000 x 20.625)
= Rs.20625.
Answer D
Answer: (D) Rs. 20,625
Question: Which of the following is closest to (8!-7!)/(8!+7!)?
(A) 0.01
(B) 0.8
(C) 0.2
(D) 1
(E) 10
Rationale: (8!-7!)/(8!+7!)
7! (8-1)/7! (8+1)
7/9 = 0.8 (approximately)
B is the answer
Answer: (B) 0.8
Question: Two pipes A and B can separately fill a tank in 12 and 15 minutes respectively. A third pipe C can drain off 45 liters of water per minute. If all the pipes are opened, the tank can be filled in 15 minutes. What is the capacity of the tank?
(A) 399
(B) 540
(C) 772
(D) 272
(E) 121
Rationale: 1/12 + 1/15 - 1/x = 1/15
x = 12
12 * 45 = 540
Answer: B
Answer: (B) 540
Question: There are seven thieves. They stole diamonds from a diamond merchant and ran away. While running, night sets in and they decide to rest in the jungle.
When everybody was sleeping, two of them woke up and decided to divide the diamonds equally among themselves. But when they divided the diamonds equally, one diamond is left.
So they woke up the 3rd thief and tried to divide the diamonds equally again but still one diamond was left. Then they woke up the 4th thief to divide the diamonds equally again, and again one diamond was left. This happened with the 5th and 6th thief – one diamond was still left.
Finally, they woke up the 7th thief and this time the diamonds were divided equally.
How many diamonds did they steal in total?
(A) 1560
(B) 1561
(C) 1559
(D) 1557
(E) None of the above
Rationale: We need a number that is a multiple of 7 that will give a remainder of 1 when divided by 2, 3, 4, 5, and 6. The least common multiple of these numbers is 60. So, we need a multiple of 7 that is 1 greater than a multiple of 60.
Answer B
Answer: (B) 1561
Question: What is the units digit of the expression 14^7−15^4?
(A)  0
(B)  8
(C)  4
(D)  6
(E)  3
Rationale: I think answer on this one should be B too. Since we know that 14^7>15^4, as Will said one should always check if the number is positive.
Answer: (B)  8
Question: Two trains are running at 40 km/hr and 20 km/hr respectively in the same direction. Fast train completely passes a man sitting in the slower train in 7 seconds. What is the length of the fast train ?
(A) 27 7/9
(B) 28 7/9
(C) 29 7/9
(D) 38 8/9
(E) None of these
Rationale: Explanation:
As Trains are moving in same direction,
So, Relative Speed = 40-20 = 20 kmph
= 20*(5/18) = 50/9 m/sec
Length of Train= Speed * Time
Length=50/9âˆ—7
=350/9
=38 8/9
Option D
Answer: (D) 38 8/9
Question: What is the smallest positive integer K such that the product of 61347 x K is a perfect square?
(A) 3
(B) 9
(C) 15
(D) 25
(E) 63
Rationale: A perfect square, is just an integer that can be written as the square of some other integer. For example 16=4^2, is a perfect square.
Now, 61347 = 13^2 * 11^2 * 3, so if k=3 then 61347 k = (13 * 11 * 3)^2, which is a perfect square (basically the least positive value of k must complete only the power of 7 to even power as powers of other primes are already even).
Answer: A.
Answer: (A) 3
Question: Leila is playing a carnival game in which she is given 4 chances to throw a ball through a hoop. If her chance of success on each throw is 1/5, what is the chance that she will succeed on at least 3 of the throws?
(A) 1/5^4
(B) 1/5^3
(C) 6/5^4
(D) 13/5^4
(E) 17/5^4
Rationale: Probability that She will succeed on at least 3 of the throws = Probability that she will succeed on exactly 3 throws + probability that she will succeed on atleast 4 throws.
