mathewhe/aqua_rat huggingface dataset:
Question: One day a car rental agency rented 3/4 of its cars, including 4/5 of its cars with CD players. If 3/5 of its cars have CD players, what percent of the cars that were not rented had CD players?
(A) 23/40
(B) 17/30
(C) 12/25
(D) 7/15
(E) 3/10
Rationale: The cars with CD players which were not rented is (1/5)(3/5) = 3/25 of all the cars.
The cars which were not rented is 1/4 of all the cars.
The percent of non-rented cars which had CD players is (3/25) / (1/4) = 12/25
The answer is C.
Answer: (C) 12/25
Question: The population of a town increased from 1,25,000 to 1,50,000 in a decade. The average percent increase of population per year is :
(A) 4.37%
(B) 2%
(C) 6%
(D) 8.75%
(E) None of these
Rationale: Solution
Increase in 10 year= (150000 - 125000) = 25000.
Increase% =( 25000/125000x 100 )% = 20%
âˆ´ Required average = ( 20/10 )% = 2%
Answer B
Answer: (B) 2%
Question: Arun spent six lucky days in Las Vegas. On his first day he won a net amount of only $20, but on each of the following days, the daily net amount he won grew by d dollars. If Arun won a total net amount of $1620 during his stay in Las Vegas, how much did he win on the last day?
(A) 330
(B) 500
(C) 520
(D) 540
(E) 620
Rationale: I drew a diagram:
1 - $20
2 -
3 -
4 - $320
5 -
6 -
Total: $1,620
Between 1 and 6 are 5 days where he won $1,600. This means he averaged $320 per day (1600/5). You can put $320 by 4 because it's the middle number. Now you just find the two points betwenn $20 and $320 (320-20 = 300 / 3 = 100). So each day, he earned $100 more. This means on day 6, Arun earned$520. Answer choice C.
Answer: (C) 520
Question: At the wholesale store you can buy an 8-pack of hot dogs for $1.55, a 20-pack for $3.05, and a 250-pack for $22.95. What is the greatest number of hot dogs you can buy at this store with $208?
(A) 1,108
(B) 2,100
(C) 2,108
(D) 2,160
(E) 2,256
Rationale: I think it should be D.
I can buy 8 250-pack for Rs 22.95*8 = $183.60
Now, I can buy 8 20-pack for 3.05*8 = $24.40
Now, I am left with only $1.15. I cannot but anything with this.
Hence Total Hotdogs = 250*8 + 20*5 = 2160
Answer: (D) 2,160
Question: In a covering a certain distance, the speeds of A and B are in the ratio of 3:4. A takes 30 minutes more than B to reach the destination. The time taken by A to reach the destination is?
(A) 8 hrs
(B) 9 hrs
(C) 2 hrs
(D) 2 hrs
(E) 9 hrs
Rationale: Ratio of speeds = 3:4
Ratio of times taken = 4:3
Suppose A takes 4x hrs and B takes 3x hrs to reach the destination.
Then, 4x - 3x = 30/60 => x = 1/2
Time taken by A = 4x hrs = 4 * 1/2 = 2 hrs.
Answer:C
Answer: (C) 2 hrs
Question: Today my car meter reads as 63736 kms. I notes that this is a palindrome. How many minimum kms i need to travel so my car meter find another palindrom.
(A) 100 kms
(B) 115 kms
(C) 110 kms
(D) 200 kms
(E) 120 kms
Rationale: D
200 kms
63736+200 = 63536 , a palindrome
Answer: (D) 200 kms
Question: If Dave throws down a set dice twice, calculate the probability that one die would be an even while the other would be odd?
(A) 1/6
(B) 1/4
(C) 1/2
(D) 1
(E) 1/3
Rationale: The number of exhaustive outcomes for each throw is 36.
For both throws is= 64
Let E be the event of getting an even number on one die and an odd number on the other for each throw.
The event of getting either both even or both odd for each throw is = 18/36 = 1/2
The event of getting either both even or both odd for both throws is = 36/64 = 1/2
P(E) = 1 - 1/2
= 1/2.
