mathewhe/aqua_rat huggingface dataset:
Question: In a 100m race, Sam beats John by 5 seconds. On the contrary, if Sam allowed John to start 35m ahead of Sam, then Sam and John reach the finishing point at the same time. How long does Sam take to run the 100m race?
(A) 13 seconds
(B) 25 seconds
(C) 29 seconds
(D) 21 seconds
(E) 6.25 seconds
Rationale: Their difference is 5 second but this difference is 0 if john allows Sam to start the race from 35m ahead . that means Jhon was 35m away from finishing line when they started together . so He will cover 35 m in 5 seconds . so his speed =35/5=7 metre / second . so time taken =100/5=20 seconds . so Sam took = 13 seconds .
correct answer = A
Answer: (A) 13 seconds
Question: The traffic lights at three different road crossings change after every 48 sec., 72 sec and 108 sec. respectively .If they all change simultaneously at 8:20:00 hours, then at what time they again change simultaneously .
(A) 8:27:12
(B) 8:25:12
(C) 8:26:12
(D) 8:24:12
(E) None of them
Rationale: Interval of change = (L.C.M of 48,72,108)sec.=432sec.
So, the lights will agin change simultaneously after every 432 seconds i.e,7 min.12sec
Hence , next simultaneous change will take place at 8:27:12 hrs.
Answer is A.
Answer: (A) 8:27:12
Question: The average age of a husband and a wife is 23 years when they were married five years ago but now the average age of the husband, wife and child is 20 years(the child was born during the interval). What is the present age of the child?
(A) 7 years
(B) 9 years
(C) 6 years
(D) 4 years
(E) 5 years
Rationale: 28 * 2 = 56
20 * 3 = 60
-----------
4 years
Answer: D
Answer: (D) 4 years
Question: If in a certain sequence of consecutive multiples of 50, the median is 525, and the greatest term is 950, how many terms that are smaller than 525 are there in the sequence?
(A) 6
(B) 9
(C) 8
(D) 12
(E) 13
Rationale: Since the median is 525 we know there must be a even number of integers because 50 is not a multiple of 525.
So the list around 525 must go.500 (525) 550 600 650 700 750 800 850 900 950
Since we know there are 9 numbers greater than 525 then there must be 9 numbers less then 525.
answer:B
Answer: (B) 9
Question: If the average marks of three batches of 49, 60 and 45 students respectively is 50, 55, 60, then the
average marks of all the students is
(A) 54.87
(B) 54.68
(C) 54.6
(D) 54.58
(E) None of these
Rationale: Explanation:
=(49*50+60*55+45*60)/(49+60+45)=54.87
Answer: Option A
Answer: (A) 54.87
Question: 1/4 of all the juniors and 2/3 of all the seniors are going on a trip. If there are 2/3 as many juniors as seniors, what fraction of the students are not going on the trip?
(A) 4/9
(B) 1/2
(C) 2/3
(D) 1/3
(E) 5/6
Rationale: J be the number of Juniors and S be the number of Seniors.
there are 2/3 as many juniors as seniors
23∗S=J
J/S=23
Going on Trip = J4+23∗S
Fraction = (J4+23S)/(J+S)
= (2/3*1/4 + 2/3 )/ (2/3 +1 )
= 1/2
Fraction not on trip = 1/2
ANSWER:B
Answer: (B) 1/2
Question: A box contains 3 blue marbles, 4 red, 6 green marbles and 2 yellow marbles. If three marbles are picked at random, what is the probability that they are all blue?
(A) 1/455
(B) 1/478
(C) 1/428
(D) 1/459
(E) 1/429
Rationale: Given that there are three blue marbles, four red marbles, six green marbles and two yellow marbles.
Probability that all the three marbles picked at random are blue
= ³C₃/¹⁵C₃ = (1 * 3 * 2 * 1)/(15 * 14 * 13)
= 1/455
Answer:A
Answer: (A) 1/455
Question: An empty fuel tank is filled with brand Z gasoline. When the tank is half empty, it is filled with brand Y gasoline. When the tank is half empty again, it is filled with brand Z gasoline. When the tank is half empty again, it is filled with brand Y gasoline. At this time, what percent J of the gasoline in the tank is brand Z?