Probability that she will succeed on exactly 3 throws:
S - succeed
F - Failure
So there are 4 possibilities
FSSS , SFSS, SSFS, SSSF
Probability os success = 1/5
Probability of failure= 1 - probability of success = 1- 1/5 = 4/5
Probability of success on at least three tries =
Probability that she will succeed on exactly 3 throws + probability that she will succeed on atleast 4 throws =
P(FSSS) + P(SFSS) + P(SSFS) + P(SSSF) + P(SSSS) =
{(4/5) *(1/5) *(1/5) *(1/5)} + {(1/5) *(4/5) *(1/5) *(1/5)} + {(1/5) *(1/5) *(4/5) *(1/5)} + {(1/5) *(1/5) *(1/5) *(4/5)} + {(1/5) *(1/5) *(1/5) *(1/5)} =
(1/5)*(1/5)*(1/5)* { (4/5) + (4/5) + (4/5) + (4/5) + (1/5) }
= 17 / 5^4
Answer:E
Answer: (E) 17/5^4
Question: The least number, which when divided by 12, 15, 20 and 54 leaves in each case a remainder of 8, is :
(A) 504
(B) 536
(C) 544
(D) 548
(E) None of these
Rationale: Explanation:
Required number = (L.C.M. of 12, 15, 20, 54) + 8
= 540 + 8
= 548. Answer: Option D
Answer: (D) 548
Question: Ram is 8 years younger than Sundar, and Mahi is thrice as old as Ram. If S is Sundar’s age and M is Mahi’s age, what is the relationship between S and M?
(A) M = 3S + 10
(B) M = 3S + 14
(C) M = 3S + 5
(D) M = 3S − 10
(E) M = 3S − 24
Rationale: R=S - 8 and M=3R --> M=3S -24
Answer E
Answer: (E) M = 3S − 24
Question: If cost of 15 eggs be 82 rupees, then find out the cost of 5 dozen eggs.
(A) 300
(B) 400
(C) 330
(D) 600
(E) 700
Rationale: Cost of 15 eggs = 82 rupees
Cost of 1 egg = 82/15 = 5.5 rupees,
Cost of 5 dozens, i.e. 5.5 x 12 = 66 x 5 = 330
Answer : C
Answer: (C) 330
Question: 4, 12, 48, 240, 1440, 10080,(...)
(A) 80640
(B) 10080
(C) 6200
(D) 10020
(E) 12500
Rationale: Explanation :
Go on multiplying the given numbers by 3, 4, 5, 6, 7,8
Answer : Option A
Answer: (A) 80640
Question: If (10^4 * 3.456789)^14 is written as a single term, how many digits would be to the right of the decimal place?
(A) 9
(B) 14
(C) 21
(D) 28
(E) 42
Rationale: 3.456789^14 has 6*14 = 84 decimal places.
10^56 moves the decimal place to the right 56 places.
(10^4 * 3.456789)^14 has 84-56 = 28 digits after the decimal point.
The answer is D.
Answer: (D) 28
Question: When m is divided by 9, the remainder is 2. When m is divided by 13, the remainder is 3. If 1 < m < 300, what is the greatest possible value of m?
(A) 173
(B) 203
(C) 233
(D) 263
(E) 293
Rationale: 13*9 = 117
Let's start with 3, and keep adding 13 until we find a number with the form 9k+2.
3, 16, 29 = 9*3+2
The next possible number is 29 + 117 = 146
The next possible number is 146 + 117 = 263
The next possible number would be greater than 300.
The answer is D.
Answer: (D) 263
Question: The ratio of numbers is 3:4 and their H.C.F is 5. Their L.C.M is:
(A) 12
(B) 16
(C) 24
(D) 60
(E) 98
Rationale: Let the numbers be 3x and 4x.
Then their H.C.F = x. So, x = 5.
So, the numbers are 15 and 20.
L.C.M of 15 and 20 = 60.
ANSWER:D
Answer: (D) 60
Question: How many different ways can you select a pilot and a co pilot if you have 100 people to choose from?
(A) 199
(B) 200
(C) 398
(D) 4950
(E) 9900
Rationale: 1) PERMUTATION:-
since it is selection, we have to find permutation..
