mathewhe/aqua_rat huggingface dataset:
Question: The greatest common factor of 16 and the positive integer n is 4, and the greatest common factor of n and 45 is 3. Which of the following could be the greatest common factor of n and 120?
(A) 5
(B) 8
(C) 12
(D) 24
(E) 30
Rationale: n includes the factors 2^2 (but not 2^3) and 3 (but not 3^2 or 5)
120 = 8*3*5
The GCF is 4*3 = 12.
The answer is C.
Answer: (C) 12
Question: If M and N are positive integers that have remainders of 1 and 3, respectively, when divided by 4, which of the following could NOT be a possible value of M+N?
(A) 76
(B) 52
(C) 36
(D) 28
(E) 10
Rationale: M=4p+1
N=4q+3
We need M+N=4p+1+4q+3=4(p+q)+4
Pick numbers for pq
Since it is an addition of pq and the answer to this expression should be an integer (because all the numbers being added are integers),
we just need to choose values so that we get integer multiples of 6 so
p+q=0 ; M+n = 4
p+q=1 ; M+N = 8
P+q=2 ; M+N = 12
and so on, so basically you get something like - 4,8,12,16,20,24,28,..... all the other options were turning up.
Then I directly tried p+q=2because it was closer to 10, i got 12,
So Answer E.
Answer: (E) 10
Question: In his pocket, a boy has 3 red marbles, 5 blue marbles, and 6 green marbles. How many will he have to take out of his pocket to ensure that he has taken out at least one of each color?
(A) 10
(B) 11
(C) 12
(D) 13
(E) 14
Rationale: The worst case scenario would be that he has taken 5 blue and 6 green, a total of 11 marbles, and still doesn't have 3 distinct colors. But the next draw, marble number 12, will surely be red as only the red marbles are left in his pocket.
The answer is C.
Answer: (C) 12
Question: A number consists of two digits. If the digits interchange places and the new number is added to the original number, then the resulting number will be divisible by :
(A) 5
(B) 7
(C) 9
(D) 11
(E) 13
Rationale: Sol.
Let the ten’s digit be x and unit’s digit be y. Then, number = 10x + y
Number obtained by interchanging the digits = 10y + x.
∴ (10x+y) + (10y + x) = 11 (x + y), which is divisible by 11.
Answer D
Answer: (D) 11
Question: Two trains are moving in the same direction at 72 kmph and 36 kmph. The faster train crosses a man in the slower train in 27 seconds. Find the length of the faster train?
(A) 290 m
(B) 270 m
(C) 220 m
(D) 260 m
(E) 250 m
Rationale: Relative speed = (72 - 36) * 5/18 = 2 * 5 = 10 mps.
Distance covered in 27 sec = 25 * 10 = 250 m.
The length of the faster train = 250 m.
ANSWER:E
Answer: (E) 250 m
Question: If the sum of five consecutive even positive integers is A, then the sum of the next five even consecutive integers in terms of A is:
(A) A+5
(B) A+10
(C) A+25
(D) A+50
(E) 2A + 5
Rationale: In Case of Consecutive Integers or Integers in Arithmetic Progression Mean = Median
I.e. Median = A/5 = Mean = Third Integer
First Integer = A/5 - 4
Second Integer = A/5 - 2
Third Integer = A/5
Fourth Integer = A/5 + 2
Fifth Integer = A/5 + 4
i.e.
Sixth Integer = A/5 + 6
Seventh Integer = A/5 + 8
Eighth Integer = A/5 + 10
Ninth Integer = A/5 + 12
Tenth Integer = A/5 + 14
Now Mean of next 5 Integers = Median = A/5 + 5
i.e. Sum of Next 5 integers = (A/5 + 10)*5 = A+50
Answer: option D
Answer: (D) A+50
Question: Out of first 20 natural numbers, one number is selected at random. The probability that it is either an even number or a prime number is?
