mathewhe/aqua_rat huggingface dataset:
Question: Car A leaves the airport at 8:00 am and travels at a constant rate of 40 km per hour. Car B leaves the airport at 8:45 am and travels in the same direction along the same highway at a constant rate of 52 km per hour. At what time will Car B be 9 km ahead of Car A?
(A) 11:00 am
(B) 11:15 am
(C) 11:30 am
(D) 11:45am
(E) 12:00 noon
Rationale: At 8:45 am, Car A will be 30 km ahead of Car B.
Car B travels at a rate 12 km per hour faster than Car A.
Car B needs to travel 39 km more than Car A in order to be 9 km ahead.
This will take 39 km/12 km per hour=3.25 hours.
Car B will be 9 km ahead at 12:00 noon.
The answer is E.
Answer: (E) 12:00 noon
Question: Find two numbers whose sum is 26 and whose product is 165.
(A) 13 and 13
(B) 10 and 16
(C) 11 and 15
(D) 14 and 12
(E) 18 and 6
Rationale: Let the two numbers be a and b and use the sum and product to write two equations with two unknowns
a + b = 26 and a b = 165
Solve the first equation for b
b = 26 - a
Substitute b in the equation a b = 165 by 26 - a
a (26 - a) = 165
Write the above equation in standard form
- a 2 + 26 a - 165 = 0
Solve the above equation for a
a = 11 and a = 15.
Use b = 26 - a to find b
when a = 11 , b = 15 and when a = 15 , b = 11.
The two numbers are 11 and 15.
correct answer C
Answer: (C) 11 and 15
Question: If taxi fares were $2.00 for the first 1/5 mile and $0.60 for each 1/5 mile there after, then the taxi fare for a 8-mile ride was
(A) $2.40
(B) $25.20
(C) $25.40
(D) $25.60
(E) $25.50
Rationale: In 8 miles , initial 1/5 mile charge is $2
rest of the distance = 8 - (1/5) = 39/5
rest of the distance charge = 39(0.6) = $23.4 (as the charge is 0.6 for every 1/5 mile)
=> total charge for 4 miles = 2+23.4 = 25.4
Answer is C
Answer: (C) $25.40
Question: In a certain archery competition, points were awarded as follows: the first place winner receives 11 points, the second place winner receives 7 points, the third place winner receives 5 points and the fourth place winner receives 2 points. No other points are awarded. John participated several times in the competition and finished first, second, third, or fourth each time. The product of all the points he received was 30800. How many times did he participate in the competition?
(A) 5
(B) 6
(C) 7
(D) 8
(E) 9
Rationale: 30800 = 2*2*2*2*5*5*7*11
John participated 8 times.
The answer is D.
Answer: (D) 8
Question: The average of 25 results is 18. The average of first 12 of them is 10 and that of last 12 is 20. Find the 13th result?
(A) 60
(B) 75
(C) 90
(D) 100
(E) 110
Rationale: 13th result = sum of 25 results - sum of 24 results
= 18*25-12*10-12*20
= 450-120-240
= 90
Answer is C
Answer: (C) 90
Question: A cistern is normally filled in 8 hrs,but takes 2 hrs longer to fill because of a leak on its bottom,if Cistern is full ,how much time citern would empty?
(A) 10 hours
(B) 20 hours
(C) 30 hours
(D) 40 hours
(E) 50 hours
Rationale: If leakage/hour=1/x, then 1/8 -1/x= 1/10, solving 1/x=1/40
So in 40 hours full cistern will be empty.
ANSWER:D
Answer: (D) 40 hours
Question: The speed at which a man can row a boat in still water is 14 kmph. If he rows downstream, where the speed of current is 2 kmph, what time will he take to cover 40 metres?
(A) 16 seconds
(B) 34 seconds
(C) 9 seconds
(D) 12 seconds
(E) 15 seconds
Rationale: Speed of the boat downstream = 14 + 2 = 16 kmph
= 16 * 5/18 = 40/9 m/s
Hence time taken to cover 40 m = 40*9/40
= 9 seconds.
Answer: C
Answer: (C) 9 seconds
Question: In the following list of numerals, how many 3s are followed by 3, but NOT preceded by 3?
