mathewhe/aqua_rat huggingface dataset:
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) 286
(B) 278
(C) 255
(D) 150
(E) 287
Rationale: Speed=(60 * 5/18) m/sec = (50/3) m/sec Length of the train
= (Speed x Time) = (50/3 * 9) m
= 150 m.
Answer:D
Answer: (D) 150
Question: Buses leave town B at 3 pm and every 10 hours after that. Buses leave town C at 4pm and every 15 hours after that. If the buses follow this schedule beginning on a Monday, what is the earliest day A on which the buses leave at the same time.
(A) A=Tuesday
(B) Wednesday
(C) Thursday
(D) Sunday
(E) A=The busses will never leave at the same time
Rationale: The answer is E.
I think the best way to do it is to look at the times on a 24 hour clock. Town B busses start at 15:00, and Town C start at 16:00. If you think about it that way, then for Town B you'd add 10 hours each time, and the number will always end in a 5. Town C you'd add 15 hours each time, and the numbers would always end in a 1 or 6. So you can see they'd never coincide.
Alternatively, you could see that if they left at the same time, they'd coincide every 30 hours, but since C is one hour ahead of B, every 30 hours C will still be one hour ahead of B.E
Answer: (E) A=The busses will never leave at the same time
Question: 78, 64, 48, 30, 10, (...)
(A) 14
(B) -14
(C) 12
(D) 0
(E) -12
Rationale: 78 - 14 = 64
64 - 16 = 48
48 - 18 = 30
30 - 20 = 10
10 - 22 = -12
Answer is E.
Answer: (E) -12
Question: In what ratio should the profit of Rs.8000 be divided if X starts a business with an investment of Rs. 20000, Y invests Rs.7500 for 4 months and Z invests Rs.15000 after 3 months from the start of the business.
(A) 16 : 2 : 3
(B) 8 : 3 : 6
(C) 16 : 2 : 9
(D) 6 : 9 : 1
(E) None of these
Rationale: Explanation:
Let the profit of X be P1, that of Y be P2 and of Z be P3.
P1:P2:P3 = 20000*12 : 7500*4 : 15000*9 = 240 : 30 : 135 = 80 : 10 : 45
= 16 : 2 : 9
ANSWER: C
Answer: (C) 16 : 2 : 9
Question: If the circus were to sell all of its 220 tickets for this month's performance at its usual price, the revenue from sales would be 10% greater than that collected last month. If the circus raised the ticket price by 5% and sold only 205 tickets as a result, what percent less would last month's revenue be compared to this month's revenue?
(A) 2
(B) 5
(C) 6100/861
(D) 110/20
(E) 9/4
Rationale: Let price be 10/ticket
then 220 tickets for this month's performance at its usual price=2200
which is 10%greater than last month(let X)---->x(1+10/100)=2200----->x=2000
now new revenue this month=205*10.5=2152.50
as per question asked 2000=2152.50(1-A/100)----->A=6100/861%
Ans C
Answer: (C) 6100/861
Question: How long does a train 180 meters long running at the rate of 54 kmph take to cross a bridge 660 meters in length?
(A) 33
(B) 56
(C) 55
(D) 82
(E) 62
Rationale: Explanation:
T = (660 + 180)/54 * 18/5
T = 56
Answer: Option B
Answer: (B) 56
Question: In the junior basketball league there are 21 teams, 1/3 of them are bad and ½ are rich. What can't be the number of teams that are rich and bad?
(A) 4.
(B) 6.
(C) 7.
(D) 8.
(E) 11.
Rationale: total teams =21
bad teams=(1/3)*21=7
rich teams=10
so maximum value that the both rich and bad can take will be 10. so E= 11 can not be that value.
ans E.
Answer: (E) 11.
Question: A certain university will select 1 of 7 candidates eligible to fill a position in the mathematics department and 2 of 10 candidates eligible to fill 2 identical positions in the computer science department. If none of the candidates is eligible for a position in both departments, how many different sets of 3 candidates are there to fill the 3 positions?
