mathewhe/aqua_rat huggingface dataset:
Question: The parameter of a square is double the perimeter of a rectangle. The area of the rectangle is 480 sq cm. Find the area of the square?
(A) 288
(B) 261
(C) 712
(D) 480
(E) 176
Rationale: Let the side of the square be a cm. Let the length and the breadth of the rectangle be l cm and b cm respectively.
4a = 2(l + b)
2a = l + b
l . b = 480
We cannot find ( l + b) only with the help of l . b. Therefore a cannot be found .
Area of the square cannot be found.
Answer: D
Answer: (D) 480
Question: A and B began business with Rs.3000 and Rs.4000 after 8 months, A withdraws Rs.1000 and B advances Rs.1000 more. At the end of the year, their profits amounted to Rs.630 find the share of A.
(A) Rs.240
(B) Rs.350
(C) Rs.340
(D) Rs.390
(E) Rs.490
Rationale: (3*8 + 2*4):(4*8 + 5*4)
8:13
8/21 * 630 = 240
ANSWER:A
Answer: (A) Rs.240
Question: For a right angle triangle the hypotenuse is 5 and base is 3. What is the area of the triangle?
(A) 6
(B) 7
(C) 8
(D) 9
(E) 10
Rationale: As we know that for a right angle triangle the are is 1/2 * base * height
We know the base = 3
We need to calculate the height
hypotenuse = h = 5
base = b = 3
height = c = ?
As per Pythagoras
h^2 = b^2 + c^2
5^2 = 3^2 + c^2
25 = 9 + c^2
C^2 = 25 - 9
c^2 = 16
c = 4
height = 4
area = 1/2 * base * height
= 1/2 * 3 * 4
= 6 square units
Ans: A
Answer: (A) 6
Question: A fair sided die labeled 1 to 6 is tossed two times. What is the probability the product of the two value is 1
(A) 1/6
(B) 7/36
(C) 1/36
(D) 9/36
(E) 11/36
Rationale: The only way you going to get a product with of one is one of the value shown on the is one. This is because any number multiply by one is one. The product of 1 is obtained if the dice shown (1,1)(1,2)(1,3)(1,4)(1,5)(1,6) or (2,1)(3,1)(4,1)(5,1)(6,1)
Answer: E
Answer: (E) 11/36
Question: Find the mean proportional between 81 & 100?
(A) A)59
(B) B)61
(C) C)63
(D) D)65
(E) E)90
Rationale: Formula = √a×b
A = 81 and B = 100
√81×100 = 9 × 10 = 90
E
Answer: (E) E)90
Question: A small college reduced its faculty by approximately 15 percent to 195 professors. What was the original number of faculty members?
(A) 182
(B) 208
(C) 224
(D) 229
(E) 302
Rationale: If x is the original number of faculty members, then after 15% reduction in faculty members number is .85x
but we are given .85x = 195
x = 229
So the original number of faculty members is 229
Correct Answer - D
Answer: (D) 229
Question: Jacob brought a scooter for a certain sum of money. He spent 10% of the cost on repairs and sold the scooter for a profit of Rs. 1100. How much did he spend on repairs if he made a profit of 20%?
(A) 27
(B) 276
(C) 500
(D) 267
(E) 234
Rationale: Let the C.P. be Rs. x. Then, 20% of x = 1100
20/100 * x = 1100 => x = 5500
C.P. = Rs. 5500, expenditure on repairs = 10%
Actual price = Rs. (100 * 5500)/110 = Rs. 5000
Expenditures on repairs = (5500 - 5000) = Rs. 500.
Answer: C
Answer: (C) 500
Question: A clock is started at noon. By 10 minutes past 4, the hour hand has turned through how many degrees?
(A) 125Â°
(B) 130Â°
(C) 135Â°
(D) 140Â°
(E) 145Â°
Rationale: The angle traced by the hour hand in 12 hrs is 360Â°
The angle traced by the hour hand in 1 hour is 30Â°
The angle traced by the hour hand in 10 minutes is 5Â°
The angle traced by the hour hand in 4 hours and 10 minutes is 4*30Â° + 5Â° = 125Â°
The answer is A.
