mathewhe/aqua_rat huggingface dataset:
Question: A boat with still water speed of a is traveling upstream where the streams speed is b. After covering certain distance s, the boat turns back and tries to come to the starting place. But the boat stops at 3/4th of the intended distance due to a technical fault. What is the ratio of the time taken for the return journey to that of the upstream journey.
(A) 3(a - b)/4(a + b)
(B) 4(a - b)/3(a + b)
(C) 3(a + b)/4(a - b)
(D) 4/3
(E) 4/8
Rationale: speed of boat upstream = a - b
speed of boat downstream = a + b
For upstream journey, time taken = distance / speed = s / (a - b)
During return journey, the boat had covered on 3/4th of s :
Therefore for return journey, time taken = distance / speed = (3s/4)/(a+b)
Ratio of time taken for return journey to the upstream journey = (3s/4)/(a+b)/ (s/(a - b)) = 3(a - b)/4(a + b)
ANSWER:A
Answer: (A) 3(a - b)/4(a + b)
Question: Two taps can separately fill a cistern 10 minutes and 15 minutes respectively and when the waste pipe is open, they can together fill it in 18 minutes. The waste pipe can empty the full cistern in?
(A) 5
(B) 6
(C) 7
(D) 9
(E) 1
Rationale: 1/10 + 1/15 - 1/x = 1/18
x = 9
Answer: D
Answer: (D) 9
Question: If p and q are the roots of the equation x2 - bx + c = 0, what is the equation if the roots are (pq + p + q) and (pq - p - q)?
(A) x2 - 2cx + (c2 - b2) = 0
(B) x2 - 2bx + (b2 + c2) = 0
(C) bcx2 - 2(b + c)x + c2 = 0
(D) x2 + 2bx - (c2 - b2) = 0
(E) None
Rationale: Explanatory Answer
In the given quadratic equation x2 - bx + c = 0,
The sum of the roots p + q = b --- (1)
And the product of the roots pq = c --- (2)
We have to formulate a quadratic equation whose roots are (pq + p + q) and (pq - p - q).
The sum of the two roots = pq + p +q + pq - p - q = 2pq
But from eqn (2), we know that pq = c
Therefore, the sum of the roots = 2c
The product of the roots = (pq + p + q)(pq - p - q)= (pq)2 - (p+q)2
From equation (1) and (2), we know that pq = c and p + q = b
Therefore, the product of the roots = c2 - b2
We know the sum of the roots and the product of the roots.
Therefore, the quadratic equation is x2 - (sum of the roots)x + product of the roots = 0
=> x2 - 2cx + c2 - b2 = 0
Answer A
Answer: (A) x2 - 2cx + (c2 - b2) = 0
Question: An amount of Rs. 100000 is invested in two types of shares. The first yields an interest of 9% p.a and the second, 11% p.a. If the total interest at the end of one year is 9 2/3 %, then the amount invested in each share was?
(A) 23777
(B) 35000
(C) 29977
(D) 26777
(E) 19871
Rationale: Let the sum invested at 9% be Rs. x and that invested at 11% be Rs. (100000 - x). Then,
(x * 9 * 1)/100 + [(100000 - x) * 11 * 1]/100 = (100000 * 29/3 * 1/100)
(9x + 1100000 - 11x)/100 = 29000/3 = 9700
(9x + 1100000 - 11x) = 970000
x = 65000
Sum invested at 9% = Rs. 65000
Sum invested at 11% = Rs. (100000 - 65000) = Rs. 35000.
Answer: B
Answer: (B) 35000
Question: The number of bacteria in a petri dish increased by 50 percent every 2 hours. If there were 108 million bacteria in the dish at 2: 00 p.m., at what time were there 32 million bacteria in the dish?
(A) 6: 00 p.m.
(B) 8: 00 p.m.
(C) 6: 00 a.m.
(D) 8: 00 a.m.
(E) 10: 00 a.m.
Rationale: Given:
The number of bacteria in a petri dish increased by 50 percent every 2 hours
There were 108 million bacteria in the dish at 2: 00 p.m
Since the bacteria is increasing by 50% every 2 hours, this means that the number is multiplied by 1.5 every 2 hours.