2 4 6 3 3 1 5 7 8 3 3 3 4 6 2 3 3 3 3 9 7 2 3
(A) 1
(B) 2
(C) 3
(D) 4
(E) 5
Rationale: 633
833
233
Ans:3
ANSWER:C
Answer: (C) 3
Question: Farm A had an average output of 300 kgs of rice per acre. Farm B had an average output of 350 kgs of rice per rice. It is known that Farm B's area is 15 acres less than Farm A's. It is also known that Farm B in total harvested 3000 kgs of rice more than Farm A. What is the area of Farm A?
(A)  130 acres
(B)  135 acres
(C)  145 acres
(D)  160 acres
(E)  180 acres
Rationale: The area of Farm A = x acres;
The area of Farm B = x-15 acres.
Total output of Farm A = 300x kgs;
Total output of Farm B = 350(x-15) kgs.
Farm B in total harvested 3000 kgs of rice more than Farm A: 300x+3000=350(x-15) --> x=180 acres.
Answer: A.
Answer: (A)  130 acres
Question: David invested certain amount in three different schemes. A, B and C with the rate of interest 10% p.a., 12% p.a. and 15% p.a. respectively. If the total interest accrued in one year was Rs. 3200 and the amount invested in scheme C was 150% of the amount invested in scheme A and 240% of the amount invested in scheme B, what was the amount invested in scheme B?
(A) 5000
(B) 2787
(C) 2679
(D) 2790
(E) 2712
Rationale: Let x, y and z be the amount invested in schemes A, B and C respectively. Then,
(x * 10 * 1)/100 + (y * 12 * 1)/100 + (z * 15 * 1)/100 = 3200
10x + 12y + 15z = 320000
Now, z = 240% of y = 12/5 y
And, z = 150% of x = 3/2 x
x = 2/3 z = ( 2/3 * 12/5) y = 8/5 y
16y + 12y + 36y = 320000
y = 5000
Sum invested in scheme B = Rs. 5000.Answer: A
Answer: (A) 5000
Question: What is the total number of prime numbers less than 60?
(A) 17
(B) 18
(C) 19
(D) 20
(E) 21
Rationale: Solution
Prime numbers less than 60 are	=17.
2,3,5,7,11,13,17,19,23,29,31,37,41,43,47,53,59
Their number is 17.
Answer A
Answer: (A) 17
Question: In how many ways can the letters of the word STATE be arranged?
(A) 60
(B) 1348
(C) 2520
(D) 3000
(E) 3478
Rationale: STATE has 5 words, but T is repeated two times. Thus ways = 5! / 2! = 60 ways
A
Answer: (A) 60
Question: A small company reduced its faculty by approximately 20 percent to 195 employees. What was the original number of employees?
(A) A)182
(B) B)208
(C) C)220
(D) D)224
(E) E)244
Rationale: If x is the original number of employees, then after 20% reduction in employees number is .80x
but we are given .80x = 195
x = 244
So the original number of employees is 244
Correct Answer - E
Answer: (E) E)244
Question: In Solution P, the proportion of water to alcohol is 5:4. In Solution Q, the proportion of water to alcohol is 7:5. If the two solutions are combined, what is the concentration of alcohol in the new solution if the original solutions were mixed in equal amounts?
(A) 35%
(B) 37%
(C) 39%
(D) 41%
(E) 43%
Rationale: Let V be the total volume of the new solution.
The amount of alcohol added from Solution P is (4/9)*V/2=(2/9)*V
The amount of alcohol added from Solution Q is (5/12)*V/2=(5/24)*V
The total amount of alcohol in the new solution is (2/9+5/24)*V=(31/72)*V
The alcohol concentration is 31/72=43% (approximately)
The answer is E.
Answer: (E) 43%
Question: If p and t are positive integers such that p > t > 1, what is the remainder when 92p × 5p+t + 11t × 6pt is divided by 10?
(A) A.0
(B) B.1
(C) C.3
(D) D.4
(E) E.5
Rationale: 92p × 5p+t + 11t × 6pt--1=B
Answer: (B) B.1
Question: How many prime numbers between 1 and 100 are factors of 1771?