100P2= 100!/(100-2)!=100*99=9900
2) COMBINATION:-
the ways to select 2 for 2 posts= 100C2
=> 100!/2!98! = 4950
But these 2 can be arranged in 2! ways..
Total= 4950*2! = 9900
3) choose for each post
First post say PILOT can be filled with any of the 100..
co-pilot can be filled by any of the remaining 99
Total = 100*99=9900..
ANS:E
Answer: (E) 9900
Question: A driving school claims an average test pass rate of 76.8 percent. What is the least number of pupils required to achieve this result?
(A) 132
(B) 127
(C) 125
(D) 152
(E) 112
Rationale: C
125
96 passes out of 125 give an average of 76.8%
Answer: (C) 125
Question: A committee is reviewing a total of 30x black-and-white films and 6y color films for a festival. If the committee selects y/x% of the black-and-white films and all of the color films, what fraction of the selected films are in color?
(A) 22/21
(B) 20/21
(C) 23/21
(D) 25/21
(E) 28/21
Rationale: Say x=y=10. In this case we would have:
30x=300 black-and-white films;
6y=60 color films.
y/x%=10/10%=1% of the black-and-white films, so 3 black-and-white films and all 60 color films, thus total of 63 films were selected.
Color films thus compose 60/63=20/21 of the selected films.
Answer:B
Answer: (B) 20/21
Question: A 900 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) 1000
(B) 1050
(C) 1060
(D) 370
(E) 380
Rationale: Speed = 900/18 = 50/1 m/sec.
Let the length of the platform be x meters.
Then, (x + 300)/39 = 50/1
=> x = 1950 m.
L=1950-900 =1050
Answer: Option B
Answer: (B) 1050
Question: A certain number when divided by 39 leaves a remainder 18, what is the remainder when the same number is divided by 13?
(A) 7
(B) 8
(C) 9
(D) 6
(E) 5
Rationale: Explanation:
39 + 18 = 57/13 = 5 (Remainder)
Answer: E
Answer: (E) 5
Question: A is thrice as efficient as B and is, therefore, able to finish a piece of work 10 days earlier than B. In how many days A and B will finish it together?
(A) 7 days
(B) 6 days
(C) 9 days
(D) 5 days
(E) 4 days
Rationale: WC = 3:1
WT = 1:3
x 3x
1/x – 1/3x = 1/10
x = 20/3
3/20 + 1/20 = 1/5 => 5 days
Answer:D
Answer: (D) 5 days
Question: Ashok secured average of 79 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) 104
(B) 27
(C) 99
(D) 17
(E) 80
Rationale: Explanation:
Number of subjects = 6
Average of marks in 6 subjects = 79
Therefore total marks in 6 subjects = 79 * 6 = 474
Now, No. of subjects = 5
Total marks in 5 subjects = 74 * 5 = 370
Therefore marks in 6th subject = 474 – 370 = 104
ANSWER: A
Answer: (A) 104
Question: Two pipes can separately fill a tank in 20 and 30 hours respectively. Both the pipes are opened to fill the tank but when the tank is full, a leak develops in the tank through which one-third of water supplied by both the pipes goes out. What is the total time taken to fill the tank?
(A) 17 hrs
(B) 16 hrs
(C) 15 hrs
(D) 13 hrs
(E) 12 hrs
Rationale: 1/20 + 1/30
= 1/12
1 + 1/3
= 4/3
1 --- 12
4/3 --- ?
4/3 * 12 = 16 hrs
Answer:B
Answer: (B) 16 hrs
Question: Three persons A, B and C started new business. A & C invested amounts in the ratio 2:1, whereas the ratio between amounts invested by A & B was 3:2, If Rs 157300 was their profit, how much amount did B receive?
(A) 35009
(B) 37900
(C) 39000
(D) 48400
(E) 52000
Rationale: A:B = 3:2 = 6:4
A:C = 2:1 = 6:3
A:B:C = 6:4:3
B share = (4/13)*157300 = 48400
(D)
Answer: (D) 48400
Question: If a,b, and c are consecutive positive integers and a>b>c, what can be the value of (a^2-b^2)(b^2-c^2)?