Answer: (A) 125Â°
Question: Before leaving for his business trip, Chad asks his assistant to choose and pack six shirts from his closet, which currently contains eight shirts. If each shirt is a different color, including one blue shirt and one pink shirt, and the assistant chooses the shirts at random, what is the probability that the pink shirt will be one of the shirts packed but the blue shirt will not?
(A) 1/7
(B) 2/11
(C) 3/14
(D) 9/28
(E) 11/56
Rationale: The total number of ways to choose 6 shirts from 8 is 8C6 = 28
The number of ways to choose a pink shirt plus 5 shirts from 6 is 6C5 = 6
P(a pink shirt but not a blue shirt) = 6/28 = 3/14
The answer is C.
Answer: (C) 3/14
Question: Find the value of (2 − 1/3) (1 − 1/4)(1 − 1/5)……… (1 − 1/99)(1 − 1/100)
(A) 1/20
(B) 3/20
(C) 5/20
(D) 7/20
(E) 9/20
Rationale: (2 − 1/3) (1 − 1/4)(1 − 1/5)..... (1 − 1/99)(1 − 1/100)
5/3 × 3/4 × 4/5 × ....... 98/99 × 99/100 = 5/100 = 1/20
Answer is A.
Answer: (A) 1/20
Question: At wipro gym class can be divided into 8 teams with an equal number of players on each team or into 12 teams with an equal number of players on each team. What is the lowest possible number of students in the class?
(A)  20
(B)  24
(C)  36
(D)  48
(E)  96
Rationale: We are given that wipro gym class can be divided into 8 teams or 12 teams, with an equal number of players on each team. Translating this into two mathematical expressions we can say, where G is the total number of students in the gym class, that:
G/8 = integer and G/12 = integer
This means that G is a multiple of both 8 and 12.
We are asked to determine the lowest number of students in the class, or the lowest value for variable “G”. Because we know that G is a multiple of 8 and of 12, we need to find the least common multiple of 8 and 12. Although there are technical ways for determining the least common multiple, the easiest method is to analyze the multiples of 8 and 12 until we find one in common.
Starting with 8, we have: 8, 16, 24, 32
For 12, we have: 12, 24
For the multiples of 12, we stopped at 24, because we see that 24 is also a multiple of 8. Thus, 24 is the least common multiple of 8 and 12, and therefore we know that the lowest possible number of students in the gym class is 24.
Answer B.
Answer: (B)  24
Question: A grocer has a sale of Rs. 5435, Rs. 5927, Rs. 5855, Rs. 6230 and Rs. 5562 for 5 consecutive months. How much sale must he have in the sixth month so that he gets an average sale of Rs. 5500?
(A) Rs. 1991
(B) Rs. 2991
(C) Rs. 3991
(D) Rs. 4991
(E) Rs. 5991
Rationale: Explanation:
Total sale for 5 months = Rs. (5435 + 5927 + 5855 + 6230 + 5562) = Rs. 29009.
Required sale = Rs. [ (5500 x 6) â€“ 29009 ]
= Rs. (33000 â€“ 29009)
= Rs. 3991.
Answer C
Answer: (C) Rs. 3991
Question: If x lies in the range (-1,0) then which of the following statements must be true?
(A) x^4 >x^3 > x^2 >x
(B) x >x^2 > x^3 > a^4
(C) x^4 >x^2 > x^3 >x
(D) x^2 >x^4 > x^3 >x
(E) x^2 > x^4 >x > x^3
Rationale: consider any number from the given range (-1-0)..let x=-1/2
then x^2= 1/4
x^3=-1/8
x^4=1/16
so we have x^2>x^4>x^3>x
Ans D
Answer: (D) x^2 >x^4 > x^3 >x
Question: The percentage increase in the area of a rectangle, if each of its sides is increased by 20% is?
(A) 44%
(B) 46%
(C) 50%
(D) 52%
(E) 54%
Rationale: Let original length = x metres and original breadth = y metres.
Original area = (xy) m2.
New length = 120	x	m	= 6	x	m.
100	5
New breadth = 120	y	m	= 6	y	m.
