mathewhe/aqua_rat huggingface dataset:
Question: There are 3 teams each with 8 basket players. How many combinations are there if we were to pick 2 players from the 3 teams such that no team was picked twice?
(A) 50
(B) 23
(C) 192
(D) 28
(E) 45
Rationale: There are altogether three arrangements, which are we can select two members each from team A and B, each from team A and C, and each from team B and C. For each arrangement, there are altogether 64 possibilities (8*8) since each team has 8 players. So there are a total of 192 possibilities (64*3). I hope this method is easier for you to understand.
Answer: (C) 192
Question: What is the smallest positive integer x such that 80-x is the cube of a positive integer
(A) 16
(B) 12
(C) 47
(D) 9
(E) 12
Rationale: Given 80-x is a perfect cube
so we will take 64= 4*4*4
80-x = 64
x =80-64 = 16
correct option is A
Answer: (A) 16
Question: A river 2m deep and 45 m wide is flowing at the rate of 3 kmph the amount of water that runs into the sea per minute is?
(A) 4500
(B) 3889
(C) 2777
(D) 1299
(E) 2791
Rationale: (3000 * 2 * 5)/60
= 4500 M3
Answer: A
Answer: (A) 4500
Question: A dealer offers a cash discount of 20%. Further, a customer bargains and receives 20 articles for the price of 15 articles. The dealer still makes a profit of 20%. How much percent T above the cost price were his articles marked?
(A) 100%
(B) 80%
(C) 75%
(D) 66+2/3%
(E) 50%
Rationale: Good question...2:11 min
Marked Price (M) = Cost Price (C) + Mark up...(EQN. A)
Selling price = 20% Discount over M = 0.8*M
Given that, a customer bargains and receives 20 articles for the price of 15 articles-->*afurther loss of 25%to the dealer--> BUT aNET PROFIT of 20%over cost price (C)
0.75* 0.8 * M =1.2 * C
Hence, M/C = 2/1 = 200%=T
From Eqn. A , (C + Mark up)/C = 200% -->Mark up / C = 100%
Ans. A
Answer: (A) 100%
Question: Given a Number 123456, from this number put any three values in numerator and remaining three are in denominator. So how many values you can make from this number less than 1/5.
(A) 2
(B) 6
(C) 7
(D) 87
(E) 81
Rationale: Explanation:
If the given value is 120, then denominator should be slightly greater than 600. If for 130, it is 650. So if we take numerator as 132, then denominator should be greater than 660 which is not possible as we have only 5 and 4 available. So numerator is less than 130. The following numbers are possible.
123/654, 123/645, 124/635, 124/653, 125/634, 125/643.
Answer:D
Answer: (D) 87
Question: A trader sells 85 meters of cloth for Rs. 8925 at the profit of Rs. 15 per metre of cloth. What is the cost price of one metre of cloth?
(A) 21
(B) 28
(C) 90
(D) 26
(E) 11
Rationale: Explanation:
SP of 1m of cloth = 8925/85 = Rs. 105
CP of 1m of cloth = SP of 1m of cloth - profit on 1m of cloth
= Rs. 105 - Rs. 15 = Rs. 90.
Answer: C
Answer: (C) 90
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.130000, find the cost of a camel?
(A) s.9800
(B) s.3800
(C) s.9800
(D) s.5200
(E) s.6880
Rationale: Cost of the camel = P
10 camels = 24 horses
16 horses = 4 oxen
6 oxen = 4 elephants
10 elephants = Rs.130000
P = Rs.[(24 * 4 * 4 * 130000)/(10 * 16 * 6 * 10)]
P = Rs.(49920000/9600) => P = Rs.5200
Answer:D
Answer: (D) s.5200
Question: If (1/5)^m * (1/4)^2 = 1/((10)^4), then m =
(A) 4
(B) 5
(C) 6
(D) 3
(E) 2
Rationale: 1/5^m *1/4^2= 1/ 2^4*5^4
2^4*5^4/2^4 =5^m or 5^4 =5^m
therefore m=4
A
Answer: (A) 4
Question: How many 1's are there preceded by 2 but not followed by 7?
