mathewhe/aqua_rat huggingface dataset:
Question: Square RSTU shown above is rotated in a plane about its center in a clockwise direction the minimum number of degrees necessary for T to be in the position where R is now shown. The number of degrees through which RSTU is rotated is
(A)  135 degree
(B)  180 degree
(C)  225 degree
(D)  270 degree
(E)  315 degree
Rationale: From the options, I am assuming the positioning of R and T relative to each other to be as shown. To replace R by T, focus on OT. Say, you rotate OT clockwise (and with it the entire square) and bring it in place of OR. How many degrees did you go? You covered 2 right angles i.e. 180 degrees.
Answer : B
Answer: (B)  180 degree
Question: A man swims downstream 35 km and upstream 20 km taking 5 hours each time, what is the speed of the man in still water?
(A) 6.5
(B) 5.5
(C) 5.2
(D) 4.6
(E) 9.7
Rationale: 35 --- 5 DS = 7
? ---- 1
20 ---- 5 US = 4
? ---- 1 M = ?
M = (7+ 4)/2 = 5.5
Answer: B
Answer: (B) 5.5
Question: The ratio of number of students studying Arts, Commerce and Science in a College is 3 : 7 :8. What is the new ratio of the number of students studying Arts, Commerce and Science respectively if there is an increase of 20%, 40% and 25% in the number of students studying Arts, Commerce and Science?
(A) 18 : 35 : 50
(B) 18 : 49 : 50
(C) 4 : 8 : 5
(D) 32 : 35 : 25
(E) None of these
Rationale: Suppose the number of students studying Arts, Commerce and Science be 3x, 7x and 8x respectively.
When their numbers are increased by 20%, 40% and 25% respectively the new ratio becomes
3x × 120% : 7x × 140% :
8x × 125% = 36 : 98 : 100
= 18 : 49 : 50
Answer B
Answer: (B) 18 : 49 : 50
Question: For an integer x greater than 1, x* denotes the product of all the integers from 1 to x inclusive. How many prime numbers are there between 7*+2 and 7*+7, inclusive ?
(A) 0
(B) 1
(C) 2
(D) 3
(E) 4
Rationale: Given that x* denotes the product of all the integers from 1 to n, inclusive so, 7* + 2 = 7! + 2 and 7* + 7 = 7! + 7.
Now, notice that we can factor out 2 our of 7! + 2 so it cannot be a prime number, we can factor out 3 our of 7! + 3 so it cannot be a prime number, we can factor out 4 our of 7! + 4 so it cannot be a prime number, ... The same way for all numbers between 7! + 2 and 7! +7, inclusive. Which means that there are no primes in this range.
Answer: A.
Answer: (A) 0
Question: An investment compounds annually at an interest rate of 33.34% What is the smallest investment period by which time the investment will more than triple in value?
(A) 1
(B) 2
(C) 3
(D) 5
(E) 4
Rationale: Assume initial amount is x
Annual Interest is 34.1% so after 1 year the amount will become x * (100+33.34)/100 => x*4/3
now we need to find n for x * (4/3)^n = 3x
or in other words n = 4
E
Answer: (E) 4
Question: In the x- y plane, there are 4 points (0,0), (0,4), (9,4), and (9,0). If these 4 points makes a rectangle, what is the probability that x+y<4?
(A) 2/5
(B) 3/5
(C) 3/7
(D) 4/7
(E) 2/9
Rationale: The line y=-x+4 intersects the rectangle and these three points of intersection (0,0), (0,4) and (4,0) form a triangle.
The points below the line y=-x+4 satisfy x+y<4.
The area of this triangle is (1/2)(4)(4)=8
The area of the rectangle is 36.
P(x+y<4) = 8/36 = 2/9
The answer is E.
Answer: (E) 2/9
Question: If (m-8) is a factor of m^2-sm-24, then s=
(A) 3
(B) 5
(C) 6
(D) 11
(E) 16
Rationale: (m-8)(m-a)=m^2-sm-24
A=-3
s=8+a=5=D=B
Answer: (B) 5
Question: A voltage will influence current only if the circuit is:
(A) 2
(B) 7
(C) 6
(D) 28
(E) 22
Rationale: Answer:E
Answer: (E) 22
Question: The radius of a wheel is 22.4 cm. What is the distance covered by the wheel in making 500 resolutions?