(A) 42
(B) 70
(C) 140
(D) 165
(E) 315
Rationale: 1C7*2C10 = 7*45 = 315
the answer is (E)
Answer: (E) 315
Question: The average age of applicants for a new job is 10, with a standard deviation of 8. The hiring manager is only willing to accept applicants whose age is within one standard deviation of the average age. Assuming that all applicants' ages are integers and that the endpoints of the range are included, what is the maximum number of different ages of the applicants?
(A) 8
(B) 16
(C) 17
(D) 18
(E) 34
Rationale: Minimum age = Average - 1 Standard deviation = 10 - 8 = 2
Maximum age = average + 1 Standard deviation = 10+ 8 = 18
Maximum number of different ages of the applicants = 18 - 2 + 1 = 17
Answer C
Answer: (C) 17
Question: Robert purchased $2000 worth of US saving bonds. If bonds are sold in $50 or $100 denominations only, which of the following CANNOT be the number of US saving bonds that Robert purchased?
(A) 20
(B) 27
(C) 30
(D) 60
(E) 70
Rationale: I started off with looking at the answer choices... 20-27-30 are in a tight range, so my guess was to look and rule out the bigger numbers.
The total amount is $3000. So with 70 bonds, each $50 = $3500 , we already exceed the $3000 limit. Hence E is the answer.
Answer: (E) 70
Question: The 8 spokes of a custom circular bicycle wheel radiate from the central axle of the wheel and are arranged such that the sectors formed by adjacent spokes all have different central angles, which constitute an arithmetic series of numbers (that is, the difference between any angle and the next largest angle is constant). If the largest sector so formed has a central angle of 80°, what fraction of the wheel’s area is represented by the third largest sector?
(A) 1/72
(B) 1/6
(C) 1/18
(D) 1/12
(E) 1/9
Rationale: Its an AP question .... it is given clearly in the question .
Let the smallest angle be a
and the circle has 8 sectors and hence 8 angle with a common difference d
hence all the angles can be written in AP form with Cd as d ,
a, a+d, a+2d, a+3d ,a+4d, a+5d, a+6d ,a+7d,
given that a+7d = 80 --------1
also
a + a+d + a+2d + a+3d +
a+4d + a+5d + a+6d + a+7d = 360 ( as sum of all the angle is 360)
which is 8a + 28d = 360 --------2
solving 1 and 2
we get a=10
We are almost done ,
now the question ask what fraction of the wheel’s area is represented by the smallest sector ?
(60/360)( pie r*r)/ (pie r*r) = 60/360= 1/6
B ans ....
Answer: (B) 1/6
Question: Find the unit digit in the product 274*318*577*313
(A) 5
(B) 2
(C) 10
(D) 26
(E) 89
Rationale: Explanation:
Required digit=Unit digit is in(4*8*7*3)=2
Answer B
Answer: (B) 2
Question: The sum of two numbers is 528 and their H.C.F is 33.The number of pairs of numbers satisfying the above conditions is:
(A) 4
(B) 6
(C) 8
(D) 12
(E) none of these
Rationale: Let the required numbers be 33a and 33b.Then,33a+33b=528,
a+b=16.
now, co-primes with sum 16 are (1,15), (3,13), (5,11)and(7,9);
required numbers are (33*1,33*15), (33*3,33*13), (33*5,33*11), (33*7, 33*9).
The number of such pairs is 4.
Correct Options:A
Answer: (A) 4
Question: In a function they are distributing noble prize. In how many ways can 3 prizes be distributed among 5 boys when No boy gets more than one prize?
(A) 12
(B) 14
(C) 17
(D) 24
(E) 60
Rationale: Sol. In this case, repetitions are not allowed. So, the first prize can be given in 5 ways. The second in 4 ways and the third in 3 ways. But fundamental principle, (5 x 4 x 3) ways = 60 ways
E
Answer: (E) 60
Question: If a: b :: 3 : 4, then what is (5a+6b): (a-2b)?
(A) 57:11
(B) -57:11
(C) 11 : 10
(D) -39 : 5
(E) -1 : 10
Rationale: a/b= 3/4
Dividing numerator & denominator of ' (5a+6b)/(a-2b) 'by b,
[5(a/b)+6]/[(a/b)-2]= [5*(3/4)+6]/[(3/4)-2]= -39/5
ANSWER:D
Answer: (D) -39 : 5
Question: If 40% of the 880 students at a certain college are enrolled in biology classes, how many students at the college are NOT enrolled in a biology class?