5 9 3 2 1 7 4 2 6 9 7 4 2 1 3 2 8 7 4 1 3 8 3 2 5 6 7 4 3 9 5 8 2 0 1 8 7 4 6 3
(A) 4
(B) 5
(C) 6
(D) 1
(E) 9
Rationale: 2 1 3
Only at these places 1 is preceded by 2 but not followed by 7
Answer: D
Answer: (D) 1
Question: What least number must be added to 1056, so that the sum is completely divisible by 23 ?
(A) 2
(B) 3
(C) 18
(D) 21
(E) None of these
Rationale: 23) 1056 (45
92
---
136
115
---
21
---
Required number = (23 - 21)
= 2.
Answer: A
Answer: (A) 2
Question: A certain car dealership offers its newest model in ten exterior and ten interior colors. If the seven interior colors are identical to the seven exterior colors, and the dealership sells every pair of colors except those that would result in a car with an identically colored interior and exterior, how many different color combinations are possible?
(A) 45
(B) 81
(C) 90
(D) 10!/2!
(E) 10!
Rationale: I lined up the 10 different colours for Exterion and Interior like this:
E: A B C D E F G H I J
I: A B C D E F G H I J
I calculated the number of combinations: 10*10= 100 combinations.
But, from these 100 we need to delete sth: the same colours.
There are 10 possible pairs of coulours that will be the same. So, I deleted these 10 pairs from 100, resulting in 45.
Mind here, that the 10 do not result in 20 colours, because 1 pair is one unit that is not allowed. So, 10 units are not allowed (surprised that 80 wasn't among the answer options to confuse test takers...).
A
Answer: (A) 45
Question: In a group of 25 factory workers, 17 have brown eyes. Six of the women do not have brown eyes. How many of the 11 men have brown eyes.
(A) 10
(B) 9
(C) 8
(D) 7
(E) 4
Rationale: Total number of worker (M+W): 25
No. of men (M): 11 (Inferred fromHow many of the 11 men)
No. of women (W): 14
Total no. of workers who have brown eyes (B): 17
No. of women who do not have brown eyes: 6
Therefore, no. of women who have brown eyes: W - 6 = 14 - 6 = 8
Remaining 9 are men. (B - 8= 17 - 8= 9)
So 9 out of 11 men have brown eyes.
B
Answer: (B) 9
Question: The ratio of two numbers is 3:4 and their sum is 28. The greater of the two numbers is?
(A) 8
(B) 10
(C) 16
(D) 18
(E) 22
Rationale: 3:4
Total parts = 7
= 7 parts --> 28 (7 × 4 = 28)
= 1 part ---->4 (1 × 4 = 4)
= The greater of the two number is = 4
= 4 parts ----> 16 (4 × 4 = 16)
C
Answer: (C) 16
Question: If Q is a positive integer, which of the following must be odd?
(A) Q+1
(B) Q^2+Q
(C) Q^2+Q+1
(D) x^2−1
(E) 3x^2−3
Rationale: A. Q+1 = can be odd or even. Since O + O =E or E + O = O
B. Q^2 + Q = Q(Q+1). Since from the above derivation we already know the term Q+1 can be Odd or Even, directly substitute here. Q(ODD) = Even (When Q is Even) or Q(EVEN) = EVEN [When Q is ODD]
C. Here's the answer. Since we know the term Q^2 + Q can always take a EVEN number, EVEN + 1 = ODD
Hence C.
Answer: (C) Q^2+Q+1
Question: Set S consists of all prime numbers less than 10. If two numbers are chosen from et S at random, what is the probability that the product of these numbers will be greater than the product of the numbers which were not chosen?
(A) 1/3
(B) 2/3
(C) 1/2
(D) 7/10
(E) 4/5
Rationale: Prime integers below 10: 2, 3, 5, 7
Total outcomes: Number of ways you can choose 2 from 4 = 4C2=6pairs4C2=6pairs
No. of ways for Event: Pairs that will have products greater than product of pairs not selected i.e. (3,5), (3,7), (5,7) =3pairs=3pairs
Probability = number of ways/Total outcomes =3/6=1/2=3/6=1/2
Hence choice(C) is correct.
