mathewhe/aqua_rat huggingface dataset:
Question: If from a group of 5 people, an old member is replaced by a new one, the average age is same as it was 3 years ago. What is the difference between the ages of the old member and the new one?
(A) 15
(B) 77
(C) 19
(D) 66
(E) 19
Rationale: Explanation:
The present average age is (x + 3) when the old member is present and it equals to x when an old member is replaced by a new one.
The difference in the ages of the old member and the new one is equal to the difference in the total age before and after the replacement = 15 years.
ANSWER:A
Answer: (A) 15
Question: a equilateral triangle having one side 5m.in this triangle there is a square of side 2m.calculate the percentage of area outside square in that triangle.
(A) 68
(B) 54
(C) 63.04
(D) 62
(E) 60
Rationale: area of triangle=âˆš3a2/4.=1.732*25/4=10.825m2.
area of square=2*2=4m2.
rest area after square=10.825-4=6.825m2.
%rest area after square=6.825/10.825*100=63.04%
answer C
Answer: (C) 63.04
Question: A palindrome is a number that reads the same forward and backward, such as 144. How many odd, 4-digit numbers are palindromes?
(A) 40
(B) 45
(C) 50
(D) 62
(E) 2500
Rationale: A palindrome is a number that reads the same forward and backward. Examples of four digit palindromes are 1221, 4334, 2222 etc
You basically get to choose the first two digits and you repeat them in opposite order. Say, you choose 45 as your first two digits. The next two digits are 54 and the number is 4554.
Also, you need only odd palindromes. This means that you need an odd digit at the end i.e. 1/3/5/7/9. This means that you need to start the number with an odd digit. Only then will it end with an odd digit.
In how many ways can you pick two digits such that the first one is an odd digit?
The first digit can be selected in 5 ways.(1/3/5/7/9)
The second digit can be selected in 10 ways.(0/1/2/3...8/9)
Total = 5*12 = 62 ways
D
Answer: (D) 62
Question: In how many ways can you sit 8 people on a bench if 4 of them must sit together?
(A) 720
(B) 2,160
(C) 2,880
(D) 4,320
(E) 40,320
Rationale: In such questions, always tie the person that have to sit together. So we have effectively 4+1= 5 persons to arrange.
They can be arranged in 5! ways.
Now the 4 persons can themselves be arranged in 4! ways.
Total ways: 5!*4! = 2880.
C is the answer.
Answer: (C) 2,880
Question: If two of the four expressions x+y, x+5y, x-y, 5x+y are chosen at random, what is the probability that their product will be of the form of x^2 - (by)^2, where b is an integer?
(A) 1/2
(B) 1/3
(C) 1/4
(D) 1/5
(E) 1/6
Rationale: There are total 4C2=64C2=6 ways to choose 2 equations out of 4 at random.
We want the product of 2 equations in format x2−(by)2x2−(by)2, where b is a constant coefficient of term y2y2. Also note equation does not contain any xyxy term.
There are only 2 equations, (x+y) & (x-y) which gives the product x2−y2x2−y2. Product of all other equations will contain term xyxy
So answer = 1/6
ANS:E
Answer: (E) 1/6
Question: The average of marks obtained by 120candidates was 35. If the avg of marks of passed candidates was 39 & that of failed candidates was 39 and that of failed candidates was 15, the no.of candidates who passed the examination is?
(A) 80
(B) 90
(C) 100
(D) 120
(E) 140
Rationale: Let the number of candidate who passed = y
Then, 39y + 15(120 - y) =120 x 35
⇒ 24y= 4200 -1800
∴ y= 2400 / 24 = 100
C
Answer: (C) 100
Question: A fair price shopkeeper takes 10% profit on his goods. He lost 20% goods during theft. His loss percent is:
(A) 10
(B) 13
(C) 12
(D) 18
(E) 19
Rationale: C
12%
Suppose he has 100 items.
Let C.P. of each item be $ 1.
Total cost = $100. Number of items left after theft = 80.