(A) 50%
(B) 40%
(C) 37.5%
(D) 331⁄3%
(E) 25%
Rationale: Work with fraction of brand Z in the tank.
1st step: brand Z is 1
2nd step: brand Z is 1/2
3rd step: brand Z is (1/2)*(1/2) + 1/2 = 3/4
4th step: brand Z is (1/2)*(3/4) J= 3/8 = 37.5%
Answer (C)
Answer: (C) 37.5%
Question: For any a and b that satisfy |a – b| = b – a and a > 0, then |a + 4| + |-b| + |b – a| + |ab| =
(A) a-b+4
(B) ab-b+4
(C) ab + 2b + 4
(D) 2ab+b+2
(E) ab+2b+2
Rationale: Observation-1: |a – b| = b – a
which is possible only when signs of a and b are Same
Since Given a > 0
so we figure out that a and b are both positive
Observation-2: |a – b| must be Non-Negative and so should be the value of b-a which is possible only when absolute value of b is greater than or equal to absolute value of a
Now you may choose the values of a and b based on above observations
e.g. b = 4 and a=1 and check the value of given functions and options
|a + 4| + |-b| + |b – a| + |ab| = |1 + 4| + |-4| + |4 – 1| + |1*4| = 16
ab + 2b + 4= 1*4+8+4=16
all other options are not equal to 16
Answer : C
Answer: (C) ab + 2b + 4
Question: The cost of 10 grams of gold was $75 in 2001. In 2015, the price had increased to $400. What was the percent increase in the cost of the 10 grams of gold?
(A) 255%
(B) 433.3%
(C) 325%
(D) 125.5%
(E) 300.98%
Rationale: Increase = 400-75 = 325
% increase = 325*100/75 = 433.3%
Answer: option B
Answer: (B) 433.3%
Question: Solve for x and check: 25x = 675
(A) 675
(B) 725
(C) 895
(D) 1025
(E) None of these
Rationale: Solution : Dividing each side by 25, we obtain
(25x/675)=(675/25)
Therefore : x=27
Check :
25x=675
(25*27)=675
675=675
ANSWER : A
Answer: (A) 675
Question: A, B and C invests Rs.2000, Rs.3000 and Rs.4000 in a business. After one year A removed his money; B and C continued the business for one more year. If the net profit after 2 years be Rs.3200, then A's share in the profit is?
(A) 276
(B) 289
(C) 220
(D) 400
(E) 278
Rationale: 2*12 : 3*12 : 4*24
1: 3: 4
1/8 * 3200 = 400
Answer: D
Answer: (D) 400
Question: a box contains 12 marbels of 3 different colours green,yellow and blue 4each,if you were to close your eyes and pick them at random how many marbels must you take out to be sure that there are at least two of each colour among the marbels you picked out?
(A) 4
(B) 5
(C) 6
(D) 7
(E) 8
Rationale: you have 12 marbles:
g g g g y y y y b b b b
In order to definitely 2 of one color --
So you take out g y b. Then the next one you take will be the 2nd for one of these marbles. So you need to take out 4.
ANSWER:A
Answer: (A) 4
Question: A batsman scored 90 runs which included 2 boundaries and 7 sixes. What percent of his total score did he make by running between the wickets.
(A) 30%
(B) 40%
(C) 44.44%
(D) 60%
(E) 80%
Rationale: Explanation:
Number of runs made by running = 90 - (2 x 4 + 7 x 6)
= 90- (50)
= 40
Now, we need to calculate 40 is what percent of 90.
=> 40/90 * 100 = 44.44 %
Option C
Answer: (C) 44.44%
Question: In a simultaneous throw of 2 dice what is the probability of getting a total of 8?
(A) 2/13
(B) 3/45
(C) 5/36
(D) 6/73
(E) 4/15
Rationale: n(S) = 6*6 = 36
E = {(2,6),(3,5),(4,4),(5,3),(6,2)}
Probability = 5/36
Answer is C
Answer: (C) 5/36
Question: A started a business with an investment of Rs. 70000 and after 6 months B joined him investing Rs. 120000. If the profit at the end of a year is Rs. 26000, then the share of A is?