Required: At what time were there 32 million bacteria in the dish?
Assume that there were n intervals of 2 hours between 32 million and 108 million.
32 * (1.5)^n = 108
(3/2)^n = 108/32 = 27/8 = (3/2)^3
Hence n = 3 intervals.
Each interval was of 2 hours. Therefore, the number of hours = 6
Subtracting 6 hours from 2 PM, we get 8 AM as the answer.
Option D
Answer: (D) 8: 00 a.m.
Question: If a and b are positive integers and x = 9^a and y = 5^b, which of the following is a possible units digit of xy?
(A) 1
(B) 4
(C) 5
(D) 7
(E) 8
Rationale: The units digit of 9^a is either 1 or 9.
The units digit of 5^b is 5.
1*5 = 5 and 9*5 = 45.
The units digit of xy is 5.
The answer is C.
Answer: (C) 5
Question: If n is a prime number greater than 3, what is the remainder when n^2 is divided by 11?
(A) 0
(B) 1
(C) 2
(D) 3
(E) 5
Rationale: There are several algebraic ways to solve this question including the one under the spoiler. But the easiest way is as follows:since we can not have two correct answersjust pick a prime greater than 3, square it and see what would be the remainder upon division of it by 11.
n=5 --> n^2=25 --> remainder upon division 25 by 11 is 3.
Answer: D.
Answer: (D) 3
Question: A train,130 metres long travels at a speed of 45 km/hr crosses a bridge in 30 seconds. What is the length of the bridge?
(A) 210
(B) 225
(C) 235
(D) 245
(E) 260
Rationale: Speed =45 km/hr=45×5/18 m/s =12.5 m/s Distance travelled = (Speed x Time)
Distance travelled = 12.5×30=375 m
length of the bridge = 375-130 = 245 m
Answer: D
Answer: (D) 245
Question: Mike is 50% less efficient than Alice. How much time will they, working together, take to complete a job which Alice alone could have done in 15 days?
(A) 5 days
(B) 10 days
(C) 9 days
(D) 18 days
(E) 15 days
Rationale: Ratio of times taken by Alice and Mike = 100 : 150 = 2 : 3.
Suppose Mike takes x days to do the work.
Then, 2 : 3 : : 15 : x â‡’ x = (15Ã—3)/2 â‡’ x = 45â„2
Aliceâ€™s 1 dayâ€™s work = 1â„15; Mikeâ€™s 1 days work = 2â„45
(Alice + Mike)â€™s 1 dayâ€™s work = (1â„15 + 2â„45) = 1â„9
âˆ´ Alice and Mike together can complete the job in 9 days.
Answer C
Answer: (C) 9 days
Question: A company organized a recruiting process for 3 vacant positions of assistant manager for its product launches. The company's efforts yielded 11 eligible candidates. How many sets of 3 candidates can the company choose to fill the 3 assistant manager positions?
(A)  2,060
(B)  1,320
(C)  165
(D)  315
(E)  220
Rationale: 11*10*9/3*2*1 = 165
C
Answer: (C)  165
Question: A man gets a simple interest of Rs.500 on a certain principal at the rate of 5% p.a in two years. Find the compound interest the man will get on twice the principal in two years at the same rate?
(A) 256.29
(B) 256.27
(C) 256.23
(D) 256.21
(E) 256.25
Rationale: Let the principal be Rs.P
S.I at 5% p.a in 8 years on Rs.P = Rs.500
(P)(8)(5)/100 = 500
P = 1250
C.I on Rs.2P i.e., Rs.2500 at 5% p.a in two years
=2500{ [1 + 5/100]2 - 1} = 2500{ 212 - 202 /202}
= 2500/400(441 - 400)
= 25/4(41) = 1025/4 = Rs.256.25
Answer:E
Answer: (E) 256.25
Question: In a race with 30 runners where 5 trophies will be given to the top 7 runners (the trophies are distinct: first place, second place, etc), how many ways can this be done?
(A) 8^8 ways
(B) 8^9 ways
(C) 7^5 ways
(D) 8^7 ways
(E) 8^6 ways
Rationale: 7 people can be prized with 5 distinct prizes in 7^5 ways
ANSWER:C
Answer: (C) 7^5 ways
Question: Fresh grapes contain 90% by weight while dried grapes contain 20% water by weight. What is the weight of dry grapes available from 40 kg of fresh grapes?