S.P. of each item = $1.10
Total sale = 1.10 * 80 = $88
Hence, loss % = 12/100 * 100 = 12%
Answer: (C) 12
Question: If a is a positive integer, then 2^a + 2^(a + 1) =
(A) 3^(a + 1)
(B) 2^(a + 1)
(C) 2a
(D) 2a^(a + 1)
(E) 3(2^a)
Rationale: If a is a positive integer, then 2^a + 2^(a + 1) =
2^a + 2^(a + 1)
2^a(1+2)
2^a(3)
E. 3(2^a)
ANSWER:E
Answer: (E) 3(2^a)
Question: If x, y, and z are all factors of 33, which of the following must be true?
(A) The product xyz > 33
(B) Either x = y, y = z, or x = z
(C) x – y – z = even
(D) The product xyz is odd
(E) yz/x is an integer
Rationale: All the factors of 33 are odd numbers.
The product of odd numbers is odd.
The answer is D.
Answer: (D) The product xyz is odd
Question: If the average (arithmetic mean) of x, x + 2, and x + 4 is 63, what is the value of x?
(A) 60
(B) 62
(C) 64
(D) 61
(E) 66
Rationale: AM of x, x + 2, and x + 4 = x + (x + 2) + (x + 4) / 3 = 3x + 6 /3 = x + 2
Given that x + 2 = 63
x = 61
Answer : D
Answer: (D) 61
Question: A goods train runs at a speed of 72 kmph and crosses a 280 m long platform in 26 seconds.What is the length of the goods train?
(A) 230 m
(B) 240 m
(C) 260 m
(D) 270 m
(E) 250 m
Rationale: s=280+x/t
72*5/18=280+x/26
x=240
ANSWER:B
Answer: (B) 240 m
Question: If 6 (A's capital) = 8 (B's capital) = 10 (C's capital). Then the ratio of their capitals is:
(A) 3:4:5
(B) 12:15:20
(C) 20:15:12
(D) 6:8:10
(E) 6:8:12
Rationale: 6A = 8B = 10 C
A:B:C = 1/6:1/8:1/10
= 20:15:12
ANSWER:C
Answer: (C) 20:15:12
Question: If an amount of Rs 11,180 is divided equally among
52 students, approximately how much amount will
each student get?
(A) Rs 215
(B) Rs 210
(C) Rs 213
(D) Rs 218
(E) None
Rationale: Amount received by each student = 11180/52 â‰ˆ Rs
215
Answer A
Answer: (A) Rs 215
Question: Three years ago , the average age of A, B and C was 27 years and that of B and C 5 years ago was 20 years. A’s present age is :
(A) 22
(B) 88
(C) 40
(D) 87
(E) 17
Rationale: Explanation:
Sum of the present ages of A, B and C = (27× 3 + 3 × 3) years = 90 years.
Sum of the present ages of B and C = (20 × 2 + 5 × 2) years = 50 years.
A's present age = 90 – 50 = 40 years.
Answer: C
Answer: (C) 40
Question: Pipes A and B can fill a tank in 4 and 6 hours. Pipe C can empty it in 8 hours. If all pipes are opened together, then the tank will be filled in?
(A) 60/17 hr
(B) 22/7 hr
(C) 52/11 hr
(D) 6 hr
(E) 63/19 hr
Rationale: Net part filled in 1 hour = 1/4 + 1/6 - 1/8= 7/22
The tank will be full in 22/7 hr
Answer is B
Answer: (B) 22/7 hr
Question: There are 4 boys and 2 girls. In how many ways can they be seated in a row so that all the two girls do not sit together?
(A) 630
(B) 716
(C) 564
(D) 846
(E) 478
Rationale: The required number of ways = (4+2)! - (4-2)!*2! = 6!-2!*2! = 720-4 = 716
Answer is B
Answer: (B) 716
Question: What is the remainder when 4990990900032 is divided by 32 ?
(A) 16
(B) 0
(C) 4
(D) 2
(E) 5
Rationale: Though i was unaware of the divisibility test for 32 but i guessed the pattern!!
divisibility rule for 4- last two digits must be divisible by 4
divisibility rule for 8- last three digits must be divisible by 8
similarly, divisibility rule for 32 - last five digits must be divisible by 32
Hence, Ans B
Answer: (B) 0
Question: Four car rental agencies A, B, C and D rented a plot for parking their cars during the night. A parked 15 cars for 12 days, B parked 12 cars for 20 days, C parked 18 cars for 18 days and D parked 16 cars for 15 days. If A paid Rs. 1125 as rent for parking his cars, what is the total rent paid by all the four agencies?
