mathewhe/aqua_rat huggingface dataset:
Question: If n is a prime number greater than 4, what is the remainder when n^2 is divided by 12?
(A) 0
(B) 2
(C) 1
(D) 3
(E) 5
Rationale: There are several algebraic ways to solve this question including the one under the spoiler. But the easiest way is as follows:since we can not have two correct answersjust pick a prime greater than 4, square it and see what would be the remainder upon division of it by 12.
n=7 --> n^2=49 --> remainder upon division 49 by 12 is 1.
Answer: C.
Answer: (C) 1
Question: A,B and C started a business by investing Rs.800/- , Rs.1,000/- and Rs.1,200/- respectively for two years.
Total profit is Rs.1000/-. Find the C's share?
(A) Rs. 600
(B) Rs. 500
(C) Rs. 400
(D) Rs. 800
(E) Rs. 900
Rationale: Solution: A : B : C = (800 * 2) : (1,000 * 2) : (12,000 * 2) = 4 : 5 : 6.
So C's share = Rs. (1000 * 6/15) = Rs. 400.
Answer: Option C
Answer: (C) Rs. 400
Question: The length of a train and that of a platform are equal. If with a speed of 72 k/hr, the train crosses the platform in one minute, then the length of the train (in meters) is?
(A) 600
(B) 758
(C) 718
(D) 750
(E) 738
Rationale: Speed = [72 * 5/18] m/sec = 20 m/sec; Time = 1 min. = 60 sec.
Let the length of the train and that of the platform be x meters.
Then, 2x/60 = 20 è x = 20 * 60 / 2
=600
Answer:A
Answer: (A) 600
Question: Working in a South Side studio at a constant rate, Kanye can drop a full-length platinum LP in 5 weeks. Working at his own constant rate, Common can drop a full-length platinum LP in x weeks. If the two emcees work together at their independent rates, they can drop a full-length platinum compilation LP in 2 weeks. Assuming no efficiency is lost or gained from working together, how many weeks would it take Common, working alone, to drop a full-length platinum LP?
(A)  3 and 1/3 weeks
(B)  3 weeks
(C)  2 and 1/2 weeks
(D)  2 and 1/3 weeks
(E)  2 weeks
Rationale: VERITAS PREPOFFICIAL SOLUTION:
Now, while your instinct may be to Go! and speed through your initial read of this rate problem, remember: slow motion (is) better than no motion. As you read each sentence, you should start jotting down variables and relationships so that by the time you get to the question mark you have actionable math on your noteboard and you don’t have to read the question all over again to get started. You should be thinking:
Working in a South Side studio at a constant rate, Kanye can drop a full-length platinum LP in 5 weeks.
Rate (K) = 1 album / 5 weeks
Working at his own constant rate, Common can drop a full-length platinum LP in x weeks.
Rate (C) = 1 album / x weeks
If the two emcees work together…
I’m adding these rates, so their combined rate is 1/5 + 1/x
…they can drop a full-length platinum compilation LP in 2 weeks.
And they’re giving me the combined rate of 1 album / 2 weeks, so 1/5 + 1/x = 1/2
Assuming no efficiency is lost or gained from working together, how many weeks would it take Common, working alone, to drop a full-length platinum LP?
I’m using that equation to solve for Common’s time, so I’m solving for x.
Now by this point, that slow motion has paid off – your equation is set, your variable is assigned, and you know what you’ve solving for. Your job is to solve for x, so:
1/5 + 1/x = 1/2, so let’s get the x term on its own:
1/x = 1/2 – 1/5. and we can combine the two numeric terms by finding a common denominator of 10:
1/x = 5/10 – 2/10
1/x = 3/10, and from here you have options but let’s cross multiply:
10 = 3x, so divide both sides by 3 to get x alone:
10/3 = x, and that doesn’t look like the answer choices so let’s convert to a mixed number: 3 and 1/3 (there’s that number again), for answer choice A.