(A) 187 m
(B) 704 m
(C) 179 m
(D) 127 m
(E) 297 m
Rationale: In one resolution, the distance covered by the wheel is its own circumference. Distance covered in 500 resolutions.
= 500 * 2 * 22/7 * 22.4
= 70400 cm
= 704 m
Answer:B
Answer: (B) 704 m
Question: By selling 150 mangoes, a fruit-seller gains the selling price of 30 mangoes. Find the gain percent?
(A) 28%
(B) 25%
(C) 95%
(D) 75%
(E) 45%
Rationale: SP = CP + g
150 SP = 150 CP + 30 SP
120 SP = 150 CP
120 --- 30 CP
100 --- ? => 25%
Answer:B
Answer: (B) 25%
Question: A card is drawn from a pack of 52 cards. The probability of getting a queen of club or a king of heart is:
(A) 1/13
(B) 2/13
(C) 1/26
(D) 2/26
(E) 1/52
Rationale: Here, n(S) = 52.
Let E = event of getting a queen of club or a king of heart.
Then, n(E) = 2.
P(E) =	n(E)/n(S)	=2/52=1/26
Option C
Answer: (C) 1/26
Question: A sales staff is composed of a sales manager and two sales people, all of whom earn commission as a percentage of sales. Each sales person earns 5% commission on sales. In a given week, the sales staff earned a total of $1,500 in commissions on $5,000 worth of sales. What commission rate did the sales manager earn during that week?
(A) 20%
(B) 30%
(C) 35%
(D) 40%
(E) 45%
Rationale: A for me.
Let managers comminsion rate be M.
m*5000+ 2*0.05*5000=1500
5000*m=1000
m=20/100=20%
Answer: (A) 20%
Question: A certain lab experiments with white and brown mice only. In one experiment, 2/5 of the mice are brown. If there are 12 white mice in the experiment, how many mice in total are in the experiment?
(A) 20
(B) 12
(C) 15
(D) 18
(E) 16
Rationale: Let total number of mice = M
Number of brown mice = 2/5M
Number of white mice = 3/5 M = 12
=> M = 20
Answer A
Answer: (A) 20
Question: The greatest number of four digits which is divisible by 15, 25, 40 and 75 is:
(A) 9000
(B) 9400
(C) 9600
(D) 9800
(E) None
Rationale: EXPLANATION
Greatest number of 4-digits is 9999.
L.C.M. of 15, 25, 40 and 75 is 600.
On dividing 9999 by 600, the remainder is 399.
Required number (9999 – 399) = 9600.
Answer C
Answer: (C) 9600
Question: What will come in place of the x in the following Number series? 46080, 3840, 384, x
(A) 48
(B) 3
(C) 4
(D) 5
(E) 6
Rationale: 46080 /12 = 3840
3840 /10 = 384
384 /8 = 48
A
Answer: (A) 48
Question: An article is bought for Rs.600 and sold for Rs.500, find the loss percent?
(A) 16 4/3%
(B) 100/3%
(C) 16%
(D) 16 2/3%
(E) 18%
Rationale: Explanation:
600 ---- 100
100 ---- ? => 16 2/3%
ANSWER IS D
Answer: (D) 16 2/3%
Question: Two pipes can fill a tank in 20 and 24 minutes respectively and a waste pipe can empty 3 gallons per minute. All the three pipes working together can fill the tank in 15 minutes. The capacity of the tank is?
(A) 887 gallons
(B) 176 gallons
(C) 120 gallons
(D) 289 gallons
(E) 976 gallons
Rationale: Work done by the waste pipe in 1 minute
= 1/15 - (1/20 + 1/24) = - 1/40
Volume of 1/40 part
= 3 gallons
Volume of whole = 3 * 40
= 120 gallons.
Answer:C
Answer: (C) 120 gallons
Question: The food in a camp lasts for 20 men for 50 days. If twenty more men join, how many days will the food last?
(A) 22 days
(B) 25 days
(C) 28 days
(D) 16 days
(E) 27 days
Rationale: one man can consume the same food in 20*50 = 1000 days.
