mathewhe/aqua_rat huggingface dataset:
Question: The length of a rectangle i s two - fifths of the radius of a circle. The radius of the circle is equal to the side of the square, whose area is 1225 sq.units. What is the area (in sq.units) of the rectangle if the rectangle if the breadth is 10 units?
(A) 140 sq.units
(B) 149
(C) 148
(D) 17
(E) 143
Rationale: Given that the area of the square = 1225 sq.units
=> Side of square = √1225 = 35 units
The radius of the circle = side of the square = 35 units Length of the rectangle = 2/5 * 35 = 14 units
Given that breadth = 10 units
Area of the rectangle = lb = 14 * 10 = 140 sq.units
Answer: Option A
Answer: (A) 140 sq.units
Question: David paid $5,000 for 100 shares of stock X and $3,000 for 100 shares of stock Y. He later sold the same shares of both stocks, gaining 3/6 the amount he paid for stock Y. If the prices he had paid for the stocks had been reversed and everything else remained the same, then the net result would have been:
(A) A loss 3 times as much
(B) A loss 2 times as much
(C) A Gain of 1.67 times as much.
(D) A loss 1.5 times as much
(E) A Gain of 2 times as much.
Rationale: A = 5000; B = 3000; Profit = (3/6)*3000 = 1500
After prices are reversed:
A = 3000; B =5000; Profit = (3/6)*5000 =2500
2500 --> Gain of 1.67 times 1500
Answer: C
Answer: (C) A Gain of 1.67 times as much.
Question: Little Texas Drilling Company has three wells, each producing oil at a constant rate. Well A produces one barrel every two minutes. Well B produces one barrel every three minutes. Well C produces one barrel every four minutes. How many hours does it take Little Texas Drilling Company to produce 265 barrels of oil?
(A) 2
(B) 3
(C) 4
(D) 5
(E) 180
Rationale: Well A produces 1/2 a barrel per minute.
Wells B and C produce 1/3 + 1/4 = 7/12 (a little more than half) a barrel per minute.
So all three wells combined produce a little more than 1 barrel per minute.
So for 265 barrels they will take a bit less than 265 mins which will be more than 4 hrs but less than 5 hrs.
Answer (D)
Answer: (D) 5
Question: The cost price of a particular amount of articles is same as the number of articles. Selling price of the articles comes out to be 20. Over the whole transaction 25% is gained. What is X?
(A) 16
(B) 77
(C) 15
(D) 18
(E) 161
Rationale: Explanation:
According to the question let n be the number of articles.
=> Cost price of n articles = n
=> Selling price of n articles = 20
=> Profit % = 25%
=> Profit % = (SP - CP)/CP X 100
Putting the values in the formula
(20-n)/n x 100 = 25
=> 5n/4 = 20
=> n = 16
ANSWER: A
Answer: (A) 16
Question: In a certain town, there are five times as many people who were born in the town’s state as there are people who were born in another state or country. The ratio of those residents born in the town’s state to the town’s total population is
(A) 1 to 4
(B) 1 to 3
(C) 1 to 2
(D) 3 to 4
(E) 5 to 6
Rationale: Town state: 5 times the whole town or country
then ratio will be 5(times)/6 total(times)
So the answer is 5/6.
E
Answer: (E) 5 to 6
Question: A company pays project contractors a rate of a dollars for the first hour and b dollars for each additional hour after the first, where a > b.
In a given month, a contractor worked on two different projects that lasted 3 and 5 hours, respectively. The company has the option to pay for each project individually or for all the projects at the end of the month. Which arrangement would be cheaper for the company and how much would the company save?
(A) Per month, with savings of $(2a + 2b)
(B) Per month, with savings of $(2a - 2b)
(C) The two options would cost an equal amount.
(D) Per project, with savings of $(2a + 2b)
(E) Per project, with savings of $(2a - 2b)
Rationale: Per Project, company will pay as follows:
For 3 hours work = a+2b
For 5 hours work = a+4b
Total = 2a+6b
Per Month, company will pay for 8 hours work = a+5b
Total per contract - total per month
3a+5b - (a+7b)
2a-2b
Since a>b Amount 3a+5b(per contract amount) > a+7b (per project amount) by 2a-2b.