Answer:c
Answer: (C) 1/2
Question: There are 7 people and 4chairs. In how many ways people can occupy the chairs?
(A) 760
(B) 840
(C) 560
(D) 740
(E) 800
Rationale: total people = 7
total chairs = 4
1st chair can be occupy in 7ways
2nd chair can be occupy in 6ways
3rd chair can be occupy in 5ways
4th chair can be occupy in 4ways
total number of ways = 7*6*5*4 = 840 ways
correct option is B
Answer: (B) 840
Question: There are 12 pieces of radioactive metal Q that look identical. 11 of the pieces give the same radiation count when measured, the 12th piece is a counterfeit and gives a different radiation level, which may be more or less than the other 11. We are given a radiation scale, which can take 2 sets of samples and compare their added up radiation levels to tell us if the sums are the same or if different, which set has the higher level of radiation. What is the minimum number of comparisons we need on this scale to identify the counterfeit sample and to also determine whether it has more or less radiation than the other samples ?
(A) 2
(B) 3
(C) 4
(D) 5
(E) 6
Rationale: First of all if you are down to just 3 pieces and you know that if the offending piece is less or more active, then it takes exactly 1 measurement to find out the offending piece. So you know you have to reduce the problem to three.
Now when you are down to either A or B after measurement 1, you need the next measurement to (a) reduce the problem set to 3 and (b) to know whether anser is more or less. Now you cannot compare a group of 4 to 4, as in the best case it will only reduce the problem to 4 elements which is not good enough.
If you have to choose a set of 3 to compare, you cannot pick any 3 on the same side from the same set (A or B) because if you do this, a quick check will show you that in every choice there is a case where you can only get down to 4 elements. Eg. If you weighed {1,2,3} v/s {5,9,10} and they were equal you're problem would only reduce to {4,6,7,8}
The easiest way to solve this then is to compare 3 to 3, and make sure each side has elements from both AB such that whatever the measurement outcome in the worst case the problem reduces to 3 elements only. Which is why the sets {1,5,9} and {2,6,7} OR {A,B,C}{A,B,B}. The extra element from C is just taken to make the problem symmetric so to say, we have 8 elements and we make it 9, to compose 3 sets of 3 each.=B
Answer: (B) 3
Question: John started a business, investing Rs.18000. After 3 months and 4 months respectively, Rose and Tom joined him with capitals of 12000 and 9000. At the end of the year the total profit was Rs.4290. What is the difference between Rose ’s and Tom ’s share in the profit?
(A) s.340
(B) s.362
(C) s.370
(D) s.382
(E) s.390
Rationale: John : Rose : Tom
Ratio of their investments = 18000 × 12 : 12000 × 9 : 9000 × 8
= 6 : 3: 2
The difference between Rose’s and Tom’s share = 1 share
:.i.e. = Rs. 4290 × 1/11 = Rs.390.
E)
Answer: (E) s.390
Question: A leak in the bottom of a tank can empty the full tank in 7 hours. An inlet pipe fills water at the rate of 6 litres a minute. When the tank is full, the inlet is opened and due to the leak, the tank is empty in 12 hours. How many litres does the cistern hold?
(A) 7580
(B) 7960
(C) 8290
(D) 6048
(E) None
Rationale: Solution
Work done by the inlet in 1 hour	= (1/7 - 1/12)
= 5/84
Work done by the inlet in 1 min.	= (5/84 × 1/60)
= 0.000992
Volume of 0.000992 part = 6 litres.
Therefore, Volume of whole	= ((1/0.000992)×6)
‹=› 6048 litres.
Answer D
Answer: (D) 6048
Question: I bought two books; for Rs.480. I sold one at a loss of 15% and other at a gain of 19% and then I found each book was sold at the same price. Find the cost of the book sold at a loss?
(A) 118
(B) 280
(C) 886
(D) 667
(E) 198
Rationale: x*(85/100) = (480 - x)119/100
x = 280
Answer: B
Answer: (B) 280
Question: The average age of three boys is 15 years and their ages are in proportion 3:5:7. What is the age in years of the youngest boy?