(A) 2
(B) 6
(C) 5
(D) 4
(E) 3
Rationale: factor of 1771= 7*11*23--- 3 prime numbers
E
Answer: (E) 3
Question: One day, Raviraj left home and cycled 20 Km southwards, turned right and cycled 10 km and turned right and cycled 20 Km and turned left and cycled 20 Km. How many kilometres will he have to cycle to reach his home straight ?
(A) 50
(B) 30
(C) 40
(D) 60
(E) 80
Rationale: Raviraj starts from home at A, moves 20 Km in south upto B. Then he turns right and moves 10 Km upto C, then he turns right and moves 20 Km upto D, then he turns lefts and moves 20 Km upto E.
So from image it is clear that, if he moves straight then he will have to move AD+DE, AD = BC = 10 Km
So, he will have to move 10 + 20 = 30 Km
ANSWER B
Answer: (B) 30
Question: When positive integer x is divided by positive integer y, the remainder is 4. If x/y = 96.16, what is the value of y?
(A) 96
(B) 75
(C) 48
(D) 25
(E) 12
Rationale: by the definition of a remainder, the remainder here is equal to 4/y. the remainder in decimal form is given as .16
therefore, 4/y = .16
solve for y and get 25.
D
Answer: (D) 25
Question: A cycle is bought for Rs.900 and sold for Rs.1260, find the gain percent?
(A) 39%
(B) 20%
(C) 40%
(D) 74%
(E) 83%
Rationale: 900 ---- 360
100 ---- ? =>
40%
Answer:C
Answer: (C) 40%
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) 2/21
(B) 3/21
(C) 5/26
(D) 4/25
(E) 5/27
Rationale: P(Both are red),
=6C213C2=6C213C2
=5/26
C
Answer: (C) 5/26
Question: The probability of a team winning a match given Matt is playing the match is 0.75. The probability of the team winning a match given Matt is not playing the match is 0.6. The probability of Matt playing any match is 0.8.
If it is known that the team has won the last match, what is the probability that Matt played the match?
(A) 0.8321
(B) 0.7
(C) 0.8571
(D) 0.8333
(E) 0.8213
Rationale: Out of 100 matches:
Matt is plays in 80 and not plays in 20.
Out of 80 matches Matt plays in, team wins 0.75*80 = 60.
Out of 20 matches Matt does not play in, team wins 0.6*20 = 12.
So, out of 100 matches 60 + 12 = 72 are won.
It is known that the team has won the last match. Out of 72 matches won, Matt is in 60: 60/72 = 0.8333...
Answer: D.
Answer: (D) 0.8333
Question: A man purchased 3 blankets @ Rs.100 each, 4 blankets @ Rs.150 each and two blankets at a certain rate which is now slipped off from his memory. But he remembers that the average price of the blankets was Rs.150. Find the unknown rate of two blankets?
(A) A)600
(B) B)350
(C) C)450
(D) D)470
(E) E)500
Rationale: Explanation:
10 * 150 = 1500
3 * 100 + 4 * 150 = 900
1500 – 900 = 600
A
Answer: (A) A)600
Question: In the kitchen of a busy restaurant, it takes M minutes to wash P pots. At this rate, how many hours does it take to wash 6P pots?
(A) 10/M
(B) M/10
(C) M/60
(D) 240M
(E) 6M
Rationale: The time it takes to wash 6P pots is 6M minutes which is 6M / 60 = M/10 hours.
The answer is B.
Answer: (B) M/10
Question: What percent of a day is 5 hours?
(A) 12Ã—1/2%
(B) 16Ã—1/2%
(C) 18Ã—2/3%
(D) 20Ã—5/6%
(E) None
Rationale: Solution
Required percentage	= (5/24Ã—100)%
= (125 / 6)%.
= 20Ã—5/6%.
Answer D
Answer: (D) 20Ã—5/6%
Question: A bus takes 4 hours to cover a distance of 340 Km. how much should the speed in Kmph be maintained to cover the same direction in 5/2th of the previous time?
(A) 34 Kmph
(B) 50 Kmph
(C) 33 Kmph
(D) 45 Kmph
(E) 70 Kmph
Rationale: Time = 4
Distance = 340
5/2 of 4 hours = 4 * 5/2 = 10 Hours
Required speed = 340/10 = 34 Kmph
A
Answer: (A) 34 Kmph
Question: Ms. Lopez deposits $ 100 in an account that pays 20% interest, compounded semiannually. How much money will there be in the account at the end of one year?