(A) 17/27
(B) 17/70
(C) 17/90
(D) 17/20
(E) 17/23
Rationale: n(S) = 20
n(Even no) = 10 = n(E)
n(Prime no) = 8 = n(P)
P(EᴜP) = 10/20 + 8/20 - 1/20 = 17/20
Answer: D
Answer: (D) 17/20
Question: Abby and Bobby type at constant rates of 70 words per minute and 60 words per minute, respectively. Bobby begins typing before Abby and has typed 600 words when Abby begins typing at 1:30 pm. If they continue typing at their respective rates, at what time will Abby have typed exactly 200 more words than Bobby?
(A) 1:40 PM
(B) 2:50 PM
(C) 2:00 PM
(D) 2:10 PM
(E) 2:20 PM
Rationale: Say time needed for Abby to type 200 more words than Bobby is t. In that time she would type 70t words and Bobby would type 60t words.
Now, total words typed by Bobby would be 600+60t and we want that number to be 200 less than 70t: 600+60t=70t-200 --> t=80.
1:30 PM + 80 minutes = 2:50 PM.
Answer: B.
Answer: (B) 2:50 PM
Question: A man swims downstream 72 km and upstream 45 km taking 3 hours each time; what is the speed of the current?
(A) 1.5
(B) 3.5
(C) 4.5
(D) 2.5
(E) 5.5
Rationale: 72 --- 3 DS = 24
? ---- 1
45 ---- 3 US = 15
? ---- 1 S = ?
S = (24 - 15)/2 = 4.5
Answer:C
Answer: (C) 4.5
Question: A trader sells 85 meters of cloth for Rs. 8925 at the profit of Rs. 25 per metre of cloth. What is the cost price of one metre of cloth?
(A) 80
(B) 28
(C) 90
(D) 26
(E) 11
Rationale: Explanation:
SP of 1m of cloth = 8925/85 = Rs. 105
CP of 1m of cloth = SP of 1m of cloth - profit on 1m of cloth
= Rs. 105 - Rs. 25 = Rs. 80.
Answer: A
Answer: (A) 80
Question: If 1 > 1 - ab > 0, which of the following must be true?
I. a/b > 0
II. ab < 1
III. a/b < 2
(A) I only
(B) II only
(C) III only
(D) I and II only
(E) I and III only
Rationale: MANHATTAN GMATOFFICIAL SOLUTION:
You can manipulate the original compound inequality as follows, making sure to perform each manipulation on every term:
1 > 1 - ab > 0
0 > -a b > -1 Subtract 1 from all three terms.
0 < ab < 1 Multiply all three terms by -1 and flip the inequality signs.
Therefore you know that 0 < ab < 1. This tells you that ab is positive, so a/b must be positive (a and b have the same sign). Therefore, I must be true. However, you do not know whether a/b < 1, so II is not necessarily true. But you do know that ab must be less than 1, so III must be true.
Therefore, the correct answer is (D).
Answer: (D) I and II only
Question: {-10, -6, -5, -4, -2.5, -1, 0, 2.5, 4, 6, 7, 10}
A number is to be selected at random from the set above. What is the probability that the number will be a solution to the equation (x-2)(x+1)(2X+5) = 0?
(A) 1/12
(B) 1/6
(C) 1/4
(D) 1/3
(E) 1/2
Rationale: x = -1
Prob = 1/12
Answer -A
Answer: (A) 1/12
Question: If the average (arithmetic mean) of 5 positive temperatures is x degrees Fahrenheit, then the sum E of the 3 greatest of these temperatures, in degrees Fahrenheit, could be
(A)  6x
(B)  4x
(C)  5x/3
(D)  3x/2
(E)  3x/5
Rationale: Note that we have 5positivetemperatures.
Next, as the average is x then the sum of the temperatures is 5x and as all the temperatures are positive then the sum of the 3 greatest must be more than (or equal to) 3x (as the average of the 3 greatest must be at least x) and less than 5x: 3x<E<5x --> only option B fits.
Answer: B.
Answer: (B)  4x
Question: What will be the result of 12^4+ 3 +2^9 +3 - 8/2 ?
(A) 58
(B) 14
(C) 145
(D) 69
(E) 74
Rationale: The multiplication(e.g. 12^4) and division(e.g. 8/2) is done first and then the sum(e.g. 48+3) and
subtraction (e.g.4-4), and the answer is 69, option D.