Hence per month payment will be cheaper by 2a-2b .
OA B
Answer: (B) Per month, with savings of $(2a - 2b)
Question: 3x<2y<0 which of the following is the greatest?
(A) 2x+3y
(B) -(3x+y)
(C) 2x-y
(D) x+y
(E) 0
Rationale: Plugging in -1 for both x and y we get
A. 2x+3y =-5
B. -(3x+y) =4
C. 2x-y =1
D. x+y =-2
E. 0 =0
Answer: B
Answer: (B) -(3x+y)
Question: In the parking lot there are 44 vehicles, 24 of them are buses, and the rest are cars. The color of 24 vehicles is red, of which 18 are buses. How many cars can be found in the parking lot which are not colored red?
(A) 11
(B) 12
(C) 13
(D) 14
(E) 15
Rationale: The number of cars is 44-24 = 20.
The number of red cars is 24-18=6.
The number of cars which are not red is 20-6=14.
The answer is D.
Answer: (D) 14
Question: If a certain sample of data has a mean of 23.0 and a standard deviation of 3.0, which of the following values is more than 2.5 standard deviations from the mean?
(A) 12.0
(B) 13.5
(C) 15.0
(D) 23.5
(E) 26.5
Rationale: Value ismore than 2.5SDfrom the mean means that the distance between the mean and the value must be more than 2.5*SD=7.5. So the value must be either less than 23-7.5=15.5or more than 23+7.5=30.5.
Answer: C.
Answer: (C) 15.0
Question: Series Problem like 4 12 x 44 46 132 134 begin of the Skype highlighting 44 46 132 134 end of the Skype highlighting. Find x?
(A) 14
(B) 15
(C) 16
(D) 17
(E) 18
Rationale: 134-132=2
46-44=2
x-12=2
x=14
ANSWER:A
Answer: (A) 14
Question: How many no.'s with 3 different digits, 2, 3, 5, 6, 7 and 9, which are divisible by 5?
(A) 18
(B) 20
(C) 25
(D) 28
(E) 31
Rationale: Since each desired number is divisible by 5, so we must have 5 at the unit place. So, there is 1 way of doing it.
The tens place can now be filled by any of the remaining 5 digits (2, 3, 6, 7, 9). So, there are 5 ways of filling the tens place.
The hundreds place can now be filled by any of the remaining 4 digits. So, there are 4 ways of filling it.
Required number of numbers = (1 x 5 x 4) = 20
B
Answer: (B) 20
Question: A plane flies 420 miles with the wind and 350 miles against the wind in the same length of time. If the speed of the wind is 23 mph, what is the speed of the plain in still air?
(A) 153mph
(B) 253mph
(C) 353mph
(D) 453mph
(E) 553mph
Rationale: The speed of the plane in still air = x miles/hour
The speed of the wind is 23 mph
Speed with the wind = (x + 23) mph
Speed against the wind = (x – 23) mph
Time = Distance/ Speed
According to the problem,
420/(x + 23) = 350/(x – 23)
420(x – 23) = 350(x + 23)
420x – 9660 = 350x + 805
420x – 350x = 8050 + 9660
70x = 17710
x = 17710/70
x = 253
Therefore, the speed of the plane in still air = 253 mph.
correct answer B)253mph
Answer: (B) 253mph
Question: The total age of A and B is 13 years more than the total age of B and C. C is how many year younger than A
(A) 11
(B) 12
(C) 13
(D) 14
(E) 15
Rationale: Explanation:
Given that A+B = 13 + B + C
=> A ? C = 13 + B ? B = 13
=> C is younger than A by 13 years
Answer: Option C
Answer: (C) 13
Question: If
1 = 6
2 = 12
3 = 18
4 = 24
5 = 30
6 = 36
7 = 42
Then 42 = ?