(A) 77
(B) 88
(C) 99
(D) 110
(E) 121
Rationale: (a^2-b^2)(b^2-c^2) = (a+b)*(a-b)*(b+c)*(b-c) = (a+b)*(-1)*(b+c)*(-1) = (a+b)*(b+c)
Therefore, the product should have factors with a difference of 2.
99 = 9*11, so this is a possible value for the original expression.
The answer is C.
Answer: (C) 99
Question: Two trains are moving at 80 kmph and 70 kmph in opposite directions. Their lengths are 150 m and 100 m respectively. The time they will take to pass each other completely is?
(A) 6 sec
(B) 7 sec
(C) 7 2/2 sec
(D) 8 sec
(E) 9 sec
Rationale: 70 + 80 = 150 * 5/18 = 125/3 mps
D = 150 + 100 = 250 m
T = 250 * 3/125 = 6 sec
Answer: A
Answer: (A) 6 sec
Question: The average of 13 numbers is 10.9. If the average of the first seven numbers is 10.5 and that of the last seven numbers is 11.4, then the middle number is
(A) 15.6
(B) 11.6
(C) 12.6
(D) 13.3
(E) 14.4
Rationale: Explanation:
Middle numbers = [(10.5 x 7 + 11.4 x 7) - 10.9 x 13] = (131.4 - 119-9) = 11.6 Answer: B
Answer: (B) 11.6
Question: The maximum number of student amoung them 1001 pens and 910 pencils can be distributed in such a way that each student gets the same number of pens and same number of pencils is :
(A) 91
(B) 910
(C) 1001
(D) 1911
(E) None of these
Rationale: Solution
Required number of student = H.C.F of 1001 and 910 = 91. Answer A
Answer: (A) 91
Question: An article is bought for Rs.675 and sold for Rs.900, find the gain percent?
(A) 33 1/2%
(B) 33 2/3%
(C) 33 1/3%
(D) 33 3/3%
(E) 32 1/3%
Rationale: 675 ---- 225
100 ---- ? => 33 1/3%
Answer:C
Answer: (C) 33 1/3%
Question: A pump can fill a tank with water in 2 hours. Because of a leak, it took 2x1/3 hours to fill the tank. The leak can drain all the water of the tank in
(A) 5 hours
(B) 7 hours
(C) 8 hours
(D) 14 hours
(E) 18 hours
Rationale: Work done by the leak in 1 hour = 1/2 - 3/7 = 1/14.
Leak will empty the tank in 14 hrs.
ANSWER:D
Answer: (D) 14 hours
Question: A parking garage rents parking spaces for $10 per week or $20 per month. How much does a person save in a year by renting by the month rather than by the week?
(A)  $140
(B)  $160
(C)  $220
(D)  $240
(E)  $280
Rationale: 10$ per week!
An year has 52 weeks.
Annual charges per year = 52* 10 = 520$
30$ per month!
An year has 12 months.
Annual charges per year = 12 * 20 = 240$
520 - 240 = 280
Ans E
Answer: (E)  $280
Question: How many words can be formed by using all letters of the word “BIHAR”
(A) 478
(B) 451
(C) 120
(D) 123
(E) 150
Rationale: The word BIHAR contains 5 different letters.
Required number of words = 5p5 = 5! = (5x4x3x2x1) = 120
Ans: C
Answer: (C) 120
Question: In a certain pond, 40 fish were caught, tagged, and returned to the pond. A few days later, 40 fish were caught again, of which 2 were found to have been tagged. If the percent of tagged fish in the second catch approximates the percent of tagged fish in the pond, what is the approximate number of fish in the pond?
(A)  1000
(B)  625
(C)  1,250
(D)  2,500
(E)  10,000
Rationale: total fish = x
percentage of second catch = (2/40)*100 = 5%
so, x * 5% = 50
x = 1000 ans.A
Answer: (A)  1000
Question: The ratio of two quantities is 1 to 2. If each of the quantities is increased by 15, what is the ratio of these 2 new quantities?