Answer: (D) 69
Question: A pet store holds cats and dogs. If the difference between the number of cats and the number of dogs is 7. What could be the ratio of Cats to dogs in the pet store?
(A) 1:3
(B) 1:4
(C) 28:35
(D) 2:5
(E) 4:6
Rationale: Say theratioof cats to dogs is a/b. Then thenumberof cats would be ax and thenumberof dogs bx, for some positive integer x.
We are told that ax - bx = 7 --> x(a - b) =7. Since 7 is a prime number it could be broken into the product of two positive multiples only in one way: x(a - b) = 1*7.
The above implies that either x = 1 and a - b = 7 or x = 7 and (a - b) = 1.
Therefore the correct answer should have the difference between numerator and denominator equal to 1 or 7.
For the original question only option which fits is E, 4:5. Cats = 7*4 = 28 and dogs = 7*5 = 35.
Answer: C.
Answer: (C) 28:35
Question: The average of 10 numbers is 40.2. Later it is found that two numbers have been wrongly copied. The first is 16 greater than the actual number and the second number added is 13 instead of 31. Find the correct average.
(A) 40.2
(B) 40.4
(C) 40.6
(D) 40.8
(E) None of the above
Rationale: Sum of 10 numbers = 402
Corrected sum of 10 numbers
= 402 – 13 + 31 – 16 = 404
Hence, new average = 404⁄10 = 40.4
Answer B
Answer: (B) 40.4
Question: When the positive integer A is divided by 9 and 5, the remainder is 3 and 4, respectively. When the positive integer B is divided by 9 and 5, the remainder is 3 and 4, respectively. Which of the following must be a factor of A-B?
(A) 32
(B) 36
(C) 40
(D) 45
(E) 50
Rationale: A = 9k+3 = 5j+4
B = 9m+3 = 5n+4
A-B = 9(k-m) = 5(j-n)
Thus A-B is a multiple of 9 and 5, so it is multiple of 45.
The answer is D.
Answer: (D) 45
Question: The 8 spokes of a custom circular bicycle wheel radiate from the central axle of the wheel and are arranged such that the sectors formed by adjacent spokes all have different central angles, which constitute an arithmetic series of numbers (that is, the difference between any angle and the next largest angle is constant). If the largest sector so formed has a central angle of 80°, what fraction of the wheel’s area is represented by the third smallest sector?
(A) 1/72
(B) 1/36
(C) 1/18
(D) 1/12
(E) 1/9
Rationale: Its an AP question .... it is given clearly in the question .
Let the smallest angle be a
and the circle has 8 sectors and hence 8 angle with a common difference d
hence all the angles can be written in AP form with Cd as d ,
a, a+d, a+2d, a+3d ,a+4d, a+5d, a+6d ,a+7d,
given that a+7d = 80 --------1
also
a + a+d + a+2d + a+3d +
a+4d + a+5d + a+6d + a+7d = 360 ( as sum of all the angle is 360)
which is 8a + 28d = 360 --------2
solving 1 and 2
we get a=10
We are almost done ,
now the question ask what fraction of the wheel’s area is represented by the smallest sector ?
(30/360)( pie r*r)/ (pie r*r) = 30/360= 1/12
D ans ....
Answer: (D) 1/12
Question: A quadratic function f(x) attains its minimum value of -15 at x=3. If f(0)=5, find the value of f(9).
(A) 65
(B) 55
(C) -25
(D) 75
(E) 25
Rationale: Explanation :
Any quadratic equation can be written as f(x) = α(x-k)2 - β
Given that minimum value of f(x) is -15 at x=3
f(x) is minimum when x=k => k=3
-15=-β => β= 15
Also given that f(0) = 5
=> 5 = α(0-3)2 - 15 => α= 20/9
Hence, f(9)=20/9(9-3)2 - 15 = 65
Answer : A
Answer: (A) 65
Question: A circular garden is surrounded by a fence of negligible width along the boundary. If the length of the fence is 1/4 of th area of the garden. What is the radius of the circular garden?
(A) 1
(B) 2
(C) 4
(D) 8
(E) 16
Rationale: as per the question-- width is negligible
now,
let L be the length of the fence =2pir
L=1/4(pir^2)
pir^2=8pir
r=8
Answer : D
Answer: (D) 8
Question: If the horse can run 10 miles/hour, how many days would it take for a horse to run from New York City to Washington. D.C.? (240 miles from NYC to D.C.)