Hint: Its a logic Riddle not a mathematical riddle
(A) 7
(B) 2
(C) 3
(D) 4
(E) 5
Rationale: A
1
As stated
7=42 => 42=7
Answer is A
Answer: (A) 7
Question: what is the angle between the hands of a clock when time is 8:40?
(A) 65deg
(B) 75deg
(C) 45deg
(D) 15deg
(E) 100deg
Rationale: Angle between two hands =
40h - 11/2 m = 40*8 - 40*11/2 = 320 - 220 = 100deg
ANSWER:E
Answer: (E) 100deg
Question: 32,0.2,160,15,0.5,30,28,0.7,?
(A) 30
(B) 40
(C) 50
(D) 60
(E) 70
Rationale: (32,0.2,160),(15,0.5,30),(28,0.7,?)
32 / 0.2 = 160,
15 / 0.5 = 30
28 / 0.7 = 40
ANSWER:B
Answer: (B) 40
Question: If 3^k is a divisor of the product of all even integers between 2 and 30 (inclusive), what is the maximum value of k?
(A) 4
(B) 6
(C) 10
(D) 13
(E) 14
Rationale: since the Q tells us 3k3k is a divisor of the product of all even integers between 2 and 30 (inclusive)
the Q basically asks us power of 3 in the product..
lets see the even multiples of 3 from 2 to 30..
6*12*18*24*30..
3^5(2*4*6*8*10)..
or 3^6*2*4*2*8*10..
ans 6
ANSWER:B
Answer: (B) 6
Question: When positive integer n is divided by 3, the remainder is 1. When n is divided by 8, the remainder is 5. What is the smallest positive integer p, such that (n + p) is a multiple of 15?
(A) 1
(B) 2
(C) 5
(D) 19
(E) 20
Rationale: When positive integer n is divided by 3, the remainder is 1 i.e., n=3x+1
values of n can be one of {1, 4, 7, 10, 13, 16, 19, 22..............49, 52, 59..................}
Similarly,
When n is divided by 8, the remainder is 5..i.e., n=7y+5
values of n can be one of {5, 13, 21, 29, 37, 45, 53, 61........}
combining both the sets we get
n={13, 37, ...........}
What is the smallest positive integer p, such that (n + p) is a multiple of 15 or 15x
in case of n=13 p=2
so for min value of p, we take min value of n.
B is the answer.
Answer: (B) 2
Question: In a certain country, 60 percent of the population likes basketball, and 33 percent of the population likes both basketball and golf. What percentage of the people who like basketball also like golf?
(A) 20%
(B) 33%
(C) 40%
(D) 55%
(E) 67%
Rationale: Correct Answer: (D).
Since this is a percent problem without concrete numbers, we can assign our own. If we assume that there are 100 people in the country, then 60 people like basketball, and 33 people like basketball and golf. We’re looking for people who like both divided by people who like basketball, so 33/60 = 55%, or choice D.
Answer: (D) 55%
Question: At Pat's Pet Shop, 25 cups of bird seed are used every 5 days to feed 20 parakeets. How many cups of bird seed would be required to feed 15 parakeets for 7 days?
(A) 35.25
(B) 15
(C) 64
(D) 104
(E) 26 1/4
Rationale: Let's go step-by-step.
25 cups are used over a 5 day period, which means 5 cups a day. This feeds 20 parakeets, which means each parakeet needs 1/4 of a cup every day.
For 15 parakeets, we need 15*1/4 cups = 3 3/4 cups a day. Over 7 days, we need 26 1/4 cups. Choice E.
Answer: (E) 26 1/4
Question: What is the greatest possible common divisor of two different positive integers which are less than 144?
Can someone explain why the answer is 71 if we assume that the integers are 143 and 142?
(A) 143
(B) 142
(C) 72
(D) 71
(E) 12
Rationale: First of all, what is the greatest common divisor of 143 and 142? It is 1. You are looking for the common divisor. 142 and 143 will have no common divisor except 1.
Think:
2 and 3 have GCD (greatest common divisor) of 1
2 and 4 have GCD of 2.
3 and 4 have GCD (greatest common divisor) of 1
So if you were to select 2 numbers less than 5 with the greatest GCD, you need to select 2 and 4, not 3 and 4.
