mathewhe/aqua_rat huggingface dataset:
Question: If 2 tables and 3 chairs cost Rs, 3500 and 3 tables and 2 chairs cost Rs. 4000, then how much does a table cost ?
(A) 2377
(B) 1000
(C) 2778
(D) 766
(E) 18811
Rationale: Let the cost of a table and that of a chair be Rs. x and Rs, y respectively.
Then, 2x + 3y = 3500 ...(i)
and 3x + 2y = 4000 .....(ii)
solving (i) and (ii) we get x = 1000, y = 500
Answer: B) 1000
Answer: (B) 1000
Question: A type A machine can complete a job in 5 hours and a type B machine can complete the job in 7 hours. How many hours will it take 2 type A machines and 3 type B machines working together and independently to complete the job?
(A) 1/5
(B) 29/35
(C) 5/6
(D) 35/29
(E) 35/12
Rationale: A needs 5 hours to complete the job
2A need 5/2 hours to complete the job,
similarly 3B need 7/3 hours to complete the job
Lets consider 2A and 3B as single entity (X, Y)
so
1/X + 1/Y = 1/Z Z is the time to complete the job if working together.
1/(2/5) + 1/(7/3) =1/Z
2/5 + 3/7 =1/Z
29/35 = 1/Z
Z = 35/29
so if 2A and 3 B working together, they would need 35/29 hours to complete the job.
ANSWER:D
Answer: (D) 35/29
Question: A boat ma goes 2km against the current of the stream in 1 hr and goes 1 km along the current in 10 min. how long will it take to go 5 km in stationary water
(A) 40 min
(B) 1hr
(C) 1hr 15 min
(D) 1hr 30 min
(E) 4 hr
Rationale: rate down stream=(1/10*60)km/hr=6km/hr
rate up stream=2km/hr
speed still water =1/2(6+2)=4km/hr
required time =(5/4)=1 1/4=1hr 15 min
Answer(C)
Answer: (C) 1hr 15 min
Question: A bowl was filled with 10 ounces of water, and 0.012 ounce of the water evaporated each day during a 50-day period. What percent of the original amount of water evaporated during this period?
(A) 0.004%
(B) 0.04%
(C) 0.40%
(D) 6%
(E) 40%
Rationale: Total amount of water evaporated each day during a 50-day period = .012 * 50
=.012 * 100/2
= 1.2/2
= .6
percent of the original amount of water evaporated during this period = (.6/10) * 100%
= 6 %
Answer D
Answer: (D) 6%
Question: By selling 12 toffees for a rupee, a man loses 20%. How many for a rupee should be sell to get a gain of 20%?
(A) 5
(B) 8
(C) 10
(D) 15
(E) 20
Rationale: Explanation:
Let S.P. of 12 toffees be Rs. x.
Then, 80:1 = 120:x or x = 120/180 = 3/2
For Rs. 3/2, toffees sold = 12.
For Re. 1, toffees sold = 12 * 2/3 = 8
ANSWER IS B
Answer: (B) 8
Question: If John invested $ 1 at 6 percent interest compounded annually, the total value of the investment, in dollars, at the end of 4 years would be
(A) (1.5)^4
(B) 4(1.5)
(C) (1.05)^4
(D) 1 + (0.05)^4
(E) (1.06)^4
Rationale: In this prompt, the answer choices show that we don't actually have to calculate anything - we just need to 'format' the calculation correctly. We're told that the interest is COMPOUNDED ANNUALLY, so we need the Compound Interest Formula, with a Principal of $1, an R of 5% (which would 'translate' as .05) and a T of 4. We'd have....
E
Answer: (E) (1.06)^4
Question: 2, -6, 18, -54, 162, (...)
(A) 486
(B) 422
(C) -422
(D) -468
(E) -486
Rationale: 2 × -3 = -6
-6 × -3 = 18
18 × -3 = -54
-54 × -3 = 162
162 × -3 = -486
Answer is E.
Answer: (E) -486
Question: A trader bought a car at 20% discount on its original price. He sold it at a 40% increase on the price he bought it. What percent of profit did he make on the original price?