(A) 540
(B) 528
(C) 530
(D) 520
(E) 510
Rationale: We know 37.5 % people study biology,therefore the no of people not studying = 100 - 40 = 60%
> Therefore the people not studying biology out of a total 880 people are = 60 % of 880
> (60/100)*880 = 528 people
B
Answer: (B) 528
Question: How many integers between 1 and 10^20 are such that the sum of their digits is 2?
(A) 190
(B) 210
(C) 211
(D) 230
(E) 231
Rationale: The integers with a sum of 2 are:
2, 20, 200,...,2*10^19 and there are 20 integers in this list.
Also, these integers have a sum of 2:
11
101, 110
1001, 1010, 1100
etc...
The number of integers in this list is 1 + 2 + ... + 19
Thus, the total number of integers is 1 + 2 + ... + 19 + 20 = 20*21/2 = 210
The answer is B.
Answer: (B) 210
Question: If g(x) = ax^5 + bx^3 + 5, and g(5) = 10, then g(–5) =?
(A)  – 10
(B)  – 8
(C)  – 6
(D)  0
(E)  4
Rationale: g(5) = 10
or, 5^5 a + 5^3 b + 5 = 10
or, 5^5 a + 5^3 b = 5
g(-5) = -5^5 a - 5^3 b + 5 = - (5^5 a + 5^3 b) + 5 = - 5 + 5 = 0 = (D)
Answer: (D)  0
Question: The average mark obtained by 22 candidates in an examination is 49. The average of the first ten is 55 while the last eleven is 40 .The marks obtained by the 11th candidate is ?
(A) 22
(B) 0
(C) 99
(D) 88
(E) 66
Rationale: It is clear that 22 x 49 = 10 x 55 + K + 11 x 40 ⇒⇒ K = 88
Answer:D
Answer: (D) 88
Question: In how many ways can a cricket eleven be chosen out of a batch of 15 players ?
(A) 1365
(B) 5263
(C) 4512
(D) 7845
(E) 1549
Rationale: Required number of ways = 15c11 = 15c(15-11) = 11c4
= 15x14x13x12/4x3x2x1 = 1365.
Ans: A
Answer: (A) 1365
Question: A shopkeeper has 280 kg of apples. He sells 50% of these at 20% profit and remaining 60% at 30% profit. Find his % profit on total.
(A) 24%
(B) 25%
(C) 26%
(D) 28%
(E) 35%
Rationale: If the total quantity was 100
Then 50X 20% + 60 X30%= 28
This profit will remain same for any total quantity unless the % of products remains the same. Hence 'D' is the answer
Answer: (D) 28%
Question: A number is doubled and 9 is added. If the resultant is trebled, it becomes 75. What is that number?
(A) 3.5
(B) 6
(C) 8
(D) None of these
(E) Cannot be determined
Rationale: Solution
Let the number be x.
Then, 3(2x + 9)	‹=› 75
‹=› 2x+9 = 25
‹=› 2x= 16
x= 8.
Answer C
Answer: (C) 8
Question: A brick measures 20 cm * 10 cm * 7.5 cm how many bricks will be required for a wall 24 m * 2 m * 0.75 m?
(A) 29798
(B) 27908
(C) 24000
(D) 25000
(E) 27991
Rationale: 24 * 2 * 0.75 = 20/100 * 10/100 * 7.5/100 * x
24 = 1/100 * x => x
= 24000
Answer: C
Answer: (C) 24000
Question: Which of the statements is true for 3111 & 1714
(A) 11
(B) 88
(C) 66
(D) 17
(E) 16
Rationale: Answer:B
Answer: (B) 88
Question: A bullet train is moving at a speed of 132 km/hr. If the length of the bullet train is 110 metres, how long will it take to cross a railway platform 165 metres long?
(A) 5 ½ sec
(B) 9 ½ sec
(C) 3 ½ sec
(D) 7 ½ sec
(E) 6 ½ sec
Rationale: D
7 ½ sec
Speed of train = 132 *(5/18) m/sec = 110/3 m/sec.