(A) 6157
(B) 6187
(C) 6128
(D) 6150
(E) 6113
Rationale: The ratio in which the four agencies will be paying the rents = 15 * 12 : 12 * 20 : 18 * 18 : 16 * 15
= 180 : 240 : 324 : 240 = 45 : 60 : 81 : 60
Let us consider the four amounts to be 45k, 60k, 81k and 60k respectively.
The total rent paid by the four agencies = 45k + 60k + 81k + 60k= 246k
It is given that A paid Rs. 1125
45k = 1125 => k = 25
246k = 246(25) = Rs. 6150
Thus the total rent paid by all the four agencies is Rs. 6150.
Answer: D
Answer: (D) 6150
Question: The base and height of a parallelogram are 12m and 6m respectively. Then its area is ======?
(A) 27Sq.m
(B) 126Sq.m
(C) 84Sq.m
(D) 18Sq.m
(E) 72Sq.m
Rationale: A= b*h => A= 12*6=72Sq.m. Answer: (E)
Answer: (E) 72Sq.m
Question: The length T of a rectangle is decreased by 15% and its width is increased by 40%. Does the area of the rectangle decrease or increase and by what percent?
(A) Decreases by 19%
(B) Decreases by 25%
(C) Increases by 6%
(D) Increases by 19%
(E) Increases by 25%
Rationale: Let the length T of the rectangle be 100x, and width be 100y. Area = 100x * 100y = 10000xy
Now after the change Length = 85x, and width = 140 y. Area = 11900xy
% Change = (11900xy - 10000xy)/(10000xy) = 19 % Increase. Hence D.
Answer: (D) Increases by 19%
Question: The floor of a rectangular room is 20 m long and 12 m wide. The room is surrounded by a veranda of width 2 m on all its sides. The area of the veranda is :
(A) 144 m2
(B) 120 m2
(C) 108 m2
(D) 158 m2
(E) None of these
Rationale: Area of the outer rectangle = 24 Ã— 16 = 384 m2
Area of the inner rectangle = 20 Ã— 12 = 240 m2
Required area = (304 â€“ 180) = 144 m2
Answer A
Answer: (A) 144 m2
Question: Pumping alone at their respective constant rates, one inlet pipe fills an empty tank to 1/2 of capacity in 6 hours and a second inlet pipe fills the same empty tank to 2/3 of capacity in 6 hours. How many hours will it take both pipes, pumping simultaneously at their respective constant rates, to fill the empty tank to capacity?
(A) 3.25
(B) 3.6
(C) 4.2
(D) 4.4
(E) 5.14
Rationale: Time taken by First tank Fill 1/2 the tank = 6 hours
i.e. Time taken by First tank to Fill 1 complete the tank =12 hours
Time taken by Second tank Fill 2/3 the tank = 6 hours
i.e. Time taken by First tank to Fill 1 complete the tank = (3/2)*6 = 9 hours
in 1 Hour, Both tanks together Fill the tank = (1/12)+(1/9) = 7/36 tank
i.e. Time taken by Both tank to Fill 1 complete the tank = 36/7 hours = 5.14 hours
Answer: option E
Answer: (E) 5.14
Question: Anup start a bike at 6am. and rides it at 60kmph. Raghu started at 7pm with his car at 70kmph. When will Raghu overtake Anup?
(A) 8:30am
(B) 9:40am
(C) 10:00am
(D) 01:00pm
(E) 11:10am
Rationale: Suppose bike is overtaken by car xhrs after 6am
Distance covered by the bike in x hrs = distance covered by the car in x-1 hr
60x = 70(x-1)
10x = 70
x = 7 hrs
Required time = 6+7 = 01:00Pm
Answer is D
Answer: (D) 01:00pm
Question: The average of first thirteen prime numbers which are odd is?