Answer: (A)  3 and 1/3 weeks
Question: A contractor undertook to do a piece of work in 10 days. He employed certain number of laboures but 5 of them were absent from the very first day and the rest could finish the work in only 13 days. Find the number of men originally employed ?
(A) 21.6
(B) 23.6
(C) 22.6
(D) 21.8
(E) 21.3
Rationale: Let the number of men originally employed be x.
10x = 13(x â€“ 5)
or x = 21.6
Answer A
Answer: (A) 21.6
Question: The ratio between the present ages of A and B is 5:3 respectively. The ratio between A's age 4 years ago and B's age 4 years hence is 1:1. What is the ratio between A's age 4 years hence and B's age 4 years ago?
(A) 3:9
(B) 3:7
(C) 3:1
(D) 3:2
(E) 3:3
Rationale: Let the present ages of A and B be 5x and 3x years respectively.
Then, (5x - 4)/(3x + 4) = 1/1
2x = 8 => x = 4
Required ratio = (5x + 4):(3x - 4) = 24:8 = 3:1
Answer: C
Answer: (C) 3:1
Question: If selling price is doubled, the profit triples. Find the profit percent.
(A) 66%
(B) 120%
(C) 105%
(D) 100%
(E) 80%
Rationale: Let C.P. be Rs. x and S.P. be Rs. y.
Then, 3(y - x) = (2y - x)
y = 2x.
Profit = Rs. (y - x) = Rs. (2x - x) = Rs. x.
Profit % =	x/x x 100% =100%
Answer is D.
Answer: (D) 100%
Question: A train speeds past a pole in 15 seconds and a platform 100 m long in 25 seconds. Its length is?
(A) 886 m
(B) 787 m
(C) 876 m
(D) 150 m
(E) 586 m
Rationale: Let the length of the train be x meters and its speed be y m/sec.
They, x / y = 15 => y = x/15
x + 100 / 25 = x / 15
x = 150 m.
Answer:D
Answer: (D) 150 m
Question: Veena ranks 79rd from the top in a class of 182. What is her rank from the bottom if 22 students have failed the examination?
(A) 88
(B) 108
(C) 82
(D) 90
(E) 93
Rationale: total student=182
failed=22
paasd student=182-22=160
from bottom her rank is=160-79+1=82
ANSWER:C
Answer: (C) 82
Question: A man buys a cycle for Rs. 1600 and sells it at a loss of 20%. What is the selling price of the cycle?
(A) 1410
(B) 1420
(C) 1430
(D) 1440
(E) 1280
Rationale: S.P. = 80% of Rs. 1600 = 80/100 x1600= Rs. 1280
answer : E
Answer: (E) 1280
Question: From a group of 6boys&4girls a Committee of 4 persons is to be formed. In how many different ways can it be done, so that the committee has at least 2 boys?
(A) 145
(B) 198
(C) 185
(D) 210
(E) 234
Rationale: The committee of 4 persons is to be so formed that it has at least 2 men. The different ways that we can choose to form such a committee are:
(i) 2m. 2w in 6C2 x 4 C1=6X5 - 2X1 X 3X3 2X1 =n an (ii) 3m. 1w in 6C3 x 4C1 =6X5X4 3X2X1 X4 _n - a ''''
(iii) 4m in 6C4 -2x1 = 15 Total no. of different ways in which a committee of 4 persons can be formed so that it has at least 2 men. = 90 + 18 + 15 = 185
C
Answer: (C) 185
Question: How many positive 5-digit integers have the odd sum of their digits?
(A) 9*10^2
(B) 9*10^3
(C) 10^4
(D) 45*10^3
(E) 9*10^4
Rationale: We are looking at numbers between 10000 and 99999 both inclusive.
There are 90000 numbers.
Now for
10000 : sum of digits is odd;
10001 :sum of digits is even;
10002 : sum of digits is odd ; so on and so forth. So every alternate number is such that the sum of digit is odd.