100	5
New Area = 6	x x	6	y	m2	= 36	xy	m2.
5	5	25
The difference between the original area = xy and new-area 36/25 xy is
= (36/25)xy - xy
= xy(36/25 - 1)
= xy(11/25) or (11/25)xy
Increase % = 11	xy x	1	x 100	%	= 44%.
25	xy
A)
Answer: (A) 44%
Question: The perimeter of one square is 48 cm and that of another is 36 cm. Find the perimeter and the diagonal of a square which is equal in area to these two combined?
(A) 13√4
(B) 13√2
(C) 23√2
(D) 12√4
(E) 15√2
Rationale: 4a = 48 4a = 36
a = 12 a = 9
a2 = 144 a2 = 81
Combined area = a2 = 225 => a = 15
d = 15√2
Answer: E
Answer: (E) 15√2
Question: Suppose son name is 120,his brother name is 150 and his mother name is 170.find out his father's name???
(A) 190
(B) 200
(C) 230
(D) 240
(E) 250
Rationale: since difference between all name is =30
so father's name will be 170+30=200.
ANSWER:B
Answer: (B) 200
Question: A grocer has 400 pounds of coffee in stock, 25 percent of which is decaffeinated. If the grocer buys another 100 pounds of coffee of which 60 percent is decaffeinated, what percent, by weight, of the grocer’s stock of coffee is decaffeinated?
(A) 28%
(B) 30%
(C) 32%
(D) 34%
(E) 40%
Rationale: 1. 25% of 400=100 pounds of decaffeinated coffee
2. 60% of 100=60 pounds of decaffeinated coffee
3. Wt have 160 pounds of decaffeinated out of 500 pounds, that means 160/500*100%=32%. The correct answer is C.
Answer: (C) 32%
Question: A solution contains 8 parts of water for every 7 parts of Lemonade syrup. How many parts of the solution should be removed and replaced with water so that the solution will now contain 40% lemonade syrup?
(A) 1.5
(B) 1.75
(C) 2.14
(D) 2.34
(E) 2.64
Rationale: Let the total solution is 150 L with 80 L water & 70 L syrup.
To make 40% syrup solution, the result solution must have 90 L syrup and 60 L syrup.
Therefore we are taking 10 L of syrup from initial solution and replacing with water.
using urinary method:
70 L syrup in 150 L solution
10 L syrup in 21.4 L solution
We started by multiplying 10
Now to get to the result we need to divide by 10 => amount of solution to be replaced with water = (21.4/10) = 2.14.
Correct option : C
Answer: (C) 2.14
Question: The Carson family will purchase three used cars. There are two models of cars available, Model A and Model B, each of which is available in five colors: blue, black, red, and green. How many different combinations of three cars can the Carsons select if all the cars are to be different colors?
(A) 24
(B) 32
(C) 48
(D) 60
(E) 100
Rationale: I have no idea how you got 8C8, 7C6 and 4C1.
I could have understood 8C1*6C1*4C1 (I have explained why this doesn't work in the post above)
The best way to solve it is by first selecting 3 colors out of the given 4 in 4C3 ways. (say, you got black, red and green)
Now for each color, you have 2 choices - model A or B
So you select a model in 2 ways.
No of ways of selecting the 3 cars = 5C3 * 2 * 2 * 2 =100
Well, my logic was
The number of ways of selecting r objects from n different objects is nCr.
We have 8 options and can select either of the 8 as the first - 8C8
One car is gone and one becomes a forbidden choice so we have 7 options and need to select either of the 6 as the first - 7C6
Two cars are gone and two becomes a forbidden choice so we have 6 options and need to select either of the 4 as the first - 6C4
E
Answer: (E) 100
Question: The weights of one liter vegetable ghee packet of two brands ‘A’ and ‘B’ are 800 gm and 850 gm respectively. If they are mixed in the ratio of 3 : 2 by volumes to form a mixture of 3 liters, what is the weight (in kg) of the mixture?