Distance covered in passing the platform = (110 + 165) m = 275 m.
Time taken =275 *(3/110) sec =15/2 sec = 7 ½ sec
Answer: (D) 7 ½ sec
Question: If x is an odd integer and y = 2x + 8, which of the following CANNOT be a divisor of y?
(A) 10
(B) 14
(C) 18
(D) 21
(E) 22
Rationale: x takes odd values as 1,3,5,7.,
y=2x+8
x is an odd term so 2x must be an even term when it adds with 8 so it must be a even integer
21 didn't follows this condition ans is D
Answer: (D) 21
Question: Due to 10% decrease in the price of sugar and John can buy 3kg more sugar in Rs100 , then find the CP of sugar?
(A) s. 1(2/9)
(B) s. 2(2/9)
(C) s. 2(1/9)
(D) s. 3(19/27)
(E) s. 4(2/9)
Rationale: Here r = 10 % ,x = 100 and A = 3 kg
Actual price of sugar = 10*100/((100-10 )*3) = Rs. 3(19/27)
D
Answer: (D) s. 3(19/27)
Question: Two trains running in opposite directions cross a man standing on the platform in 27 seconds and 17 seconds respectively and they cross each other in 23 seconds. The ratio of their speeds is:
(A) 1 : 3
(B) 3 : 2
(C) 3 : 4
(D) 4:2
(E) None of these
Rationale: Explanation:
Let the speeds of the two trains be x m/sec and y m/sec respectively. Then, length of the first train = 27 x meters, and length of the second train = 17 y meters. (27 x + 17 y) / (x + y) = 23 ==> 27 x + 17 y = 23 x + 23 y ==> 4 x = 6 y ==> x/y = 3/2.
ANSWER IS B
Answer: (B) 3 : 2
Question: A bag contains 7 red, 9 blue and 5 green balls. If 3 balls are picked at random, what is the probability that both are red?
(A) 2/21
(B) 3/41
(C) 5/26
(D) 1/38
(E) 5/32
Rationale: P(Both are red),
=7C3/21C3=(7*6*5)/21*20*19
=1/38
D
Answer: (D) 1/38
Question: In what ratio should a variety of rice costing Rs. 6 per kg be mixed with another variety of rice costing Rs. 8.75 per kg to obtain a mixture costing Rs. 7.50 per kg?
(A) 5/6
(B) 6/5
(C) 7/3
(D) 5/9
(E) 5/3
Rationale: Let us say the ratio of the quantities of cheaper and dearer varieties
= x : y
By the rule of allegation,
x/y = (87.5 - 7.50) / (7.50 - 6) = 5/6
Answer:A
Answer: (A) 5/6
Question: If 18 persons can build a wall 140 m long in 42 days, the number of days that 30 persons will take to complete a similar wall 100 m long, is.
(A) 18
(B) 21
(C) 24
(D) 28
(E) 30
Rationale: Explanation :
(Length 140:100) : (Persons 30:18) :: 42 : x
=> 140 * 30 * x = 100 * 18 * 42
=> or x = 18
Answer : A
Answer: (A) 18
Question: The wheel of an engine 30/7 metres in circumference makes seven revolutions in 4seconds. Find the speed of the train in km per hour?
(A) 15km/hr
(B) 25km/hr
(C) 32km/hr
(D) 18km/hr
(E) 27km/hr
Rationale: Distance travelled by the train in 4 seconds = 30*7/7 = 30 metres
speed of the train = 30/4 = 15/2 m/s = 27 km/hr
Answer is E
Answer: (E) 27km/hr
Question: At what rate percent of simple interest will a sum of money double itself in 44 years?
(A) 6.54 %
(B) 4.54 %
(C) 8 .2 %
(D) 4.94 %
(E) 2.27 %
Rationale: Let sum = x. Then, S.I. = x.
Rate = (100 * S.I.) / (P * T) = (100 * x) / (x * 44)
= 100/44 = 2.27 %
ANSWER:E
Answer: (E) 2.27 %
Question: The side of a square is increased by 25% then how much % does its area increases?