(A) s.14028
(B) s.14000
(C) s.14003
(D) s.14029
(E) s.24029
Rationale: Ratio of investments of A and B is (70000 * 12) : (120000 * 6) = 7 : 6
Total profit = Rs. 26000
Share of B = 7/13 (26000) = Rs.14000
Answer: B
Answer: (B) s.14000
Question: city A to city B, Andrew drove for 1 hour at 50 mph and for 3 hours at 60 mph. What was the average speed for the whole trip?
(A) 45
(B) 57.5
(C) 58
(D) 59.5
(E) 61
Rationale: The total distance is 1×50+3×60=2301×50+3×60=230. And the total time is 4 hours. Hence,
Average Speed=(Total DistanceTotal Time)=2304=57.5
B
Answer: (B) 57.5
Question: A man’s current age is (2/5) of the age of his father. After 8 years, he will be (1/2) of the age of his father. What is the age of father at now?
(A) 40
(B) 45
(C) 38
(D) 50
(E) 39
Rationale: A
40
Let, father’s current age is A years.
Then, Man’s current age =[ (2/5)A ]years.
Therefore, [ (2/5)A + 8 ]= (1/2)(A + 8)
2(2A + 40) = 5(A + 8)
A = 40
Answer: (A) 40
Question: A and B started business in partnership investing Rs. 20,000 and Rs. 15,000 respectively. After six months, C joined them with Rs. 20,000. What will be B's share in the total profit of Rs. 25,000 earned at the end of 2 years from the starting of the business?
(A) 7500
(B) 7509
(C) 7507
(D) 7505
(E) 7502
Rationale: A:B:C = (20000 * 24) : (15000 * 24) : (20000 * 18) = 4:3:3
B's share = 25000 * 3/10 = Rs. 7500.
Answer: A
Answer: (A) 7500
Question: When a person aged 39 is added to a group of n people, the average age increases by 2. When a person aged 15 is added instead, the average age decreases by 1. What is the value of E?
(A)  7
(B)  8
(C)  9
(D)  10
(E)  11
Rationale: A simple and elegant solution.
As addition of 39, shifts mean by 2, and addition of 15, shifts mean by 1 to the other side, we have the mean lying between 3915, and in a ratio of 2:1
39-15 = 24
24 divide by 3 is 8.
Meaning mean of the n terms is 15+8 = 39-16 = 23
Now, from first statement, When a person aged 39 is added to a group of n people, the average age increases by 2.
E*23 +39 = 25*(E+1)
E = 7
Ans. (A)
Answer: (A)  7
Question: The average age of 4 boys is 25 years and their ages are in the proportion 3:5:7. The age of the youngest boy is?
(A) 10years
(B) 15years
(C) 20years
(D) 25years
(E) 18years
Rationale: Total age of 4 boys = 25*4 = 100
ratio of their ages = 3:5:7
Age of the youngest = 100*3/15 = 20 years
Answer is C
Answer: (C) 20years
Question: A garden center sells a certain grass seed in 5-pound bags at $13.82 per bag, 10-pound bags at $20.43 per bag, and 25-pound bags $32.25	per bag. If a customer is to buy at least	65 pounds of the grass seed,	but no more than 80 pounds,	what is the least possible cost of the grass seed that the customer will buy?
(A) $94.03
(B) $96.75
(C) $98.75
(D) $102.07
(E) $105.3
Rationale: there can be 2 cases
1)25+25+10+5=$98.75 or
2)25+25+25=$96.75
C
Answer: (C) $98.75
Question: The greatest possible length which can be used to measure exactly the lengths 7 m, 3 m 85 cm, 12 m 95 cm is:
(A) 15 cm
(B) 25 cm
(C) 35 cm
(D) 40 cm
(E) 42 cm
Rationale: Required length = H.C.F. of 700 cm, 385 cm and 1295 cm = 35 cm
Answer: Option C
Answer: (C) 35 cm
Question: If x>y>0, which of the following must be true:
I. x^2<y^2
II. x^3 > y^3
III. |x|<y
(A) I only
(B) II only
(C) III only
(D) II and III
(E) I, II and III
Rationale: Assuming x and y to be integers
X=3,Y=2
X^2=3^2=9
Y^2=2^2=4
So I is true
Now lets look at option III because if option 3 is true E is the answer or else A
As per question X>Y>0 Hence |X| >Y
So OA=B
Answer: (B) II only
Question: 2.505/10.02 =
(A)  0.35
(B)  0.3505
(C)  0.25
(D)  0.351
(E)  0.3527
Rationale: 2.505 / 10.02
2505 / 1002 = 2.5
move the comma two places to the left as we have 2 decimal places from the divisor: 0.25. Answer: C
Answer: (C)  0.25
Question: 45 men can complete a work in 15 days. Six days after they started working, 30 more men joined them. How many days will they now take to complete the remaining work?