(A) 3.84
(B) 1.75
(C) 3.52
(D) 2.46
(E) None of these
Rationale: Here's how I did it. My notes from reading the problem were:
1L A = 800 gm
1L B = 850 gm
We are mixing five parts (3 parts A plus 2 parts B, 5 parts total) to get 3L, so 5x = 3 ---> x = 3/5. Each part is 3/5 of a liter.
So if we have 3 parts A, we have 800*3*(3/5) = 1440
If we have 2 parts B, we have 850*2*(3/5) = 1020
1440 + 1020 = 2460
Solving for units gives us 2.46
So the answer is D
Answer: (D) 2.46
Question: Little John had $8.50. He spent $1.25 on sweets and gave to his two friends $1.20 and $2.20. How much money was left?
(A) $5.85
(B) $6.85
(C) $ 3.85
(D) $2.85
(E) $4.85
Rationale: John spent and gave to his two friends a total of
1.25 + 1.20 + 2.20 = $4.65
Money left
8.50 -4.65 = $3.85
correct answer is C) $ 3.85
Answer: (C) $ 3.85
Question: A make a wall in 9 hour. B makes a wall in 10 hour. When doing together 10 more bricks are required and together make a wall in 5 hour. How many bricks r there in the wall?
(A) 180 bricks
(B) 190 bricks
(C) 170 bricks
(D) 160 bricks
(E) 195 bricks
Rationale: Time taken by Aand B together to complete same brick job = 1/(1/9 +1/10) = 90/19 hrs.
Actual time taken = 5 hrs
extra time taken for 10 bricks job = 5-90/19 = 5/19 hrs
so 5/19 hrs are reqd for 10 bricks
5 hrs are reqd for 190 bricks.
so initially 180 bricks were reqd.
Finally 190 bricks are used.
ANSWER:B
Answer: (B) 190 bricks
Question: The speed of a car increases by 2 kms after every one hour. If the distance travelling in the first one hour was 35 kms. what was the total distance travelled in 12 hours?
(A) 252 kms
(B) 152 kms
(C) 552 kms
(D) 752 kms
(E) 152 kms
Rationale: Explanation:
Total distance travelled in 12 hours =(35+37+39+.....upto 12 terms)
This is an A.P with first term, a=35, number of terms,
n= 12,d=2.
Required distance = 12/2[2 x 35+{12-1) x 2]
=6(70+23)
= 552 kms.
Answer: C
Answer: (C) 552 kms
Question: The heights of a wall is six times its width and the length of the wall is seven times its height. If volume of the wall be 16128 cu .m, its width is
(A) 4 m
(B) 4.5 m
(C) 5 m
(D) 6 m
(E) None
Rationale: Solution
Let the width of the wall be x metres.
Then, Height = (6x)m and length= (42x)m.
42x × x ×6x	= 16128
x3‹=› (16128 / 42 × 6)= 64
‹=› x= 4.
Answer A
Answer: (A) 4 m
Question: A bag contains 4 blue, 5 white and 6 green balls. Two balls are drawn at random. What is the probability that one ball is white?
(A) 3/4
(B) 2/35
(C) 1/2
(D) 3/7
(E) 10/21
Rationale: 1 white ball can be drawn from 5 white balls in 5C1 = 5 ways
1 ball from the remaining 10 balls can be drawn in 10C1 = 10 ways
Hence, one white ball and one other colour ball can be drawn in 5 × 10 = 50 ways
i.e.,n(E) = 50
n(S) = Number of ways in which 2 balls can be drawn from 15 balls (∵ 4 + 5 + 6 = 15)
= 15C2
P(E) = n(E)/n(S)=50/15C2
=50(15×14/2×1)=50×2/15×14=10×2/3×14=10/3×7=10/21
ANSWER:E
Answer: (E) 10/21
Question: A number when divided by a certain divisor left remainder 241, when twice the number was divided by the same divisor, the remainder was 102. Find the divisor?
(A) 370
(B) 365
(C) 380
(D) 456
(E) 460
Rationale: Easy solution:
N= Dq1+241
2N = 2Dq1 + 482 - (1)
2N = Dq2 + 102 - (2)
As (1) = (2) = 2N
D*(q2-2q1) = 380
D * Some integer = 380
Checking all options only (C) syncs with it.