(A) $118.00
(B) $120.00
(C) $121.00
(D) $122.00
(E) $140.00
Rationale: et me explain the concept for those who are not familiar with compounded semi annually/ quarterly etc..
it basically means, here, that the interest will be paid twice, after 6 months and at the end of year..so twice..
but interest is 20%, which will get distributed semiannually that is 10%...
so the Q literally means ..
after 6 months..
100*10/100 + 100=110..
at the end of year
110*10/100 + 110= 121..
or we put it in compound interest formula..
where CI=10%, T is 2 and P=100..
so amount = 100(1 + 10/100)^2=100*1.1*1.1=121..
ANSWER:C
Answer: (C) $121.00
Question: In a parking lot, there are some cars with a spare tire others don't. All together there are 43 tires and 9 cars. How many cars have a spare tire?
(A) 5
(B) 6
(C) 7
(D) 8
(E) 9
Rationale: Let's assume we are talking about 4 wheels car only.
9 cars, 4 tires per car, 9 x 4 = 36 tires.
There are total of 43 tires, 43 - 36 = 7 extra tires.
Let's assume each car has only one spare tire. ==> 7 cars with a spare tire
Answer C
Answer: (C) 7
Question: In how many different number of ways a Committee of 4 person of can be selected from 6 boys and 4girls such that at least 1 girl is included in the committee
(A) 195
(B) 200
(C) 80
(D) 15
(E) NONE OF THESE
Rationale: 1G 3B 2G 2B 3G B 4G
= (4C1*6C3)+(4C2*6C2)+(4C3*6C1)+4C4
= (4*20)+(6*150+(4*6)+1
= 80+90+24+1=195
Total 5M 3W
10C4=210
6C4=15
At least one girl = total - with out girl
At least one girl = 210-15=195
A)
Answer: (A) 195
Question: If doubling a number and adding 20 to the result gives the same answer as multiplying the number by 8 and taking away 4 from the product, the number is
(A) 2
(B) 3
(C) 4
(D) 5
(E) 6
Rationale: Sol.
Let the number be x.
Then, 2x + 20 = 8x - 4
⇔ 6x = 24
⇔ x = 4.
Answer C
Answer: (C) 4
Question: The perimeter of one square is 48 cm and that of another is 20 cm. Find the perimeter and the diagonal of a square which is equal in area to these two combined?
(A) 13√7
(B) 13√2
(C) 13√1
(D) 13√6
(E) 23√5
Rationale: 4a = 48 4a = 20
a = 12 a = 5
a2 = 144 a2 = 25
Combined area = a2 = 169 => a = 13
d = 13√2
Answer: B
Answer: (B) 13√2
Question: A class has 10 students.Teacher decided to go the tour.But the seats are available only 7.What is the probability that 7 students have to go out of 10 students?
(A) 150
(B) 125
(C) 120
(D) 105
(E) 110
Rationale: out of 10 students, 7 students must be go to tour.
The probablity is 10C7=120
120 possible ways to go to tour
Answer: (C) 120
Question: The sum of five numbers is 800. The average of the first two numbers is 100 and the third number is 150. Find the average of the two numbers?
(A) 225
(B) 250
(C) 240
(D) 260
(E) 270
Rationale: Let the five numbers be P, Q, R, S and T.
=> P + Q + R + S + T = 800
(P + Q)/2 = 100 and R = 150
P + Q = 200 and R = 150
P + Q + R = 350
S + T = 800 - (P + Q + R) = 450
Average of the last two numbers
= (S + T)/2 = 225
Answer:A
Answer: (A) 225
Question: In a class of students, the ratio of girls to boys is 2:5. If 4 more girls joined the class, the ratio would be 3:5. How many students are in the class?
(A) 16
(B) 20
(C) 24
(D) 28
(E) 32
Rationale: Let x be the number of students in the class.
(2/7)*x=(3/8)(x+4)-4
16x=21x+84-224
5x=140
x=28
The answer is D.
Answer: (D) 28
Question: 1=5,2=4,3=253,4=2,6=15 , then 15= ?