Now think: 143 = 11 * 13
The greatest possible divisor it will have with another number less than 144 will be either 11 or 13. Let's move on.
142 = 2*71
The greatest possible divisor it can have with another number less than 144 can be 71 (say, if the other selected integer is 71)
Do you think another number less than 144 could have a GCD of greater than 71? No because when you split a number into two factors, one of them will be at least 2. If it is greater than 2, the other factor will obviously be less than 71.
Answer: (D) 71
Question: A number Y is chosen at random from the numbers 1, -3, -1, 0, 1, 2, 3. What is the probability that |X|<3?
(A) 3/7
(B) 1/4
(C) 1/5
(D) 1/7
(E) 2/5
Rationale: |X||X| can take 7 values.
To get |X|<2|X|<2 ( i.e., −2<x<+2−2<x
⇒ P(|X|<2)= Favourable CasesTotal CasesP(|X|<2)= Favourable CasesTotal Cases
= 3/7
A
Answer: (A) 3/7
Question: The present worth of a certain sum due sometimes hence is Rs.1600 and the true discount is Rs.160.The banker's gain is
(A) Rs.16
(B) Rs.24
(C) Rs.20
(D) Rs.12
(E) None
Rationale: Solution
B.G
Given,T.D = 160, P.w= 1600	= (T.D)² / P.W
= Rs(160 x 160 / 1600)
= Rs.16.
Answer A
Answer: (A) Rs.16
Question: The length of a rectangular field is 7/5 its width. If the perimeter of the field is 288 meters, what is the width of the field?
(A) 50
(B) 60
(C) 70
(D) 80
(E) 90
Rationale: Let L be the length and W be the width. L = (7/5)W
Perimeter: 2L + 2W = 288, 2(7/5)W + 2W = 288
Solve the above equation to find: W = 60 m and L = 84 m.
correct answer B)60
Answer: (B) 60
Question: A clock shows the time as 11 a.m. If the minute hand gains 5 minutes every hour, how many minutes will the clock gain by 6 p.m.?
(A) 45 minutes
(B) 55 minutes
(C) 35 minutes
(D) 25 minutes
(E) 40 minutes
Rationale: there are 7 hours in between 11 a.m. to 6 p.m.
7*5=35 minutes.
ANSWER:C
Answer: (C) 35 minutes
Question: In a panel of 10 light bulbs, the odds of any light bulb to burn out are 0.08 at any given 10 minutes. Should a light bulb burn out, the whole panel would instantly turn off. What are the odds that the panel would be turned off within the first 10 minutes after it was switched on?
(A) 1-0.06^10
(B) 1-0.92^10
(C) (1-0.94)^10
(D) 0.06
(E) 1-10*0.06
Rationale: ans B.
Prob that light will not turned off = 0.92^10. Hence prob (turn off) = 1 - prob (not turn off).
Answer: (B) 1-0.92^10
Question: |x+3| – |4-x| = |8+x| How many X solutions will this equation have?
(A) 0
(B) 1
(C) 2
(D) 3
(E) 4
Rationale: X=|x| = x when x >= 0 (x is either positive or 0)
|x| = -x when x < 0 (note here that you can put the equal to sign here as well x <= 0 because if x = 0,
|0| = 0 = -0 (all are the same)
So the '=' sign can be put with x > 0 or with x < 0. We usually put it with 'x > 0' for consistency.A
Answer: (A) 0
Question: A library has an average of 510 visitors on Sundays and 240 on other day. The average number of visitors in a month of 10 days starting with sunday is
(A) 280
(B) 285
(C) 290
(D) 855
(E) 275
Rationale: Explanation:
As the month begin with sunday, so there will be five sundays in the month. So result will be:
=(510×5+240×25/10)=(8550/10)=855
Answer: Option D
Answer: (D) 855
Question: The average of 20 numbers is zero. Of them, at the most, how many may be greater than zero?
(A) 0
(B) 1
(C) 10
(D) 19
(E) 2
Rationale: Average of 20 numbers = 0.