Answer C
Answer: (C) 380
Question: A train running at the speed of 60 km/hr crosses a pole in 6 seconds. Find the length of the train.
(A) 150 m
(B) 145 m
(C) 100 m
(D) 135 m
(E) 155 m
Rationale: Speed = 60*(5/18) m/sec = 50/3 m/sec
Length of Train (Distance) = Speed * Time
(50/3) * 6 = 100 meter
ANSWER: C
Answer: (C) 100 m
Question: Bradley owns b video game cartridges. If Bradleyâ€™s total is two-thirds the total owned by Andrew and five times the total owned by Charlie, how many video game cartridges do the three of them own altogether, in terms of b?
(A) 16/3)b
(B) 17/4)b
(C) 13/4)b
(D) 27/10)b
(E) 7/12)b
Rationale: Step 1: Categorize the problem
This problem is testing basic algebra and equations, with an extra layer of complexity by having variables in the answer choices.
Step 2: Think like the test maker
What is the key detail or key details in the problem? The key detail to immediately recognize is that the problem gives you Andrew and Charlieâ€™s totals in relation to Bradleyâ€™s total rather than giving you Bradleyâ€™s total in relation to the other two; and then the problem asks you to solve the problem in terms of b. This means that you have to relate Andrew and Charlieâ€™s values in relation to Bradleyâ€™s total. The test maker is attempting to force you to structure the problem in the opposite way that most people are used to structuring information. By gaining this insight, it makes it easier to solve the problem.
Step 3: Solve the problem
b = Bradleyâ€™s total
(3/2)b = Andrewâ€™s total
(1/5)b = Charlieâ€™s total
Add each total
b + (3/2)b+ (1/5)b = (10/10)b + (15/10)b + (2/10)b= (27/10)b
Therefore,choose D.
Answer: (D) 27/10)b
Question: At a certain conference, 52% of the attendees registered at least two weeks in advance and paid their conference fee in full. If 30% of the attendees who paid their conference fee in full did not register at least two weeks in advance, what percent of conference attendees registered at least two weeks in advance?
(A)  18.0%
(B)  62.0%
(C)  79.2%
(D)  74.28%
(E)  82.0%
Rationale: Refer to the table in the attachment:
Let x= No. of members who have paid in Full
30 % members paid in full and did not register in advance = 0.3x
52 % registerd in advance and paid in full.
So if total No. of members = 100, then 52 members paid Full and registered in advance.
Hence total members who paid full amount = 0.3x + 52 =x
0.7x =52
Hence x = 74.28
i.e. 74.28 out of 100 or 74.28 %
Ans. D
Answer: (D)  74.28%
Question: Two trains running in opposite directions cross a man standing on the platform in 27 seconds and 17 seconds respectively and they cross each other in 21 seconds. The ratio of their speeds is?
(A) 3/7
(B) 2/3
(C) 3/5
(D) 3/1
(E) 3/3
Rationale: Let the speeds of the two trains be x m/sec and y m/sec respectively. Then, length of the first train = 27 x meters, and length of the second train = 17 y meters. (27 x + 17 y) / (x + y) = 21
==> 27 x + 17 y = 21 x + 21 y ==> 6 x = 4 y ==> x/y
= 2/3.
Answer: B
Answer: (B) 2/3
Question: The average of eleven ten prime numbers which are odd is?
(A) 17.72
(B) 18.52
(C) 19.63
(D) 16.53
(E) 15.63
Rationale: Explanation:
Sum of first 11 prime no. which are odd = 195
Average = 195/11 = 17.72
Answer:A
Answer: (A) 17.72
Question: The pilot of a small aircraft with a 40-gallon fuel tank wants to fly to Cleveland, which is 480 miles away. The pilot recognizes that the current engine, which can fly only 5 miles per gallon, will not get him there. By how many miles per gallon must the aircraft’s fuel efficiency be improved to make the flight to Cleveland possible?
(A) 2
(B) 4
(C) 12
(D) 40
(E) 7
Rationale: Actual miles/gallon is = 480/40 = 12 miles/gallon.