(A) 0.6
(B) 0.8
(C) 1
(D) 1.2
(E) 1.4
Rationale: The horse runs 10 miles/hour, thus it would take the horse 240 miles/10 miles/hour to = 24 hours to run from NYC to D.C. There are 24 hours in a day, so days it take would be 24hours/24hours/day = 1 day. Correct Option: 1
Answer: (C) 1
Question: Anil can do a work in 15 days while Sunil can do it in 25 days. How long will they take if both work together?
(A) 4 3/8 days
(B) 7 3/8 days
(C) 9 3/8 days
(D) 8 3/8 days
(E) 11 3/8 days
Rationale: C
9 3/8 days
1/15 + 1/25 = 8/75
75/8 = 9 3/8 days
Answer: (C) 9 3/8 days
Question: 2^2*3^3*2^2*3^6 =
(A) 3^5*2^5
(B) 2^9*3^4
(C) 2^4*3^9
(D) 5^8
(E) 6^10
Rationale: 2^2*3^3*2^2*3^6 =
A) 3^5*2^5
B) 2^9*3^4
C) 2^4*3^9
D) 5^8
E) 6^10
If the base is same, powers are added so that follows C) 2^4*3^9.
Hence the answer is C
Answer: (C) 2^4*3^9
Question: Trapezoid JKLM in the x-y plane has coordinates J = (–2, –4), K = (–2, 1), L = (6, 7), and M = (6, –4). What is its perimeter?
(A) 34
(B) 36
(C) 38
(D) 40
(E) 42
Rationale: This one may look challenging initially, but all kinds of simplifying tricks. First of all, J & K have the same x-coordinate, so that’s a vertical segment, and the length is JK = 1 – (–4) = 5. L & M also have the same x-coordinate, so that’s also a vertical segment, and the length is LM = 7 – (–4) = 11. J & M have the same y-coordinate, so that’s also a horizontal segment, and the length is JM = 6 – (–2) = 8. Right there, we have the lengths of three of the four sides.
The last side to find is KL. From K = (–2, 1), we have to go over 8 and up 6 to get to L = (6, 7), so 6 and 8 the legs of the right triangle, and KL is the hypotenuse. We recognize another common Pythagorean triplet — (6, 8, 10), which is a multiple of the (3, 4, 5) triplet. Thus, without further calculations, we immediately know KL = 10.
Perimeter = JK + KL + LM + JM = 5 + 10 + 11 + 8 = 34
Answer = A
Answer: (A) 34
Question: In a garden, carrots are planted in rows. In each row there are as many carrots as the number of rows in the garden. If each plant attracts as many bunnies as the number of carrots in each row and if the total number of bunnies is n, then :
(A) n is a perfect square
(B) n is an odd number
(C) n is an even number
(D) n is a perfect cube
(E) none
Rationale: For example, if there were 4 carrot rows, the garden would have a 4x4 arrangement. If each carrot attracts 4 bunnies, the number of bunnies would be (4*4)*4 = 64 pieces, which is a cube of 4.
Answer: D
Answer: (D) n is a perfect cube
Question: The ratio of investments of A and B is 8 : 7 and the ratio of their yearend profits is 20 : 21. If B invested for 12 months, then find the period of investment of A:
(A) 6 months
(B) 8 months
(C) 10 months
(D) 12 months
(E) None
Rationale: Let A invest for x months ; A = 8x months,
B = 7 × 12 = 84 months
8x/84 = 20/21
⇒ x = 10.
Answer: C
Answer: (C) 10 months
Question: What is the place value of 7 in the numeral 7529
(A) 2500
(B) 3400
(C) 3500
(D) 3000
(E) 7000
Rationale: Option 'E'
7 * 1000 = 7000
Answer: (E) 7000
Question: A woman complete a journey in 30 hours. She 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) 334 km.
(B) 216 km.
(C) 314 km.
(D) 224 km.
(E) 672 km.
Rationale: 0.5x/21 + 0.5x/24 = 30
--> x/21 + x/24 = 60
--> x = 672 km.