(Exception for the above statement :
When it is 10009 the sum is even and for 10010 again the sum is even; But if you look at 10019 :sum is odd; 10020 : sum is odd
and this pattern continues so basically the number of odd sum of digits and even sum of digits are equal)
This means exactly half of the numbers will have odd sum of their digits. i.e 45000
Answer : D
Answer: (D) 45*10^3
Question: The function f is defined for all positive integers V by the following rule. f(V) is the number of positive integers each of which is less than V and has no positive factor in common with V other than 1. If Y is any prime, number then f(Y)=
(A) Y-1
(B) Y-2
(C) (Y+1)/2
(D) (Y-1)/2
(E) 2
Rationale: If not the wording the question wouldn't be as tough as it is now. The GMAT often hides some simple concept in complicated way of delivering it.
This question for instance basically asks: how many positive integers are less than given prime number Y which have no common factor with Y except 1.
Well as Y is a prime, all positive numbers less than Y have no common factors with Y (except common factor 1). So there would be Y-1 such numbers (as we are looking number of integers less than Y).
For example: if Y=3 how many numbers are less than 3 having no common factors with 3: 1, 2, 3, --> 3-1=2.
Answer: A.
Answer: (A) Y-1
Question: Ajay can ride 50km in 1 hour. In how many hours he can ride 1250km?
(A) 10hrs
(B) 15hrs
(C) 20hrs
(D) 25hrs
(E) 18hrs
Rationale: 1 hour he ride 50km
he ride 1250km in = 1250/50 * 1 = 25hours
Answer is D
Answer: (D) 25hrs
Question: To be considered for “movie of the year,” a film must appear in at least 1/4 of the top-10-movies lists submitted by the Cinematic Academy’s 795 members. What is the smallest number of top-10 lists a film can appear on and still be considered for “movie of the year”?
(A) 191
(B) 199
(C) 193
(D) 212
(E) 213
Rationale: Total movies submitted are 795.
As per question we need to take 1/4 of 795 to be considered for top 10 movies = 198.75
approximate the value we 199.
IMO option B is the correct answer...
Answer: (B) 199
Question: Two boys starts from the same place walking at the rate of 5 kmph and 5.5 kmph respectively in the same direction. What time will they take to be 8.5 km apart?
(A) 10 hr
(B) 12 hr
(C) 15 hr
(D) 18 hr
(E) 17 hr
Rationale: speed = 5.5-5 = 0.5 kmph
dist = 8.5 km
time = dist/speed = 8.5/0.5 = 17 hr
ANSWER E
Answer: (E) 17 hr
Question: If an average hard drive had a capacity of 0.7 TB in 2000, and average hard drive capacities double every 5 years, what will be the average hard drive capacity in 2050?
(A) 256
(B) 512
(C) 768
(D) 1024
(E) 7168
Rationale: 0.7*2^10=0.7*1024=716.8
The answer is E.
Answer: (E) 7168
Question: In a box, there are 10 red, 6 blue and 5 green balls. One ball is picked up randomly. What is the probability that it is neither red nor green?
(A) 4/51
(B) 10/21
(C) 7/12
(D) 11/31
(E) 13/17
Rationale: Total number of balls = 10+6+5 = 21
E = event that the ball drawn is neither red nor green
= event that the ball drawn is red
n(E) = 10
P(E) = 10/21
Answer is B
Answer: (B) 10/21
Question: In a class of 50 students, 40 % are girls. Find the number of girls and number of boys in the class?
(A) 33
(B) 237
(C) 36
(D) 88
(E) 30
Rationale: Number of girls in the class = 40 % of 50
= 40/100 × 50
= 2000/100
= 20
Number of boys in the class = Total number of students in the class - Number of girls
= 50 – 20
= 30
Answer:E
Answer: (E) 30
Question: A number is doubled and 9 is added. If the resultant is trebled, it becomes 81. What is that number?
(A) 3.5
(B) 6
(C) 8
(D) 7
(E) 9
Rationale: Let the number be x. Then,
3(2x + 9) = 81
2x = 18 => x = 9
ANSWER:E
Answer: (E) 9
Question: John purchased some shirts and trousers for $1550. He paid $250 less for the shirts than he did for the trousers. If he bought 5 shirts and the cost of a shirt is $20 less than that of a trouser, how many trousers did he buy?