Answer: (C) 1/2
Question: A paint store mixes 3/4 pint of red paint and 2/3 pint of white paint to make a new paint color called Perfect Pink. How many pints of red paint would be needed to make 36 pints of Perfect Pink paint?
(A) 9
(B) 16
(C) 19
(D) 25 1/3
(E) 28 1/2
Rationale: 3/4 pint is required to make 3/4 + 2/3 = 17/12 pint of perfect pink
so 17/12 pint requires 3/4 pint of red..
1 pint will require 3/4 * 12/17=9/17..
36 pints will require 9/17 * 36= 19 pints..
C
Answer: (C) 19
Question: How many combinations of three letters taken from letters (b, b, c, c, d,d) are possible?
(A) 12
(B) 13
(C) 5
(D) 6
(E) 7
Rationale: So 3C3 for bcd - 1 choice
2 more for dd(b,c )
2 more for bb(d,c )
2 more for cc(d,b )
total 7
Ans :E
Answer: (E) 7
Question: There are 6 more women than there are men on a local co-ed softball team. If there are a total of 16 players on the team, what is the ratio of men to women?
(A) 10/16
(B) 6/16
(C) 4/16
(D) 6/10
(E) 5/11
Rationale: w = m+6
w+m = 16
m+6+m = 16
2m = 10
m = 5
w = 11
ratio:5:11
Ans: E
Answer: (E) 5/11
Question: A quantity of tea is sold at Rs. 5.75 per kilogram. The total gain by selling the tea at this rate is Rs. 60. Find the quantity of tea being sold if a profit of 15% is made on the deal.
(A) 80kg.
(B) 90kg.
(C) 70kg.
(D) 60kg.
(E) 50kg.
Rationale: say total cost price of tea is x.
then total profit at a rate of 15% is=(15x/100)
according to question,
15x/100=60
so x=400
c.p of the tea is 400.so total selling price will be=(400+60)=460
so the quantity of the tea will be=(460/5.75)=80kg.
ANSWER:A
Answer: (A) 80kg.
Question: Last year, sales at Company Dopler were 10% greater in February than in January, 5% less in March than in Feb, 5% greater in April than in March, 10% less in May than in April, and 10% greater in June than in May. In which month were sales closest to Jan?
(A) Feb
(B) April
(C) Mar
(D) May
(E) June
Rationale: Jan = $100
10% greater in February than in January ---> Feb = $110
10% less in March than in Feb ---> Mar = $99
5% greater in April than in March ---> Apr = $103.95
10% less in May than in April ---> May $93.55
10% greater in June than in May --->Jun = $102.90
Answer : C
Answer: (C) Mar
Question: A watch passes through three hands and each person gains 25%. If the third person sells it for $375, what did the first person pay for it?
(A) $184
(B) $188
(C) $192
(D) $196
(E) $200
Rationale: 1.25*1.25*1.25 * original price = 375
(5/4)^3 * original price = 375
original price = 64*375 / 125 = $192
The answer is C.
Answer: (C) $192
Question: A train 280 m long, running with a speed of 63 km/hr will pass a tree in?
(A) 17 sec
(B) 16 sec
(C) 18 sec
(D) 14 sec
(E) 12 sec
Rationale: Speed = 63 * 5/18
= 35/2 m/sec
Time taken = 280 * 2/35
= 16 sec
Answer: B
Answer: (B) 16 sec
Question: What approximate value should come in the place of question mark(?) in the following equation?
98.98 ÷ 11.03 + 7.014 × 15.99 = (?)2
(A) 131
(B) 144
(C) 12
(D) 121
(E) 11
Rationale: 98.98 ÷ 11.03 + 7.014 × 15.99 = (?)2
Suppose ? = x
Then 99 ÷ 11 + 7 × 16 + ≈ 121
(taking approximate value)
∴ x = 11
Answer E
Answer: (E) 11
Question: The value of a machine depreciates at 24% per annum. If its present value is $1,50,000, at what price should it be sold after two years such that a profit of $24,000 is made?