E
Answer: (E) 672 km.
Question: Find the face value of 9 in 79864
(A) 90
(B) 900
(C) 90000
(D) 9000
(E) 9
Rationale: Face value is the value of digit itself
face value of 9 = 9
Answer : E
Answer: (E) 9
Question: A certain automobile company’s best-selling model is the Speedster. The Speedster, like all of their other models, comes in coupe and convertible styles. 2/3 of the current inventory is Speedsters, of which 4/5 are convertibles. If there are 50 vehicles that are not Speedsters, how many Speedster convertibles are there?
(A) 30
(B) 48
(C) 60
(D) 80
(E) 90
Rationale: Total Vehicle = 2/3 of speedster + 1/3 of others.
Speedster convertibles = 2/3 total vehicle * 4 /5
Given : 1/3 constitutes 50 Vehicles. hence 2/3 constitutes 100
Speedster convertibls = 100 * 4/5 = 80
D
Answer: (D) 80
Question: A table is bought for Rs.600/- and sold at a loss of 10% find its selling price
(A) Rs.500/-
(B) Rs.530/-
(C) Rs.540/-
(D) Rs.600/-
(E) Rs.700/-
Rationale: 100 % ------> 600 (100 * 6 = 600)
90 % ------> 540 (90 * 6 = 540)
Selling price = Rs.540/-
C
Answer: (C) Rs.540/-
Question: speed of a bus is 54kmph and including stoppages, it is 45kmph. For how many minsdoes the bus stop per hour?
(A) 10 min
(B) 15 min
(C) 20 min
(D) 25 min
(E) 40 min
Rationale: speed of the bus excluding stoppages = 54 kmph
speed of the bus including stoppages = 45 kmph
Loss in speed when including stoppages = 54 - 45 = 9kmph
=> In 1 hour, bus covers 9 km less due to stoppages
Hence, time that the bus stop per hour = time taken to cover 9 km
=distancespeed=954 hour=16 hour = 606 min=10 min
A
Answer: (A) 10 min
Question: The no 2.52, when written as a fraction and reduced to lowest terms,the sum of the numeratr n denominator is :
(A) 7
(B) 141
(C) 29
(D) 349
(E) 359
Rationale: the actual question has bar on decimal part. Hence the number is 2.5252525252..... .
So let x=2.525252..
then 100x= 252.525252
100x-x=250
x=250/99
so ans=num+den=349
ANSWER:D
Answer: (D) 349
Question: On a certain day, Joey, the ice-cream seller sold his ice creams to four different kids in a manner that each of the kids purchased half of the remaining ice creams and half ice-cream more.
If we tell you that the fourth kid bought just a single ice cream, can you find out how many ice creams were sold by Joey that day?
(A) 15
(B) 20
(C) 22
(D) 12
(E) 8
Rationale: A
Joey sold 15 ice creams that day.
The fourth kid bought a single ice cream. Therefore, we have the following equation:
Total - (Total / 2 + 1/2) = 1
Solving it, we get the total as 3.
Let's work this method till we reach the first kid.
The first kid bought 15 / 2 + 1/2 = 8 (leaving 7)
The second kid bought 7 / 2 + 1/2 = 4 (leaving 3)
The third kid bought 3 / 2 + 1/2 = 2 (leaving 1)
The fourth kid bought 1 / 2 + 1/2 = 1
Adding all of them together, we get
8 + 4 + 2 + 1 = 15.
Answer: (A) 15
Question: If f(y)=y^2 and y is a positive integer, which of the following CANNOT be the value of f(f(y))?
(A) 625
(B) 1296
(C) 256
(D) 350
(E) 16
Rationale: f(y)=y^2
f(f(y)) = (y^2)^2 = y^4
Therefore f(f(y)) will be numbers that are 4th power of other numbers.
Checking the options:
625 = 6^4
1296 = 6^4
256 = 4^4
350. This cannot be written as the 4th power of any number
16 = 2^4
Answer: D
Answer: (D) 350
Question: A can complete the job in 5 hours and B can complete the same job in 3 hours. A works for 1 hour and then B joins and both complete the job. What fraction of the job did B complete
(A) 1/8
(B) 3/10
(C) 1/2
(D) 5/6
(E) 8/9
Rationale: A=1/8
Answer: (A) 1/8
Question: If x is an integer and (x)(x^2)(x^3)(x^6) is positive, which of the following could be negative?