(A) 5:6
(B) 25:27
(C) 15:16
(D) 20:21
(E) It cannot be determined from the information given
Rationale: The ratio cannot be straight way added any quantity...
1:2means 1X:2X...
So when you add a quantity, it becomes 1x + 15 : 2x +15..
So value of x is must..
Ans E
Answer: (E) It cannot be determined from the information given
Question: Line k is in the rectangular coordinate system. If the a-intercept of k is -2, and the y-intercept is 3, which of the following is an equation of line k?
(A) -3a + 2y = 6
(B) 3a + 2y = -6
(C) 3a - 2y = 6
(D) 2a - 3y = 6
(E) -2a - 3y = 6
Rationale: This question can be solved in much simpler way.
To find the a intercept
Put y=0 in the equation of the line.
To find the y-intercept
Put a=0 in the equation of the line.
So
Sub a=0 in the answer choices check whether you are getting y=3.
A. -3a + 2y = 6 --- y = 3
B. 3a + 2y = -6 --- y = -3
C. 3a - 2y = 6 ----- y = -3
D. 2a - 3y = 6 --- y = -2
E. -2a - 3y = 6 --- y =-2
Eliminate answer B,C,D and E.
So the answer is A.
Answer: (A) -3a + 2y = 6
Question: In 1979 approximately 1/3 of the 37.3 million airline passengers traveling to or from the United States used Kennedy Airport. If the number of such passengers that used Miami Airport was 1/3 the number that used Kennedy Airport and 4 times the number that used Logan Airport, approximately how many millions of these passengers used Logan Airport that year?
(A)  18.6
(B)  9.3
(C)  6.2
(D)  3.1
(E)  1.01
Rationale: number of
passengers using Kennedy airport = 37/3 =~12.43
Passengers using Miami airport = 12.43/3=~4.14
passengers using logan airport = 4.14/4 =~1.01
so E
Answer: (E)  1.01
Question: At a certain fruit stand, the price of each apple is 50 cents and the price of each orange is 60 cents. Mary selects a total of 10 apples and oranges from the fruit stand, and the average (arithmetic mean) price of the 10 pieces of fruit is 56 cents. How many oranges must Mary put back so that the average price of the pieces of fruit that she keeps is 52 cents?
(A) 1
(B) 2
(C) 3
(D) 4
(E) 5
Rationale: Let number of Apples = A
number of oranges = B
A+B=10 --- 1
.56 =(.5A + .6 B)/10
=> 56 = 5A + 6B ----2
Solving 1 and 2, we get
A= 4
B= 6
Let the number of oranges put back = C
52*(10-c) = 50*4 + 60(6-C)
=> C= 5
Answer E
Answer: (E) 5
Question: A 300 m long train crosses a platform in 39 sec while it crosses a signal pole in 26 sec. What is the length of the platform?
(A) 389 m
(B) 150 m
(C) 289 m
(D) 299 m
(E) 219 m
Rationale: Speed = 300/26 = 150/13 m/sec.
Let the length of the platform be x meters.
Then, (x + 300)/39 = 150/13
=> x = 150 m.
Answer:B
Answer: (B) 150 m
Question: A is twice as good a workman as B. Together they finish a piece of work in 18 days. Then B can do a similar work by himself in :
(A) 54 days
(B) 27 days
(C) 29 days
(D) 17 days
(E) 37 days
Rationale: B can complete work in 54 days and A can complete work in 27 days.
It is simple to get the ans.
If 3B ( A+B= 2B+B) can do work in 18 days,
one B will complete work in 54 days.
ANSWER:A
Answer: (A) 54 days
Question: The sum of the ages of 4 children born at the intervals of 4 years each is 48 years. What is the age of the youngest child?
(A) 2 years
(B) 4 years
(C) 6 years
(D) 8 years
(E) 10 years
Rationale: Let the ages of the children be x, (x + 4), (x + 4)and (x + 12) years.
