mathewhe/aqua_rat huggingface dataset:
Question: The total cost of a vacation was divided among 3 people. If the total cost of the vacation had been divided equally among 4 people, the cost per person would have been $30 less. What was the total cost cost of the vacation?
(A) $200
(B) $360
(C) $400
(D) $500
(E) $600
Rationale: C for cost.
P price per person.
C= 3*P
C=4*P-120
Substituting the value of P from the first equation onto the second we get P = 120.
Plugging in the value of P in the first equation, we get C= 360. Which leads us to answer choice B
Answer: (B) $360
Question: The length of the bridge, which a train 475 metres long and travelling at 90 km/hr can cross in 30 seconds, is:
(A) 200 m
(B) 225 m
(C) 245 m
(D) 250 m
(E) 275 m
Rationale: Speed = [90 X 5/18] m/sec = [25] m/sec
Time = 30 sec
Let the length of bridge be x metres.
Then, (475 + x)/30 = 25 => 475 + x= 750 => x = 275
Answer : E
Answer: (E) 275 m
Question: If y is 75% greater than x, than x is what % less than y?
(A) 30.6%
(B) 34.4%
(C) 38.7%
(D) 42.9%
(E) 46.5%
Rationale: y = 1.75x
x = y/1.75 = 100y/175 = 4y/7
x is 3/7 less which is about 42.9% less than y.
The answer is D.
Answer: (D) 42.9%
Question: While planning their outing, Abhishek understood that their boat could travel with a speed of 12kmph in still water.The group decided to travel 24 minutes downstream. Aarti had prior experience in that route and mentioned that the speed of stream was 4kmph.How many kms will the group travel downstream?
(A) 6.4
(B) 3.2
(C) 4
(D) 4.8
(E) 4.4
Rationale: Downstream speed= boat speed in still water + speed of stream
Boat speed in Downstream = 12 + 4= 16 km/h
Time spend = 24 min = 24/60 h = 2/5 h
Distance Travel = 16 * 2/5 = 6.4 km
Answer:a
Answer: (A) 6.4
Question: A train 540 meters long is running with a speed of 54 kmph. The time taken by it to cross a tunnel 180 meters long is?
(A) 40
(B) 48
(C) 45
(D) 50
(E) 25
Rationale: D = 540 + 180 = 720
S = 54 * 5/18 = 15 mps
T = 720/15 = 48 sec
ANSWER B
Answer: (B) 48
Question: Out of 6 consonants and 3 vowels, how many words of 4 consonants and 2 vowels can be formed?
(A) 1050
(B) 25200
(C) 32400
(D) 5800
(E) 6800
Rationale: Number of ways of selecting (4 consonants out of 6) and (2 vowels out of 3)
= 6C4 * 3C2
= 6C2 * 3C1
= 6*5 *3
2*1
= 15*3= 45
Number of groups, each having 4 consonants and 2 vowels= 45.
Each group consists of 6 letters.
Number of ways of arranging 6 letters among themselves
= 6! = (6*5*4*3*2*1)= 720
Therefore, Required number of words= 45*720= 32400
ANSWER:C
Answer: (C) 32400
Question: The probability of Sam passing the exam is 1/4. The probability of Sam passing the exam and Michael passing the driving test is 1/7. What is the probability of Michael passing his driving test?
(A) 1/24.
(B) 1/2.
(C) 4/7.
(D) 2/3.
(E) 2/5
Rationale: 1/4 *1/m= 1/7 , 1/m = 4/7
Answer C
Answer: (C) 4/7.
Question: If 8^x = 2^21, what is x?
(A) 2
(B) 3
(C) 4
(D) 5
(E) 7
Rationale: 2^3x= 2^21
3x=21, therefore x=7
Answer E
Answer: (E) 7
Question: An old priest fell on a bottom of the well of a church.
The well is 15 inches deep.
At day time, the old priest climbs 5-inches but when at dark he slip back 4 inches.
In how many days priest will come out of the well ?