(A) $250640
(B) $430640
(C) $120640
(D) $110640
(E) $150640
Rationale: The value of the machine after two years = 0.76 * 0.76 * 1,50,000 = $86,640
SP such that a profit of $24,000 is made = 86,640 + 24,000 = $1,10,640
D
Answer: (D) $110640
Question: You and your friend are playing Russian Roulette. Of course, the gun is filled with fake pellets. Three bullets are placed inside three consecutive chambers. The cylinder is then spun once. It won't be spun again.
As per the rules, the gun will be passed from one person to other until a pellet is shot. If you want to win this game, would you go first or second ?
(A) 1st
(B) 3rd
(C) 4th
(D) 2nd
(E) 5th
Rationale: D
2nd
When the cylinder is spun for the first and last time, the following six outcomes are possible:
First:
First chamber is fired first. The first player loses.
Second:
Second chamber is fired first. The first player loses.
Third:
Third chamber is fired first. The first player loses.
Fourth:
Fourth chamber is fired first. The second player loses. (First shot, player 1, chamber 4 empty. Second shot player 2, chamber 5, empty. Third shot player 1, chamber 6 empty. Fourth shot player 2, chamber 1 not empty.)
Fifth:
Fifth chamber is fired first. The first player loses. (First shot, player 1, chamber 5 empty. Second shot player 2, chamber 6, empty. Third shot player 1, chamber 1 not empty.)
Sixth:
Sixth chamber is fired first. The second player loses. (First shot, player 1, chamber 6 empty. Second shot, player 2, chamber 1, not empty)
Thus, if you analyze, you will find that the second player has a 4/6 chance of winning. Therefore if you want to win the game, going second gives you better shot at it.
Answer: (D) 2nd
Question: If the first half of the English alphabet is reversed and then next portion of English alphabet is reversed so as 'A' takes the portion of 'M' and 'N' takes the portion of 'z' then which letter will be 6th to the left of 17th letter to the right of 7th leter from the left?
(A) Y
(B) V
(C) J
(D) G
(E) K
Rationale: Explanation:
6th to the left of 17th letter to the right of 7th letter from the left = 6th to the left of (17+7 =) 24th letter from the left = (24-6 =) 18th letter from the left.
Thus, we have to count from the left and we have to find out 18th letter from the left that falls into the second section of English alphabet.
Here, both the first half and the second half of the English alphabet have been reversed and we have to count from the left end, then the required letter can be found out using the formula given below. Suppose , the first and the second reversed sections of the English alphabet are and respectively.Then,
The required letter =
Therefore, The required letter = 26 + 13 + 1 - 18 = 22 = V
Answer: B
Answer: (B) V
Question: Sum of the numbers from 1 to 45 is
(A) 1789
(B) 1035
(C) 1025
(D) 1009
(E) None of these
Rationale: Explanation: Sum of first n natural numbers = 1 + 2 + 3 + ..... n = n(n+1)/2
Substitute n = 45.
So S20=45Ã—46/2=1035
Correct Option: B
Answer: (B) 1035
Question: Maxwell leaves his home and walks toward Brad's house at the same time that Brad leaves his home and runs toward Maxwell's house. If the distance between their homes is 60 kilometers, Maxwell's walking speed is 4 km/h, and Brad's running speed is 6 km/h, what is the distance traveled by Brad?
(A) 16
(B) 36
(C) 20
(D) 24
(E) 30
Rationale: Time taken = Total Distance / Relative Speed
Total Distance = 60 kms
Relative Speed (Opposite side) (As they are moving towards each other speed would be added ) = 6+ 4 = 10 kms/hr
Time taken = 60 / 10 = 6 hrs
Distance traveled by Brad = Brad's speed * time taken = 6 * 6 = 36 kms... Answer - B
Answer: (B) 36
Question: Two brother X and Y appeared for an exam. The probability of selection of X is 1/7 and that of B is 2/5. Find the probability that both of them are selected.
(A) 2/69
(B) 2/60
(C) 2/63
(D) 2/35
(E) 2/38
Rationale: Explanation:
Let A be the event that X is selected and B is the event that Y is selected.