(A) 1
(B) 255
(C) 345
(D) 445
(E) 6
Rationale: 1=5,2=4,3=253,4=2,6=15 , then 15= ?
15=6
check the fifth eqn.
ANSWER:E
Answer: (E) 6
Question: The amount of water (in ml) that should be added to reduce 9 ml. Lotion, containing 50% alcohol, to a lotion containing 45% alcohol, is?
(A) 1
(B) 4
(C) 5
(D) 6
(E) 7
Rationale: 4.5 4.5
45% 55%
45% ----- 4.5
55% ------? => 5.5 - 4.5 = 1 ml
ANSWER:A
Answer: (A) 1
Question: The base of a parallelogram is twice its height. If the area of the parallelogram
is 72 sq. cm, find its height.
(A) 5 cm
(B) 6 cm
(C) 7 cm
(D) 8 cm
(E) 9 cm
Rationale: Let the height of the parallelogram be x. cm. Then, base = (2x) cm.
2x X x =72 => 2x^2 = 72
X ^2=36
x=6
Hence, height of the parallelogram = 6 cm
Option B
Answer: (B) 6 cm
Question: A and B can do a piece of work in 7 days. With the help of C they finish the work in 5 days. C alone can do that piece of work in?
(A) 76 days
(B) 86 days
(C) 30 days
(D) 57 days
(E) 46 days
Rationale: C = 1/5 – 1/6 = 1/30
=> 30 days
Answer: C
Answer: (C) 30 days
Question: At an Iron factory, each employee working the second shift produced 2/3 as many widgets as each employee working the first shift. If the first shift has 3/4 as many employees, what fraction of the total widgets did the second shift produce?
(A) 8/17
(B) 1/2
(C) 8/9
(D) 9/8
(E) 17/8
Rationale: At an Iron factory, Let the first shift have 3 employee and each produce 3 widgets, so the total number of widgets produced by the first shift is 3*3=9;
Then the second shift would have 4 employees and each second shift employee would produce 3*2/3=2 widgets, so the total number of widgets produced by the second shift employees would be 4*2=8;
The ratio of the second shift production to the total is 8/(9+8)=8/17.
Answer: A.
Answer: (A) 8/17
Question: When Tom works alone he chops 3 lb. salad in 2 minutes, and when Tammy works alone she chops 2 lb. salad in 3 minutes. They start working together, and after some time finish chopping 65 lb. of salad. Of those 80 lb., the salad quantity chopped by Tammy is what percent Lesser than the quantifying chopped by Tom?
(A) 44%
(B) 100%
(C) 15%
(D) 125%
(E) 400%
Rationale: Tom chops 4 lbs in 6 minutes
Tammy chops 9 lbs in 6 minutes
So in the same amount of time, Tammy chops 125% more than Tom, since 9 is 125% greater than 4. So 125% is the answer.
Note that the actual time doesn't matter. If you multiply the time each work by x, you'll multiply the work each does by x, and 9x is still 125% greater than 4x.
125% lesser than Tom
Ans:D
Answer: (D) 125%
Question: A and B put in Rs.300 and Rs.400 respectively into a business. A reinvests into the business his share of the first year's profit of Rs.210 where as B does not. In what ratio should they divide the second year's profit?
(A) 39:40
(B) 39:45
(C) 39:49
(D) 39:44
(E) 39:41
Rationale: 3: 4
A = 3/7*210 = 90
390: 400
39:40
Answer: A
Answer: (A) 39:40
Question: A bag contains 6 black balls and 8 white balls. One ball is drawn at random. What is the probability that the ball drawn is white?
(A) 2/3
(B) 3/5
(C) 4/7
(D) 5/9
(E) 7/11
Rationale: Total number of balls = 6+8 = 14
no. of white balls = 8
probability of drawing a white ball = 8/14 = 4/7
Answer is C
Answer: (C) 4/7
Question: A train has a length of 150 metres. It is passing a man who is moving at 22 km/hr in the same direction of the train, in 33 seconds. Find out the speed of the train.