(A) 20.15
(B) 21.15
(C) 22.15
(D) 23.15
(E) 24.15
Rationale: Explanation:
Sum of first 13 prime no. which are odd = 275
Average = 275/13 = 21.15
Answer:B
Answer: (B) 21.15
Question: A train passes a station platform in 48 seconds and a man standing on the platform in 20 seconds. If the speed of the train is 54 km/hr, what is the length of the platform?
(A) 123
(B) 166
(C) 420
(D) 157
(E) 198
Rationale: Speed = [54 * 5/18] m/sec = 15 m/sec.
Length of the train = (15 * 20) m = 300 m.
Let the length of the platform be x meters.
Then, (x + 300) / 48 = 15
x + 300 = 720
x = 420 m.
Answer: C
Answer: (C) 420
Question: What profit percent is made by selling an article at a certain price, if by selling at 2/3rd of that price, there would be a loss of 20%?
(A) 20%
(B) 28%
(C) 27%
(D) 40%
(E) 70%
Rationale: SP2 = 2/3 SP1
CP = 100
SP2 = 80
2/3 SP1 = 80
SP1 = 120
100 --- 20 => 20%
Answer:A
Answer: (A) 20%
Question: A Car comes with 7 different possible exterior colors and 6 different interior colors. How many different color combinations are there?
(A) 26
(B) 42
(C) 7!6!/2!
(D) 7!6!
(E) 13!/2!
Rationale: For each exterior color out of 7 there are 6 different interior colors possible, so there are total of 7*6=42 color combinations. This is basically the same as Principle of Multiplication: if one event can occur in mm ways and a second can occur independently of the first in nn ways, then the two events can occur in mnmn ways.
Answer: B.
Answer: (B) 42
Question: Two goods trains each 750 m long are running in opposite directions on parallel tracks. Their speeds are 45 km/hr and 30 km/hr respectively. Find the time taken by the slower train to pass the driver of the faster one?
(A) 72
(B) 45
(C) 48
(D) 51
(E) 44
Rationale: Relative speed = 45 + 30 = 75 km/hr.
75 * 5/18 = 125/6 m/sec.
Distance covered = 750 + 750 = 1500 m.
Required time = 1500 * 6/125 = 72 sec.
Answer: Option A
Answer: (A) 72
Question: Tough and Tricky questions: Combinations.
seven contestants representing four different countries advance to the finals of a fencing championship. Assuming all competitors have an equal chance of winning, how many possibilities are there with respect to how a first-place and second-place medal can be awarded?
(A) 6
(B) 7
(C) 12
(D) 16
(E) 21
Rationale: Four contestants representing four different countries advance to the finals of a fencing championship. Assuming all competitors have an equal chance of winning, how many possibilities are there with respect to how a first-place and second-place medal can be awarded?
We have 2 slots to be filled using 7 contestants:7 options for slot1*3 option for slot2
= 7* 3
= 21
Ans. E) 21
Answer: (E) 21
Question: Average of five numbers is -10, and the sum of three of the numbers is 16, wat is the average of the other 2 no's?
(A) -33
(B) 23
(C) -34
(D) -39
(E) 32
Rationale: Let the five numbers be a, b, c, d, e. Then their average is (a+b+c+d+e5)=10.(a+b+c+d+e5)=10.
Now three of the numbers have a sum of 16, say, a+b+c=16a+b+c=16.
So substitute 16 for a+b+ca+b+c in the average above: (16+d+e5)=10.(16+d+e5)=10.
Solving this equation for d+ed+e gives d+e=−66d+e=−66.
Finally, dividing by 2 (to form the average) gives (d+e2)=−33.(d+e2)=−33.
Hence, the answer is A: -33
Answer: (A) -33
Question: A, B and C enter into a partnership. A initially invests Rs. 25 lakhs and adds another Rs. 10 lakhs after one year. B initially invests Rs. 35 lakhs and withdraws Rs. 10 lakhs after 2 years and C invests Rs. 30 lakhs. In what ratio should the profits be divided at the end of 3 years ?
(A) 11:10:15
(B) 20:17:23
(C) 19:19:18
(D) 5:4:9
(E) None of these
Rationale: Explanation:
A:B:CA:B:C =(25 lakhsÃ—Ã—1)+(35 lakhsÃ—Ã—2) :(35 lakhsÃ—Ã—2+25 lakhsÃ—Ã—1) :(30 lakhsÃ—Ã—3)
= 95 lakhs : 95 lakhs : 90 lakhs =19:19:18=19:19:18.