Sum of 20 numbers (0 x 20) = 0.
It is quite possible that 19 of these numbers may be positive and if their sum is a then 20th number is (-a).
ANSWER:D
Answer: (D) 19
Question: Set R has a mean of 14 and a standard deviation of 1.5. We are going to add two additional numbers to Set S. Which pair of numbers would decrease the standard deviation the most?
(A) {13,15}
(B) {18,19}
(C) {11,19}
(D) {15,19}
(E) {14,25}
Rationale: The lesser the variance( values closer to mean) ,lower the standard deviation. As discussed in question the mean is 14,the values (13,15) are closer than others.
Hence Answer : A
Answer: (A) {13,15}
Question: 90, 180, 12, 50, 100, 200, ?, 2, 50, 4, 25, 2, 6, 30, 3
(A) 130
(B) 150
(C) 180
(D) 100
(E) 220
Rationale: 30*3=90
6*30=180
6*2=12
25*2=50
4*25=100
50*4=200
2*50=100 ans is 100
ANSWER:D
Answer: (D) 100
Question: Tom planted vegetables in a rectangular garden that was 23 feet long and 15 feet wide. He used
1/3 of the area for corn and 1/5 of it for peas. How many square feet are left for other vegetables?
(A) 155 sq. ft.
(B) 156 sq. ft.
(C) 161 sq. ft.
(D) 168 sq. ft.
(E) 179 sq. ft.
Rationale: area of garden is 23 x 15 = 345 sq. ft.
1/3 x 345 = 115 sq. ft. for corn
1/5 x 345 = 69 sq. ft. for peas
115 + 69 = 184 sq. ft. used
345 - 184 = 161 sq. ft. left over
correct answer C
Answer: (C) 161 sq. ft.
Question: What will be the product of (50-1)*(50-2)*(50-3)*..............*(50-79)*(50-80)?
(A) less than -100,000
(B) -2500
(C) 0
(D) 2500
(E) more than 100,000
Rationale: One of the terms is (50-50) so the product is 0.
The answer is C.
Answer: (C) 0
Question: The factorial expression 9!/2! is not divisible by which of the following integers?
(A) 3
(B) 5
(C) 6
(D) 7
(E) None of these
Rationale: 9!/2! => 9 x 8 x7 x 6 x 5 x 4x3
(A) 3 Can divide 12 or 9
(B) 5 Can divide 5
(C) 6 Can divide 12
(D) 7 can divide 7,21,28
Hence answer will be (E)
Answer: (E) None of these
Question: When a natural number N is successively divided by 1,2,3,4 the remainders are 5,6,7,8. What will be the sum of the remainders if the order of the division is reversed?
(A) 11
(B) 12
(C) 10
(D) 2
(E) 7
Rationale: 1 2 3 4
5 6 7 8
leave the top right- most number 8
start with bottom right-most number 5
8*3+7=31
31*2+6=68
68*1+5=73
this is the number required
Now, do the successive division in the reverse order
The sum of the remainders is 10
Hence, the correct option is C
Answer: (C) 10
Question: A man goes from A to B at a speed of 14 kmph and comes back to A at a speed of 10 kmph. Find his average speed for the entire journey?
(A) 11.6 kmph
(B) 12.9 kmph
(C) 12.8 kmph
(D) 11.9 kmph
(E) 12.6 kmph
Rationale: Distance from A and B be 'd'
Average Speed = total distance/total time
Average Speed = (2d)/[(d/14) + (d/10]
= (2d)/[12d/70) => 11.6 kmph.
Answer:A
Answer: (A) 11.6 kmph
Question: In a certain city, 40% of the registered voters are democrats and the rest are republicans.In a mayoral race, if 75% of the registered voters who are democrats and 20% of the registered voters who are republicans are expected to vote for candidate A,What % of the registered voters are expected to vote for candidate A?