(A) 16-days
(B) 14-days
(C) 11-days
(D) 19-days
(E) 10-days
Rationale: C
11-days
In 10-days, he will climb 10-inch and when he climbs 5 inch more, he will be out of the well :-)
Answer: (C) 11-days
Question: Company S produces two kinds of stereos: basic and deluxe. Of the stereos produced by Company S last month, 2/3 were basic and the rest were deluxe. If it takes 6/5 as many hours to produce a deluxe stereo as it does to produce a basic stereo, then the number of hours it took to produce the deluxe stereos last month was what fraction of the total number of hours it took to produce all the stereos?
(A) 6/16
(B) 14/31
(C) 7/15
(D) 17/35
(E) 1/2
Rationale: # of basic stereos was 2/3 of total and # of deluxe stereos was 1/3 of total, let's assume total=15, then Basic=10 and Deluxe=5.
Now, if time needed to produce one Deluxe stereo is 1 unit than time needed to produce one Basic stereo would be 6/5 units. Total time for Basic would be 10*1=10 and total time for Deluxe would be 5*6/5=6 --> total time for both of them would be 10+6=16 --> deluxe/total=6/16.
Answer: A.
Answer: (A) 6/16
Question: If 6a = 7b = 20, then 84ab =
(A) 50
(B) 100
(C) 625
(D) 800
(E) 1250
Rationale: 6a * 7b = 20 * 20 = 400
42 ab = 400
i.e. 84 ab = 800
Answer: Option D
Answer: (D) 800
Question: A gang of 8 boys goes on an tour in 2 cars, of which 1 canseat 5 & the other only 4. In how many ways can they travel?
(A) 110
(B) 123
(C) 126
(D) 154
(E) 165
Rationale: There are 8 students and the maximum capacity of the cars together is 9.
We may divide the 8 students as follows
Case I: 5 students in the first car and 3 in the second
Or Case II: 4 students in the first car and 4 in the second
Hence, in Case I: 8 students are divided into groups of 5 and 3 in8C3 ways.
Similarly, in Case II: 8 students are divided into two groups of 4 and 4 in 8C4ways.
Therefore, the total number of ways in which 8 students can travel is:
\inline {\color{Blue}8C_{3}+8C_{4}}=56 + 70= 126
C
Answer: (C) 126
Question: If a certain number is divisible by 25 and 38, it is NOT necessarily divisible by which of the following?
(A) 5
(B) 10
(C) 19
(D) 20
(E) 95
Rationale: If a certain number is divisible by 25 and 38, it is NOT necessarily divisible by which of the following?
let the certain number be 950, which is both divisible by 25 and 38.
950/20 = 95/2
D. 20
Answer: (D) 20
Question: An aeroplane covers a certain distance at a speed of 240 kmph in 5 hours. To cover the same distance in 1 hours, it must travel at a speed of:
(A) 150
(B) 720
(C) 160
(D) 80
(E) 12
Rationale: Explanation:
Speed = Distance/Time
Speed =1200(5/3)km/hr
Required speed =(1200*(3/5))km/hr=720 km/hr
Answer B
Answer: (B) 720
Question: The sector of a circle has radius of 21 cm and central angle 135o. Find its perimeter?
(A) 91.5 cm
(B) 91.8 cm
(C) 61.8 cm
(D) 91.6 cm
(E) 92.5 cm
Rationale: Perimeter of the sector = length of the arc + 2(radius)
= (135/360 * 2 * 22/7 * 21) + 2(21)
= 49.5 + 42 = 91.5 cm
Answer:A
Answer: (A) 91.5 cm
Question: The “d-number” of a number x is defined as the ones digit of 2^x. Antony rolls a die with 6 sides labeled with the integers from 1 to 6, each of which has an equal probability of landing face-up. He then takes 3^d, where d is the d-number of the result of his die roll, and plots 3^d on a number line as the point A. Finally, he repeats this entire process, this time plotting the result as the point B. What is the probability that the distance between A and B is greater than the value of B?
(A)  3/8
(B)  13/36
(C)  17/36
(D)  19/36
(E)  23/36
Rationale: If you calculate 3^d for 1st roll, all 6 results will be 9, 81, 6561, 729, 9, 81. This result is the same for 2nd roll. 9, 81, 6561, 729, 9, 81.
About distance: If the first result is 9 and the second is also 9, the distance is 9-9=0 which is smaller than 9. If the first result is 9 and the second is 81, the distance is 81-9=72 which is also smaller than B which has the value of 81. If the first result is 81 and the second is 9, the distance will be greater than B. Distance 81-9=72>9.