ANSWER IS C
Answer: (C) 19:19:18
Question: A bag contains 7 green and 8 white balls. If two balls are drawn simultaneously, the probability that both are of the same colour is ?
(A) 7/14
(B) 7/18
(C) 7/12
(D) 7/11
(E) 7/15
Rationale: Drawing two balls of same color from seven green balls can be done in ⁷C₂ ways.
Similarly from eight white balls two can be drawn in ⁸C₂ ways.
P = ⁷C₂/¹⁵C₂ + ⁸C₂/¹⁵C₂ = 7/15
Answer:E
Answer: (E) 7/15
Question: If k^3 is divisible by 84, what is the least possible value of integer k?
(A) 36
(B) 42
(C) 48
(D) 56
(E) 60
Rationale: k^3 = 84*x = 2^2*3*7*x
The factors of k must at minimum include 2*3*7 = 42.
The answer is B.
Answer: (B) 42
Question: The seating chart of an airplane shows 30 rows of seats. Each row has 3 seats on each side of the center aisle, and one of the seats on each side is a window saet. The view from the window seats in 20 of the rows is obscured by the wings of the airplane. If the first person to be assigned a seat is assigned a window seat and thw window seat is assigned randomly, what is the probability that the person will get a seat with an unobscured view?
(A) 1/6
(B) 1/3
(C) 2/3
(D) 5/6
(E) 17/18
Rationale: priyalr
6 seats per row, think of a boeing 737. We have 30 rows, therefore window 30 seats one one side and 30 window seats on the other, totaling 60 window seats on the whole plane.
the view of the window of 20 rows is blocked. two wings, therefore 40 window seats are blocked.
Total window seats = 60
Total blocked window seats = 40
Total unblocked seats = 20
We know that a window seat was given, therefore probability for not window seat is 20/60 =1/3
ANS B
Answer: (B) 1/3
Question: A pool which was 1/5 full to begin with, was filled at a constant rate for 6/5 hours until it was until it was 8/9 full. At this rate, how much time would it take to completely fill this pool if it was empty to begin with?
(A) 8 hrs 45 mins.
(B) 9 hrs.
(C) 9 hrs 30 mins.
(D) 1 hrs 45 mins.
(E) 15 hrs 30 mins
Rationale: The pool was 1/5 full initially.
In 6/5 hrs, it was filled to 8/9 of its capacity.
Therefore, in 6/5 hrs, 8/9 - 1/5 was the amount of volume filled.
So, 6/5 hrs = 8/9 - 1/5 = 31/45
Therefore, for filling the vessel from empty to full, you would require 6/5 * 45/31 = 1 Hrs 45 Mins.
Hence D
Answer: (D) 1 hrs 45 mins.
Question: The difference between the number and its three fifth is 40, what is the number?
(A) 80
(B) 100
(C) 90
(D) 120
(E) 130
Rationale: Explanation:
Let the number be x. Then,
x - (3/5)x = 40
(2/5)x = 40
x = (40 x 5)/2 = 100
Answer: Option B
Answer: (B) 100
Question: The three digits of a number add up to 26. The number is divisible by 5. The leftmost digit is double the middle digit. What is the product of the three digits?
(A) 450
(B) 460
(C) 500
(D) 520
(E) 490
Rationale: Say the three-digit number is abc.
The leftmost digit is double the middle digit --> a=2b;
The number is divisible by 5 --> c is either 0 or 5;
The three digits of a number add up to 26 --> a+b+c=26
So, either a+b+c=2b+b+0=26 or a+b+c=2b+b+5=26. The first equation does not give an integer value of b, so it's not the case. From the second we get that b=7 --> a=14 and c=5 --> a*b*c=490.
Answer: E.
Answer: (E) 490
Question: A trader sells 40 metres of cloth for Rs.8200 at a profit of Rs.25 per metre of cloth. How much profit will the trder earn on 40 metres of cloth?