(A) a) 50%
(B) b) 53%
(C) c) 54%
(D) d) 55%
(E) e) 57%
Rationale: Let total voters = 100
so D= 60, vote for the mayor 60*75%=45 (60*3/4)
R= 40, vote for the mayor 40*20%= (40*1/5)
45+8=53
53/100*100=55%
D
Answer: (D) d) 55%
Question: If the product of 6 integers is negative, at most how many of the integers can be negative?
(A) 2
(B) 3
(C) 4
(D) 5
(E) 6
Rationale: product of even number of -ve numbers is positive so it cant be 6 .
ANSWER:D
Answer: (D) 5
Question: If n divided by 7 has a remainder of 1, what is the remainder when 3 times n is divided by 7?
(A) 1
(B) 2
(C) 3
(D) 5
(E) 6
Rationale: As per question => N=7P+1 for some integer p
hence 3N => 21Q + 3 => remainder => 6 for some integer Q
Alternatively => N=2 > 3N=> 3 => 3 divided by 7 will leave a remainder 3
hence C
Answer: (C) 3
Question: A train crosses a platform of 120 m in 15 sec, same train crosses another platform of length 180 m in 18 sec. then find the length of the train?
(A) 298m
(B) 180m
(C) 287m
(D) 297m
(E) 261m
Rationale: Length of the train be ‘X’
X + 120/15 = X + 180/18
6X + 720 = 5X + 900
X = 180m
Answer: B
Answer: (B) 180m
Question: In a particular state, 62% of the counties received some rain on Monday, and 54% of the counties received some rain on Tuesday. No rain fell either day in 28% of the counties in the state. What percent of the counties received some rain on Monday and Tuesday?
(A) 25%
(B) 44%
(C) 56%
(D) 62%
(E) 70%
Rationale: 62 + 54 + 28 = 144%
The number is 44% above 100% because 44% of the counties were counted twice.
The answer is B.
Answer: (B) 44%
Question: In a game of billiards, A can give B 20 points in 60 and he can give C 30 points in 60. How many points can B give C in a game of 100?
(A) 25
(B) 15
(C) 65
(D) 82
(E) 95
Rationale: Explanation:
A scores 60 while B score 40 and C scores 30.
The number of points that C scores when B scores 100 = (100 * 30)/40 = 25 * 3 = 75.
In a game of 100 points, B gives (100 - 75) = 25 points to C.
ANSWER A
Answer: (A) 25
Question: The “s-number” of a number x is defined as the ones digit of 2^x. Antony rolls a die with 6 sides labeled with the integers from 1 to 6, each of which has an equal probability of landing face-up. He then takes 3^s, where s is the s-number of the result of his die roll, and plots 3^s on a number line as the point A. Finally, he repeats this entire process, this time plotting the result as the point B. What is the probability that the distance between A and B is greater than the value of B?
(A)  3/8
(B)  13/36
(C)  17/36
(D)  19/36
(E)  23/36
Rationale: If you calculate 3^s for 1st roll, all 6 results will be 9, 81, 6561, 729, 9, 81. This result is the same for 2nd roll. 9, 81, 6561, 729, 9, 81.
About distance: If the first result is 9 and the second is also 9, the distance is 9-9=0 which is smaller than 9. If the first result is 9 and the second is 81, the distance is 81-9=72 which is also smaller than B which has the value of 81. If the first result is 81 and the second is 9, the distance will be greater than B. Distance 81-9=72>9.
On the first roll, the probability of getting result 9 is 2/6. In this case no other alternative values for second roll which would make the distance greater than B. So probability is 0. So next estimations are:
probability of getting 81 on the first roll (2/6) * probability of getting 9 on the second roll (2/6) = 1/9
probability of getting 729 on the first roll (1/6) * probability of getting 9, 81 on the second roll (4/6) = 1/9
probability of getting 6561 on the first roll (1/6) * probability of getting 9, 81, 729 on the first roll (5/6) = 5/36
All together: 1/9 + 1/9 + 5/36 = 13/36=B
Answer: (B)  13/36
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) 210 kms
(E) 120 kms
Rationale: A
100 kms
63736+100 = 63636, a palindrome
Answer: (A) 100 kms
Question: The sum of three numbers is 98. The ratio of the first to the second is 2/3, and the ratio of the second to the third is 5/8. The second number is:
(A) 15
(B) 20
(C) 30
(D) 32
(E) 33
Rationale: Let the three numbers be x, y and z.