20 more men join, the total number of men = 40
The number of days the food will last = 1000/40 = 25 days.
Answer:B
Answer: (B) 25 days
Question: What sum of money will produce Rs.70 as simple interest in 4 years at 3 1/2 percent?
(A) Rs.525
(B) Rs.500
(C) Rs.550
(D) Rs.555
(E) Rs.625
Rationale: Explanation:
70 = (P*4*7/2)/100
P = 500
Answer IS B
Answer: (B) Rs.500
Question: How many even number in the range between 25 to 100 inclusive are not divisible by 3
(A) 27
(B) 30
(C) 31
(D) 33
(E) 46
Rationale: We have to find the number of terms that are divisible by 2 but not by 6( as the question asks for the even numbers only which are not divisible by 3)
For 2,
26,28,30...100
using AP formula, we can say 100 = 10 + (n-1) *2
or n=38.
For 6,
36, 42,...96
using AP formula, we can say 96 = 12 + (n-1) *6
or n=11.
Hence, only divisible by 2 but not 3 = 38-11= 27. hence, Answer A
Answer: (A) 27
Question: A train 110 meters long is running with a speed of 60 kmph. In what time will it pass a man who is running at 6 kmph in the direction opposite to that in which the train is going?
(A) 3
(B) 6
(C) 7
(D) 8
(E) 9
Rationale: Speed of train relative to man = (60 + 6) km/hr = 66 km/hr
[66 * 5/18] m/sec = [55/3] m/sec.
Time taken to pass the man = [110 * 3/55] sec = 6 sec
Answer:B
Answer: (B) 6
Question: Express 25 mps in kmph?
(A) 16
(B) 76
(C) 90
(D) 87
(E) 12
Rationale: 25 * 18/5
= 90 kmph
Answer: C
Answer: (C) 90
Question: A woman begins bicycling with a pace of 10 kmph and she increases her pace every two hours by 2 kmph. She rests from bicycling 2 hours after her pace reaches her maximum speed of 14 kmph. She does a cool-down for the final 8 km at a pace of 2 kmph. How far in km did she bicycle?
(A) 96 km
(B) 100 km
(C) 106 km
(D) 116 km
(E) 126 km
Rationale: Distance covered in first two hours = 10 Ã— 2 = 20 km
Distance covered in next two hours = 12 Ã— 2 = 24 km
Distance covered in next two hours = 14 Ã— 2 = 48 km
Distance covered in first six hours
20 + 24 + 48 = 92 km
Remaining distance = 8 km
92 + 8 = 100 km
Answer B
Answer: (B) 100 km
Question: How many multiples of 2 are there between 1 and 58, exclusive?
(A) 21
(B) 22
(C) 24
(D) 26
(E) 28
Rationale: 28
multiples of 2 between 1 and 58 exclusive.
from 2 * 1 upto 2*28, (1,2,3,4,...,28). Hence, 28 multiples !
correct option is E
Answer: (E) 28
Question: In a series of five football matches between Germany and Argentina , the probability of Germany winning a match is 1/3 and the probability that the match ends in a draw is 1/4. If a win gets the team 2 points, a draw 1 point and a loss 0 Points, What is the probability that Germany will end up in 5 draws in the series?
(A) 24/576
(B) 125/864
(C) 1/25
(D) 1/1024
(E) 1/5
Rationale: Since the probability of a draw is 1/4, then the probability of 5 draws in 5 matches is (1/4)^5=1/1024.
Answer: D.
Answer: (D) 1/1024
Question: Number of ways in which the letters of word GALE can be arranged with vowels in alphabetical order, is
(A) 360
(B) 240
(C) 12
(D) 480
(E) None of these
Rationale: Solution
Order of vowels of fixed
âˆ´ required number of ways are 4!/2!.
Answer C
Answer: (C) 12
Question: Anand and Deepak started a business investing Rs. 2250 and Rs. 3200 respectively. Out of a total profit of Rs. 1380, Deepak's share is:
(A) 3776
(B) 810.27
(C) 815.21
(D) 688.12
(E) 267.1
Rationale: Ratio of their shares = 2250 : 3200 = 45:64
Deepak's share = 13800 * 64/109= Rs. 810.27.