(A) 5 kg
(B) 2.4 kg
(C) 2.5 kg
(D) 10 kg
(E) none of these
Rationale: The weight of non-water in 20 kg of fresh grapes (which is 100-90=10% of whole weight) will be the same as the weight of non-water in x kg of dried grapes (which is 100-20=80% of whole weight), so 40âˆ—0.1=xâˆ—0.8--> x=5
Answer: A
Answer: (A) 5 kg
Question: A can do half the work in one day where as B can do it full. B can also do half the work of C in one day. Ratio in their efficiency will be?
(A) 1:2:6
(B) 1:2:9
(C) 1:2:5
(D) 1:2:4
(E) 1:3:4
Rationale: WC of A: B = 1:2
B: C = 1:2
---------------------
A: B: C = 1:2:4
Answer: D
Answer: (D) 1:2:4
Question: How many integers C are prime numbers in the range 200 < C < 220?
(A)  1
(B)  2
(C)  3
(D)  4
(E)  5
Rationale: My friend, every single odd number greater than can be written either as 4C+1 or as 4C+3. If you divide any odd number by 4, you will get a remainder of either 1 or 3. That's not a rule unique to prime numbers at all.
The 6C+1 or 6C-1 rule is basically every odd number that is not divisible by three, so it narrows the search a little.
Here's how I thought about the problem. First, eliminate all the even numbers and the odd multiples of 5 in that range. That leaves us with:
{201, 203, 207, 209, 211, 213, 217, 219}
Eliminate the four multiples of 3. Notice that 21 is a multiple of 3, so 210 is also a multiple of 3. If we add or subtract 3 or 9, we get more multiples of three. When we eliminate those, we are left with.
{203, 209, 211, 217}
Now, notice that a cool thing about this range is that 210 is also a multiple 7 (again, because 21 is a multiple of 7). This means that
210 - 7 = 203
210 + 7 = 217
Those two numbers are also multiples of 7, so eliminate them from the list. Now, we are left with
{209, 211}.
We've already checked all the prime numbers less than 10, so we know that neither of these numbers is divisible by anything less than 10. We have to check 11 now. We know that 22 is a multiple of 11, so 220 is also a multiple of 11. This means that
220 - 11 = 209
is also a multiple of 11. We can eliminate this from the list also.
That leaves us with just 211. There's no zero option in the question, so this must be a prime number.
Answer = (A)
Answer: (A)  1
Question: In order to obtain an income of Rs. 650 from 10% stock at Rs. 96, one must make an investment of
(A) Rs. 3100
(B) Rs. 6500
(C) Rs. 6240
(D) Rs. 9600
(E) Rs. 9800
Rationale: Explanation :
Market Value = Rs. 96.
Required Income = Rs. 650.
Here face value is not given. Take face value as Rs.100 if it is not given in the question
To obtain Rs.10 (ie,10% of the face value 100), investment = Rs.96
To obtain Rs.650, investment = 96/10×650=6240
Answer : Option C
Answer: (C) Rs. 6240
Question: The product of the ages of Syam and Sunil is 240. If twice the age of Sunil is more than Syam's age by 4 years, what is Sunil's age?
(A) 8
(B) 9
(C) 10
(D) 11
(E) 12
Rationale: we can solve the quadratic equation by factorization as,
x(x−2)=120⇒x2−2x−120=0⇒(x−12)(x+10)=0⇒x=12 or −10
Since x is age and cannot be negative, x=12
Answer is E.
Answer: (E) 12
Question: The edge of a cube is 6a cm. Find its surface?
(A) 116a2 cm2
(B) 126a2 cm2
(C) 256a2 cm2
(D) 150a2 cm2
(E) 216a2 cm2
Rationale: 6a2 = 6 * 6a * 6a = 216a2
Answer:E
Answer: (E) 216a2 cm2
Question: 252 can be expressed as a product of primes as:
(A) 2 x 2 x 3 x 3 x 7
(B) 2 x 2 x 3 x 3 x 8
(C) 2 x 2 x 3 x 3 x 6
(D) 2 x 2 x 3 x 3 x 1
(E) 2 x 2 x 3 x 3 x 2
Rationale: Clearly, 252 = 2 x 2 x 3 x 3 x 7.