(A) 4
(B) 5
(C) 6
(D) 7
(E) 8
Rationale: Given that the total purchase of two items cost 1550.
So the average purchase of one item will cost 1550/2 =775.
Its given as total shirt cost 250$ less. Hence Total Shirt cost = 775 - 125 and Total trouser cost = 775 + 125
5 shirts =650$ ==> One shirt =130$
One trouser = 130 + 20 =150$
Total trousers = 900 / 150 =6.
C
Answer: (C) 6
Question: If (2^x)(3^y) = 324, where x and y are positive integers, then (2^x-1)(3^y-2) equals:
(A) 16
(B) 18
(C) 48
(D) 96
(E) 144
Rationale: So I would start attacking this problem by quickly performing the prime factorization of 288. With that it is easy to count the 5 twos and the 2 threes that are the prime factors. So x=2, y=4. now quickly 2^1(3^2)=18. Than answer should be number 2.
B
Answer: (B) 18
Question: When positive integer a is divided by 6, the remainder is 1. Which of the following must be true?
I. a is a prime number
II. a is odd
III. a is divisible by 7
(A) I only
(B) II only
(C) III only
(D) I and II only
(E) II and III only
Rationale: a=6q+1
Examine II) put q=0,1,2,3....... we have a=1,7,13,...25 so a must be odd
Examine III) 14/6 has reminder 249/7 has reminder 1 so not always true
Examine I) a= 7 true but while 2 is prime, it does not give reminder 1
Answer: B
Answer: (B) II only
Question: Find the area of a rhombus one side of which measures 20 cm and one diagonal is 23 cm.
(A) 100cm2
(B) 150cm2
(C) 300cm2
(D) 368cm2
(E) 400cm2
Rationale: Explanation: Let other diagonal = 2x cm.
Since diagonals of a rhombus bisect each other at right angles, we have:
(20)2 = (12)2 + (x)2 =>x =√(20)2 – (12)2= √256= 16 cm. _I
So, other diagonal = 32 cm.
Area of rhombus = (1/2) x (Product of diagonals) =(1/2× 23 x 32) cm2 = 368 cm2
Answer: Option D
Answer: (D) 368cm2
Question: Mrs. Rodger got a weekly raise of $145. If she gets paid every other week, write an integer describing how the raise will affect her paycheck.
(A) $ 130
(B) $ 145
(C) $ 115
(D) $ 120
(E) $ 150
Rationale: Let the 1st paycheck be x (integer).
Mrs. Rodger got a weekly raise of $ 145.
So after completing the 1st week she will get $ (x+145).
Similarly after completing the 2nd week she will get $ (x + 145) + $ 145.
= $ (x + 145 + 145)
= $ (x + 290)
So in this way end of every week her salary will increase by $ 145.
correct answer B
Answer: (B) $ 145
Question: The price of an article is cut by 10%. To restore it to the former value. The new price must be increased by ?
(A) 10%
(B) 9 1/11
(C) 11 1/9
(D) 11%
(E) None of these
Rationale: Answer
Let original price = Rs. 100.
Then, new price = Rs. 90.
∴ Increased on Rs. 90 = Rs. 10
Required increase % = (10 x 100) / 90 % = 111/9%
Correct Option: C
Answer: (C) 11 1/9
Question: A committee has 4 men and 7 women. What are the number of ways of selecting 3 men and 4 women from the given committee?
(A) 110
(B) 120
(C) 130
(D) 140
(E) 150
Rationale: The number of ways to select three men and four women = 4C3 * 7C4 = 4 * 35 = 140
The answer is D.
Answer: (D) 140
Question: Each of three charities in Novel Grove Estates has 8 persons serving on its board of directors. If exactly 4 persons serve on 3 boards each and each pair of charities has 5 persons in common on their boards of directors, then how many distinct persons serve on one or more boards of directors?