On the first roll, the probability of getting result 9 is 2/6. In this case no other alternative values for second roll which would make the distance greater than B. So probability is 0. So next estimations are:
probability of getting 81 on the first roll (2/6) * probability of getting 9 on the second roll (2/6) = 1/9
probability of getting 729 on the first roll (1/6) * probability of getting 9, 81 on the second roll (4/6) = 1/9
probability of getting 6561 on the first roll (1/6) * probability of getting 9, 81, 729 on the first roll (5/6) = 5/36
All together: 1/9 + 1/9 + 5/36 = 13/36=B
Answer: (B)  13/36
Question: A can run 4 times as fast as B and gives B a start of 75 m. How long should the race course be so that A and B might reach in the same time?
(A) 70 m
(B) 60 m
(C) 100 m
(D) 65 m
(E) 75 m
Rationale: Speed of A:Speed of B=4:1
means in a race of 4m A gains 3m.
then in a race of 75m he gains 75*(4/3)
I.e 100m
ANSWER:C
Answer: (C) 100 m
Question: A's speed is 15/13 times that of B. If A and B run a race, what part of the length of the race should A give B as a head start, so that B beats A by 40% of the length of the race?
(A) 44%
(B) 48%
(C) 52%
(D) 42%
(E) 46%
Rationale: First calculate the distance, B has covered with his speed in the time, in which A reached 60% of the race.
Then Add the remaining distance as head start for B to win the race.
Its best to apply Ratios concept here.
Since A's speed is 15/13 of B, therefore, B's speed is 13/15 of A
Distance covered by B = speed x time = (13/15) x (0.6) = 0.52%
(Which means B would have covered 0.52 of the race length during the time in which A has covered 0.6 of the race length.
Therefore to win, B needs a headstart of (1 - 0.52 = ) 0.48 of the race length.
So the answer is B
Answer: (B) 48%
Question: By selling an article at Rs.800, a shopkeeper makes a profit of 25%. At what price should he sell the article so as to make a loss of 25%?
(A) 237
(B) 480
(C) 882
(D) 271
(E) 211
Rationale: SP = 800
Profit = 25%
CP = (SP)*[100/(100+P)]
= 800 * [100/125]
= 640
Loss = 25% = 25% of 640 = Rs.160
SP = CP - Loss = 640 - 160 = Rs.480
Answer:B
Answer: (B) 480
Question: A, B and C can do a piece of work in 7 days, 21 days and 28 days respectively. How long will they taken, if all the three work together?
(A) 2
(B) 4 8/19
(C) 5
(D) 67
(E) 9
Rationale: 1/7 + 1/21 + 1/28 = 19/84 => 84/19 => 4 8/19 days
Answer: B
Answer: (B) 4 8/19
Question: A man can row his boat with the stream at 24 km/h and against the stream in 10 km/h. The man's rate is?
(A) 1 kmph
(B) 6 kmph
(C) 7 kmph
(D) 4 kmph
(E) 9 kmph
Rationale: Explanation:
DS = 24
US = 10
S = ?
S = (24-10)/2 =7 kmph
Answer: C
Answer: (C) 7 kmph
Question: The cost of 9 kgs. of sugar is Rs.279. What is the cost of .153 kgs. of sugar?
(A) Rs.3.377
(B) Rs.4.473
(C) Rs.4.377
(D) Rs.4.743
(E) None of these
Rationale: Explanation:
The cost of .153 kgs. of sugar = 279x .153/9 = Rs.4.743
Answer: Option D
Answer: (D) Rs.4.743
Question: It is required to fix a pipe such that water flowing through it at a speed of 7 metres per minute fills a tank of capacity 440 cubic metres in 10 minutes. The inner radius of the pipe should be :
(A) √2 m
(B) 2 m
(C) 1⁄2 m
(D) 1⁄√2 m
(E) None of these
Rationale: Let inner radius of the pipe be r.
Then, 440 = 22⁄7 × r2 × 7 × 10
or r2=440/22×10=2
or r = √2 m
Answer A
Answer: (A) √2 m
Question: What is the next number of the following sequence.
6, 9, 18, 45, 108, 351, ..