(A) 6
(B) 9
(C) 6
(D) 4
(E) 1
Rationale: 3x + 5x + 7x = 45
x =3
3x = 9
Answer:B
Answer: (B) 9
Question: 10, 18, x, 14
The median of the list of positive integers above is 12. Which of the following could be the average (arithmetic mean) of the list?
(A) 12
(B) 5.5
(C) 6.25
(D) 7
(E) 7.5
Rationale: GivenThe median of the list of positive integers above is 12
So arranging the numbers from lowest to highest, avg of 2 middle terms needs to be 12
so the sequence will be x 10 14 18
Lets say x = 6, which gives us mean = sum/4 = 12
A is correct
Answer: (A) 12
Question: If 20 liters of chemical X are added to 80 liters of a mixture that is 20% chemical X and 80% chemical Y, then what percentage of the resulting mixture is chemical X?
(A) 30%
(B) 33%
(C) 36%
(D) 39%
(E) 42%
Rationale: The amount of chemical X in the solution is 20 +0.2(80) = 36 liters.
36 liters / 100 liters = 36%
The answer is C.
Answer: (C) 36%
Question: Albert and Bob are painting rooms at constant, but different rates. Albert takes 1 hour longer than Bob to paint n rooms. Working side by side, they can paint a total of 3n/2 rooms in 4/3 hours. How many hours would it take Albert to paint 3n rooms by himself?
(A) 6
(B) 9
(C) 11
(D) D.13
(E) 15
Rationale: rate of bob to paint n rooms is n/T(bob)
rate of Albert to paint n rooms is n/T(albert).
albert paints the room 1 hour slower than bob, so T (albert) = T(bob) -1
Together they paint the 3n/5 rooms in 4/3 hours. Rate is equal to work over time
Therefore
n/x + n/x-1 = (3n/5)/(4/3) =
n/x + n/x-1 = 9n/20. Fastest way for me is to think how would make the denominator 20. 4*5 = 20 and it fits x and x-1 or you can solve the quadratic
4n/20 + 5n/20 = 9n/20. Therefore you know it takes Albert 5 hours to paint n room, since Albert's rate is n/5.
2*3 = 3n
6 = 3n.
Answer is A
Answer: (A) 6
Question: If y > 0, (7y)/20 + (3y)/10 is what percent of y?
(A) 40%
(B) 50%
(C) 65%
(D) 70%
(E) 80%
Rationale: can be reduced to 7y/20+6y/20 =13y/20=65%
Answer C
Answer: (C) 65%
Question: If 65 percent of a class answered the first question on a certain test correctly, 50 percent answered the second question on the test correctly, and 20 percent answered neither of the questions correctly, what percent answered both correctly?
(A) 25%
(B) 30%
(C) 35%
(D) 40%
(E) 45%
Rationale: 65% answered the first question correctly and 20% answered neither correctly.
Then 15% missed the first question but answered the second question correctly.
Then the percent who answered both correctly is 50% - 15% = 35%.
The answer is C.
Answer: (C) 35%
Question: A fill pipe can fill 1/2 of cistern in 30 minutes. In how many minutes, it can fill 1/2 of the cistern?
(A) 15 min
(B) 20 min
(C) 25 min
(D) 30 min
(E) 35 min
Rationale: Required time = 30*2*1/2 = 30 minutes
Answer is D
Answer: (D) 30 min
Question: Siddharth wants to borrow Rs.6000 at rate of interest 6% p.a. at S.I and lend the same amount at C.I at same rate of interest for two years. What would be his income in the above transaction?
(A) Rs.21.60
(B) Rs.21.29
(C) Rs.22.29
(D) Rs.21.26
(E) Rs.21.12
Rationale: Amount of money Siddharth borrowed at S.I at 6% p.a. for two years = Rs.6,000
He lend the same amount for C.I at 6% p.a. for two years.