Then, x + (x + 4) + (x + 8) + (x + 12) = 48
4x = 24 => x = 6.
Age of youngest child = x = 6 years.
ANSWER:C
Answer: (C) 6 years
Question: The product of the prime integers between 23 and 35, inclusive, is:
(A) 50! – 40!
(B) 99,029
(C) 2,303
(D) 22,011
(E) 2,000
Rationale: only prime number bet ween 23 and 35 inclusive are 23, 29, 33
thus 23*29*33 =22,011
Ans: D
Answer: (D) 22,011
Question: A flagpole 18 meters high casts a shadow of length 45 meters. If a building under similar conditions casts a shadow of length 65 meters, what is the height of the building (in meters)?
(A) 22
(B) 24
(C) 26
(D) 28
(E) 30
Rationale: The height:length ratio will be equal in both cases.
18 / 45 = x / 65
x = 26
The answer is C.
Answer: (C) 26
Question: If the L.C.M of two numbers is 600 and their product is 18000, find the H.C.F of the numbers.
(A) 50
(B) 30
(C) 125
(D) 25
(E) None of these
Rationale: H.C.F = (Product of the numbers) / (Their L.C.M) = 18000/600 = 30.
ANSWER:B
Answer: (B) 30
Question: What will come in place of the x in the following Number series? 46080, 3840, 384, 48, 8, x
(A) 2
(B) 3
(C) 4
(D) 5
(E) 6
Rationale: 46080 /12 = 3840
3840 /10 = 384
384 /8 = 48
48 /6 = 8
8/4 = 2
A
Answer: (A) 2
Question: There are 4 different letters and 4 addressed envelopes.In how many ways can the letters be put in the envelopes so that atleast one letter goes to the correct address ?
(A) 349
(B) 77
(C) 2087
(D) 27066
(E) 2811
Rationale: Answer:B
Answer: (B) 77
Question: A certain number of workers can do a work in 75 days. If there were 10 workers more it could be finished in 10 days less. How many workers are there?
(A) 65
(B) 30
(C) 28
(D) 24
(E) 32
Rationale: number of workers = 10* (75-10)/10 = 65
Answer is A
Answer: (A) 65
Question: If a fair 6-sided die is rolled three times, what is the probability that exactly one 5 is rolled?
(A) 25/216
(B) 50/216
(C) 25/72
(D) 25/36
(E) 5/6
Rationale: Total ways in which a 6-sided die can be rolled three times = 6*6*6 = 216
To get exactly one 5, there are three ways:
A 5 on the first roll and non 5 on other two rolls. This can be done in 1*5*5 = 25 ways.
The 5 could be on the second or third roll too. So total favorable cases = 25*3 = 75
Required Probability = 75/216 = 25/72
Answer (C)
Answer: (C) 25/72
Question: An empty container is filled with pure alcohol. The alcohol is slowly allowed to run out and when the container is 1/4 empty ,it is replaced with water . Next, when the container is half empty it is again filled with water. Finally, when it is empty, it is again filled with water. What percentage of container is alcohol now?
(A) 81/2%
(B) 113/4%
(C) 93/8 %
(D) 143/8%
(E) none of these
Rationale: Ratio of quantity of alcohol left to total quantity
=>1/1 x (3/4)/1 x (1/2)/1 x (1/4)/1
=>3/32
Alcohol percentage=3/32 x 100 => 93/8%
ANSWER:C
Answer: (C) 93/8 %
Question: A train passes a man standing on the platform. If the train is 170 meters long and its speed is 72 kmph, how much time it took in doing so?
(A) 7 1/2
(B) 5 1/2
(C) 2 1/2
(D) 8 1/2
(E) 8 2/2
Rationale: D = 170
S = 72 * 5/18 = 20 mps
T = 170/20 = 8 1/2 sec
Answer: D
Answer: (D) 8 1/2
Question: In a regular week, there are 5 working days and for each day, the working hours are 8. A man gets Rs. 2.40 per hour for regular work and Rs. 3.20 per hours for overtime. If he earns Rs. 432 in 4 weeks, then how many hours does he work for ?