(A) 952
(B) 972
(C) 985
(D) 548
(E) 856
Rationale: For odd place values
6*3=18
18*6=108
108*9=972
and for even place values
6*1+ 3^1=9
18*2+3^2=45
108*3+3^3=351
972*4+3^4=39699(so ans is 972)
ANSWER:B
Answer: (B) 972
Question: If x/4 – (x – 3)/5 = 1, then find the value of x.
(A) 3
(B) 6
(C) 8
(D) 11
(E) 12
Rationale: Explanation:
x/4 – (x - 3)/5 = 1
(5x – 4(x – 3))/20 = 1
5x - 4x + 12 = 20
x = 8
ANSWER: C
Answer: (C) 8
Question: In the first M games of a team's season, the ratio of the team's wins to its losses was 1:3. In the subsequent N games, the ratio of the team´s wins to losses was 2:3. If M:N = 4:5, what was the ratio of the team's wins to its losses for all M+N games?
(A) 7:18
(B) 3:7
(C) 1:2
(D) 2:5
(E) 4:9
Rationale: M = 4/9 of total games
N = 5/9 of total games
Wins = 1/4*4/9 + 2/5*5/9 = 1/9 + 2/9 = 1/3
Losses = 1 - 1/3 = 2/3
The ratio of wins to losses is 1:2.
The answer is C.
Answer: (C) 1:2
Question: 10 camels cost as much as 24 horses, 16 horses cost as much as 4 oxen and 6 oxen as much as 4 elephants. If the cost of 10 elephants is Rs.170000, find the cost of a camel?
(A) Rs.6867
(B) Rs.6818
(C) Rs.6810
(D) Rs.6800
(E) Rs.6192
Rationale: Cost of the camel = P
10 camels = 24 horses
16 horses = 4 oxen
6 oxen = 4 elephants
10 elephants = Rs.170000
P = Rs.[(24 * 4 * 4 * 170000)/(10 * 16 * 6 * 10)]
P = Rs.(65280000/9600) => P = Rs.6800
Answer: D
Answer: (D) Rs.6800
Question: P and Q are both positive integers. When P is divided by Q, the remainder is some positive integer D, and when P is divided by (Q + 8), the remainder is also D. If P/Q = 1020.75 and P/(Q + 8) = 816.6, then which of the following gives the correct set of {D, Q}?
(A) {6, 12}
(B) {6, 15}
(C) {9, 12}
(D) {9, 15}
(E) {24, 32}
Rationale: p/q= d=p/q+8
d= .75 q
d= .6(q+8)
we get d = 24 and q = 32. Answer = E.
Answer: (E) {24, 32}
Question: A 12% item produces 20%. The market value of the item is:
(A) Rs. 55
(B) Rs. 60
(C) Rs. 40
(D) Rs. 65
(E) Rs. 70
Rationale: Let the face value of the item is Rs.100
It produces Rs.12
Market value of the stock=(12/20)*100=Rs.60
ANSWER:B
Answer: (B) Rs. 60
Question: What is the value of âˆš25% ?
(A) 10%
(B) 50%
(C) 25%
(D) 45%
(E) 68%
Rationale: Explanation: br>âˆš25%
=âˆš25/âˆš100
=5/10
=50/100=50%
correct answer is B)50%
Answer: (B) 50%
Question: A man can row 6 kmph in still water. When the river is running at 1.2 kmph, it takes him 1 hour to row to a place and black. What is the total distance traveled by the man?
(A) 5.79
(B) 5.73
(C) 5.76
(D) 5.75
(E) 5.71
Rationale: M = 6
S = 1.2
DS = 7.2
US = 4.8
x/7.2 + x/4.8 = 1
x = 2.88
D = 2.88 * 2 = 5.76
\Answer:C
Answer: (C) 5.76
Question: The sale price sarees listed for Rs.400 after successive discount is 15% and 5% is?
(A) 338
(B) 323
(C) 342
(D) 882
(E) 212
Rationale: 400*(85/100)*(95/100) = 323
Answer: B
Answer: (B) 323
Question: If a, b and c are even integers, which of the following could be the value of a^2 + b^2 + c^2?
(A) a)98
(B) b)101
(C) c)102
(D) d)204
(E) e)202
Rationale: a, b and c are even integers which means that, supposing that x, y and z are integers, then a=2x, b=2y and c=2z
Therefore we have: a^2+b^2+c^2=2^2*x^2+2^2*y+2^2*z=4x^2+4y^2+4z^2=4(x^2+y^2+z^2).