(A) Rs.950
(B) Rs.1500
(C) Rs.1000
(D) Rs.1200
(E) None of these
Rationale: Explanation:
SP of 1 metre cloth = 8200/40 = Rs.205.
CP of 1 metre cloth = Rs.205 – 25 = Rs.180
CP on 40 metres = 180 x 40 = Rs.7200
Profit earned on 40 metres cloth = Rs.8200 – Rs.7200 = Rs.1000.
Answer: Option C
Answer: (C) Rs.1000
Question: Three 6 faced dice are thrown together. The probability that all the three show the same number on them is
(A) 1/87
(B) 1/36
(C) 1/18
(D) 1/76
(E) 1/10
Rationale: It all 3 numbers have to be same basically we want triplets. 111, 222, 333, 444, 555 and 666. Those are six in number. Further the three dice can fall in 6 * 6 * 6
= 216 ways.
Hence the probability is 6/216
= 1/36
Answer: B
Answer: (B) 1/36
Question: If the seventh day of a month is three days earlier than Friday, What day will it be on the nineteenth day of the month?
(A) Saturday
(B) Monday
(C) Sunday
(D) Wednesday
(E) Friday
Rationale: Explanation:
Given that seventh day of a month is three days earlier than Friday
=> Seventh day is Tuesday
=> 14th is Tuesday
=> 19th is Sunday
Answer: Option C
Answer: (C) Sunday
Question: A man buys two articles for Rs.1980 each and he gains 10% on the first and loses 10% on the next. Find his total gain or loss percent?
(A) 9
(B) 7
(C) 4
(D) 8
(E) 3
Rationale: (30*30)/100
= 9%loss
Answer:A
Answer: (A) 9
Question: How many 4 digit even numbers do not use any digit more than once
(A) 1720
(B) 2160
(C) 2240
(D) 2460
(E) 2520
Rationale: A B C D ( thousand , hundreds, tens, units)
D can be 0 2 4 6 8 ( any of the 5 digits )
A can be anything except (D or 0) so 8 possibilities
C can be anything except A and B so 8 possibilities
B can be anything except ( A D C ) so 7 possibilities
total ways are 8 * 7 * 8 * 5 = 2240
ANS:C
Answer: (C) 2240
Question: 242 students represent x percent of the boys at a school. If the boys at the school make up 50% of the total school population of x students, what is x?
(A) 120
(B) 150
(C) 180
(D) 200
(E) 220
Rationale: Let B be the number of boys in the school.
242 = xB/100
B = 0.5x
24200=0.5x^2
x^2 = 48400
x = 220
The answer is E.
Answer: (E) 220
Question: A water tank is two-fifth full. Pipe A can fill a tank in 10 minutes and pipe B can empty it in 6 minutes. If both the pipes are open, how long will it take to empty or fill the tank completely?
(A) 6 min. to empty
(B) 6 min. to full
(C) 9 min. to empty
(D) 9 min. to full
(E) 8 min. to full
Rationale: Clearly, pipe B is faster than pipe A and so, the tank will be emptied.
Part to be emptied = 2/5
Part emptied by (A + B) in 1 minute = (1/6 - 1/10) = 1/15
1/15 : 2/5 :: 1 : x
x = (2/5 * 1 * 15) = 6 min.
So, the tank will be emptied in 6 min.
ANSWER:A
Answer: (A) 6 min. to empty
Question: If 13 = 13w/(1-w) ,then (4w)2 =
(A) 1/4
(B) 1/2
(C) 1
(D) 2
(E) 4
Rationale: 13-13w=13w
26w=13
w=1/2
4w=2
4w*2=2*2=4
ANSWER:E
Answer: (E) 4
Question: The positive number a is w percent greater than the positive number b, which is p percent less than a itself. If a is increased by p percent, and the result is then decreased by w percent to produce a positive number c, which of the following could be true?
I. c > a
II. c = a
III. c < a
(A) I only
(B) II only
(C) III only
(D) I and II only
(E) II and III only
Rationale: Let w = 10% then p = 100/11 %
let b = 100 then a = 110
after increasing a by p and decreasing by w we get c= 108
therefore c<a
C it is answer
Answer: (C) III only
Question: How many seconds will a 500 meter long train take to cross a man walking with a speed of 3 km/hr in the direction of the moving train if the speed of the train is 63 km/hr?