(A) 12%
(B) 19%
(C) 15%
(D) 14%
(E) 22%
Rationale: Original price = 100
CP = 80
S = 80*(140/100) = 112
100 - 112 = 12%
Answer:A
Answer: (A) 12%
Question: A man can row his boat with the stream at 22 km/h and against the stream in 10 km/h. The man's rate is?
(A) 1 kmph
(B) 6 kmph
(C) 7 kmph
(D) 4 kmph
(E) 9 kmph
Rationale: Explanation:
DS = 22
US = 10
S = ?
S = (22 - 10)/2 =6 kmph
Answer: B
Answer: (B) 6 kmph
Question: Every year an amount increases by 1/8th of itself. How much will it be after two years if its present value is Rs.2880?
(A) 8100
(B) 3388
(C) 7767
(D) 2009
(E) 3645
Rationale: 2880* 9/8 * 9/8
= 3645
Answer: E
Answer: (E) 3645
Question: Rahim travels 4 Kms in 15 minutes and another 4 Kms in 5 mins. Deepak travels at the average speed of Rahim. Then what could be the distance covered by him in 50 minutes:
(A) 10.m.
(B) 12 km.
(C) 20 km.
(D) 13.5km.
(E) 15.5km.
Rationale: Distence=8kms,time=20mins;
the ditence covered by him in 50mins=50*8/20=20km
ANSWER:C
Answer: (C) 20 km.
Question: If the positive integer x is a multiple of 3 and the positive integer y is a multiple of 3, then xy must be a multiple of which of the following?
I. 3
II. 12
III. 9
(A) II only
(B) I and III only
(C) I and II only
(D) II and III only
(E) I, II, and III
Rationale: x=3a
y=3b
xy=9ab
where a,b are integers
Hence , xy will always be divisible by 3,9 .
B is the answer.
Answer: (B) I and III only
Question: A man buys a cycle for Rs. 800 and sells it at a loss of 15%. What is the selling price of the cycle?
(A) s. 1090
(B) s. 1160
(C) s. 680
(D) s. 520
(E) s. 700
Rationale: S.P. = 85% of Rs. 800 = Rs.85/100x 800 = Rs. 680
ANSWER :C
Answer: (C) s. 680
Question: If n divided by 7 has a remainder of 2, what is the remainder when 5 times n is divided by 7?
(A) 1
(B) 2
(C) 3
(D) 5
(E) 6
Rationale: As per question => N=7P+2 for some integer p
hence 5N => 35Q + 10 => remainder =>10 for some integer Q
Alternatively => N=2 > 5N=> 10 => 10 divided by 7 will leave a remainder 3
hence C
Answer: (C) 3
Question: If the simple interest on a sum of money for 2 years at 5% per annum is Rs.50, what is the compound interest on the same at the same rate and for the same time?
(A) Rs.51.25
(B) Rs.52
(C) Rs.54.25
(D) Rs.60
(E) None
Rationale: Solution
Sum	=Rs.(50 x 100/2x5)
= Rs. 500.
Amount	=[Rs.(500 x(1+5/100)²]
= Rs(500x21/20x21/20).
=Rs. 551.25
C.I	= Rs. (551.25 - 500)
= Rs. 51.25
Answer A
Answer: (A) Rs.51.25
Question: Find the product of the local value and absolute value of 6 in 564823
(A) 8000
(B) 16000
(C) 12000
(D) 18000
(E) 360000
Rationale: Explanation:
Place value = Local value
Face value = Absolute value
The place value of 6 in 564823 is 6 x 10000 = 60000
The face value of 6 in 564823 is nothing but 6.
=> 60000 x 6 = 360,000
Answer: Option E
Answer: (E) 360000
Question: In how much time will a train of length 130 m, moving at 36 kmph cross an electric pole?
(A) sec
(B) sec
(C) sec
(D) sec
(E) sec
Rationale: Convert kmph to mps. 36 kmph = 36 * 5/18 = 10 mps.
The distance to be covered is equal to the length of the train.
Required time t = d/s = 130/10 = 13 sec.
Answer:D
Answer: (D) sec
Question: The original price of a certain TV set is discounted by s percent, and the reduced price is then discounted by 2s percent. If P is the original price of the TV Set, which of the following represents the price of the television set after the two successive discounts?