(A) 5.4
(B) 10
(C) 1.5
(D) 7
(E) 8
Rationale: 45*15 men can complete the work in 1 day
1 man's 1 day work = 1/675
45 men 6 days work = 6*1/15 = 2/5
remaining work = 1-2/5 = 3/5
75 men's 1 day's work = 75/675 = 1/9
3/5 work is done by them in 9 *3/5 = 5.4 days
Answer is A
Answer: (A) 5.4
Question: Rajeev's age after 15years will be 5 times his age 5years back. What is the present age of Rajeev?
(A) 10years
(B) 15years
(C) 18years
(D) 20years
(E) 19years
Rationale: Let Rajeev's present age be x
Rajeev's age after 15 years = x+15
Rajeev's age 5 years back = x-5
x+15 = 5(x-5)
x = 10
Rajeev's present age = 10 years
Answer is A
Answer: (A) 10years
Question: In the fifth grade at Parkway elementary school there are 420 students. 320 students are boys and 250 students are playing soccer. 86% of the students that play soccer are boys. How many girl student are in Parkway that is not playing soccer?
(A) 69.
(B) 73.
(C) 81
(D) 65
(E) 108
Rationale: Total students = 420
Boys = 320, Girls = 100
Total playing soccer = 250
86%of 250 = 215 are boys who play soccer.
Girls who play soccer = 35.
Total girls who do not play soccer = 100 - 35 = 65.
Correct option: D
Answer: (D) 65
Question: The ratio, by weight, of coffee to sugar to water in a pot of coffee is 5:2:15. The ratio is then altered so that the ratio of coffee to sugar is halved while the ratio of coffee to water is doubled. If the altered pot of coffee contains 12 grams of sugar, how many grams of water does it contain after alteration?
(A) 22.5
(B) 20
(C) 17.5
(D) 15
(E) 12.5
Rationale: The new ratio of coffee to sugar is 2.5:2 = 5:4
The new ratio of coffee to water is 10:15.
The new ratio of coffee to sugar to water is 10:8:15.
If there are 12 grams of sugar, then there are (15/8)*12=22.5 grams of water.
The answer is A.
Answer: (A) 22.5
Question: 4+7=1281
4+6=1240
8+3=1241
9+9=?
(A) 1717
(B) 1818
(C) 1817
(D) 1718
(E) 1854
Rationale: x+y = ABCD
BC = x*y
AD=x+y
e.g. 4+7
BC=4*7=28
AD=4+7=11
ABCD = 1281
..
.
similarly
9+9=1818
4+7=1281
4+6=1240
8+3=1241
9+9=1818
ANSWER:B
Answer: (B) 1818
Question: Find the unit digit in 264^102+264^103?
(A) 0
(B) 2
(C) 3
(D) 4
(E) 6
Rationale: Required unit's digit = unit's digit in 4102+4103.4102+4103.
Now, 4242 gives unit digit 6.
⇒ 41024102 gives unit digit 6.
⇒ 41034103 gives unit digit of the product 6×46×4 i.e., 4.
Hence, unit's digit in 264102+264103264102+264103
= unit's digit in (6+4)=0
A
Answer: (A) 0
Question: 10 women are equal to as many men as are equal to 7 boys. All of them earn Rs.30 only. Women’s wages are?
(A) 1
(B) 5
(C) 2
(D) 7
(E) 2
Rationale: 10w = xm = 7b
10w+xm+7b ----- 30 Rs.
10w+10w+10w ----- 30 Rs.