P(A) = 1/7, P(B) = 2/5.
Let C be the event that both are selected.
P(C) = P(A) Ã— P(B) as A and B are independent events:
= (1/7) Ã— (2/5) = 2/35
Answer: D) 2/35
Answer: (D) 2/35
Question: In a division, a student took 42 as divisor instead of 36. his answer was 24 . The correct answer is-
(A) 42
(B) 32
(C) 48
(D) 28
(E) 38
Rationale: X/42 = 24.
X = 24 *42.
So correct answer would be,
(24 *42) /36 = 38.
ANSWER : E
Answer: (E) 38
Question: An woman swims downstream 81 km and upstream 36 km taking 9 hours each time; what is the speed of the current?
(A) 0.5
(B) 1.5
(C) 2.5
(D) 3.5
(E) 4.5
Rationale: 81 --- 9 DS = 9
? ---- 1
36 ---- 9 US = 4
? ---- 1 S = ?
S = (9 - 4)/2 = 2.5
Answer:C
Answer: (C) 2.5
Question: A train speeds past a pole in 15 sec and a platform 140 m long in 25 sec, its length is?
(A) 50 m
(B) 150 m
(C) 210 m
(D) 300 m
(E) None of these
Rationale: Let the length of the train be x m and its speed be y m/sec.
Then, x/y = 15 => y = x/15
(x + 140)/25 = x/15 => x = 210 m.
ANSWER:C
Answer: (C) 210 m
Question: The average of six number is 3.99. The average of two of them is 3.4, while the average of the other two is 3.85. what is the average of the remaining two number ?
(A) 4.5
(B) 4.6
(C) 4.72
(D) 4.8
(E) None of these
Rationale: solution:
Sum of the remaining two numbers = (3.99 × 6) - [(3.4 × 2) + (3.85 ×2)]
=23.94 -(6.8 + 7.7) = 23.94 - 14.5 = 9.44.
∴ Required average =9.44/2 = 4.72 Answer C
Answer: (C) 4.72
Question: 50 men can complete a work in 65 days.Five days after started the work, 20 men left the group. In how many days can the remaining work be completed?
(A) 277
(B) 268
(C) 260
(D) 276
(E) 100
Rationale: After 5 days, the following situation prevails.
50 men can complete the work in 60 days.
30 men can complete the work in ? days.
M1 D1 = M2 D2
=> 50 * 60 = 30 * D2
=> D2 = (50 * 60)/30 = 100 days.
Answer: E
Answer: (E) 100
Question: In how many ways can an answer key for a quiz be written if the quiz contains 3 true-false questions followed by 3 multiple-choice questions with 4 answer choices each, if the correct answers to all true-false questions cannot be the same?
(A) 164
(B) 224
(C) 280
(D) 384
(E) 476
Rationale: There are 2^3 = 8 possibilities for the true-false answers.
However we need to remove two cases for TTT and FFF.
There are 4*4*4 = 64 possibilities for the multiple choice questions.
The total number of possibilities is 6*64 = 384.
The answer is D.
Answer: (D) 384
Question: How many of the following numbers are divisible by 132 ?
264, 396, 462, 792, 968, 2178, 5184, 6336
(A) 4
(B) 5
(C) 6
(D) 7
(E) 8
Rationale: 132 = 4 x 3 x 11
So, if the number divisible by all the three number 4, 3 and 11, then the number is divisible by 132 also.
264 -> 11,3,4 (/)
396 -> 11,3,4 (/)
462 -> 11,3 (X)
792 -> 11,3,4 (/)
968 -> 11,4 (X)
2178 -> 11,3 (X)
5184 -> 3,4 (X)
6336 -> 11,3,4 (/)
Therefore the following numbers are divisible by 132 : 264, 396, 792 and 6336.
Required number of number = 4.
Answer:A
Answer: (A) 4
Question: Merry and Mich play a card game. In the beginning of the game they have an equal number of cards. Each player, at her turn, gives the other a third of her cards. Mich plays first, giving Merry a third of her cards. Merry plays next, and Mich follows. Then the game ends. Merry ended up with 14 more cards than Mich. How many cards did each player have originally?