(A) P(1 - 0.03x + 0.02x^2)
(B) P(1 - 0.03s + 0.0002s^2)
(C) P(1 - 0.03x + 0.002x^2)
(D) P(1 - 2x^2)
(E) P(1 - 3x + 2x^2)
Rationale: Youcansolve this problem with number plugging.
Say the original price was $10 and s=50. Then after the first reduction the price would become $5 and after the second reduction of 2*50=100% the rprice would become $0.
Now, since P is not zero, then the expression in the brackets must be zero for s=50. Only answer choice B works.
Answer: B.
On this problem - number pluggin is not giving me the answer.. I initially used s = 10, then 2s = 20 and P = 100. Answer should after both consecutive discounts = 72. I plug in the respective values and I keep getting 68. Can you double check my math.
100 (1-0.03(10) + 0.0002 (10)^2)
100 (1-0.3 + 0.0002 (100))
100 (0.7 + 0.02)
100 (0.68) = 68????
double check my math. Am I missing something? I also plugged in your numbers and still did not get zero as final answer with choice B..
Answer: (B) P(1 - 0.03s + 0.0002s^2)
Question: A, B and C play a cricket match. The ratio of the runs scored by them in the match is A:B = 1:3 and B:C = 1:5. If the total runs scored by all of them are 95, the runs scored by C are?
(A) 20.23
(B) 20.13
(C) 75
(D) 20.93
(E) 10.93
Rationale: A:B = 1:3
B:C = 1:5
A:B:C = 1:3:15
15/19 * 95 = 75
ANSWER:C
Answer: (C) 75
Question: There are 15 stamps from which two stamps will be selected. Tom has five stamps which are same as five of the ten stamps to be selected. What is the probability that two stamps selected will not be one of the stamps that Tom has?
(A) 3/7
(B) 8/15
(C) 6/17
(D) 5/18
(E) 7/15
Rationale: the highlighted portion is NOT clear and poorly written, But I believe you mean that Tom has five stamps of the 15 from which two are being selected..
so we have ONLY 10 which can be selected..
P=10/15∗9/14=3/7
ANSWER:A
Answer: (A) 3/7
Question: During the first two weeks of June, the total rainfall in Springdale was 40 inches. If the rainfall during the second week was 1.5 times the rainfall during the first week, what was the rainfall in inches during the second week of June?
(A) 15
(B) 18
(C) 21
(D) 24
(E) 27
Rationale: Let x be the rainfall in the first week. Then 1.5x was the rainfall in the second week.
2.5x = 40
x = 16
The rainfall during the second week was 1.5 * 16 = 24 inches
The answer is D.
Answer: (D) 24
Question: On selling 17 balls at Rs. 720, there is a loss equal to the cost price of 5 balls. The cost price of a ball is:
(A) Rs. 45
(B) Rs. 50
(C) Rs. 55
(D) Rs. 60
(E) Rs. 60
Rationale: (C.P. of 17 balls) - (S.P. of 17 balls) = (C.P. of 5 balls)
C.P. of 12 balls = S.P. of 17 balls = Rs.720.
C.P. of 1 ball = Rs.720/12	= Rs. 60.
Answer: Option D
Answer: (D) Rs. 60
Question: A sock drawer contains 3 socks, each one a different solid color. The colors of the socks are red, orange and violet. If a person reaches into the drawer and pulls out two socks, how many different color combinations are possible in the selected pair of socks?
(A) 12
(B) 15
(C) 21
(D) 3
(E) 42
Rationale: Since the order in which we select the socks does not matter , we can use combinations.
We can select 2 socks from 3 socks in 3C2 ways.
3C2 = 3
Answer : D
Answer: (D) 3
Question: A shopkeeper buys two articles for Rs.1000 each and then sells them, making 60% profit on the first article and 60% loss on second article. Find the net profit or loss percent?
(A) 200
(B) 278
(C) 282
(D) 202
(E) 600
Rationale: Profit on first article = 60% of 1000 = 600.
This is equal to the loss he makes on the second article. That, is he makes neither profit nor loss.
Answer: E
Answer: (E) 600
Question: A train 360 m long is running at a speed of 45 km/hr. In what time will it pass a bridge 265 m long?