=> Siddharth's income = C.I - S.I
= p[1 + r/ 100]n - p - pnr/100
= p{ [1 + r/ 100]2 - 1 - nr/100
= 6,000{ [1 + 6/100]2 - 1 - 12/100}
= 6,000 {(1.06)2- 1 - 0.12} = 6,000(1.1236 - 1 - 0.12)
= 6,000 (0.0036) = 6 * 3.6 = Rs.21.60
Answer: A
Answer: (A) Rs.21.60
Question: A bag contains 6 black and 8 white balls. One ball is drawn at random. What is the probability that the ball drawn is white?
(A) 4/9
(B) 4/7
(C) 4/6
(D) 4/1
(E) 4/2
Rationale: Explanation:
Let number of balls = (6 + 8) = 14.
Number of white balls = 8.
P (drawing a white ball) = 8 /14 = 4/7.
Answer: B) 4/7
Answer: (B) 4/7
Question: A package contains 8 black and 6 white balls. One ball is drawn at random. What is the probability that the ball drawn is white?
(A) 3/5
(B) 3/7
(C) 6/8
(D) 7/9
(E) 1/3
Rationale: Let number of balls = (8+6) = 14.
Number of white balls = 6.
P (drawing a white ball) =	6/14=3/7
B
Answer: (B) 3/7
Question: If a number is 20% more than the another, how much % is the smaller number less than the first ?
(A) 12(1/3)%
(B) 16(2/3)%
(C) 16(1/3)%
(D) 16(4/3)%
(E) none of these
Rationale: Take a number 100,
Then the other number is 120
% the smaller number is less than the first = [(20/(120)) x 100]% = 16(2/3)%.
ANSWER:B
Answer: (B) 16(2/3)%
Question: If daily wages of a man is double to that of a woman, how many men should work for 25 days to earn Rs.14400? Given that wages for 40 women for 30 days are Rs.21600.
(A) 12
(B) 14
(C) 16
(D) 18
(E) 20
Rationale: Explanation :
Wages of 1 woman for 1 day = 21600/40×30
Wages of 1 man for 1 day = 21600×2/40×30
Wages of 1 man for 25 days = 21600×2×25/40×30
Number of men = 14400/(21600×2×25/40×30)=144/(216×50/40×30)=144/9=16
Answer : Option C
Answer: (C) 16
Question: For all integers a and b, a%b = (a + b)(a - b). If 6%x = 11, then which of the following could be a value of x?
(A) -4
(B) -3
(C) 2
(D) 5
(E) 6
Rationale: 6%x = (6+x)(6-x)
36-x^2 = 11
x^2 = 25
x=-5,5
Ans: D
Answer: (D) 5
Question: What percentage of numbers from 1 to 70 have squares that end in the digit 1?
(A) 1
(B) 14
(C) 17
(D) 20
(E) None
Rationale: Solution
Clearly, the numbers which have 1 or 9 in the unit's digit, have squares that end in the digit 1. Such numbers from 1 to 70 are 1, 9, 11, 19, 21, 29, 31, 39, 41, 49, 51, 59, 61, 69.
Number of such numbers = 14.
Required percentage = [14 / 70 x 100]%
= 20%.
Answer D
Answer: (D) 20
Question: A certain list of 200 test scores has an average (arithmetic mean) of 84 and a standard deviation of d, where d is positive. Which of the following two test scores, when added to the list, must result in a list of 202 test scores with a standard deviation less than d ?
(A)  84 and 84
(B)  80 and 85
(C)  80 and 90
(D)  85 and 85
(E)  85 and 90
Rationale: The standard deviation of a set shows how much variation there is from the mean, how widespread a given set is. So, a low standard deviation indicates that the data points tend to be very close to the mean, whereas high standard deviation indicates that the data are spread out over a large range of values.
So when we add numbers, which are far from the mean we are stretching the set making SD bigger and when we add numbers which are close to the mean we are shrinking the set making SD smaller.
According to the aboveadding two numbers which are closest to the mean will shrink the set most, thus decreasing SD by the greatest amount.
Closest to the mean are 84 and 84 (actually these numbers equal to the mean) thus adding them will definitely shrink the set, thus decreasing SD most.