30w ------ 30 Rs. => 1Mw= 1Rs.
Answer: A
Answer: (A) 1
Question: If two dice are thrown together, the probability of getting an even number on one die and an odd number on the other is -.
(A) 1/3
(B) 1/2
(C) 7/8
(D) 3/4
(E) 7/3
Rationale: Answer: Option B
The number of exhaustive outcomes is 36.
Let e be the event of getting an even number on one die and an odd number on the other. Let the event of getting either both even or both odd then = 18/36 = 1/2
P(e) = 1 - 1/2 = 1/2.
Answer: (B) 1/2
Question: Sari and Ken climb up a mountain. At night, they camp together. On the day they are supposed to reach the summit, Sari wakes up at 08:00 and starts climbing at a constant pace. Ken starts climbing only at 10:00, when Sari is already 700 meters ahead of him. Nevertheless, Ken climbs at a constant pace of 500 meters per hour, and reaches the summit before Sari. If Sari is 50 meters behind Ken when he reaches the summit, at what time did Ken reach the summit?
(A) 13:00
(B) 13:30
(C) 14:00
(D) 15:00
(E) 15:30
Rationale: Both Sari and Ken climb in the same direction.
Speed of Sari = 700/2 = 350 meters/hr (since she covers 700 meters in 2 hrs)
Speed of Ken = 500 meters/hr
At 8:00, distance between Ken and Sari is 700 meters. Ken needs to cover this and another 50 meters.
Time he will take = Total distance to be covered/Relative Speed = (700 + 50)/(500 - 350) = 5 hrs
Starting from 10:00, in 5 hrs, the time will be 15:00
Answer (D)
Answer: (D) 15:00
Question: The length of rectangle is thrice its breadth and its perimeter is 96 m, find the area of the rectangle?
(A) 432 sq m
(B) 356 sq m
(C) 452 sq m
(D) 428 sq m
(E) 528 sq m
Rationale: 2(3x + x) = 96
l = 36 b = 12
lb = 36 * 12 = 432
ANSWER:A
Answer: (A) 432 sq m
Question: A five digit number divisible by 7 becomes divisible by 3 when 13 is added to it. The largest such number is :
(A) 54375
(B) 54354
(C) 54336
(D) 54341
(E) 54012
Rationale: Out of all the 5 options, only 54341 is NOT divisible by 3. All others are divisible
So Answer = D (No further calculation required)
Addition of any two non-divisible numbers by 3 gives the resultant divisible by 3
13 is non-divisible by 3; we are adding a number to that so that the resultant becomes divisible by 3
Applying the above rule,It means that the number which we are going to add should be non-divisible by 3
So comes the answer = 54341
Answer : D
Answer: (D) 54341
Question: 34.98 + 240.016 + 23.98 = ?
(A) 298.976
(B) 298.694
(C) 289.496
(D) 289.469
(E) 298.964
Rationale: 34.98
240.016
+ 23.98
--------
298.976
Answer is A.
Answer: (A) 298.976
Question: A batsman in his 17th innings makes a score of 80, and thereby increases his average by 2. What is his average after the 17th innings? He had never been ’not out’.
(A) 48
(B) 37
(C) 39
(D) 43
(E) 42
Rationale: Average score before 17th innings
= 80 - 2 × 17= 46
Average score after 17th innings
=> 46 + 2 = 48
ANSWER:A
Answer: (A) 48
Question: The average monthly salary of 8 workers and one supervisor in a factory was $$430. When the supervisor, whose salary was $$870 per month, retired, a new person was appointed and then the average salary of 9 people was $$400 per month. The salary of the new supervisor is:
(A) 233
(B) 600
(C) 287
(D) 771
(E) 191
Rationale: Explanation:
Total salary of 8 workers and supervisor together = 9 × 430 = 3870
Now total salary of 8 workers = 3870 − 870 = 3000
Total salary of 9 workers including the new supervisor = 9 × 400 = 3600
Salary of the new supervisor = 3600 − 3000 = 600
Answer: B
Answer: (B) 600
Question: Pipes A, B and C can fill a tank in 30, 60 and 120 minutes respectively. Pipes B and C are kept open for 10 minutes, and then Pipe B is shut while Pipe A is opened. Pipe C is closed 10 minutes before the tank overflows. How long does it take to fill the tank?