Current engine miles/gallon is 5 miles/gallon.
Additional 7 miles/gallon is required to match the actual mileage.
IMO option E.
Answer: (E) 7
Question: A certain school principal must choose 5 students to attend a field trip out of a group of 8 students. In addition, out of the 5 chosen students, the principal must select a note-taker and a treasurer. How many different ways are there for the principal to select the 5 students and then select the treasurer and the note-taker?
(A) 1,120
(B) 2,520
(C) 5,040
(D) 6,020
(E) 10,080
Rationale: 5 students can be selected out of 8 students in 8C5 ways.
out of the remaining 5 students,Note taker can be chosen in 5 ways.
Finally only 4 students remain from which we can choose a treasurer in 4 ways.
Total number of ways = 56* 5 *4 = 1120
correct answer - A
Answer: (A) 1,120
Question: Dan has a total of 12 bill in his wallet.
Some are $5 bills and the rest are $10 bills.
The total value of the 12 bills is $115.
How many $5 bills and how many $10 bills does he have?
(A) 2 $5 Bill & $11 Bill
(B) 5 $5 Bill & 10 $11 Bill
(C) 4 $5 Bill & 6 $11 Bill
(D) 1 $5 Bill & 9 $11 Bill
(E) 1 $5 Bill & 10 $11 Bill
Rationale: Total bills in Wallet =12
Total value of 12 Bills =$115
If we can select Option E we will get the following.
Total Value of $5 Bill = $5 *1 = $5
Total value of $10 Bill = $10*11= $110
So the total is $5 + $110 = $115
Answer is E
Answer: (E) 1 $5 Bill & 10 $11 Bill
Question: What sum of money will produce Rs.210 as simple interest in 4 years at 3 1/2 percent?
(A) Rs.2500
(B) Rs.1500
(C) Rs.1400
(D) Rs.1600
(E) Rs.1300
Rationale: 210 = (P*4*7/2)/100
P = 1500
Answer: B
Answer: (B) Rs.1500
Question: The average of five consecutive odd numbers is 61. What is the difference between the highest and lowest numbers ?
(A) 9
(B) 8
(C) 7
(D) 6
(E) 1
Rationale: Let the numbers be x, x + 2, x + 4, x + 6 and x + 8.
Then [x + (x + 2) + (x + 4) + (x + 6) + (x + 8) ] / 5 = 61.
or 5x + 20 = 305 or x = 57.
So, required difference = (57 + 8) - 57 = 8
Answer: B) 8
Answer: (B) 8
Question: A single discount equivalent to the discount series of 30%, 10% and 5% is?
(A) 40.15
(B) 31.7
(C) 31.6
(D) 31.5
(E) 31.1
Rationale: 100*(70/100)*(90/100)*(95/100) = 59.85
100 - 59.85 = 40.15
Answer:A
Answer: (A) 40.15
Question: A man can row upstream at 5kmph and downstream at 15kmph. Find man's rate in still water ?
(A) 5km/hr
(B) 15km/hr
(C) 10km/hr
(D) 20km/hr
(E) 7.5km/hr
Rationale: Rate in still water = 1/2 (5+15) = 10km/hr
Answer is C
Answer: (C) 10km/hr
Question: Two numbers are in the ratio 2 : 3. If eight is added to both the numbers, the ratio becomes 3 : 4. The numbers are ?
(A) 15 and 20.
(B) 16 and 24.
(C) 13 and 17.
(D) 17 and 9.
(E) none of these
Rationale: Let x and y be the two numbers
Therefore, (x/y) = (2/3),
(x + 8)/(y + 8) = 3/4
=> x = 16, y = 24
ANSWER:B
Answer: (B) 16 and 24.
Question: Employees at a company will vote for an executive team of five people from eight qualified candidates. The executive team consists of a president, a treasurer, and three warrant officers. If an executive team is considered different if any of the same people hold different offices, then how many possible executive teams D could be selected from the eight candidates?
(A) 56
(B) 120
(C) 210
(D) 1120
(E) 6720
Rationale: If an executive team is considered different if any of the same people hold different offices,....
so you will not have answer as 6720..
president could be by any of 8 person..
treasurer could be any out of remaining 7 person..
remaining three order does not matter, so we have to choose 3 out of 6=6c3=20..
total ways D= 8*7*20=1120..
ans D...