(A) 879 meters
(B) 678 meters
(C) 500 meters
(D) 126 meters
(E) 107 meters
Rationale: Let length of tunnel is x meter
Distance = 800+x meter
Time = 1 minute = 60 seconds
Speed = 78 km/hr = 78*5/18 m/s = 65/3 m/s
Distance = Speed*Time
800+x = (65/3) * 60
800+x = 20 * 65 = 1300
x = 1300 - 800 = 500 meters
Answer:C
Answer: (C) 500 meters
Question: The banker's discount on a bill due 4 months hence at 15% is Rs. 420. The true discount is:
(A) 400
(B) 276
(C) 129
(D) 176
(E) 186
Rationale: T.D.
=	B.D. x 100
100 + (R x T)
= Rs. 420 x 100
100 + 15 x	1
3
= Rs. 420 x 100
105
= Rs. 400.
Answer: A
Answer: (A) 400
Question: Tom drives from town W to town B, driving at a constant speed of 60 miles per hour. From town B Tom immediately continues to town C. The distance between W and B is twice the distance between B and C. If the average speed of the whole journey was 36 mph, then what is Tom's speed driving from B to C in miles per hour?
(A) 12
(B) 20
(C) 24
(D) 30
(E) 36
Rationale: Let's assume that it takes 4 hours to go from point W to B. Then the distance between them becomes 240 which makes distance between B and C 120. (240+120)/(4+x) gives us the average speed which is 36. You find x=6. So the question simplifies itself to 120/6=20
Hence the answer is B.
Answer: (B) 20
Question: If a card is drawn from a well shuffled pack of cards, the probability of drawing a spade or a king is ?
(A) 4/17
(B) 4/18
(C) 4/76
(D) 4/13
(E) 4/29
Rationale: P(SᴜK)
= P(S) + P(K) - P(S∩K), where S denotes spade and K denotes king.
P(SᴜK)
= 13/52 + 4/52 - 1/52
= 4/13
Answer: D
Answer: (D) 4/13
Question: If 36 men can do a piece of work in 25 hours, in how many hours will 10 men
do it ?
(A) 65 hours
(B) 90 hours
(C) 30 hours
(D) 62 hours
(E) 66 hours
Rationale: Let the required number of hours be x. Then,
Less men, More hours	(Indirect Proportion)
10 : 36 : : 25 : x	(10 x x) = (36 x 25)	(36 x 25)/10 = 90
Hence, 15 men can do it in 60 hours.
Answer is B.
Answer: (B) 90 hours
Question: A box contains 100 balls, numbered from 1 to 100. If 3 balls are selected at random and with replacement from the box. If the 3 numbers on the balls selected contain two odd and one even. What is the probability R that the first ball picked up is odd numbered?
(A) 	0
(B) 	1/3
(C) 	1/2
(D) 	2/3
(E) 	1
Rationale: Answer-D
Selecting the balls either Even or Odd is having probability 50/100=1/2
We have already selected 3 balls with 2 odd numbers and 1 even number.
So we have 3 combinations OOE, OEO, EOO. We have 3 outcomes and 2 are favourable as in 2 cases 1st number is odd. So probability R is 2/3.D
Answer: (D) 	2/3
Question: Find the odd man out? 3, 7, 15, 17, 22, 27, 29
(A) 15
(B) 17
(C) 22
(D) 27
(E) 0
Rationale: Each of the numbers is odd number except 22. The number 22 is the only even number.
ANSWER: C
Answer: (C) 22
Question: To fill a tank, 20 buckets of water is required. How many buckets of water will be required to fill the same tank if the capacity of the bucket is reduced to one-fifth of its present ?
(A) 100
(B) 200
(C) 300
(D) 400
(E) 500
Rationale: Let the capacity of 1 bucket = x.
Then, the capacity of tank = 20x.
New capacity of bucket = 1/5 x
Therefore, Required number of buckets = (20x)/(1x/5)
= (20x) x 5/1x
= 100/1
= 100
Answer is A.
Answer: (A) 100