(A) 56.28
(B) 56.25
(C) 56.27
(D) 56.29
(E) 56.21
Rationale: a = 100 a2 = 10000
a = 125 a2 = 15625
----------------
10000 --------- 5625
100 -------? => 56.25 %
Answer:B
Answer: (B) 56.25
Question: Excluding stoppages, the speed of a train is 45 kmph and including stoppages it is 35 kmph. Of how many minutes does the train stop per hour?
(A) 73
(B) 83
(C) 12
(D) 13
(E) 28
Rationale: Explanation:
T = 10/45 * 60 = 13
Answer: Option D
Answer: (D) 13
Question: A rectangular field has a length 10 meters more than it is width. If the area of the field is 171, what is the length (in meters) of the rectangular field?
(A) 17
(B) 19
(C) 21
(D) 23
(E) 25
Rationale: area = l * w = (L) * (L-10) = 171
trial and error:
20*10 = 200 (too high)
19*9 = 171
The length is 19 meters.
The answer is B.
Answer: (B) 19
Question: Two goods trains each 500 m long are running in opposite directions on parallel tracks. Their speeds are 30 km/hr and 90 km/hr respectively. Find the time taken by the slower train to pass the driver of the faster one?
(A) 48
(B) 30
(C) 26
(D) 23
(E) 12
Rationale: Relative speed = 90 + 30 = 120 km/hr.
120 * 5/18 = 100/3 m/sec.
Distance covered = 500 + 500 = 1000 m.
Required time = 1000 * 3/100 = 30 sec.
Answer:B
Answer: (B) 30
Question: Dames school has 2000 boys and 5000 girls. What is the percentage increase from boys to total attendance and girls to total attendance?
(A) 40%
(B) 10%
(C) .4%
(D) 50%
(E) 12%
Rationale: Ratio of boys to total attendance (2/7)
Ratio of girls to total attendance (5/7)
percentage increase is (difference/initial quantity)*100
(2/7)/(5/7 )* 100= 40%
Correct answer is A
Answer: (A) 40%
Question: What is the minimum number of people to join into this group so that when they are grouped into 5, none will remain ungrouped ? Without newcomers when they are grouped into 6, 4 of them remain ungrouped and when they are grouped into 9, 7 of then reamin ungrouped.
(A) 2
(B) 4
(C) 6
(D) 8
(E) 10
Rationale: P = 6a+4 = 9b+7
6a= 9b+3 --> min (a,b) = (2,1) so that number of people in this group is
P= 6*2+4 = 16
5k = 16 + x so that none will be ungrouped --> min( k) = 4 then
5*4 = 20 16 + x
X= 4 newcomers should join to this group
ANSWER: B
Answer: (B) 4
Question: Look at this series: 22, 21, 23, 22, 24, 23, ... What number should come next?
(A) 30
(B) 19
(C) 25
(D) 5
(E) 20
Rationale: In this simple alternating subtraction and addition series; 1 is subtracted, then 2 is added, and so on.
so 23+2=25
Option C
Answer: (C) 25
Question: A shopkeeper sold an article offering a discount of 5% and earned a profit of 31.1%. What would have been the percentage of profit earned if no discount had been offered?
(A) 38
(B) 27.675
(C) 30
(D) Data inadequate
(E) None of these
Rationale: Giving no discount to customer implies selling the product on printed price. Suppose the cost price of the article is 100.
Then printed price = 100Ã—(100+31.1)/(100âˆ’5)
= 138
Hence, required % Profit = 138 â€“ 100 = 38%
Answer A
Answer: (A) 38
Question: Alfred buys an old scooter for Rs. 4700 and spends Rs. 800 on its repairs. If he sells the scooter for Rs. 5800, his gain percent is:
(A) 12/11 %
(B) 10 %
(C) 5 5/11%
(D) 6/7 %
(E) 10/11 %
Rationale: Explanation:
Cost Price (C.P.) = Rs. (4700 + 800) = Rs. 5500.
Selling Price (S.P.) = Rs. 5800.
Gain = (S.P.) - (C.P.) = Rs.(5800 - 5500) = Rs. 300.