Answer: A
Answer: (A) 2 x 2 x 3 x 3 x 7
Question: If x > 0, x/5 + x/25 is what percent of x?
(A) 6%
(B) 24%
(C) 37 1/2%
(D) 60%
(E) 75 %
Rationale: Just plug and chug. Since the question asks for percents, pick 100. (but any number will do.)
100/5 + 100/25= 20+4 =24
24 is 24% of 100=B
Answer: (B) 24%
Question: One card is drawn from a pack of 52 cards. What is the probability that the card drawn is a queen of club or a king of heart?
(A) 2/7
(B) 1/26
(C) 3/17
(D) 4/19
(E) 5/27
Rationale: Out of 52 cards there will be one queen of club and one king of heart are there
Total 2
probability = 2/52 = 1/26
Answer is B
Answer: (B) 1/26
Question: In how many different number of ways 5 men and 3 women can sit on a shopa which can accommodate persons?
(A) 42
(B) 230
(C) 240
(D) 250
(E) 260
Rationale: 7p2 = 7 Ã— 6 = 42
A
Answer: (A) 42
Question: Right now, the ratio between the ages of Sandy and Molly is 4:3. After 6 years, Sandy’s age will be 34 years. What is Molly's age right now?
(A) 12
(B) 15
(C) 18
(D) 21
(E) 24
Rationale: Now, Sandy is 34 - 6 = 28
Molly's age is (3/4) * 28 = 21
The answer is D.
Answer: (D) 21
Question: What is the length of the longest pole which can be kept in a room 12 m long, 5 m broad and 3 m high?
(A) 7
(B) 9
(C) 11
(D) 13.34
(E) None
Rationale: Explanation:
d2 = 122 + 52 + 32 = 13.34
D)
Answer: (D) 13.34
Question: an article with cost price of 245 is sold at 34% profit. what is the selling price?
(A) 328
(B) 320
(C) 300
(D) 207
(E) 310
Rationale: sp=1.34*245=328
ANSWER:A
Answer: (A) 328
Question: For any positive integer n, the sum of the first n positive integers equals [n(n+1)]/2.
What is the sum of all the even integers between 99 and 181?
(A) 4360
(B) 4890
(C) 5280
(D) 5740
(E) 6320
Rationale: 100 + 102 +...+ 180 = 41*100 + (2+4...+80) = 41*100 + 2(1+2+...+40) =
41*100 + 2(40)(41)/2 = 140*41 = 5740
The answer is D.
Answer: (D) 5740
Question: Find the roots of the quadratic equation: x2 + 2x - 15 = 0?
(A) -5, 3
(B) 3, 5
(C) -3, 5
(D) -3, -5
(E) 5, 2
Rationale: Explanation:
x2 + 5x - 3x - 15 = 0
x(x + 5) - 3(x + 5) = 0
(x - 3)(x + 5) = 0
=> x = 3 or x = -5.
ANSWER IS A
Answer: (A) -5, 3
Question: What is the probability of creating a three digit number with exactly two consecutive primes as digits?
(A) 3/100
(B) 9/250
(C) 9/125
(D) 21/250
(E) 51/500
Rationale: For numbers between 100- 199
For 1 st digit we just have 1 option
For second digit we have 3 options (2,3,5) and for all these 3 options we have one option ( i.e for 2 we have 3, for 3 we have 5 and for 5 we have 7)
Hence for numbers between 100-199 we have in total 3 options
Now for numbers between 200-299
For 1st digit again we have only one option but now for 2nd we have either 1 option i.e 3 or we have 8 options i.e when 3rd digit is 3 ( so when 3rd digit is 3 we have 8 options for 2nd digit.)
Hence in total 1* 2* 8 ( 2 because we 2 places for placing 3 ) = 16
Now, similarly for numbers starting from 300-399 we will have same 32 options and same goes for other numbers
So now using POE we can clearly see the total numbers will be more than 21 for sure,
Hence E
Answer: (E) 51/500
Question: Which of the following is not a perfect square of an integer?