(A) 8
(B) 13
(C) 16
(D) 24
(E) 27
Rationale: A intersect B intersect C = 4
A intersect B but not C = 1
B intersect C but not A = 1
C intersec A but not B = 1
A only is 2; B only is 2; C only is 2
Therefore, total 13 members serve on one or more boards of directors.
ANSWER:B
Answer: (B) 13
Question: Dropbox charges $3.10 for first 1/5 of a month for 500 GB storage, plus $0.40 for each additional 1/5 of a month. What would Dropbox charge for a data storage of 500 GB for 8 months ?
(A) $15.60
(B) $16.00
(C) $17.80
(D) $18.70
(E) $19.10
Rationale: first 1/5 month charge = $3.10
rest of the months = 8 - (1/5) = 39/5
charge for the rest of the months = 39 *0.4 = 15.6
total charge = 3.10+15.6 = 18.7
Answer is D.
Answer: (D) $18.70
Question: A cistern of capacity 8000 litres measures externally 3.3 m by 2.6 m by 1.1 m and its walls are 5 cm thick. The thickness of the bottom is:
(A) 9
(B) 1
(C) 2
(D) 4
(E) 6
Rationale: Answer: B) 1 dm
Answer: (B) 1
Question: Mica covers a distance in 20 min , if she drives at a speed of 60 km/h on an average. Find the speed at which she must drive at to reduce the time of the journey by 40%.
(A) 50 km/h
(B) 90 km/h
(C) 75 km/h
(D) 80 km/h
(E) 100 km/h
Rationale: Given Speed = 60 Kmph.
It means Mica covered 60 km in 60 min (1 hour). So, in 20 min he will cover 20 km.
40% time reduced = 20 - 40% of 20= 12 min.
Thus, Mica needs to cover 20 km in 12 min (0.2 hour).
Speed * Time = Distance.
Speed * 0.2 = 20
Speed = 100 kmph.
ANSWER : OPTION E
Answer: (E) 100 km/h
Question: A box contains ELEVEN bulbs out of which 5 are defective. If four bulbs are chosen at random, find the probability that atleast one bulb is good?
(A) 325/330
(B) 325/420
(C) 369/430
(D) 546/558
(E) 124/131
Rationale: Required probability= 1-5C4/11C4= 1 - 5/330= 325/330Answer:A
Answer: (A) 325/330
Question: A certain gallery is hanging a series of 6 paintings. All the paintings will be exhibited in a row along a single wall. Exactly 2 of the paintings are on panel, the remainder are on canvas. In how many ways can the paintings be exhibited if the works on panel must be the second and sixth in the row?
OE
(A) 240
(B) 200
(C) 122
(D) 48
(E) 16
Rationale: We need to consider them separately because the question specifies:
1. Panel paintings have to be placed only at 2nd and 6th place.
2. Implies that Canvas has to be placed 1,3,4,5th place.
So we have two separatebucketsto consider.
So panels can be ordered in 2!
Canvas can be ordered in 4!
since relative position of panels to canvas is fixed (Panels 2nd and 6th) the answer is 2! x 4! = 48
D
Answer: (D) 48
Question: The time taken by a man to row his boat upstream is twice the time taken by him to row the same distance downstream. If the speed of the boat in still water is 42 kmph, find the speed of the stream?
(A) 76 kmph
(B) 17 kmph
(C) 14 kmph
(D) 18 kmph
(E) 10 kmph
Rationale: The ratio of the times taken is 2:1.
The ratio of the speed of the boat in still water to the speed of the stream = (2+1)/(2-1) = 3/1
= 3:1
Speed of the stream = 42/3 = 14 kmph.
Answer: C
Answer: (C) 14 kmph
Question: The roof of an apartment building is rectangular and its length is 3 times longer than its width. If the area of the roof is 588 feet squared, what is the difference between the length and the width of the roof?
(A) 28.
(B) 40.
(C) 42.
(D) 44.
(E) 46.
Rationale: Answer is A: 28
Let w be the width , so length is 3w. Therefore : w*3w = 588, solving for, w = 14 , so 3w-w = 2w = 2*14 = 28
Answer: (A) 28.