Gain % =(300/5500*100)%=5 5/11%
Answer:C
Answer: (C) 5 5/11%
Question: A and B start a business, with A investing the total capital of Rs.25000, on the condition that B pays A interest @ 10% per annum on his half of the capital. A is a working partner and receives Rs.250 per month from the total profit and any profit remaining is equally shared by both of them. At the end of the year, it was found that the income of A is twice that of B. Find the total profit for the year?
(A) A)22500
(B) B)33500
(C) C)22510
(D) D)33510
(E) E)11500
Rationale: Interest received by A from B = 10% of half of Rs.25000 = 10% * 12500 = 1250.
Amount received by A per annum for being a working partner = 250 * 12 = Rs.3000.
Let 'P' be the part of the remaining profit that A receives as his share. Total income of A = (1250 + 3000 + P)
Total income of B = only his share from the remaining profit = 'P', as A and B share the remaining profit equally.
Income of A = Twice the income of B
(1250 + 3000 + P) = 2(P)
P = 4250
Total profit = 2P + 3000
= 2*4250 + 3000 = 11500
Answer:E
Answer: (E) E)11500
Question: In the first round of the elections, the only two candidates got exactly the same number of votes. During the second round, 21,000 votes switched from the first candidate to the second one. The total number of votes remained the same in both rounds, and no other votes switched sides. If, in the second round, the winning candidate got four times as many votes as the other candidate, how many people have voted in each round?
(A) 70,000
(B) 25,000
(C) 40,000
(D) 50,000
(E) 60,000
Rationale: Let A be the first candidate and B be the second one.
Given x+21000 = 4(x-21000)=>x=35000
2x = 70000
IMO option A.
Answer: (A) 70,000
Question: If x and y are positive integers and 3 + x + y + xy = 17, what is the value of x + y?
(A) 3
(B) 5
(C) 6
(D) 8
(E) 9
Rationale: Try each answer choice.
For A: 3 + 3 + xy = 17; xy = 11 (impossible, 11 prime number. 1 + 11 doesn't equal 3)
For B: 3 + 5 + xy = 17; xy = 9 (no combination of xy = 9 and x + y = 5)
For C: 3 + 6 + xy = 17; xy = 8 (x + y = 6; x = 2, y = 4 or x = 4, y = 2)
For D: 3 + 8 + xy = 17; xy = 6 (no combination of xy = 6 and x + y = 8)
For E: 3 + 9 + xy = 17; xy = 5 (impossible, 5 prime number. 1 + 5 doesn't equal 9)
Therefore, answer C.
Answer: (C) 6
Question: What will come in place of the x in the following Number series? 18, 22, 30, 46 ,78, X
(A) 35
(B) 56
(C) 142
(D) 87
(E) 98
Rationale: (C)
The pattern is +4, +8, +16, +32, +64
So the missing term is = 142
Answer: (C) 142
Question: What approximate value should come in place of question mark (?) in the following equation?
33 1⁄3% of 768.9 + 25% of 161.2 – 68.12 = ?
(A) 230
(B) 225
(C) 235
(D) 220
(E) 240
Rationale: ? = 33 1⁄3% of 768.9 + 25% of 161.2 – 68.12
= 1⁄3 of 768.9 + 1⁄4 of 161.2 – 68.12
= 256.3 + 40.3 – 68.12 ≈ 230
Answer A
Answer: (A) 230
Question: The game of blackjack is played with a deck consisting of 13 cards (one of each of the numbers 2-10, one jack, one queen, one king, and one of ace) in each of four suits: clubs, diamonds, hearts, and spades.
In a game of blackjack, if your first card is a spade, what are the odds that it is an ace?
(A) 1/52
(B) 1/26
(C) 1/13
(D) 1/4
(E) 5/13
Rationale: There are 13 spades, the probability that the spade we already have is an ace is therefore 1/13.
Answer: C.
Answer: (C) 1/13
Question: John and Steve are speed walkers in a race. John is 15 meters behind Steve when he begins his final push. John blazes to the finish at a pace of 4.2 m/s, while Steve maintains a blistering 3.7 m/s speed. If John finishes the race 2 meters ahead of Steve, how long was John’s final push?