(A) 64
(B) 529
(C) 441
(D) 450
(E) 484
Rationale: A. 8*8=64
B.23*23=529
C.21*21=441
D.22*22=484
Here 450 is not a square of an integer
so answer is D
Answer: (D) 450
Question: A man has Rs. 560 in the denominations of one-rupee notes, five-rupee notes and ten-rupee notes. The number of notes of each denomination is equal. What is the total number of notes that he has ?
(A) 33
(B) 105
(C) 37
(D) 90
(E) 28
Rationale: Let number of notes of each denomination be x.
Then x + 5x + 10x = 560
⇒ 16x = 560
∴ x = 35.
Hence, total number of notes = 3x = 105
Answer:B
Answer: (B) 105
Question: Pipe A can fill a tank in 16 minutes and pipe B cam empty it in 24 minutes. If both the pipes are opened together after how many minutes should pipe B be closed, so that the tank is filled in 30 minutes?
(A) 76
(B) 87
(C) 76
(D) 56
(E) 21
Rationale: Let the pipe B be closed after x minutes.
30/16 - x/24 = 1 => x/24 = 30/16 - 1 = 14/16
=> x = 14/16 * 24 = 21.
Answer: E
Answer: (E) 21
Question: How many multiples of 3 are there between 81 and 358?
(A) 94
(B) 95
(C) 93
(D) 97
(E) 98
Rationale: 3 * 27 = 81
3 * 119 = 357
Total multiples of 3 = (119 - 27) + 1
= 93
Answer is C.
Answer: (C) 93
Question: At what price must an article costing Rs.47.50 be marked in order that after deducting 5% from the list price. It may be sold at a profit of 25% on the cost price?
(A) 62.5
(B) 69.5
(C) 67.5
(D) 62.5
(E) 22.5
Rationale: CP = 47.50
SP = 47.50*(125/100) = 59.375
MP*(95/100) = 59.375
MP = 62.5
Answer:A
Answer: (A) 62.5
Question: Population is 21000. Population increases by 10% every year, then the population after 3 years is?
(A) 26630
(B) 27951
(C) 36621
(D) 26621
(E) 26821
Rationale: population after 1st year = 21000*10/100 = 2100 ===> 21000+2100 = 23100
population after 2nd year = 23100*10/100 = 2310 ===> 23100+2310 = 25410
population after 3rd year = 254100*10/100 = 2541 ===> 25410+2541 = 27951
ANSWER:B
Answer: (B) 27951
Question: If Leo gains 10 pounds, he will weigh 50% more than his sister Kendra. Currently their combined weight is 150 pounds. What is Leo's current weight?
(A) 80
(B) 86
(C) 92
(D) 98
(E) 104
Rationale: L+K = 150 and so K = 150-L
L+10 = 1.5K = 1.5(150-L)
2.5L = 215
L = 86
The answer is B.
Answer: (B) 86
Question: A man can row 6 kmph in still water. When the river is running at 1.2 kmph, it takes him 1 hour to row to a place and black. How far is the place?
(A) 2.89
(B) 2.88
(C) 2.86
(D) 2.82
(E) 2.81
Rationale: M = 6
S = 1.2
DS = 6 + 1.2 = 7.2
US = 6 - 1.2 = 4.8
x/7.2 + x/4.8 = 1
x = 2.88.Answer: B
Answer: (B) 2.88
Question: A rectangular field is to be fenced on three sides leaving a side of 30 feet uncovered.If the area of the field is 600 sq.ft, how many feet of fencing will be required ?
(A) 70feet
(B) 52feet
(C) 32feet
(D) 12feet
(E) 55feet
Rationale: Explanation:
We are given with length and area, so we can find the breadth.
as Length * Breadth = Area
=> 30 * Breadth = 600
=> Breadth = 20 feet
Area to be fenced = 2B + L = 2*20 + 30
= 70 feet
Answer: Option A
Answer: (A) 70feet
Question: Beth received 1/10 of the votes cast in a certain election. What fraction of the other votes cast would she have needed in order to have received 1/2 of the votes cast?