(A) 50
(B) 99
(C) 88
(D) 77
(E) 21
Rationale: :
Speed = 45 * 5/18 = 25/2 m/sec
Total distance covered = 360 + 265 = 625 m
Required time = 625 * 2/25 = 50 sec
Answer:A
Answer: (A) 50
Question: -20 , -16 , -12 , -8 ....
In the sequence above, each term after the first is 3 greater than the preceding term. Which of the following could not be a term in the sequence?
(A) 0
(B) 200
(C) 441
(D) 663
(E) 762
Rationale: Ans : B
Since 762 is not divisible by 3 , all the other options are divisible by 3
Answer: (B) 200
Question: If x and y are integers such that |y + 3| ≤ 3 and 2y – 3x + 6 = 0, what is the least possible value T of the product xy?
(A) 	-12
(B) 	-3
(C) 	0
(D) 	2
(E) 	None of the above
Rationale: How to deal with inequalities involving absolute values? First example shows us the so callednumber case
In this case we have |y + 3| ≤ 3 which is generalized |something| ≤ some number. First we solve as if there were no absolute value brackets:
y + 3 ≤ 3
y ≤ 0
So y is 0 or negative
Second scenario - remove the absolute value brackets. Put a negative sign around the other side of the inequality,ANDflip the sign:
y + 3 >= -3
y >= -6
Therefore we have a possible range for y: -6=<y<=0
Ok, so far so good, we're half way through. What about x?
Here's the formula: 2y – 3x + 6 = 0, rewrite it as 2y + 6 = 3x.
You can say that 2y + 6 is a multiple of 3 (=3x). So all values which must be integer must also satisfy this constraint. I'm just saying that, so it's easier to evaluate all the possible numbers (-6, -3, 0). If you plug in y = 0, x will be 2 and xy = 0 as the lowest possible value T.
Hence, Answer Choice C is the one to go.
Answer: (C) 	0
Question: In a certain alphabet, 8 letters contain a dot and a straight line. 24 letters contain a straight line but do not contain a dot. If that alphabet has 40 letters, all of which contain either a dot or a straight line or both, how many letters contain a dot but do not contain a straight line?
(A) 4
(B) 8
(C) 14
(D) 20
(E) 28
Rationale: We are told that all of the letters contain either a dot or a straight line or both, which implies that there are no letters without a dot and a line (no line/no dot box = 0).
First we find the total # of letters with lines: 8 +24 = 32;
Next, we find the total # of letters without line: 40 - 32= 8;
Finally, we find the # of letters that contain a dot but do not contain a straight line:8- 0 = 8.
B
Answer: (B) 8
Question: A man invests Rs. 6,000 at the rate of 5% per annum. How much more should he invest at the rate of 8%, so that he can earn a total of 6% per annum?
(A) Rs. 1200
(B) Rs. 1300
(C) Rs. 1500
(D) Rs. 3000
(E) None of these
Rationale: Explanation :
Interest on Rs.6000 at 5% per annum = ( 6000 × 5 × 1) / 100 = Rs. 300
Let his additional investment at 8% = x
Interest on Rs.x at 8% per annum = ( x × 8 × 1 ) / 100 = 2x/25.
To earn 6% per annum for the total, interest = (6000 + x) × 6 × 1/100.
=> 300 + 2x/25 = (6000 + x) × 6 × 1/100.
=> 30000 + 8x = (6000 + x) × 6.
=> 30000 + 8x = 36000 + 6x.
=> 2x=6000.
=> x=3000.
Answer : D
Answer: (D) Rs. 3000
Question: When a certain number X is divided by 63, the remainder is 11. What is the remainder when X is divided by 9?
(A) 2
(B) 3
(C) 4
(D) 5
(E) 6
Rationale: When a certain number X is divided by 63, the remainder is 11. What is the remainder when X is divided by 9?
Putting a value say x = 11 we get remainder as 11 when divided by 63.
When 11 divided by 9 we get 2 as remainder.
A is the answer.
Answer: (A) 2
Question: Three pipes of same capacity can fill a tank in 8 hours. If there are only two pipes of same capacity, the tank can be filled in.
(A) 17 hours
(B) 12 hours
(C) 16 hours
(D) 24 hours
(E) None of these
Rationale: Explanation:
The part of the tank filled by three pipes in one hour = 1/8
=> The part of the tank filled by two pipes in 1 hour = 2/3 * 1/8 = 1/12.