(A) 13 seconds
(B) 17 seconds
(C) 26 seconds
(D) 34 seconds
(E) 51 seconds
Rationale: Let t be the time that John spent for his final push.
Thus, per the question,
4.2t = 3.7t+15+2 ---> 0.5t = 17 ---> t = 34 seconds.
D is the correct answer.
Answer: (D) 34 seconds
Question: If a coin is tossed 3 times what is the probability that it will land either heads 3 times or tails 3 times?
(A) 1/4
(B) 1/16
(C) 1/2
(D) 1/8
(E) 1/32
Rationale: The probability of 3 heads is (1/2)^3 = 1/8
The probability of 3 tails is (1/2)^3 = 1/8
The probability of 3 heads or 3 tails is 1/8 + 1/8 = 1/4
The answer is A.
Answer: (A) 1/4
Question: The number of sequences in which 7 players can throw a ball, so that the youngest player may not be the last is ?
(A) 2389
(B) 2778
(C) 4320
(D) 1987
(E) 1212
Rationale: Explanation:
x Not younger_______ â†‘
The last ball can be thrown by any of the remaining 6 players. The first 6 players can throw the ball in â¶Pâ‚† ways.
The required number of ways = 6(6!) = 4320
Answer:C
Answer: (C) 4320
Question: The average of runs of a cricket player of 20 innings was 32. How many runs must he make in his next innings so as to increase his average of runs by 8 ?
(A) 96
(B) 200
(C) 128
(D) 116
(E) 122
Rationale: Average = total runs / no.of innings = 32
So, total = Average x no.of innings = 32 * 20 = 640
Now increase in avg = 4 runs. So, new avg = 32+8 = 40 runs
Total runs = new avg x new no. of innings = 40 * 21 = 840
Runs made in the 11th inning = 840-640 = 200
ANSWER:B
Answer: (B) 200
Question: 3 people, harry, john , and Cassie, have speeds of 3 mph, 4 mph and 6 mph respectively. They run a race in which john gives harry a head start of 2 hrs. If both john and Cassie overtake harry at the same time, what head start did Cassie give harry?
(A) 3 hours
(B) 4 hours
(C) 5 hours
(D) 9 miles
(E) 10 miles
Rationale: Question clearly states that A started first. B started after 2 hours and we need to determine When did C start.
As per the question, we know that All three meet at the same point.
So, we can determine when did A and B meet. The point they will meet would be the same at which C will be present at that time.
So,
A and B will meet after t = 6/(4-3) = 6 hours.
In these 6 hours, B would have covered 4*6=24 miles.
=> C would also have covered 24 miles and that would be in 24/6=4 hours.
Thus, C started 2 hours after B or 4 hours after A. hence, answer is B.
Answer: (B) 4 hours
Question: A college has classes from 10:00 AM until 1:45 PM. In this duration, there are five periods. If 5 minutes are provided between each period to leave one class and enter the next class, how many minutes long is each period?
(A) 38 min
(B) 41 min
(C) 40 min
(D) 42 min
(E) 52 min
Rationale: The total time is 225 minutes.
There are four breaks of five minutes between the classes for a total of 20 minutes.
The total class time is 205 minutes.
205 / 5 classes = 41 minutes per class
The answer is B.
Answer: (B) 41 min
Question: If x and y are odd integers, which of the following must always be a non-integer
(A) xy
(B) xy/4
(C) x/y
(D) y/x
(E) -x^2y
Rationale: as X and Y are odd, multiplication of x and y would result in odd integer
(Odd Integer)/4 will always be non integer
B
Answer: (B) xy/4
Question: What is the unit digit in {(6374)^1793 x (625)^317 x (341^491)}?
(A) 0
(B) 2
(C) 3
(D) 5
(E) 6
Rationale: Unit digit in (6374)^1793 = Unit digit in (4)^1793
= Unit digit in [(42)^896 x 4]
= Unit digit in (6 x 4) = 4
Unit digit in (625)^317 = Unit digit in (5)^317 = 5
Unit digit in (341)^491 = Unit digit in (1)^491 = 1
Required digit = Unit digit in (4 x 5 x 1) = 0.
Answer:A
Answer: (A) 0