(A) 1/5
(B) 2/7
(C) 3/10
(D) 7/20
(E) 4/9
Rationale: Let the total votes be 100. Beth received 10 votes, other votes 100-10=90. In order to have received 1/2 of the votes she needed 50 votes so 40 more, which is 40/90=4/9 of the other votes.
Answer: E
Answer: (E) 4/9
Question: Three numbers which are co-prime to each other are such that the product of the first two is 551 and that of the last two is 1073. The sum of the three numbers is:
(A) 80
(B) 85
(C) 90
(D) 95
(E) 100
Rationale: Let three numbers are a, b and c.
Given:
The product of a and b is 551.
The product of b and c is 1073.
b is common in both the product
b = H.C.F. of 551 and 1073 = 29;
a = (551/29) = 19.
c = (1073/289) = 37.
The sum of three number is 85.
answer :B
Answer: (B) 85
Question: A jar contains 12 marbles consisting of an equal number of red, green, and blue marbles. Three marbles are removed from the jar and discarded. What is the probability that only two colors will remain in the jar after the Three marbles have been removed?
(A) 1/495
(B) 1/165
(C) 1/81
(D) 11/31
(E) 3/220
Rationale: Jar contains {3-red, 3-green, 3-blue} marbles. We are asked to find the probability that after removing 3 marbles only 2 colours remain in the jar, i.e., the probability of removing EITHER red, OR green, OR blue.
Sample space = 12C3 = 220.
Probability of choosing 3 red = 3C3/12C3 = 1/220.
Probability of choosing 3 green = 3C3/12C3 = 1/220.
Probability of choosing 3 blue = 3C3/12C3 = 1/220.
Required probability = 1+1+1/220 = 3/220 Ans (E).
Answer: (E) 3/220
Question: x and y are integers. x + y < 11 , and x > 6. What is the smallest possible value of x - y ?
(A) 1
(B) 2
(C) 4
(D) -2
(E) -4
Rationale: Because x & y are integers, the two equations can be simply written as :
x+y<= 10 --- eq. 1
x>= 7 ---- eq. 2
For smallest value of x-y, x has to be the smallest whereas y has to be the largest.
From the above eq. 2, smallest value of x = 7
Plugging it in eq. 1: 7+y<=10, or y<=3
Therefore, largest value of y=3 & smallest values of x=7
x-y = 7 - 3 = 4
Answer is C
Answer: (C) 4
Question: The product of two numbers is 120 and the sum of their squares is 289. Find the sum?
(A) 23
(B) 20
(C) 15
(D) 26
(E) 28
Rationale: Nos A and B
AB=120 and A2+B2=289
(A+B)2=529
A+B=Root(529)=23
ANSWER A
Answer: (A) 23
Question: In a certain state, gasoline stations compute the price per gallon p, in dollars, charged at the pump by adding a 7 percent sales tax to the dealer's price per gallon d, in dollars, and then adding a gasoline tax of $0.18 per gallon. Which of the following gives the dealer's price per gallon d in terms of the price per gallon p charged at the pump?
(A) d = p/1.07 - 0.18
(B) d = p-0.25
(C) d= (p-0.18)/1.07
(D) d = p/1.25
(E) d = (p-0.07)/1.18
Rationale: Let dealers price (d) be 1. so adding 7% to dealers price is d+ 7% of d. i.e. 1 + 7% of 1 which is1 + 0.07. then add 0.18 to the value.
Now 1.07 + 0.18. this is now 1.25. you have the gasoline stations price (p) as 1.25 dollars.
Now sub 1.25 in the options to know which option gave you d = 1. d must equal 1 because you earlier picked 1 as the value of d in the question.
PS: always remember to start from E upwards.
Answer : C
Answer: (C) d= (p-0.18)/1.07
Question: Each of the three people individually can complete a certain job in 3, 5, and 6 hours, respectively. What is the lowest fraction of the job that can be done in 1 hour by 2 of the people working together at their respective rates?
(A) 4/15
(B) 7/30
(C) 11/30
(D) 7/18
(E) 5/18
Rationale: The two slowest people work at rates of 1/5 and 1/6 of the job per hour.