Answer: A
Answer: (A)  84 and 84
Question: The average weight of 16 men in a committe is 50.25 kg and that of the remaining 8 men are45.15 kg. Find the average weights of all the men in the committe?
(A) 42
(B) 48.55
(C) 49.2
(D) 50.1
(E) 51.2
Rationale: Required average
= 50.25 x 16 + 45.15 x 8
16 + 8
= 804 + 361.20
24
=	1165.20
24
= 48.55
B
Answer: (B) 48.55
Question: The cash difference between the selling prices of an article at a profit of 4% and 6% is Rs. 3. The ratio of the two selling prices is:
(A) 51:52
(B) 52:53
(C) 51:53
(D) 52:55
(E) 52:56
Rationale: Let C.P. of the article be Rs. x.
Then, required ratio = 104% of x / 106% of x
= 104/106 = 52/53 = 52:53
ANSWER:B
Answer: (B) 52:53
Question: Suresh started a business, investing Rs.18000. After 3 months and 4 months respectively, Rohan and Sudhir joined him with capitals of 12000 and 9000. At the end of the year the total profit was Rs.3982. What is the difference between Rohan’s and Sudhir’s share in the profit?
(A) Rs.362
(B) Rs.383
(C) Rs.398
(D) Rs.399
(E) Rs.400
Rationale: Suresh : Rohan : Sudhir
Ratio of their investments = 18000 × 12 : 12000 × 9 : 9000 × 8
= 6 : 3: 2
The difference between Rohan’s and Sudhir’s share = 1 share
:.i.e. = Rs. 3982 × 1/11 = Rs.362.
A)
Answer: (A) Rs.362
Question: Raj invested an amount of Rs.17400 for two years. Find the rate of compound interest that will fetch him an amount of Rs.1783.50 at the end of two years?
(A) 8% p.a.
(B) 6% p.a.
(C) 4% p.a.
(D) 5% p.a.
(E) None of these
Rationale: Let the rate of interest be R% p.a.
17400[1 + R/100]2 = 17400 + 1783.50
[1 + R/100]2 = (17400 + 1783.50)/17400
= 1 + 1025/10000 = 1 + 41/400
= 441/400 = [21/20]2
[1 + R/100] = 21/20
R/100 = 1/20
Therefore R = 5
ANSWER:D
Answer: (D) 5% p.a.
Question: 3 buffaloes eat as much as 4 cows or 2 oxen. At a farm there are 15 buffaloes, 8 oxen and 24 cows. The fodder for these cattle is available for 24days. If 8 more cows & 9 more buffaloes are brought in, how long will the fodder last?
(A) 16
(B) 17
(C) 19
(D) 18
(E) 24
Rationale: Sol. 2 oxen = 3 buffaloes = 4 cows 8 oxen = 16 cows and 15 buffaloes = 20 cows 16 cows + 20 cows + 24 cows = 60 cows Since fodder is available for 60 cows for 24 days
So fodder will be available for (60 + 8 + 12) = 80 cows c 24x60 .0 .
for-^—=18 days.
D
Answer: (D) 18
Question: A and B invests Rs.8000 and Rs.9000 in a business. After 4 months, A withdraws half of his capital and 2 months later, B withdraws one-third of his capital. In what ratio should they share the profits at the end of the year?
(A) 32:46
(B) 32:98
(C) 32:45
(D) 32:27
(E) 32:42
Rationale: A : B
(8000*4)+(4000*8) : (9000*6)+(6000*6)
64000 : 90000
32 : 45
Answer:C
Answer: (C) 32:45
Question: A shopkeeper sold an article at $100 with 20% profit. Then find its cost price?
(A) $120
(B) $100
(C) $91
(D) $83
(E) $69
Rationale: cost price = selling price *100/(100+profit)
C.P. = 100*100/120 = $83(approximately)
Answer is D
Answer: (D) $83
Question: In a two digit number, the digit in the units place is five times the digit in ten's place and sum of the digits is equal to six. What is the number?