Question: A cubical tank is filled with water to a level of 3 feet. If the water in the tank occupies 75 cubic feet, to what fraction of its capacity is the tank filled with water?
(A) 1/2
(B) 2/3
(C) 3/4
(D) 2/5
(E) 3/5
Rationale: The volume of water in the tank is H*L*B = 75 cubic feet.
Since H = 3, then L*B = 25 and L = B = 5.
Since the tank is cubical, the capacity of the tank is 5*5*5 = 125.
The ratio of the water in the tank to the capacity is 75/125 = 3/5
The answer is E.
Answer: (E) 3/5
Question: If x, 6, 7, 8 are there and the range and median of them are the same, what is the value of x?
(A) 0
(B) 1
(C) 2
(D) 3
(E) 7
Rationale: Try taking the values of x as you suggested and then see if the median and the range are equal.
Once you do that, you will get the answer yourself.
Tried substituting values starting with 6, 7, 8...
only x = 7 satisfies the condition.
E
Answer: (E) 7
Question: What value will replace the question mark in the following equation ? 5172.49 + 378.352 + ? = 9318.678
(A) 3767.836
(B) 3677.863
(C) 3767.863
(D) 3767.683
(E) None of them
Rationale: Let 5172.49 + 378.352 + x = 9318.678
Then , x = 9318.678 – (5172.49 + 378.352) = 9318.678 – 5550.842 = 3767.836
Answer is A.
Answer: (A) 3767.836
Question: If n is a prime number greater than 11, what is the remainder when n^2 is divided by 12 ?
(A) 0
(B) 1
(C) 2
(D) 3
(E) 5
Rationale: There are several algebraic ways to solve this question, but the easiest way is as follows:since we cannot have two correct answers just pick a prime greater than 11, square it and see what would be the remainder upon division of it by 12.
n=17 --> n^2=289 --> remainder upon division 289 by 12 is 1.
Answer: B.
Answer: (B) 1
Question: A and B together can do a piece of work in 6 days and A alone can do it in 12 days. In how many days can B alone can do it?
(A) 11 days
(B) 15 days
(C) 12 days
(D) 21 days
(E) 22 days
Rationale: Explanation:
A and B can do work 1/6 in 1 day
A alone can do 1/12 work in 1 day
B alone can do (1/6 -1/12) =1/12 work in 1 day
=> complete work can be done in 12 days by B
Answer: Option C
Answer: (C) 12 days
Question: In a group of hats consisting of only blue hats, green hats, and purple hats, the ratio of blue hats to green hats to purple hats is 7:4:12. If there are a total of 115 hats in this group, how many of these hats are not blue?
(A) 28
(B) 42
(C) 48
(D) 64
(E) 80
Rationale: B:G:P = 7:4:12 --> total of 23 parts.
Not blue = (G + P)/(total)*92 = 16/23*115 = 80.
Answer: E.
Answer: (E) 80
Question: What is the smallest positive perfect square that is divisible by 9, 21, and 49?
(A) 225
(B) 324
(C) 441
(D) 529
(E) 900
Rationale: The number needs to be divisible by 3^2, 3*7, and 7^2.
The smallest such perfect square is 3^2*7^2 = 441
The answer is C.
Answer: (C) 441
Question: 32 is divided into two parts in such a way that seventh part of first and ninth part of second are equal. Find the smallest part?
(A) 66
(B) 26
(C) 42
(D) 27
(E) 14
Rationale: x/7 = y/9 => x:y = 7:9
7/16 * 32 = 14
Answer: E
Answer: (E) 14
Question: A box measuring 35 inches long by 20 inches wide by 10 inches deep is to be filled entirely with identical cubes. No space is to be left unfilled. What is the smallest number of cubes that can accomplish this objective?
(A) 17
(B) 18
(C) 54
(D) 56
(E) 864
Rationale: least number of cubes will be required when the cubes that could fit in are biggest.
5 is the biggest number that could divide all three, 35, 20 and 10.