(A) 182 km/hr
(B) 180 km/hr
(C) 152 km/hr
(D) 169 km/hr
(E) 190 km/hr
Rationale: Explanation:
Length of the train =150=150 m
Speed of the man =2=2 km/hr
Relative speed =1503=50 m/s=1503=50 m/s
=50Ã—185=180 km/hr=50Ã—185=180 km/hr
Relative speed = Speed of train - Speed of the man (as both are moving in the same direction). Therefore,
Speed of the train = Relative speed + Speed of the man
=180+2=182 km/hr=180+2=182 km/hr
ANSWER IS A
Answer: (A) 182 km/hr
Question: In how many a committee of 5 members can be selected from 6men 5 ladies consisting of 3 men and 2 ladies
(A) 451
(B) 175
(C) 154
(D) 200
(E) 120
Rationale: (3 men out of 6) and (2 ladies out of 5) are to be chosen
Required number of ways
=(6C3 * 5C2)
= 200
Ans: D
Answer: (D) 200
Question: Each of the integers from 2 to 9, inclusive, is written on a separate slip of blank paper and the ten slips are dropped into hat. If the slips are then drawn one at a time without replacement, how many must be drawn to ensure that the numbers on two of the slips drawn will have a sum of 10?
(A) 3
(B) 4
(C) 5
(D) 6
(E) 7
Rationale: Answer is 5. In the worst case, you could end up drawing 2,3,4,5. 7th draw will result in either of 6,7,8,9 which would result in the numbers adding to 10.
C
Answer: (C) 5
Question: If number x is 10% less than another number y and y is 10% more than 125, then find out the value of x
(A) 123.85
(B) 130.5
(C) 120.2
(D) 150.4
(E) 200.2
Rationale: Consider as w
x=10%
y=10%+125
==>123.85
ANSWER A
Answer: (A) 123.85
Question: P alone can complete a piece of work in 11 days. Work done by Q alone in one day is equal to one-third of the work done by P alone in one day. In how many days can the work be completed if P and Q work together?
(A) 6 (1/4) days
(B) 33/4) days
(C) 7 (3/4) days
(D) 8 (3/4) days
(E) 9 (3/4) days
Rationale: Work done by P alone in one day = 1/11 th of the total work done by Q alone in one day = 1/3(of that done by P in one day) = 1/3(1/11 of the total) = 1/33 of the total.
Work done by P and Q, working together in one day = 1/11 + 1/33 = 4/33 of the total
They would take 33/4 days to complete the work working together.
ANSWER:B
Answer: (B) 33/4) days
Question: The perimeter of a rhombus is 68 cm and one of its diagonals is 16 cm. Find its area?
(A) 229
(B) 240
(C) 228
(D) 218
(E) 219
Rationale: 4a = 68 => a = 17
172 – 82 = 152
1/2 * 16 * 30 = 240
Answer: B:
Answer: (B) 240
Question: What is the greatest possible length which can be used to measure exactly the lengths 12 m, 6 m and 40 m?
(A) 2m
(B) 5m
(C) 3m
(D) 10 m
(E) 20 m
Rationale: Required length = HCF of 12 m, 6 m, 40m = 2m
Answer is A
Answer: (A) 2m
Question: If $0.60 is the commission for sales of $2,000, what percent of the sales amount is the commission?
(A) 3%
(B) 0.3%
(C) 0.03%
(D) 0.003%
(E) 0.0003%
Rationale: % of sales amount of commission
= (Commission/Total Value) *100
= (0.6/2000) * 100
= 0.03%
The answer is C.
Answer: (C) 0.03%
Question: Raju and Reenu are standing in a row there are 9 peoples. what is the probability that at least 3 people will stand between Raju and Reenu
(A) 5/12
(B) 6/12
(C) 7/12
(D) 8/12
(E) 9/12
Rationale: 9C2=36
3 people between Raju and Reena 7+5+3=15
15/36=5/12
ANSWER:A
Answer: (A) 5/12
Question: The banker's gain on a sum due 3 years hence at 12% per annum is Rs. 360. The banker's discount is:
(A) Rs. 1360
(B) Rs. 1000
(C) Rs. 360
(D) Rs. 640
(E) None of these
Rationale: Explanation :
BG = Rs. 360
T = 3 years
R = 12%
TD = (BG ×100)/TR = (360×100)/(3×12) = Rs. 1000
BG = BD – TD
=> BD = BG + TD = 360 + 1000 = Rs. 1360 Answer : Option A
Answer: (A) Rs. 1360
Question: In Smithtown, the ratio of right-handed people to left-handed people is 3 to 1 and the ratio of men to women is 3 to 2. If the number of right-handed men is maximized, then what q percent of all the people in Smithtown are left-handed women?