Which means that the total a^2+b^2+c^2 must be divisible by 4.
The only choice which is divisible by 4 is: D)
204=10^2+10^2+2^2
Answer: D.
Answer: (D) d)204
Question: A train traveling at 36 kmph crosses a platform in 30 seconds and a man standing on the platform in 12 seconds. What is the length of the platform in meters?
(A) 120 meters
(B) 360 meters
(C) 420 meters
(D) 600 meters
(E) Cannot be determined
Rationale: Answer
Distance covered by the train when crossing a man and when crossing a platform
When a train crosses a man standing on a platform, the distance covered by the train is equal to the length of the train.
However, when the same train crosses a platform, the distance covered by the train is equal to the length of the train plus the length of the platform.
The extra time that the train takes when crossing the platform is on account of the extra distance that it has to cover. i.e., length of the platform.
Compute length of platform
Length of the platform = speed of train * extra time taken to cross the platform.
Length of platform = 36 kmph * 12 seconds
Convert 36 kmph into m/sec
1 kmph = 5/18 m/s (This can be easily derived. But if you can remember this conversion, it saves a good 30 seconds).
∴ 36 kmph = 5/18∗36 = 10 m/sec
Therefore, length of the platform = 10 m/s * 12 sec = 120 meters.
Choice A
Answer: (A) 120 meters
Question: The probability that a number selected at random from the first 50 natural numbers is a composite number is
(A) 17/28
(B) 17/25
(C) 17/26
(D) 17/22
(E) 17/21
Rationale: :The number of exhaustive events = ⁵⁰C₁ = 50.
We have 15 primes from 1 to 50.
Number of favourable cases are 34.
Required probability = 34/50 = 17/25.
Answer:B
Answer: (B) 17/25
Question: Two trains of equal are running on parallel lines in the same direction at 48km/hr and 36 km/hr. The faster train passes the slower train in 36 sec. The length of each train is?
(A) 50
(B) 88
(C) 60
(D) 55
(E) 22
Rationale: Let the length of each train be x m.
Then, distance covered = 2x m.
Relative speed = 48 - 36 = 12 km/hr.
= 12 * 5/18 = 10/3 m/sec.
2x/36 = 10/3 => x = 60.
Answer:C
Answer: (C) 60
Question: If p/q = 3/11 , then 2p+q= ?
(A) 12
(B) 14
(C) 17
(D) 15
(E) 16
Rationale: let p=3, q=11 then 2*3+11=17
so 2p+q=17.
ANSWER:C
Answer: (C) 17
Question: Two trains 140 m and 180 m long run at the speed of 60 km/hr and 40 km/hr respectively in opposite directions on parallel tracks. The time which they take to cross each other is?
(A) 10.9 sec
(B) 13.8 sec
(C) 53.8 sec
(D) 10.8 sec
(E) 11.52 sec
Rationale: Relative speed = 60 + 40 = 100 km/hr.
= 100 * 5/18 = 250/9 m/sec.
Distance covered in crossing each other = 140 + 180 = 320 m.
Required time = 320 * 9/250 = 11.52 sec.
Answer: E:
Answer: (E) 11.52 sec
Question: Simplify
25+[5âˆ’(6+2(7âˆ’8âˆ’5Â¯Â¯Â¯Â¯Â¯Â¯Â¯Â¯Â¯Â¯Â¯))]
(A) 23
(B) 25
(C) 28
(D) 30
(E) 16
Rationale: Explanation:
=25+[5âˆ’(6+2(7âˆ’8+5))]
(Please check due to overline, sign has been changed)
=25+[5âˆ’(6+2Ã—4))]
=25+[âˆ’9]=25-9=16
Option E
Answer: (E) 16
Question: If the integer n has exactly five positive divisors, including 1 and n, how many positive divisors does √n have?