Answer: B
Answer: (B) 810.27
Question: Evaluate: |4 - 8(3 - 12)| - |5 - 11| =
(A) 40
(B) 50
(C) 60
(D) 70
(E) 80
Rationale: According to order of operations, inner brackets first. Hence
|4 - 8(3 - 12)| - |5 - 11| = |4 - 8*(-9)| - |5 - 11|
According to order of operations, multiplication within absolute value signs (which may be considered as brackets when it comes to order of operations) next. Hence
= |4 + 72| - |5 - 11|
= |76| - |-6|
= 76 - 6 = 70
correct answer is D) 70
Answer: (D) 70
Question: Jack and Jill work at a hospital with 6 other workers. For an internal review, 2 of the 8 workers will be randomly chosen to be interviewed. What is the probability that Jack and Jill will both be chosen?
(A)  1/3
(B)  1/4
(C)  1/15
(D)  1/28
(E)  2/3
Rationale: 1/8C2=1/28.
Answer: D.
Answer: (D)  1/28
Question: If six persons sit in a row, then the probability that three particular persons are always together is?
(A) 1/6
(B) 1/1
(C) 1/5
(D) 1/9
(E) 1/2
Rationale: Six persons can be arranged in a row in 6! ways. Treat the three persons to sit together as one unit then there four persons and they can be arranged in 4! ways. Again three persons can be arranged among them selves in 3! ways. Favourable outcomes
= 3!4! Required probability
= 3!4!/6!
= 1/5
Answer: C
Answer: (C) 1/5
Question: Richard has to paint a mural with seven horizontal stripes. He only has enough paint for four brown stripes, four red stripes, four blue stripes, four white stripes, four black stripes, and four yellow stripes. If his patron wants at most two different colors in the mural, how many different ways can he paint the wall?
(A) 120
(B) 350
(C) 1050
(D) 2,520
(E) 5,040
Rationale: Number of ways to choose 2 colors among 6 - 6c2
Number of ways that the chosen colors can be painted for 7 horizontal stripes - 2 (either (4,3) or (3,4))
Now the order,
the number of ways in which a particular color among the 2 chosen colors can be painted for 4 stripes is - 7c4
[Note: We don't need to calculate the ways for the remaining 3 stripes as they are obvious and already counted under this]
Total number of combinations - 6c2 * 2* 7c4 = 1050
C
Answer: (C) 1050
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 is even
(D) n*n is odd
(E) n*n is odd
Rationale: n is odd and n*n is even
Option A
Answer: (A) n is odd and n*n is even
Question: A team of eight entered for a shooting competition. The best marks man scored 82 points. If he had scored 92 points, the average scores for. The team would have been 85. How many points altogether did the team score?
(A) 662
(B) 672
(C) 652
(D) 642
(E) 670
Rationale: 8 * 85 = 680 – 10 = 670
ANSWER:E
Answer: (E) 670
Question: Roger can read a book in k minutes. What part of the book can he read in 4 minutes? (k>8)
(A) 8+k
(B) 8/k
(C) k/8
(D) (k+ 8)/k
(E) (k-8) / k
Rationale: Let's sayk = 24
That is, it takes 24 minutes to read the entire book.
So, in 8 minutes, Roger can read1/3of the book
So, we're looking for the answer choice that yields an OUTPUT of1/3whenk = 24
A) 8+24=32ELIMINATE
B) 8/24=1/3KEEP
C)24/8 =3ELIMINATE
D) (24+ 8)/24=32/24 = 4/3ELIMINATE
E) (24-8) /24=16/24 = 2/3ELIMINATE
Answer: A
Answer: (A) 8+k
Question: A person goes to a bank and Quotes x Rs and y paise on a cheque. The cashier misreads it and gives y Rs and x paise. The man comes out and donates 5 paise to a begger. Now, the man has exactly double the amount he has quoted on the cheque. .