(A) x^4
(B) (x)(x^3)
(C) (x)(x)
(D) x + x^7
(E) 3x^2
Rationale: A) X^4 - always positive (or 0).
B) X(X^3) = X^4 - Again always positive (or 0).
C) (x)(x) = X^2 - Again always positive (or 0).
D) x+x^7 - Could be -ve if x is -ve.
E) 3X^2 - again always positive (or 0)
Answer D.
Answer: (D) x + x^7
Question: A six-sided die is rolled once. What is the probability that the number rolled is greater than 4?
(A) 2 / 3
(B) 2 / 6
(C) 3 / 3
(D) 4 / 5
(E) 2 / 4
Rationale: Only 5 & 6 so, 2 / 6
correct answer B
Answer: (B) 2 / 6
Question: Sam’s car was fined when he gave Joe and Peter a ride, so they decided to help Sam pay the fine. Joe paid $4 more than 1/4 of the fine and Peter paid $4 less than 1/3 of the fine, leaving pay $5 less than 1/2 the fine to complete the payment. What fraction of the fine did Sam pay?
(A) $30
(B) $25
(C) $35
(D) $40
(E) $45
Rationale: Call the fine F. Joe paid (1/4)F + 4 and Peter paid (1/3)F – 4, leaving (1/2)F – 5 left. If we add those three up, they should add up to F.
F = [(1/4)F + 4] + [(1/3)F – 4] + [(1/2)F – 5]
F = (1/4)F + (1/3)F + (1/2)F – 5
Multiply all terms by 12 to clear the fractions.
12F = 3F + 4F + 6F – 60
12F = 13 F – 60
–F = – 60
F = 60
Well, if the fine cost $60, then Sam paid the part not covered by Joe or Peter. Half the fine is $30, and Sam paid $5 less than this: $25.
Answer = B
Answer: (B) $25
Question: The product of the first seven positive multiples of three is closest to which of the following powers of 10?
(A) 10^9
(B) 10^8
(C) 10^7
(D) 10^6
(E) 10^5
Rationale: The product will be 3^7 * 1 * 2 * 3 * 4 * 5 * 6 * 7
=3^7 * 5140
= 9^3 * 15420
= ~135000 * 9 * 9
= ~1220000 * 9
= ~11000000 which is very close to 10^7
The correct answer is therefore (C)
Answer: (C) 10^7
Question: Calculate the number of tanks of 50x50x20m size needed to discharge crude oil from a cargo ship of volume 120000 m3 and is 90% full, if the tanks can only be filled up to 95%.
(A) 1
(B) 2
(C) 3
(D) 4
(E) 5
Rationale: Volume of the tank that needed to be filled=50x50x20x0.95=47500
Volume of the crude in ship=120000x0.9=108000
No. of tanks needed to discharge the ship=108000/47500= 2.27
Which is 3 tanks
Answer: C
Answer: (C) 3
Question: A bag contains 6 black and 9 white balls. One ball is drawn at random. What is the probability that the ball drawn is white?
(A) 4
(B) 4/3
(C) 4/5
(D) 4/9
(E) 3/5
Rationale: Let number of balls = (6 + 9) = 15.
Number of white balls = 9.
P (drawing a white ball) = 9/15=3/5
Hence Answer is E
Answer: (E) 3/5
Question: Average age of boys in a class is 16 years and average age of girls is 15 years, what is the average age of all
(A) 15.5
(B) 15
(C) 16
(D) Cant be computed
(E) 17
Rationale: Explanation:
As number of girls and boys is not given so result cant be computed
Answer: Option D
Answer: (D) Cant be computed
Question: The C.P of 10 pens is equal to the S.P of 5 pens. Find his gain % or loss%?