(A) 6
(B) 5
(C) 2
(D) 3
(E) 4
Rationale: take the example of 16...
it has 3 positive divisors (1,2,4,8,16)
Now, take the example of 4...
it has only 3 divisors..
so D is the ans
Answer: (D) 3
Question: Find the value of x from the below equation? : x^2+5x+25 = 0
(A) No answer
(B) 25
(C) 1
(D) 0
(E) -2
Rationale: a = 1, b = 5, c = 25
x1,2 = (-5 Â± âˆš(5^2 - 4Ã—1Ã—25)) / (2Ã—1) = (-5 Â± âˆš(25-100)) / 2 = (-5 Â± âˆš -75) / 2
No real roots
A
Answer: (A) No answer
Question: A person purchased a TV set for Rs. 25000 and a DVD player for Rs. 8000. He sold both the items together for Rs. 42900. What percentage of profit did he make?
(A) 48%
(B) 70%
(C) 40%
(D) 45%
(E) 30%
Rationale: The total CP = Rs. 256000 + Rs. 8000
= Rs. 33000 and SP
= Rs. 42900
Profit(%)
= (42900 - 33000)/33000 * 100
= 30%
Answer: E
Answer: (E) 30%
Question: In how many different number of ways 4 men and 1 women can sit on a shopa which can accommodate persons?
(A) A)160
(B) B)17
(C) C)19
(D) D)21
(E) E)20
Rationale: 5p3 =5 x4= 20
Option 'E'
Answer: (E) E)20
Question: P started from his house towards west. After walking a distance of 25 m. He turned to the right and walked 10 m. He then again turned to the right and walked 15 m. After this he is to turn right at 1350 and to cover 30 m. In which direction should he go?
(A) West
(B) South
(C) South-west
(D) South-East
(E) east
Rationale: south east
ANSWER:D
Answer: (D) South-East
Question: The standard deviation of a normal distribution of data is 2, and 3 standard deviations below the mean is greater than 47. What is a possible value for the mean of the distribution?
(A) 46
(B) 54
(C) 48
(D) 49
(E) 50
Rationale: The standard deviation ({SD}) = 2;
3 standard deviations below the mean is greater than 47:
{Mean} - 3*{SD} > 47;
{Mean} - 6 > 47;
{Mean} > 53.
Answer: B.
Answer: (B) 54
Question: Employees of a certain company are each to receive a unique 6-digit identification code consisting of the digits 0, 1, 2, 3, 4, and 5 such that no digit is used more than once in any given code. In valid codes, the second digit in the code is exactly twice the first digit. How many valid codes are there?
(A) 48
(B) 56
(C) 64
(D) 72
(E) 80
Rationale: There are 4! ways to make codes starting with 12.
There are 4! ways to make codes starting with 24.
The number of codes is 2*4! = 48.
The answer is A.
Answer: (A) 48
Question: An artist who needs to buy only paint and canvas finds that the cost of canvas has decreased by 40 percent and the cost of paint has decreased by 60 percent. If paint previously accounted for 4 times as much of the expense of painting as did canvas, by what percent did the total cost for paint and canvas decrease?
(A) 40%
(B) 44%
(C) 50%
(D) 56%
(E) 60%
Rationale: Paint:Canvas cost is 4:1.
So, paint accounts for 80% of cost and canvas accounts for 20%.
Canvas, after decrease by 40% will be (100-40)% of 20% => 60% of 20% => 12% of original
Paint, after decrease by 60% will be (100-60)% of 80% => 40% of 80% => 32% of original
New cost as a % of old cost = 32+12 = 44% of original.
So, overall cost saving = 100-44 = 56%
Therefore, (D)
Answer: (D) 56%
Question: Out of four numbers ,the average of first three is 16 and that of the last three is 15. If the last number is 21,the first number is :
(A) 22
(B) 21
(C) 77
(D) 99
(E) 24
Rationale: Explanation:
Let the numbers be a,b,c,d
Given, a + b + c = 48, b + c + d = 45
Now, d = 21
thus, b + c + 21 = 45 ⇒ b + c = 24
Putting the value of b + c in a + b + c = 48
a + 24 = 48 ⇒ a = 24
Answer: E
Answer: (E) 24
Question: The average earning of amechanic for the first 4days of a week is Rs.11 and for the last four days is Rs.22. If heearns Rs.20 on the fourth day, his average earning forthe whole week is?