(A) 31 rs 63 paise
(B) 30 rs 63 paise
(C) 31 rs 33 paise
(D) 31 rs 3 paise
(E) 33 rs 63 paise
Rationale: he gets 100y+x paise instead of 100x+y paise
(100y+x) - (100x+y) - 5 = (100x+y)
99y -99x - 5 = 100x + y
98y = 199x + 5
y = 2x + (3x+5)/98
only an integer value of x = 31
will make y an integer
with the constraints that both x & y < 100
substituing, y = 2*31 + 1 = 63
ans: 31 rs 63 paise
ANSWER:A
Answer: (A) 31 rs 63 paise
Question: Two dice are tossed. The probability that the total score is a prime number is?
(A) 1/2
(B) 5/12
(C) 7/9
(D) 1/6
(E) 1/12
Rationale: Clearly, n(S) = (6 x 6) = 36.
Let E = Event that the sum is a prime number.
Then E= { (1, 1), (1, 2), (1, 4), (1, 6), (2, 1), (2, 3), (2, 5), (3, 2), (3, 4), (4, 1), (4, 3),
(5, 2), (5, 6), (6, 1), (6, 5) }
n(E) = 15.
P(E) =n(E)/n(S)=15/36=5/12
hence:B
Answer: (B) 5/12
Question: An art gallery owner is hanging paintings for a new show. Of the nine paintings she has to choose from, she can only hang three on the main wall of the gallery. Assuming that she hangs as many as possible on that wall, in how many ways can she arrange the paintings?
(A) 18
(B) 30
(C) 64
(D) 60480
(E) 216
Rationale: Arrangement means permutations questions..
9P3 = 9!/3! = 60480
.
ANS option D is correct answer..
Answer: (D) 60480
Question: 1=5,2=25,3=253,4=254,5=?
(A) 1
(B) 255
(C) 345
(D) 445
(E) 235
Rationale: 1=5,2=25,3=253,4=254,5=?
5=1
check the first eqn.
ANSWER:A
Answer: (A) 1
Question: A bag is filled with pennies and nickels in the ratio of 4 to 2. There are 30 nickles in the bag, how many coins are there in that bag?
(A) 90
(B) 50
(C) 65
(D) 70
(E) 80
Rationale: A ratio of pennies to nickels of 4 to 2 means that we can write the number of pennies and nickels in the form
number of pennies = 4x and number of nickels = 2x
But we know the number of nickels, 30. Hence
2x = 30
Solve for x
x = 15
The total number of coins is given by
4x + 2x = 6x = 6 × 15 = 90
Answer : A
Answer: (A) 90
Question: If 70% of a number is equal to two-third of another number, what is the ratio of first number to the second number?
(A) 5:7
(B) 18:23
(C) 17:19
(D) 20:21
(E) 2:3
Rationale: Let 70% of A = 2/3 B. Then,
70A/100 = 2B/3 => 7A/10 = 2B/3
A/B = (2/3 * 10/7) = 20/21
A:B = 20:21.
Answer: D
Answer: (D) 20:21
Question: C invested $600 in a business and D invested $400 in a business. At the end of the year they got $2000 as the profit. Find their share?
(A) $800,$1200
(B) $900,$1000
(C) $700,$1100
(D) $1200,$800
(E) $600,$1000
Rationale: C:D = 600:400
C:D = 3:2
C's share = 2000*3/5 = $1200
D's share = 2000*2/5 = $800
Answer is D
Answer: (D) $1200,$800
Question: With both valves open, the pool will be filled with water in 48 minutes. The first valve alone would fill the pool in 2 hours. If the second valve emits 50 cubic meters of water more than the first every minute, then what is the capacity T of the pool?
(A) 9000 cubic meters
(B) 10500 cubic meters
(C) 11750 cubic meters
(D) 12000 cubic meters
(E) 12500 cubic meters
Rationale: D. 12000 cubic meters.
If both hte valves fill the pool in 48 minutes and valve 1 only fills in 120 minutes then valve 2 alone will fill the pool in (48*120)/(120-48) = 80 minutes.
Now, if valve 1 admits x cubic meter of water per minute then the capacity of pool will be 120x and also 80 (x+50).
or, 120x = 80 (x + 50).
or x = 100.
Hence, the capacity of pool = 120x = 12000 cubic meters.
Answer: (D) 12000 cubic meters
Question: Can you find a six digit number under 5 lakh such that the sum of it's digits is 43 ?