(A) 15
(B) 28
(C) 32
(D) 36
(E) 38
Rationale: Solution
Let the ten digits be x. Then,units digit=5x
Therefore x +5x = 6
‹=›6x = 6
‹=›x= 1
So, ten's digit = 1, unit's digit = 5.
Hence, the required number is 15.
Answer A
Answer: (A) 15
Question: Half the people on a bus get off at each stop after the first, and no one gets on after the first stop. If only one person gets off at stop number 9, how many people got on at the first stop?
(A) 128
(B) 64
(C) 32
(D) 16
(E) 256
Rationale: 7 - > 1
6 - > 2
5 - > 4
4 - > 8
3 - > 16
2 - > 32
1 - > 64
because people get off after the first stop
=> the formula will be : 2^(n-1) where n is the stop number
in this case n = 9
=> 2^(9-1) = 2^8 = 256
=> answer is E
Answer: (E) 256
Question: The length of a rectangular floor is more than its breadth by 200%. If Rs. 240 is required to paint the floor at the rate of Rs. 3 per sq m, then what would be the length of the floor?
(A) 65
(B) 44
(C) 18
(D) 15.49
(E) 14
Rationale: Let the length and the breadth of the floor be l m and b m respectively.
l = b + 200% of b = l + 2b = 3b
Area of the floor = 240/3 = 80 sq m
l b = 80 i.e., l * l/3 = 240
l2 = 240 => l =15.49
Answer:D
Answer: (D) 15.49
Question: A rectangular plot measuring 90 metres by 50 metres is to be enclosed by wire fencing. If the poles of the fence are kept 5 metres apart, how many poles will be needed ?
(A) 55
(B) 56
(C) 57
(D) 58
(E) None of these
Rationale: Solution
Perimeter of the plot = 2(90 + 50) = 280 m.
∴ Number of poles = [280/5] =56m Answer B
Answer: (B) 56
Question: How many ways can 8 friends be arranged around a circular dinner table?
(A) A)16
(B) B)48
(C) C)96
(D) D)5040
(E) E)720
Rationale: The number of arrangements of n distinct objects in a row is given by n!n!.
The number of arrangements of n distinct objects in a circle is given by (n−1)!(n−1)!.
The difference between placement in a row and that in a circle is following: if we shift all object by one position, we will get different arrangement in a row but the same relative arrangement in a circle. So, for the number of circular arrangements of n objects we have:
n!n=(n−1)!n!n=(n−1)!.
So, the answer is (8 - 1)! = 7! = 5040.
Answer: D.
Answer: (D) D)5040
Question: The owner of a local jewelry store hired two watchmen to guard his diamonds, but a thief still got in and stole some diamonds. On the way out, the thief met each watchman, one at a time. To each he gave 1/2 of the diamonds he had then, and 2 more besides. He escaped with two diamonds. How many did he steal originally?
(A) 20
(B) 36
(C) 25
(D) None of these
(E) Cannot be determined
Rationale: Explanation :
Since, thief escaped with 2 diamonds,
Before 2nd watchman, he had ( 2 + 2 ) x 2 = 8 diamonds.
Before 1st watchman, he had ( 8 + 2 ) x 2 = 20 diamonds.
Answer : A
Answer: (A) 20
Question: Find the fraction which has the same ratio to 2/13 that 5/34 has to 7/48.
(A) 240/1587
(B) 240/1545
(C) 240/1547
(D) 240/1542
(E) 240/1512
Rationale: P : 2/13 = 5/34 : 7/48
As the product of the means is equal to the product of the extremes.
P*7/48 = 2/13 * 5/34
P*7/48 = 10/442
P = 480/3094 => P = 240/1547
Answer: C
Answer: (C) 240/1547
Question: If 6 women can color 180 m long cloth in 3 days, then 5 women can color 200 m long cloth in?
(A) 6 days
(B) 5 days
(C) 4 days
(D) 2 days
(E) 3 days
Rationale: The length of cloth painted by one woman in one day = 180/ 6× 3 = 10 m
No. of days required to paint 200 m cloth by 5 women = 200/ 5 × 10 = 4 days
Answer : C
Answer: (C) 4 days
Question: If a*b denotes the greatest common divisor of a and b, then ((12*15)*(18*24)) = ?