(A) 50%
(B) 40%
(C) 30%
(D) 60%
(E) 20%
Rationale: 10 CP = 5 SP
10 --- 5 CP gain
100 --- ? => 50%(gain)
Answer: A
Answer: (A) 50%
Question: The first photo shoot takes 3 minutes long and then the following shoots are taken at a rate of 23 seconds/shoot as the model is already at the scene. What is the maximum number of photo shoots taken under 10 minutes ?
(A) 13
(B) 14
(C) 15
(D) 16
(E) 19
Rationale: a must be an integer as it is the number shoots at a rate of 23sec/shoot
3*60 + 23a = 10*60
23a = 420
a = 18
The total number of shoots -->1 +18 = 19 and
20th shoot will be taken at 617 seconds which is above 10 minutes
ANSWER: E
Answer: (E) 19
Question: The average age of a group of 10 students is 20 years. If 2 more students join the group, the average age increases by 1 year. The average age of the new students is
(A) 23
(B) 21
(C) 19.5
(D) 20
(E) 22.5
Rationale: Total age of 10 students = 10 * 20 = 200 and the total age of 16 students = 21*15 = 315.
Let the average age of 2 new students be x.
Therefore total age of the new students = 2x.
So total age of 12 student =200 +5x=315, x=23
Hence, the correct answer is A.
Answer: (A) 23
Question: Three candidates contested in an election and received 6136, 7636, 11628 votes respectively. What is the percentage of the total votes did the winning candidate get?
(A) 46%
(B) 49%
(C) 57%
(D) 51%
(E) 62%
Rationale: Total number of votes polled = 6136+7636+11628 = 25400
Required percentage = 11628*100/25400 = 46%
Answer is A
Answer: (A) 46%
Question: A sock drawer contains seven socks, each one a different solid color. The colors of the socks are red, orange, yellow, green, blue, indigo, and violet. If the socks are laid next to each other, how many different arrangements of socks could be made?
(A) 24
(B) 240
(C) 1,024
(D) 2,520
(E) 5,040
Rationale: I see no condition for arrangement.
So 7! ways - 5,040
ANS option E is correct answer..
Answer: (E) 5,040
Question: A farming field can be ploughed by 6 tractors in 4 days. When 6 tractors work together, each of them ploughs 120 hectares a day. If two of the tractors were moved to another field, then the remaining 4 tractors could plough the same field in 5 days. How many hectares a day would one tractor plough then?
(A) 111
(B) 184
(C) 122
(D) 144
(E) 166
Rationale: If each of 6 tractors ploughed 120 hectares a day and they finished the work in 4 days, then the whole field is: 120*6*4=720*4=2880hectares. Let's suppose that each of the four tractors ploughed x hectares a day. Therefore in 5 days they ploughed
5*4*x=20*x hectares, which equals the area of the whole field, 2880 hectares.
So, we get 20x=2880
x=2880/20=144. Hence, each of the four tractors would plough 144 hectares a day.
Answer is D.
Answer: (D) 144
Question: (1/1*2)+(1/2*3)+(1/3*4)+(1/4*5)+ .............+(1/99*100)=
(A) 98/100
(B) 99/100
(C) 97/100
(D) 96/100
(E) 95/100
Rationale: (1/1*2)+(1/2*3)+(1/3*4)+(1/4*5)+ .............+(1/99*100)= 1-1/100= 99/100
ANSWER:B
Answer: (B) 99/100
Question: The length of a rectangular floor is more than its breadth by 200%. If Rs. 324 is required to paint the floor at the rate of Rs. 3 per sq m, then what would be the length of the floor?
(A) 28
(B) 37
(C) 18
(D) 38
(E) 39
Rationale: Let the length and the breadth of the floor be l m and b m respectively.
l = b + 200% of b = l + 2b = 3b
Area of the floor = 324/3 = 108 sq m
l b = 108 i.e., l * l/3 = 108
l2 = 324 => l = 18.
Answer:C
Answer: (C) 18
Question: How many numbers amongst the numbers 5 to 30 are there which are exactly divisible by 6 but not by 4?
(A) Nil
(B) 1
(C) 2
(D) 3
(E) More than 3
Rationale: 6,12,18,24,30 are divisible by 6.
12, 24 are divisible by 4 also.
So there are 3 numbers exactly divisible by 6 but not by 4
ANSWER:D
Answer: (D) 3