The tank can be filled in 12 hours.
ANSWER IS B
Answer: (B) 12 hours
Question: The ratio between the present ages of P and Q is 6:7. If Q is 4 years old than P, what will be the ratio of the ages of P and Q after 4 years?
(A) 7:5
(B) 7:0
(C) 7:3
(D) 7:2
(E) 7:8
Rationale: Let P's age and Q's age be 6x and 7x years respectively.
Then, 7x - 6x = 4 => x = 4
Required ratio = (6x + 4) : (7x + 4)
28 : 32 = 7:8.Answer: E
Answer: (E) 7:8
Question: Three unbiased coins are tossed. What is the probability of getting at most two heads?
(A) 3/4
(B) 1/4
(C) 3/8
(D) 7/8
(E) 5/8
Rationale: Explanation:
Here S = {TTT, TTH, THT, HTT, THH, HTH, HHT, HHH}
Let E = event of getting at most two heads.
Then E = {TTT, TTH, THT, HTT, THH, HTH, HHT}.
P(E) =n(E)/n(S)= 7/8	.
ANSWER : D
Answer: (D) 7/8
Question: Two numbers are in the ratio 3:5. If 9 be subtracted from each, they are in the ratio of 9:17. The first number is:
(A) 36
(B) 77
(C) 88
(D) 55
(E) 221
Rationale: (3x-9):(5x-9) = 9:17
x = 12 => 3x = 36
Answer: A
Answer: (A) 36
Question: How many 4-digit numbers (ABCD) can be formed such that |A – D| = 2?
(A) 2,000
(B) 1,900
(C) 1,800
(D) 1,600
(E) 1,500
Rationale: Digit A can be filled in 9 ways (excluding 0)
Digit B can be filled in 10 ways
Digit C can be filled in 10 ways
Digit D can be filled in 2 ways (because of modulus A-D )
The answer will be 9*10*10*2 = 1800
Ans C
Answer: (C) 1,800
Question: The time taken by a man to row his boat upstream is twice the time taken by him to row the same distance downstream. If the speed of the boat in still water is 45 kmph, find the speed of the stream?
(A) 15
(B) 88
(C) 14
(D) 12
(E) 17
Rationale: The ratio of the times taken is 2:1.
The ratio of the speed of the boat in still water to the speed of the stream = (2+1)/(2-1) = 3/1 = 3:1
Speed of the stream = 45/3 = 15 kmph.
Answer:A
Answer: (A) 15
Question: Village X has a population of 68000, which is decreasing at the rate of 1200 per year. Village Y has a population of 42000, which is increasing at the rate of 800 per year .in how many years will the population of the two villages be equal?
(A) 13
(B) 15
(C) 16
(D) 12
(E) 11
Rationale: Let the population of two villages be equal after p years
Then,68000-1200p=42000+800p
2000p=26000
p=13
Answer is A.
Answer: (A) 13
Question: Shweta buys a product at 25% discount rate. At what % over the cost price should she sell the product to make an overall 25% profit over the listed price?
(A) 66.67%
(B) 66.69%
(C) 66.63%
(D) 66.64%
(E) 66.61%
Rationale: Let the listed price of the product be x
Hence, at 25% discount rate the Cost Price will become: 3x/4
Now to make an overall profit of 25% over listed price:
SP = CP+(25/100)CP
=> SP = x+x/4
=>SP = 5x/4
=>Selling Price over Cost price: (5x/4)-(3x/4)
=>x/2
=>%Selling price over Cost price: (x/2)/(3x/4)*100
=>
ANSWER: A
Answer: (A) 66.67%
Question: If each year the population of the country grows by 10%, how many years will elapse before the population of the country doubles?
(A) 3
(B) 4
(C) 5
(D) 7
(E) 8
Rationale: Till Year 2000, population is 100 .
Year 2001: Population becomes 110 ............. 1 Year elapsed
Year 2002: Population becomes 121 ............. 2 Year elapsed
Year 2003: Population becomes>133 ............. 3 Year elapsed
Year 2004: Population becomes> 146 .................. 4 year elapsed
Year 2005: Population becomes> 160 .................. 5 year elapsed
Year 2006: Population becomes> 176 .................. 6 year elapsed
Year 2007: Population becomes> 193 .................. 7 year elapsed
Year 2008: Population > 200 .................. 8 year elapsed
Answer:E
Answer: (E) 8
Question: The ratio of the present ages of P and Q is 3:4. 5 years ago, the ratio of their ages was 5:7. Find the their present ages?