The sum of these rates is 1/5 + 1/6 = 11/30 of the job per hour.
The answer is C.
Answer: (C) 11/30
Question: Machine–A produces 40% of the total output and Machine-B produces 60% of the total output. An average of nine units out of a thousand goods manufactured by Machine-A and one unit of 300 units produced by Machine-B prove to be defective. What is the probability that a unit chosen at random from the total daily output of the factory is defective?
(A) a. 0.56
(B) b. 0.056
(C) c. 0.0056
(D) d. 0.00056
(E) e. 0.000056
Rationale: Let total Production be 10000 units....
A produces 4000 units and 36 units are defective
B produces 6000 units and 20 units are defective
So, Out of total 10,000 units 56 units are defective...
So the required probability = 56/10000 => 0.0056
Answer will be (C)
Answer: (C) c. 0.0056
Question: Find large number from below question The difference of two numbers is 1515. On dividing the larger number by the smaller, we get 16 as quotient and the 15 as remainder
(A) 1209
(B) 1615
(C) 1245
(D) 1300
(E) 1635
Rationale: Let the smaller number be x. Then larger number = (x + 1515).
x + 1515 = 16x + 15
15x = 1500
x = 100
Large number = 100+1515 = 1615
Answer : B
Answer: (B) 1615
Question: A man can row his boat with the stream at 6 km/h and against the stream in 4 km/h. The man's rate is?
(A) 1 kmph
(B) 5 kmph
(C) 2 kmph
(D) 9 kmph
(E) 4 kmph
Rationale: DS = 6
US = 4
S = ?
S = (6 - 4)/2
= 1 kmph
Answer: A
Answer: (A) 1 kmph
Question: Bob invested one half of his savings in a bond that paid simple interest for 2 years and received $450 as interest. He invested the remaining in a bond that paid compound interest (compounded annually) for the same 2 years at the same rate of interest and received $605 as interest. What was the annual rate of interest?
(A)  68%
(B)  10%
(C)  12%
(D)  15%
(E)  20%
Rationale: First divide $450/2years to get 225$/yr non-compounding interest.
Next, subtract from the total compound after 2 years to see the interest gained in the second year. This can be done because the same amount has been invested in both accounts and the interest gained for the first year will be the same. So, $605-$225= $380.
To find the difference in interest gained, $380-$225= $155 increase in interest after the first year through compounding.
From this information we can set up the equation $225 * X% = $155=68% giving us answer choice A.
Answer: (A)  68%
Question: Suppose 8 monkeys take 8 minutes to eat 8 bananas. How many monkeys would it take to eat 48 bananas in 48 minutes
(A) 5 monkeys
(B) 6 monkeys
(C) 7 monkeys
(D) 8 monkeys
(E) 9 monkeys
Rationale: 8 monkeys take 8 minutes to eat 8 bananas means each monkey takes 8 min for 1 banana
in 48 mins one monkey can eat 6 bananas....which means that 8 monkeys can eat 48 bananas in 48 minutes
so answer is 8 monkeys
ANSWER:D
Answer: (D) 8 monkeys
Question: How many odd 4-digit positive integers E that are multiples of 5 can be formed without using the digit 3?
(A) 648
(B) 729
(C) 900
(D) 1296
(E) 3240
Rationale: I choose A.
Possible n° of 1st digit: 8 (0 can't be the first number, or else it wouldn't have 4 digits. 3 is exlcuded)
Possible n° of 2nd digit: 9 (3 is excluded)
Possible n° of 3rd digit: 9 (3 is excluded)
Possible n° of 4th digit: 1 (a number is a multiple of 5 if it ends in 5 or 0, here we are asked for the odd numbers, hence the last digit can't be 0)
So, E=8*9*9*1=648 (A)
Answer: (A) 648
Question: The average age of a husband and his wife was 23 years at the time of their marriage. After five years they have a one-year old child. The average age of the family now is
(A) 12 years
(B) 27 years
(C) 19 years
(D) 18 years
(E) 37 years
Rationale: Sum of the present ages of husband, wife and child
= (23 * 2 + 5 * 2) + 1 = 57 years.
Required average = (57/3) = 19 years.
Answer: C
Answer: (C) 19 years