(A) 160
(B) 175
(C) 190
(D) 200
(E) 210
Rationale: Suppose the man works overtime for x hours.
Now, working hours in 4 weeks = (5 x 8 x 4) = 160.
160 x 2.40 + x x 3.20 = 432
3.20x = 432 - 384 = 48
x = 15.
Hence, total hours of work = (160 + 15) = 175.
answer :B
Answer: (B) 175
Question: What is the probability of getting a number less than 4 when a die is rolled?
(A) 8/7
(B) 4/5
(C) 6/7
(D) 2/4
(E) 1/2
Rationale: Explanation :
Total number of outcomes possible when a die is rolled = 6
n(S) = 6
E = Getting a number less than 4 = {1, 2, 3}
Hence, n(E) = 3
P(E)=n(E)/n(S)=3/6=1/2
E
Answer: (E) 1/2
Question: A circular rim A having a diameter of 54 inches is rotating at the rate of x inches/min. Another circular rim B with a diameter of 27 inches is rotating at the rate of y inches/min. What is the value of y in terms of x, if both the rims reach their starting positions at the same time after every rotation.
(A) 2x
(B) 3x
(C) 4x
(D) 5x
(E) 6x
Rationale: t = S1/V1 = S2/V2
or, 54/x = 27/y
or, y = 54x/27 = 2x (Answer A)
Answer: (A) 2x
Question: A jogger running at 9 km/hr along side a railway track is 240 m ahead of the engine of a 130 m long train running at 45 km/hr in the same direction. In how much time will the train pass the jogger?
(A) 28 sec
(B) 16 sec
(C) 37 sec
(D) 18 sec
(E) 17 sec
Rationale: Speed of train relative to jogger = 45 - 9 = 36 km/hr.
= 36 * 5/18 = 10 m/sec.
Distance to be covered = 240 + 120 = 370 m.
Time taken = 370/10 = 37 sec.
Answer:C
Answer: (C) 37 sec
Question: The average of first eight prime numbers which are odd is?
(A) 12.25
(B) 15.7
(C) 15.2
(D) 15.8
(E) 15.1
Rationale: Sum of first 8 prime no. which are odd = 98
Average = 98/8 = 12.25
Answer:A
Answer: (A) 12.25
Question: (856942 x 555) = ?
(A) 484638125
(B) 474638130
(C) 474638135
(D) 475602810
(E) 484638145
Rationale: 856942 x 555=475602810Ans D
Answer: (D) 475602810
Question: There were 35 students in a hostel. Due to the admission of 7 new students, the expenses of mess were increased by 42 per day while the average expenditure per head diminished by 1. What was the original expenditure of the mess?
(A) 400
(B) 400
(C) 445
(D) 465
(E) None of the above
Rationale: Let the original average expenditure be `x.
Then,
42(x – 1) – 35x = 42 ⇔ 7x = 84 ⇒ x = 12.
∴ Original expenditure = (35 × 12)= 420.
Answer B
Answer: (B) 400
Question: The ratio 6 : 3 expressed as a percent equals
(A) 12.5%
(B) 40%
(C) 80%
(D) 200%
(E) None
Rationale: Solution
6 : 3	= 6/3
= (6/3 x 100)%.
= 200 %.
Answer D
Answer: (D) 200%
Question: In an election only two candidates contested. A candidate secured 70% of the valid votes and won by a majority of 192 votes. Find the total number of valid votes?
(A) 430
(B) 438
(C) 436
(D) 480
(E) 422
Rationale: Let the total number of valid votes be x.
70% of x = 70/100 * x = 7x/10
Number of votes secured by the other candidate = x - 7x/100 = 3x/10
Given, 7x/10 - 3x/10 = 192 => 4x/10 = 192
=> 4x = 1920 => x = 480.
Answer:D
Answer: (D) 480