(A)  50%
(B)  40%
(C)  25%
(D)  20%
(E)  10%
Rationale: looking at the ratio we can take total number of people q=20..
ans 5/20 or 25% C
Answer: (C)  25%
Question: Two dice are thrown together.What is the probability that the sum of the number on the two faces divided by 4?
(A) 3/9
(B) 4/9
(C) 1/9
(D) 2/9
(E) 5/9
Rationale: n(s)=6*6=36
Let e be the event that the sum of the numbers on the two faces is divisible by 4
E={(1,3),(2,2),(3,1),(2,6),(3,5),(4,4),(5,3),(6,2)}
n(e)=8
p(e)=n(e)/n(s)
=8/36
=2/9
Answer is option D
Answer: (D) 2/9
Question: What number times (1⁄5)^2 will give the value of 5^3?
(A) 5
(B) 25
(C) 125
(D) 625
(E) 3125
Rationale: x*(1/5)^2 = 5^3
x = 5^2*5^3 = 5^5 = 3125
The answer is E.
Answer: (E) 3125
Question: A cab on its way to Bangalore overtakes an auto also going in the same direction at 11 am. The cab reaches Bangalore at 1.30 pm and starts the return journey after taking a break of 1 hour. On its way back it meets the auto at 3 pm. At what time will the auto reach Bangalore?
(A) 8 p.m
(B) 7 p.m
(C) 4 p.m
(D) 1 p.m
(E) 2 p.m
Rationale: Explanation:
The time interval is shown below with an interval of half hour.
11 am ------- 11:30 ------- 12 ------- 12:30 ------- 1-------1:30
At 11 the cab overtakes the auto and reaches Bangalore at 1:30. Hence, the cab travels 5 segments in two and a half hour assuming the cab to be travelling at constant
speed.
On its way back, the cab commences its journey at 2:30 and meets the auto at 3 p.m. In half an hour the cab travels one segment and hence the auto in one segment away
from Bangalore.
Therefore, the auto travels 4 segments from 11 am to 3 pm assuming it to be travelling at a constant speed. Hence, the speed of auto is 4/4 = 1 segment per hour.
As the auto is one segment away from Bangalore, it will take another 1 hour for the auto to reach Bangalore and hence the auto will reach Bangalore at 4 p.m.
ANSWER:C
Answer: (C) 4 p.m
Question: 3 men or 6 women can do a piece of work in 25 days. In how many days will 12 men and 8 women do the same work?
(A) 15/9 days
(B) 15/4 days
(C) 18/4 days
(D) 11/4 days
(E) 75/16 days
Rationale: 3M = 6W ---- 25 days
12M + 8W -----?
24W + 8 W = 32W ---?
6W ---- 25 32 -----?
6 * 25 = 32 * x => x = 75/16 days
Answer:E
Answer: (E) 75/16 days
Question: Two men and three women working 7 hours a day finish a work in 5 days. Four men and four women working 3 hours a day complete the work in 7 days. The number of days in which only 7 men working 4 hours a day will finish the work is?
(A) 6 days
(B) 2 days
(C) 7 days
(D) 5 days
(E) 1 days
Rationale: D
2M + 3W ----- 35 h
4M + 4W ------- 21 h
7M -------? d
70M + 105W = 84M +84M
21W = 14M => 2M = 3W
4 * 35 = 7 * x => x = 20 hours
20/4 = 5 days
Answer: (D) 5 days
Question: If I walk at 6 km/h, I miss the bus by 12 minutes. If I walk at 5 km/h, I reach 14 minutes before the arrival of the bus. How far I walk to reach the bus stand ?
(A) 13km
(B) 12 km
(C) 11 km
(D) 6.5 km
(E) 5.5 km
Rationale: d = product of speed difference of time /difference of speed
[Here, â€“ve sign indicates before the schedule time]
d = 6Ã—5/60[12âˆ’(âˆ’14)/6-5]
â‡’ d = 13 km
Answer A
Answer: (A) 13km