(A) 30,40
(B) 25,30
(C) 50,60
(D) 20,40
(E) 10,20
Rationale: Answer: Option A
Their present ages be 3X and 4X.
5 years age, the ratio of their ages was 5:7, then (3X - 5):(4X - 5) = 5:7
X = 35 - 25 => X = 10.
Their present ages are: 30, 40.
Answer: (A) 30,40
Question: The number of cars present at a particular time was measured at 2,999 different locations on Tuesday and on Wednesday. The number of locations that had more cars on Wednesday was 10% higher than the number of locations that had more cars on Tuesday. How many of the locations had more cars on Tuesday?
(A) 1,428
(B) 1,633
(C) 1,860
(D) 2,460
(E) 2,829
Rationale: The question states that all these 2,999 locations were measured twice, once on each day.
It also breaks the 2,999 into two groups, the higher-on-Tuesday locations and the higher-on-Wednesday locations, which we can call T and W.
Therefore, we can write two equations:
For each of the first and second day count of locations, T + W = 2999
But, for the second day count, W = 1.10 T
i.e. for Second day count, T + 1.10T = 2999
i.e. 2.10 T = 2999
i.e. T = 1428
A
Answer: (A) 1,428
Question: On dividing a certain number by 234, we get 43 as remainder. If the same number is divided by 13, what will be the remainder?
(A) 6
(B) 9
(C) 4
(D) 7
(E) 8
Rationale: Description :
Solution : suppose that on dividing the given number by 234,
we get quotient=x and remainder= 43
then, number= 234*x+43----> (1).
=> (13*18x)+(13*3)+4
=> 13*(18x+3)+4.
So, the number when divided by 13 gives remainder=4.
Answer :(C)
Answer: (C) 4
Question: The average mark of the students of a class in a particular exam is 80. If 5 students whose average mark in that exam is 50 are excluded, the average mark of the remaining will be 90. Find the number of students who wrote the exam.
(A) 20
(B) 27
(C) 25
(D) 99
(E) 21
Rationale: Let the number of students who wrote the exam be x.
Total marks of students = 80 x.
Total marks of (x - 5) students = 90(x - 5)
80x - (5 * 50) = 90(x - 5)
200 = 10x => x = 20.Answer: A
Answer: (A) 20
Question: Two pipes A and B can fill a tank in 4 and 5 hours respectively. If they are turned up alternately for one hour each, the time taken to fill the tank is?
(A) 4 hrs 27 min
(B) 4 hrs 24 min
(C) 4 hrs 74 min
(D) 4 hrs 54 min
(E) 4 hrs 21 min
Rationale: 1/4 + 1/5 = 9/20
20/9 = 2 2/9
9/20 * 2 = 9/10 ---- 4 hours
WR = 1 - 9/10 = 1/10
1 h ---- 1/4
? ----- 1/10
2/5 * 60 = 24 = 4 hrs 24 min
Answer:B
Answer: (B) 4 hrs 24 min
Question: The perimeters of two squares are 80 cm and 64 cm. Find the perimeter of a third square whose area is equal to the difference of the areas of the two squares.
(A) 42cm
(B) 44cm
(C) 46cm
(D) 48cm
(E) 49cm
Rationale: Explanation:
Side of first square = (80/4) = 20 cm;
Side of second square = (64/4)cm = 16 cm.
Area of third square = [(20)2 - (16)2] cm2 = (400 - 256) cm2 = 144 cm2.
Side of third square = (144)(1/2) cm = 12 cm.
Required perimeter = (12 x 4) cm = 48 cm.
Answer: Option D
Answer: (D) 48cm
Question: The work done by a woman in 8 hours is equal to the work done by a man in 6 hours and by a boy in 12 hours. If working 6 hours per day, 9 men can complete a work in 6 days then in how many days can 12 men, 12 women and 12 boys together finish the same work by working 8 hours per day?