Answer: (D) 1120
Question: If a train, travelling at a speed of 90 kmph, crosses a pole in 5 sec, then the length of train is?
(A) 177 m
(B) 125 m
(C) 188 m
(D) 178 m
(E) 777 m
Rationale: D = 90 * 5/18 * 5
= 125 m
Answer: B
Answer: (B) 125 m
Question: A batsman scored 60 runs which included 2 boundaries and 2 sixes. What percent of his total score did he make by running between the wickets.
(A) 30%
(B) 33.33%
(C) 40%
(D) 60%
(E) 50%
Rationale: Explanation:
Number of runs made by running = 60- (2 x 4 + 2 x 6)
= 60 - (20)
= 20
Now, we need to calculate 20 is what percent of 60.
=> 20/60 * 100 = 33.33 %
Option B
Answer: (B) 33.33%
Question: The product of two numbers is 2028 and their H.C.F is 13. The number of such pairs is:
(A) 1
(B) 2
(C) 3
(D) 4
(E) 5
Rationale: Let the numbers be 13a and 13b.
Then, 13a * 13b = 2028 => ab = 12.
Now, co-primes with product 12 are (1, 12) and (3, 4).
So, the required numbers are (13 * 1, 13 * 12) and (13 * 3, 13 * 4).
Clearly, there are 2 such pairs.
ANSWER:B
Answer: (B) 2
Question: Fom the integer n, if n*n*n is odd, then what is true from below options?
(A) n is odd and n*n is even
(B) n is odd
(C) n*n is odd
(D) n is even
(E) n*n is even
Rationale: n is odd and n*n is even
Option A
Answer: (A) n is odd and n*n is even
Question: The area of a rectangular plot is 23 times its breadth. If the difference between the length and the breadth is 10 metres, what is its breadth?
(A) 13 metres
(B) 5 metres
(C) 7.5 metres
(D) Data inadequate
(E) None of these
Rationale: L × B = 23 × B
∴ L = 23 m
and L – B = 10
∴ B = 23 – 10 = 13 m
Answer A
Answer: (A) 13 metres
Question: 10 camels cost as much as 24 horses, 16 horses cost as much as 4 oxen and 6 oxen as much as 4 elephants. If the cost of 10 elephants is Rs. 170000, find the cost of a camel?
(A) 3278
(B) 2669
(C) 2770
(D) Rs.6800
(E) 2791
Rationale: Cost of the camel = P
10 camels = 24 horses
16 horses = 4 oxen
6 oxen = 4 elephants
10 elephants = Rs.170000
P = Rs.[(24 * 4 * 4 * 170000)/(10 * 16 * 6 * 10)]
P = Rs.(65280000/9600) => P = Rs.6800
Answer: D
Answer: (D) Rs.6800
Question: A gang of 8 boys goes on an tour in 2 cars, of which 1 canseat 5 & the other only 4. In how many ways can they travel?
(A) 90
(B) 100
(C) 126
(D) 154
(E) 167
Rationale: There are 8 students and the maximum capacity of the cars together is 9.
We may divide the 8 students as follows
Case I: 5 students in the first car and 3 in the second
Or Case II: 4 students in the first car and 4 in the second
Hence, in Case I: 8 students are divided into groups of 5 and 3 in8C3 ways.
Similarly, in Case II: 8 students are divided into two groups of 4 and 4 in 8C4ways.
Therefore, the total number of ways in which 8 students can travel is:
\inline {\color{Blue}8C_{3}+8C_{4}}=56 + 70= 126
C
Answer: (C) 126
Question: A composer’s guild is planning its spring concert, and twelve pieces have been submitted for consideration. The director of the guild knows that they will only have time to present eight of them. If the pieces can be played in any order, how many combinations of pieces are possible?
(A) 402
(B) 210
(C) 109
(D) 504
(E) 495
Rationale: Combination question..
12C8 = 495..
IMO option E is correct..
Answer: (E) 495