(A) 588338
(B) 499449
(C) 399826
(D) 788392
(E) 622975
Rationale: B
The required number is 499449.
The maximum sum of a number under 5 lakh will be of the number 499999 i.e. 49.
Thus the required number must be close to 499999.
The root of 499999 ~ 707.106
By calculating the square of 707, we get 499849 which is the answer.
Answer: (B) 499449
Question: In a certain deck of cards, each card has a positive integer written on it. In a multiplication game, a child draws a card and multiples the integer on the card by the next larger integer. If each possible product is between 26 and 200, then the least and greatest integers on the card could be
(A) 3 and 15
(B) 3 and 20
(C) 5 and 13
(D) 4 and 14
(E) 5 and 14
Rationale: There child draws one number then multiplies that number by the number above it. The number must be more than 15 and less than 200.
x * (x+1)
Answer gives us choices of 3,4 and 5 (JUST ABOVE 26)
3*(3+1) =12 <- WRONG
4*(4+1) =20 <- WRONG
5*(5+1) =30 <- CORRECT AS IT IS ABOVE 26
Answer gives us choices 13,14,15 and 20 (BELOW 200)
Immediately by knowing squares you should be able to rule out 15 (225) and 20 (400). And common sense dictates that as 14^2 is 196 that 14*(14+1) is above 200.
13*(13+1)=182 <- CORRECT
Answer is C) 5 and 13
Answer: (C) 5 and 13
Question: A and B undertake to do a piece of work for Rs. 1200. A alone can do it in 6 days while B alone can do it in 8 days. With the help of C, they finish it in 3 days. Find the share of C.
(A) 150
(B) 450
(C) 750
(D) 800
(E) None of them
Rationale: C's 1 day's work = 1/3-(1/6+1/8)=24
A : B : C = Ratio of their 1 day's work = 1/6:1/8:1/24= 4 : 3 : 1.
A’s share = Rs. (1200 *4/8) = Rs.600, B's share = Rs. (1200 *3/8) = Rs. 450
C's share = Rs. [1200 - (300 + 225») = Rs. 150.
Answer is A
Answer: (A) 150
Question: What is the present worth of Rs. 121 due in 2 years at 5% simple interest per annum
(A) 110
(B) 120
(C) 130
(D) 140
(E) None of these
Rationale: Explanation:
Let the present worth be Rs.x
Then,S.I.= Rs.(121 - x)
= (x*5*2/100) = 121 - x
= 10x = 12100 - 100x
= 110x = 12100
x= 110
Answer:A
Answer: (A) 110
Question: If |x-12| = 100, what is the sum of all the possible values of x?
(A) -12
(B) -22
(C) 24
(D) 36
(E) 42
Rationale: There will be two cases
x-12 = 100 or x-12 = -100
=> x = 112 or x= -88
sum of both the values will be -88 + 112 = 24
Answer is C
Answer: (C) 24
Question: There are two positive numbers in the ratio 5:8. If the larger number exceeds the smaller by 45, then find the smaller number?
(A) 25
(B) 66
(C) 77
(D) 88
(E) 75
Rationale: Let the two positive numbers be 5x and 8x respectively.
8x - 5x = 45
3x = 45 => x = 15
=> Smaller number = 5x = 75.
Answer: E
Answer: (E) 75
Question: A can be divided by 11 with no remainder. Which of the following expressions could be divided by 11 leaving a remainder of 1?
(A) A-20.
(B) A-12.
(C) A-9.
(D) A-10.
(E) A-13.
Rationale: We could use the following logic:
since A is a multiple of 11, we could very well say A = 11K (where K is 1,2...n).
The condition here should now be
11K + 1 = <operation> such that it gives us an integer
11k +1 = A -20 => A = 11K + 21 Not divisible by 11
11K +1 = A -12 => A = 11K + 31 Not Divisible by 11
11K +1 = A -9 => A = 11K + 10 Not Divisible by 11
11K +1 = A -10 => A = 11K + 11Divisible by 11
11K +1 = A -13 => A = 11K + 14 Not Divisible by 11
Answer therefore is A -10 (D)
Answer: (D) A-10.
Question: Find out the number of ways in which 6 rings of different types can be worn in 3 fingers?