(A) 1 1⁄3 days
(B) 3 2⁄3 days
(C) 3 days
(D) 1 1⁄2 days
(E) None of these
Rationale: 8W = 6M = 12B
12M + 12W + 12B Þ 12M + 9M + 6M = 27M
\9 men can complete the work by working 1 hour per day in 6 × 6 days
\27 men working 8 hours per day = 6×6×9/27×8=112days
Answer D
Answer: (D) 1 1⁄2 days
Question: What is the dividend? Divisor is 9, the quotient is 49, and the remainder is 52.
(A) Undetermined
(B) 0
(C) 1
(D) 546
(E) 493
Rationale: Dividend= Divisor * Quotient + Remainder
?= 9 * 49 + 52
441 + 52
?= 493
(e.g. Answer: E)
Answer: (E) 493
Question: A, B and C started a business with investment of Rs. 8000. Rs. 20000 and Rs. 32000. What is the share of B in the total profit of Rs. 5400 at the end of 1 year?
(A) Rs. 2880
(B) Rs. 720
(C) Rs. 1800
(D) Rs. 1650
(E) None of these
Rationale: Explanation:
Ratio of capitals of A, B and C
= 8000 : 20000 : 32000 = 2 : 5 : 8
.: B's share = Rs. [(5/15) × 5400] = Rs. 1800
Answer: Option C
Answer: (C) Rs. 1800
Question: Integer m has 4 different prime factors and n has 3 different prime factors. If m and n has the greatest common factor of 15, how many different prime factors does mn have?
(A)  4
(B)  5
(C)  6
(D)  7
(E)  8
Rationale: As m and n has GCF of 15, 3*5 should be common factor for both m and n.
m=3*5*p1*p2
n=3*5*p3
mn=3^2*5^2*p1*p2*p3
mn has prime numbers of 3,5,p1,p2p3
B
Answer: (B)  5
Question: A, Band C can do a piece of work in 11 days, 5 days and 55 days respectively, working alone. How soon can the work be done if A is assisted by Band C on alternate days?
(A) 5 days
(B) 8 days
(C) 9 days
(D) 10 days
(E) 11 days
Rationale: (A+B)'s 1 day's work = 1/11+1/5 = 16/55
(A+C)'s 1 day's work = 1/11+1/55 = 6/55
work done in 2 day's = 16/55+6/55 = 2/5
2/5th work done in 2 days
work done= 5/2*2 = 5 days
ANSWER:A
Answer: (A) 5 days
Question: Which one of the given numbers is divisible by 11?
(A) 4823718
(B) 8423718
(C) 8432718
(D) 4132788
(E) 4852718
Rationale: Explanation:
4132788 = (4+3+7+8) – (1+2+8) = 11
So, the given number is divisible by 11
Answer:D
Answer: (D) 4132788
Question: Cn = 2Cn-1 + 4 and Qn = 4Qn-1 + 8 for all n > 1. If C5 = Q4 and C7 = 316, what is the first value of n for which Qn is an integer?
(A)  1
(B)  2
(C)  3
(D)  4
(E)  5
Rationale: Assuming I have understood the symbols used correctly answer is C- 3
C7 = 2S6 +4 = 316
C6 = 312/2 = 156 = 2C5 + 4
C5 = 152/2 = 76 = Q4
Q4 = 4Q3 + 8 = 76
Q3 = 68/4 = 17
Q3 = 4Q2 + 8 = 17
Q2 = 9/4 = 2.25
Q2 = 4Q1 + 8
Q1 will not be integer
Answer: (C)  3
Question: Find the value of y from (12)^3 x 6^4 ÷ 432 = y?
(A) 2134
(B) 2245
(C) 3450
(D) 4500
(E) 5184
Rationale: Given Exp. = (12)3 x 64 = (12)3 x 64 = (12)2 x 62 = (72)2 = 5184
432 12 x 62
E
Answer: (E) 5184
Question: RAJA complete a journey in 10 hours. He travels first half of the journey at the rate of 21 km/hr and second half at the rate of 24 km/hr. Find the total journey in km.
(A) 200 km
(B) 250 km
(C) 224 km
(D) 255 km
(E) 260 km
Rationale: consider x -- > (1/2)x/21 + (1/2)x/24 = 10
==> x/21+x/24 = 20
15x = 168 * 20
==> 224km
ANSWER C
Answer: (C) 224 km