(A)  24
(B)  12
(C)  6
(D)  4
(E)  3
Rationale: The greatest common divisor of 12 and 15 is 3. Hence 12*15 = 3 (note that * here denotes the function not multiplication).
The greatest common divisor of 18 and 24 is 6. Hence 18*24 = 6.
Hence ((12*16)*(18*24)) = 3*6.
The greatest common divisor of 3 and 6 is 3.
Answer; E.
Answer: (E)  3
Question: The cost of 4 bags and 12 purses is Rs.620, what is the cost of 10 bags and 30 purses?
(A) Rs.3600
(B) Rs.3500
(C) Rs.3800
(D) Rs.3900
(E) Rs.1550
Rationale: Explanation:
Cost of 4 bags + 12 purses = Rs.620
Multiply each term by 5/2, we get,
Cost of 10 bags + 30 purses = Rs.1550.
Answer: Option E
Answer: (E) Rs.1550
Question: X men can do a work in 120 days. If there were 20 men less, the work would have taken 60 days more. What is the value of X?
(A) 60
(B) 99
(C) 77
(D) 55
(E) 22
Rationale: We have M1 D1 = M2 D2
120X = (X - 20)180
=> 2X = (X - 20) 3 => 2X = 3X - 60
=> X = 60
Answer:a
Answer: (A) 60
Question: P and Q invested in a business. They earned some profit which they divided in the ratio of 2:3. If P invested Rs.50, 000, the amount invested by Q is:
(A) Rs. 65,000
(B) Rs. 70,000
(C) Rs. 75,000
(D) Rs. 90,000
(E) Rs. 60,000
Rationale: Q invested = 50000/2*3 = 75000
Answer : C
Answer: (C) Rs. 75,000
Question: If x and y are positive integers, and x^3*y^4 = 10125, which of the following is the value of xy?
(A) 6
(B) 10
(C) 14
(D) 15
(E) 21
Rationale: 10125 = 3*3375 = 3^2*1125 = 3^3*375 = 3^4*125 = 3^4*5^3
xy = 3*5 = 15
The answer is D.
Answer: (D) 15
Question: Three of the following four are alike in a certain way and hence form a group. Which is the one that does not belong to that group?
(A) Shirt
(B) Shoe
(C) Ring
(D) Cobbler
(E) FRR
Rationale: Explanation:
Cobbler is human being while all others are used by human beings.
Answer: D
Answer: (D) Cobbler
Question: In a race of 1000 m, A can beat by 100 m, in a race of 800m, B can beat C by 100m. By how many meters will A beat C in a race of 600 m?
(A) 927.5 m
(B) 127.5 m
(C) 167.5 m
(D) 128.5 m
(E) 127.1 m
Rationale: When A runs 1000 m, B runs 900 m and when B runs 800 m, C runs 700 m.
When B runs 900 m, distance that C runs = (900 * 700)/800 = 6300/8 = 787.5 m.
In a race of 1000 m, A beats C by (1000 - 787.5) = 212.5 m to C.
In a race of 600 m, the number of meters by which A beats C = (600 * 212.5)/1000 = 127.5 m.
Answer:B
Answer: (B) 127.5 m
Question: 'a' and 'b' are positive integers such that their LCM is 20 and their HCF is 1. What is the difference between the minimum and maximum possible values of 'a + b'?
(A) 0
(B) -24
(C) -32
(D) -20
(E) -12
Rationale: possible values of a and b can be 5,4; 4,5 (which are same for a+b) and 1,20; 20,1 (same result for a+b)
so 9-21 = -12. ans E.
Answer: (E) -12
Question: What is the sum of the first 22 natural numbers (starting from 1)?
(A) 223
(B) 233
(C) 243
(D) 253
(E) 263
Rationale: The sum of n natural numbers = n*(n+1) / 2 = 22*23/2 = 253
The answer is D.
Answer: (D) 253