(A) 120
(B) 720
(C) 125
(D) 729
(E) None of these
Rationale: Explanation :
The first ring can be worn in any of the 3 fingers
=> There are 3 ways of wearing the first ring
Similarly each of the remaining 5 rings also can be worn in 3 ways
Hence total number of ways
=3×3×3×3×3×6=36=729. Answer : Option D
Answer: (D) 729
Question: The winning relay team in a high school sports competition clocked 48 minutes for a distance of 13.2 km. Its runners A, B, C and D maintained speeds of 17 kmph, 18 kmph, 19 kmph, and 20 kmph respectively. What is the ratio of the time taken by B to than taken by D?
(A) 5:16
(B) 5:17
(C) 9:8
(D) 10:9
(E) None of these
Rationale: Explanation :
Since it is a relay race, all the runners ran the same distance.
Hence for a same distance, (ratio of times) = 1/(ratio of speeds).
Hence ratio of times taken by B t& D =20 : 18 = 10 : 9.
Answer : D
Answer: (D) 10:9
Question: A train of length 560 metres takes 90 seconds to cross a tunnel of length 340 metres. What is the speed of the train in km/hr?
(A) 36 km/hr.
(B) 46 km/hr.
(C) 30 km/hr.
(D) 48 km/hr.
(E) None
Rationale: Sol.
Speed = [560+340 / 90] m/sec = [900 / 90 * 18/5] km/hr = 36km/hr.
Answer A
Answer: (A) 36 km/hr.
Question: In the coordinate plane, points (x, 5) and (9, y) are on line k. If line k passes through the origin and has slope 5/9, then x - y =
(A) 4
(B) 6
(C) 5
(D) 8
(E) 7
Rationale: Line k passes through the origin and has slope 1/4 means that its equation is y=5/9*x.
Thus: (x, 5)=(9, 5) and (9, y) = (9,5) --> x-y=9-5=4.
Answer: A
Answer: (A) 4
Question: A bus can hold 120 passengers. If there are 12 rows of seats on the bus, how many seats are in each row?
(A) 10
(B) 12
(C) 45
(D) 8
(E) 9
Rationale: No. of seats = 120/12 = 10
There are 10 seats in each row
Answer : A
Answer: (A) 10
Question: A starts business with a capital of Rs.1200 B and C join with some investments after 3 and 6 months respectively. If the end of a year, the profit is divided in the ratio 2:3:5 respectively. What is B's investment in the business?
(A) 2400
(B) 2408
(C) 2406
(D) 2403
(E) 2401
Rationale: 1200 * 12: x * 9 = 2:3
x = 2400
Answer: A
Answer: (A) 2400
Question: A typist can type 120 words in 100 seconds. At that rate, how many seconds would it take her to type 258 words?
(A) 205
(B) 210
(C) 215
(D) 220
(E) 225
Rationale: 120/100=258/n
120* n=258*100
120n	=25800
n=215
Answer:C
Answer: (C) 215
Question: A bag contains 12 red jellybeans and 12 blue jellybeans. If 3 jellybeans are removed one at a time, at random and are not replaced, what is the probability that all 3 jellybeans removed from the bag are blue?
(A) 9/100
(B) 2/19
(C) 1/8
(D) 3/20
(E) 3/10
Rationale: Method-1
10 red jellybeans and 10 blue jellybeans
Total Outcomes = No. of ways to choose 3 Jelly bean at random out of a total 20 jellybeans = 20C3 = 1140
Favourable Outcomes = No. of ways to choose 3 Jelly bean such that they are all Blue out of 10 Blue = 10C3 = 120
Probability = Favourable Outcomes / Total Outcomes = 10C3 / 20C3
Probability = 120 / 1140 = 2/19
Answer: option B
Method-2
Probability of First jelly bean to be Blue = 10/20 [Total 10 Blue out of total 20 jellybeans]
Probability of Second jelly bean to be Blue = 9/19 [Total 9 Blue remaining out of total 19 jellybeans remaining]
Probability of Third jelly bean to be Blue = 8/18 [Total 8 Blue remaining out of total 18 jellybeans remaining]
Required Probability = (10/20)*(9/19)*(8/18) = 3/10
Answer: option E
Answer: (E) 3/10