(A) 40 minutes
(B) 28 minutes
(C) 30 minutes
(D) 36 minutes
(E) 34 minutes
Rationale: DETAILED SOLUTION
Let us assume that the tank has a capacity of 120 litres. So, the pipes discharge the following amounts of water:
(A) 4 litres per minute
(B) 2 litres per minute
(C) 1 litre per minute.
Part 1: B and C (3 litres/min) are kept open for 10 minutes, filling 3 × 10 = 30 litres. 90 litres remain to be filled in the tank.
Part 2: Now, B is shut and A is opened. Effectively, this means that A and C are filling the tank together (5 litres / minute). We don’t yet know how long A and C are open together.
Part 3: C is closed 10 minutes before the tank overflows. This means that only A works for the last 10 minutes, filling 40 litres (working@4 litres/min)
Since 30 litres are filled in Part 1 and 40 litres in Part 3, the balance (50 litres) should have been filled in Part 2.
Working together, A and C fill 5 litres per minute in Part 2. This means that they would have taken 10 minutes to fill 50 litres.
So, the entire time it took to fill the tank is:
10 + 10 + 10 = 30 mins.
Answer choice (c)
Alternate Solution
In one minute, A fills (1/30)th of the tank, B fills (1/60)th of the tank, and C fills (1/120)th of the tank.
(B + C) work for 10 minutes, followed by (A + C), which works for “t” minutes, followed by A, which work for 10 minutes. This ensures that the tank gets filled. This can be written in an equation form:
10 x (1/60 + 1/120) + t x (1/30 + 1/120) + 10 x (1/30) = 1
10 x (1/40) + t x (1/24) + 10 x (1/30) = 1.
Or, 1/4 + t/24 + 1/3 = 1. Or t = 10.
So, the entire tank was filled in 30 mins.
Answer choice (C).
Answer: (C) 30 minutes
Question: Ram professes to sell his goods at the cost price but he made use of 900 grms instead of a kg, what is the gain percent?
(A) 11 1/6%
(B) 11 7/9%
(C) 11 1/9%
(D) 11 1/8%
(E) 11 2/9%
Rationale: 900 --- 100
100 --- ? => 11 1/9%
Answer:C
Answer: (C) 11 1/9%
Question: The compound ratio of 2/3, 6/7, 1/3 and 1/8 is given by?
(A) 1/56
(B) 1/42
(C) 1/40
(D) 1/41
(E) 1/47
Rationale: 2/3 * 6/7 * 1/3 * 1/8 = 1/42
Answer:B
Answer: (B) 1/42
Question: The speed at which a man can row a boat in still water is 15 kmph. If he rows downstream, where the speed of current is 3 kmph, what time will he take to cover 120 metres?
(A) 16 seconds
(B) 34 seconds
(C) 14 seconds
(D) 12 seconds
(E) 24 seconds
Rationale: Speed of the boat downstream = 15 + 3 = 18 kmph
= 18 * 5/18 = 5 m/s
Hence time taken to cover 120 m = 120/5
= 24 seconds.
Answer: E
Answer: (E) 24 seconds
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 8 sec. What is the length of the fast train?
(A) 27 7/6
(B) 277/5
(C) 27 7/2
(D) 400/9
(E) 27 7/1
Rationale: Relative speed = (40 - 20) = 20 km/hr.
= 20 * 5/ 18 = 50/9 m/sec.
Length of faster train = 50/9 * 8 = 400/9
= 27 7/9 m.
Answer:D
Answer: (D) 400/9
Question: One pipe can fill a tank three times as fast as another pipe. If together the two pipes can fill tank in 36 min, then the slower pipe alone will be able to fill the tank in?
(A) 187 min
(B) 289 min
(C) 144 min
(D) 278 min
(E) 287 min
Rationale: Let the slower pipe alone fill the tank in x min.
Then, faster pipe will fill it in x/3 min.
1/x + 3/x = 1/36
4/x = 1/36 => x = 144 min.