(A) s. 14
(B) s. 20
(C) s. 30
(D) s. 16
(E) s. 21
Rationale: Total earning for the week = Sum of earning of first four days + Sum of earning of last four days - Earning of 4th day
= 4 x 11 + 4 x 22 -20
= Rs. 112
âˆ´ Average earning = 112/ 7
= Rs. 16
D
Answer: (D) s. 16
Question: On a ranch, a rancher can place a loop of rope, called a lasso, once in every 2 throws around a cow’s neck. What is the probability that the rancher will be able to place a lasso around a cow’s neck at least once in 6 attempts?
(A) 3/4
(B) 7/8
(C) 15/16
(D) 31/32
(E) 63/64
Rationale: P(missing all 6)=(1/2)^6=1/64
P(success on at least one attempt)=1-1/64=63/64
The answer is E.
Answer: (E) 63/64
Question: A 415 m long train is running at 63 km/hr. In how much time will it cross a tunnel 285 m long?
(A) 25
(B) 35
(C) 45
(D) 60
(E) 40
Rationale: Speed of the train= ( 63 * 5 / 18) m/sec = 35/2 m/sec. Distance travelled = (Speed x Time)
Time = (Distance travelled / Speed)
Distance travelled = Length of the train + Length of the Tunnel
=415+285 = 700m
Time = (700 / 35/2)= 40 sec
Answer: E
Answer: (E) 40
Question: When a certain number X is divided by 72, the remainder is 19. What is the remainder when X is divided by 8?
(A) 3
(B) 2
(C) 4
(D) 1
(E) 5
Rationale: Let possible value of x is 91
least possible value of x/8 is 91/8 => 11 quotient with remainder 3
Thus answer is (A) 3
Answer: (A) 3
Question: In how many ways a President, VP and Water-boy can be selected from a group of 10 people.
(A) 10C3
(B) 10P3
(C) 240
(D) 360
(E) None
Rationale: Solution:
We are selecting three different posts here, so order matters.
Thus, total ways of selecting a President, VP and Water-boy from a group of 10 people would be 10P3.
Answer: Option B
Answer: (B) 10P3
Question: Difference between the length &breadth of a rectangle is 2 m. If its perimeter is 76 m, then its area is??
(A) 2000 m^2
(B) 2340 m^2
(C) 2520 m^2
(D) 2556 m^2
(E) 360 m^2
Rationale: We have: (l - b) = 2 and 2(l + b) = 76 or (l + b) = 38
so 2 l = 40 = > l = 20 & b = 18
Area = 20 * 18 = 360 m^2
Answer : E
Answer: (E) 360 m^2
Question: A certain galaxy is known to comprise approximately 5 x 10^11 stars. Of every 50 million of these stars, one is larger in mass than our sun. Approximately how many stars in this galaxy are larger than the sun?
(A) 800
(B) 1,250
(C) 8,000
(D) 12,000
(E) 10,000
Rationale: Total no. of stars on galaxy = 5 * 10^11
Of every 50 million stars, 1 is larger than sun.
1 million = 10^6 therofore, 50 million = 50 * 10^6
total no. of stars larger than sun = 5 * 10^11 / 50 * 10^6
=50 * 10^3 /5
= 10000
therefore answer is E
Answer: (E) 10,000
Question: A man traveled from the village to the post-office at the rate of 25 kmph and walked back at the rate of 4 kmph. If the whole journey took 5 hours 48 minutes, find the distance of the post-office from the village ?
(A) 70 m
(B) 80 km
(C) 20 km
(D) 10 km
(E) 73 km
Rationale: Explanation:
Average speed = , here a=25 b=4
= 2x25x4/(25+4) = 200/29 km/hr.
Distance covered in 5 hours 48 minutes
= Speed x time = (200/29)x (29/5) Distance covered in 5 hours 48 minutes = 40kms.
Distance of the post office from the village = (40/2) = 20 km.
Answer: C
Answer: (C) 20 km
Question: The average age of a group of 10 persons was decreased by 3 years when one person, whose age was 42 years, was replaced by a new person. Find the age of the new person?
(A) 18
(B) 56
(C) 12
(D) 17
(E) 14
Rationale: Initial average age of the 10 persons be P.
Age of the new person Q.
Sum of the ages of the initial 10 persons = 10P
New average
= (P-3) 10(P-3)
= 10P - 42 + Q
=> Q = 12
Answer:C
Answer: (C) 12