Sum of the numbers is 98.
x + y + z = 98………………(i)
The ratio of the first to the second is 2/3.
x/y = 2/3.
x = 2/3 ? y.
x = 2y/3.
The ratio of the second to the third is 5/8.
y/z = 5/8.
z/y = 8/5.
z = 8/5 ? y.
z = 8y/5.
Put the value of x = 2y/3 and z = 8y/5 in (i).
2y/3 + y + 8y/5 = 98
49y/15 = 98.
49y = 98 ? 15.
49y = 1470.
y = 1470/49.
y = 30 .
Therefore, the second number is 30
correct answer C
Answer: (C) 30
Question: The retirement plan for a company allows employees to invest in 10 different mutual funds. Six of the 10 funds grew by at least 10% over the last year. If Sam randomly selected 4 of the 10 funds, what is the probability T that 3 of Sam’s 4 funds grew by at least 10% over last year?
(A)  6C3 / 10C4
(B)  6C3 * 4C1 / 10C4
(C)  6C3 * 4C1 / 10P4
(D)  6P3 * 4P1 / 10C4
(E)  6P3 * 4P1 / 10P4
Rationale: Look at the answers. B is the only answer choice that uses only combination formulas and takes into account all the factors.
We know this is a combination, not a permutation. This rules out choices C, DE.
A clearly isn't the answer because T= 6C3 only accounts for 3 of the funds he chose. 10C4, the denominator, is correct, so the numerator must be wrong.
B it is.
Answer: (B)  6C3 * 4C1 / 10C4
Question: Roy is now 8 years older than Julia and half of that amount older than Kelly. If in 2 years, Roy will be twice as old as Julia, then in 2 years what would be Roy’s age multiplied by Kelly’s age?
(A) 160
(B) 168
(C) 176
(D) 184
(E) 192
Rationale: R = J+8 = K+4
R+2 = 2(J+2)
(J+8)+2 = 2J+4
J = 6
R = 14
K = 10
In 2 years (R+2)(K+2) = 16*12 = 192
The answer is E.
Answer: (E) 192
Question: Ravi invested certain amount for two rates of simple interests at 6% p.a. and 7% p.a. What is the ratio of Ravi's investments if the interests from those investments are equal?
(A) 7:9
(B) 7:5
(C) 7:2
(D) 7:6
(E) 7:1
Rationale: Let x be the investment of Ravi in 6% and y be in 7%
x(6)(n)/100
= y(7)(n)/100
=> x/y = 7/6
x : y = 7 : 6
Answer: D
Answer: (D) 7:6
Question: A can do a work in 15 days and B in 20 days. If they work on it together for 4 days, then the fraction of the work that is left is?
(A) 8
(B) 8/11
(C) 8/13
(D) 8/15
(E) None
Rationale: A's 1 day's work =	1	;
15
B's 1 day's work =	1	;
20
(A + B)'s 1 day's work =	(	1	+	1	)	=	7	.
15	20	60
(A + B)'s 4 day's work =	(	7	x 4	)	=	7	.
60	15
Therefore, Remaining work =	(	1 -	7	)	=	8	.
15	15
Option D
Answer: (D) 8/15
Question: The greatest number by which the product of three consecutive multiples of 3 is always divisible is
(A) 54
(B) 76
(C) 152
(D) 162
(E) None of these
Rationale: Solution
Required number	= Product of first three multiplies of 3
= (3 × 6 × 9)= 162.
Answer D
Answer: (D) 162
Question: For a drama, Jack need to select 5 dramatist from a team of 8 members. What is the possible way to select dramatist?
(A) 60
(B) 56
(C) 48
(D) 25
(E) 10
Rationale: The question is out of 8 members, john needs 5 members.
So the combination is 8C5.
8C5=8!/3!*5!
=8*7*6*5!/5!*3*2*1
=56 ways to select.
Option B is answer
Answer: (B) 56