Thus side of cube must be 5, and total number of cubes = 35/5 * 20/5*10/5 = 56
Ans D it is.
Answer: (D) 56
Question: In an election, candidate Douglas won 64 percent of the total vote in Counties X and Y. He won 76 percent of the vote in County X. If the ratio of people who voted in County X to County Y is 2: 1, what percent of the vote did candidate Douglas win in County Y?
(A) 10%
(B) 25%
(C) 30%
(D) 35%
(E) 40%
Rationale: given voters in ratio 2:1
let X has 200 votersY has 100 voters
for X 76% voted means 76*200=152 votes
combined for XY has 300 voters and voted 64% so total votes =192
balance votes=192-152=40
As Y has 100 voters so 40 votes means 40% of votes required
Ans E
Answer: (E) 40%
Question: A line that passes through (–1, –4) and (4, k) has a slope = k. What is the value of k?
(A)  3/4
(B)  1
(C)  4/3
(D)  2
(E)  7/2
Rationale: Slope = (y2-y1)/(x2-x1)
=> k = (k+4)/(4+1)
=> 5k = k+4
=> k =1
Ans B it is!
Answer: (B)  1
Question: In how many different ways can the letters of the word 'OPTICAL' be arranged so that the vowels always come together?
(A) 520
(B) 720
(C) 890
(D) 870
(E) 1098
Rationale: The word 'OPTICAL' contains 7 different letters.
When the vowels OIA are always together, they can be supposed to form one letter.
Then, we have to arrange the letters PTCL (OIA).
Now, 5 letters can be arranged in 5! = 120 ways.
The vowels (OIA) can be arranged among themselves in 3! = 6 ways.
Required number of ways = (120 x 6) = 720.
ANSWER B 72
Answer: (B) 720
Question: A train 325 m long passes a man, running at 10 km/hr in the same direction in which the train is going, in 45 sec. The speed of the train is?
(A) 12 km/hr
(B) 13 km/hr
(C) 14 km/hr
(D) 15 km/hr
(E) 16 km/hr
Rationale: Speed of the train relative to man = 325/45 = 65/9 m/sec.
= 65/9 * 18/5 = 26 km/hr
Let the speed of the train be x km/hr. Then, relative speed = (x - 10) km/hr.
x - 10 = 26 => x = 16 km/hr.
Answer: E
Answer: (E) 16 km/hr
Question: A, B and C started a business with capitals of Rs. 8000, Rs. 10000 and Rs. 12000 respectively. At the end of the year, the profit share of B is Rs. 1500. The difference between the profit shares of A and C is?
(A) Rs.628
(B) Rs.629
(C) Rs.629
(D) Rs.600
(E) Rs.629
Rationale: Ratio of investments of A, B and C is 8000 : 10000 : 12000 = 4 : 5 : 6
And also given that, profit share of B is Rs. 1500
=> 5 parts out of 15 parts is Rs. 1500
Now, required difference is 6 - 4 = 2 parts
Required difference = 2/5 (1500) = Rs.600'
Answer: D
Answer: (D) Rs.600
Question: For a race a distance of 224 meters can be covered by P in 14 seconds and Q in 32 seconds. By what distance does P defeat Q eventually?
(A) 232m
(B) 288m
(C) 324m
(D) 231m
(E) 236m
Rationale: Explanation:
This is a simple speed time problem. Given conditions:
=>Speed of P= 224/14 = 16m/s
=>Speed of Q=224/32 = 7m/s
=>Difference in time taken = 18 seconds
Therefore, Distance covered by P in that time= 16m/s x 18 seconds = 288 metres
ANSWER: B
Answer: (B) 288m
Question: The list price of an article is Rs.65. A customer pays Rs.56.16 for it. He was given two successive discounts, one of them being 10%. The other discount is?
(A) 1
(B) 4
(C) 5
(D) 6
(E) 8
Rationale: 65*(90/100)*((100-x)/100) = 56.16
x = 4%
Answer: B
Answer: (B) 4