(A) 60
(B) 58
(C) 56
(D) 55
(E) 54
Rationale: Game Mich Merry
Initially 54 54 assume
After game 1 36 72
After game 2 60 48
After game 3 40 68
Now Merry has 28 cards more than Mich. This option gives us exactly what number of cards they had initially.
So the answer is E
Answer: (E) 54
Question: On dividing 172 by a number, the quotient is 10 and the remainder is 2. Find the divisor.
(A) 9
(B) 11
(C) 13
(D) 15
(E) 17
Rationale: d = (D-R)/Q
= (172 - 2)/10
= 170/10 = 17
E
Answer: (E) 17
Question: 10^190 - 10^9 = Which of the following best approximates the value of the expression above?
(A) 10^170
(B) 10^180
(C) 10^160
(D) 10^181
(E) 10^190
Rationale: 10^190 - 10^9 =
Which of the following best approximates the value of the expression above?
Yes, answer 10^190 is correct. Note that we need approximate value of the given expression and as 10^(190) is much larger number than 10^(9) then 10^(9) is pretty much negligible in this case: 10^(190)-10^(9)=~10^(190).
Answer : E
Answer: (E) 10^190
Question: If 5 cars park in 5 parking place.there are 3 red colour car,1 blue and 1 green then how many ways we can arrange the cars differently
(A) 10
(B) 20
(C) 30
(D) 40
(E) 50
Rationale: total car=5
place =5
means cars are place any 5 position means its 5!=120
but 3 cars r red and 1 blue and 1 green
then its arrange 3!,1!,1!
so,
=120/6*1*1
=20
ANSWER:B
Answer: (B) 20
Question: A can contains a mixture of two liquids A and B in the ratio 7 : 5. When 9 litres of mixture are drawn off and the can is filled with B, the ratio of A and B becomes
7 : 9. How many litres of liquid A was contained by the can initially?
(A) 10
(B) 20
(C) 21
(D) 25
(E) 26
Rationale: Suppose the can initially contains 7x and 5x litres of mixtures A and B respectively
Quantity of A in mixture left
= (7x - 7/12 x 9) litres = (7x - 21/4) litres.
Quantity of B in mixture left
= (5x - 5/12 x 9) litres = (5x - 15/4) litres.
(7x - 21/4) / [(5x - 15/4)+9] = 7/9 = › 28x - 21/20x + 21 = 7/9 =› 252x - 189 = 140x + 147
=› 112x = 336 =’ x = 3.
So, the can contained 21 litres of A.
Answer C
Answer: (C) 21
Question: 40 people attend a party. 11 men are single and the rest are there with their wives. There are no children in the party. In all 22 women are present. Then the number of married men at the party is ?
(A) 5
(B) 6
(C) 7
(D) 11
(E) 9
Rationale: Total people = number of men + number of women
40 = 7 + number of married men + 22
number of married men = 40- 22-7= 11 men
ANSWER:D
Answer: (D) 11
Question: The length of a rectangle is 2 cm more than the width of the rectangle. The perimeter of the rectangle is 20 cm. Find the length and the width of the rectangle.
(A) l=2,w=9
(B) l=5,w=8
(C) l=6,w=4
(D) l=1,w=7
(E) l=2,w=3
Rationale: Let length l=x, width w=x−2and perimeter =p
∴p=2l+2w
=2x+2(x−2)
20=2x+2x−4
4x=24
x=6
l=6 cm and w=l−2=4cm
Answer is C.
Answer: (C) l=6,w=4
Question: If f(x)= 5x^2- 2x+6 and g(y)= 3y-7, then g(f(x))
(A) 82x^2-9x+38
(B) 15x^2-6x+11
(C) 58x^2-4x+58
(D) 87x^2-5x+96
(E) 98x^2-7x+94
Rationale: g(f(x))=3(5x^2-2x+6)-7
=15x^2-6x+18-7
=15x^2-6x+11
the answer is B
Answer: (B) 15x^2-6x+11
Question: Manoj borrowed Rs.3450 from Anwar at 6% p.a. simple interest for three years. He then added some more money to the borrowed sum and lent it to Ramu for the same time at 9% p.a. simple interest. If Manoj gains Rs.824.85 by way of interest on the borrowed sum as well as his own amount from the whole transaction, then what is the sum lent by him to Ramu?