Answer:C
Answer: (C) 144 min
Question: A wheel that has 6 cogs is meshed with a larger wheel of 18 cogs. When the smaller wheel has made 21 revolutions, then the number of revolutions mad by the larger wheel is:
(A) 49
(B) 4
(C) 12
(D) 7
(E) 27
Rationale: Let the required number of revolutions made by larger wheel be x.
Then, More cogs, Less revolutions (Indirect Proportion)
18 : 6 :: 21 : x 18 * x = 6 x 21
x =	(6 x 21)/18
x = 7.
Answer is D.
Answer: (D) 7
Question: A car driver travels from the plains to the hill station, which are 200 km apart at an average speed of 40km/hr. in return trip, he covers the same distance at an average speed of 20km/hr. the average speed of the car over the entire distance of 400 km is
(A) 8.95km/hr
(B) 26.7km/hr
(C) 27.8km/hr
(D) 37.9km/hr
(E) 8.45km/hr
Rationale: average speed = (2*40*20)/40+20 km/hr
=(1600/60)km/hr =26.7 km/hr
Answer (B)
Answer: (B) 26.7km/hr
Question: The ratio of the volumes of two cubes is 1331 : 2197. What is the ratio of their total surface areas?
(A) 121 : 169
(B) 169 : 122
(C) 81 : 124
(D) 81 : 126
(E) 81 : 129
Rationale: Ratio of the sides = 3√1331 : 3√2197 = 11 : 13
Ratio of surface areas = 11^2 : 13^2 = 121 : 169
Answer: Option A
Answer: (A) 121 : 169
Question: A circular garden is surrounded by a fence of negligible width along the boundary. If the length of the fence is 1/5 of th area of the garden. What is the radius of the circular garden?
(A) 1
(B) 2
(C) 10
(D) 8
(E) 16
Rationale: as per the question-- width is negligible
now,
let L be the length of the fence =2pir
L=1/5(pir^2)
pir^2=10pir
r=10
Answer : C
Answer: (C) 10
Question: 38, 69, 22,73, 31,47, 90, 82
Which of the following numbers is greater than three-fourth of the numbers but less than one-fourth of the numbers in the list above?
(A) a- 56
(B) b- 68
(C) c- 69
(D) d- 71
(E) e- 77.5
Rationale: Important:- Arrange the numbers in ascending order first.
22, 31, 38, 47, 69, 73, 82, 90
3/4th of the number list represents- 73 (6th number)
remaining 1/4th list represents 82 (7 th number)
77.5 fits in between above 2
Answer:- E
Answer: (E) e- 77.5
Question: Of the 3,600 employees of Company X, 3/4 are clerical. If the clerical staff were to be reduced by 4/5, what percent of the total number of the remaining employees would then be clerical?
(A) 37%
(B) 22.2%
(C) 20%
(D) 12.5%
(E) 11.1%
Rationale: Let's see, the way I did it was
3/4 are clerical out of 3600 so 2700 are clerical
2700 reduced by 4/5 is 2700*4/5
so it reduced 2160 people , so there is 540 clerical people left
but since 2160 people left, it also reduced from the total of 3600 so there are 1440 people total
since 540 clerical left / 1440 people total
you get (A) 37%
Answer: (A) 37%
Question: A die is thrown three times. Events X and Y are defined as below:
X : 4 on the third throw
Y : 6 on the first and 5 on the second throw
What is the probability of X given that Y has already occurred.
(A) 1/5
(B) 1/6
(C) 2/7
(D) 3/7
(E) 3/11
Rationale: The sample space has 216 outcomes.
Now X =
(1,1,4) (1,2,4) ... (1,6,4) (2,1,4) (2,2,4) ... (2,6,4)
(3,1,4) (3,2,4) ... (3,6,4) (4,1,4) (4,2,4) ...(4,6,4)
(5,1,4) (5,2,4) ... (5,6,4) (6,1,4) (6,2,4) ...(6,5,4) (6,6,4)
Y = {(6,5,1), (6,5,2), (6,5,3), (6,5,4), (6,5,5), (6,5,6)}
and X n Y = {(6,5,4)}.
Now P(Y) = 6/216
and P (X n Y) = 1/216
Then P(X|Y) = (1/216)/(6/216) = 1/6.
B)
Answer: (B) 1/6