(A) Rs.5625
(B) Rs.5355
(C) Rs.5365
(D) Rs.5345
(E) Rs.5395
Rationale: Let the sum lent by Manoj to Ramu be Rs.P.
Amount gained by Manoj = P. 3.9 /100 = 3450.3.6/100 = Rs.824.85
27P = 62100 = 82485
P = (82485 + 62100)/27 = 3055 + 2300 = Rs.5355
Option B
Answer: (B) Rs.5355
Question: The average age of a group of person going for picnic is 16 years. Twenty new persons with an average age of 15 years join the group on the spot due to which their average becomes 15.5 years. Find the number of persons initially going for picnic.
(A) 20
(B) 18
(C) 22
(D) 19
(E) None of the above
Rationale: Let the number of persons, initially going for Picnic = x
∴ Sum of their ages = 16x
Also, 16x+15×20/x+20 = 15.5
⇒ 0.5x = 10 ⇒ x = 20 years.
Answer A
Answer: (A) 20
Question: I spend 40 hours a week (5 days) at work and like to organize my time so that I spend an equal number of hours on the two tasks I currently have. Currently, I am spending 5 hours a day on Task 1 and 3 on Task 2. How many hours a week less do I need to spend on Task 1 in order to evenly distribute my time?
(A) 5
(B) 3
(C) 7
(D) 1
(E) 6
Rationale: 5 x 5 = 25
25 - 5 = 20
The answer is A.
Answer: (A) 5
Question: The total of the ages of Mahesh, Suresh, Ramesh is 129 years. Ten years ago, the ratio of their ages was 2:3:4. What is the present age of Mahesh?
(A) 32years
(B) 54years
(C) 42years
(D) 35years
(E) 30years
Rationale: Let ages of Mahesh, Suresh, Ramesh 10years ago be 2x,3x,4x
2x+10 + 3x+10 +4x+10 = 129
x = 11
Ramesh present age = 4*11+10 = 54 years
Answer is B
Answer: (B) 54years
Question: If the radius of a cylinder is doubled and height 5 times, what is the new volume of the cylinder divided by the old one?
(A) 8.
(B) 2.
(C) 6.
(D) 20.
(E) 10.
Rationale: let v and v' be the original and the changed volume
now
v=pir^2h
v'=pi(2r)^2(5h)
v'=20v
D) 20
Answer: (D) 20.
Question: The price of a T.V. set worth Rs. 40000 is to be paid in 20 installments of Rs. 1000 each. If the rate of interest be 6% per annum, and the first installment be paid at the time of purchase, then the value of the last installment covering the interest as well will be?
(A) 22678
(B) 26699
(C) 26788
(D) 19000
(E) 39000
Rationale: Money paid in cash = Rs. 1000
Balance payment = (40000 - 1000) = Rs. 39000
Answer: E
Answer: (E) 39000
Question: How many four-digit numbers are there such that all four digits are different and the first digit is not zero?
(A) 1504
(B) 2648
(C) 3720
(D) 5832
(E) 8105
Rationale: All four digits are different and first digit is not zero.
So first digit can be filled in 9 ways.
And, second digit can be filled in 9 ways.
And, third digit can be filled in 9 ways.
And, fourth digit can be filled in 8 ways.
Total ways = 9*9*9*8
= 5832
Hence option (D).
Answer: (D) 5832
Question: The radius of a wheel is 16.8 cm. What is the distance covered by the wheel in making 300 resolutions?
(A) 754 m
(B) 316.512 m
(C) 311.512 m
(D) 311.518 m
(E) 313.512 m
Rationale: In one resolution, the distance covered by the wheel is its own circumference. Distance covered in 300 resolutions.
= 300* 2 * 22/7 * 16.8 = 31651.2 cm
= 316.512 m
Answer:B
Answer: (B) 316.512 m