mathewhe/aqua_rat huggingface dataset:
Question: Two pipes A and B can fill a tank in 15 min and 21 min respectively. Both the pipes are opened together but after 4 min, pipe A is turned off. What is the total time required to fill the tank?
(A) 14 min 19 sec
(B) 14 min 42 sec
(C) 14 min 20 sec
(D) 14 min 40 sec
(E) 15 min 12 sec
Rationale: :
Part filled in 4 minutes = 4(1/15 + 1/20) = 7/15
Remaining part = 1 - 7/15 = 8/15
Part filled by B in 1 minute = 1/21
1/21 : 8/15 :: 1 ; x
x = 8/15 * 1 * 21 = 11 1/5 min = 11 min 12 sec.
The tank will be full in (4 min. + 11 min. 12 sec) = 15 min 12 sec.Answer: E
Answer: (E) 15 min 12 sec
Question: A and B can do a piece of work in 12 days and 16 days respectively. Both work for 3 days and then A goes away. Find how long will B take to complete the remaining work?
(A) 15 days
(B) 12 days
(C) 10 days
(D) 9 days
(E) 8 days
Rationale: Explanation:
3/12 + (3 + x)/16 = 1
x = 9 days
Answer: D
Answer: (D) 9 days
Question: A number when divided by D leaves a remainder of 8 and when divided by 3D leaves a remainder of 21 . What is the remainder left, when twice the number is divided by 3D?
(A) 13
(B) 12
(C) 3
(D) 2
(E) 42
Rationale: making eqn as per the question
a=Dx+8......1
a=3Dy+21....2
multiplying 3 in eqn 1 we get eqn 3
3a=3Dx+24....3
a=3Dy+21......2
now subtract 2 from 3 we get..
2a=3D(x-y)+3
so here's the remainder we got is 3
ANSWER:C
Answer: (C) 3
Question: A batsman makes a score of 90 runs in the 17th inning and thus increases his averages by 3. What is his average after 17th inning?
(A) 39
(B) 35
(C) 42
(D) 40.5
(E) 42
Rationale: let the average after 16th inning =x
then total run after 16th inning=16x
then total run after 17th inning=16x+90
then average run after 17th inning=(16x+90)/17
(16x+90)/17=x+3 => 16x+90 = 17x+51 => x=39
x=39;
average after 17th inning =39+3=42
ANSWER:E
Answer: (E) 42
Question: On a certain road, 10% of the motorists exceed the posted speed limit and receive speeding tickets, but 60% of the motorists who exceed the posted speed limit do not receive speeding tickets. What percent of the motorists on that road exceed the posted speed limit?
(A) 10.5%
(B) 12.5%
(C) 15%
(D) 25%
(E) 30%
Rationale: suppose there are X motorists.
10% of them exceeded the speed limit and received the ticket, i.e. X/10.
Again, suppose total no. of motorists who exceeded the speed limit are Y.
60% of Y exceeded the speed limit but didn't received the ticket, i.e. 3Y/5.
it means 2Y/5 received the ticket.
hence, 2Y/5 = X/10
or Y/X=1/4
or Y/X * 100= 1/4 * 100= 25%
D
Answer: (D) 25%
Question: A shopping cart contains only apples, oranges, and pears. If there are four times as many oranges as apples, and five times as many pears as oranges, then the apples are equivalent to what fraction of the pears?
(A) 1/8
(B) 1/9
(C) 1/12
(D) 1/16
(E) 1/20
Rationale: O = 4A
P = 5O = 20A
A = P/20
The answer is E.
Answer: (E) 1/20
Question: Which of the following correctly lists the data sets in order of least to greatest standard deviation?
I. 2, 2, 2 3, 3, 2
II. 32, 32, 32, 30, 30, 32
III. 37, 38, 39, 40, 44, 42
(A) I, II, III
(B) I, III, II
(C) II, I, III
(D) II, III, I
(E) III, II, I
Rationale: (D) To answer a question such as this, you DO NOT need to know how to calculate standard deviation. You simply need to understand how to compare standard deviations of different sets. The more spread out the numbers are, the greater the standard deviation will be. Even one or two numbers that are much larger or smaller than the others will cause the standard deviation to rise drastically.
sequence lowest to highest = I,II,III
A
Answer: (A) I, II, III
Question: How many 3-letter words can be formed using the letters of the English alphabet that contain 1 different vowels and 2 different consonants?
(A) 4!*5c2 *21c2
(B) 4!*5c3 *21c2
(C) 3!*5c1 *21c2
(D) 5!*5c2 *21c2
(E) 6!*5c2 *21c2
Rationale: combination for 1 vowels out of 5 =5c1 ways
combination for 2 consonants of 21 = 21c2 ways
Additionally the arrangement can be = 3!
total arrangements =3!*5c1 *21c2
C
Answer: (C) 3!*5c1 *21c2
Question: If (x+4)2−−−−−−−√=3(x+4)2=3, which of the following could be the value of x−4x−4?
(A) -11
(B) -7
(C) -4
(D) -3
(E) 5
Rationale: X+4)2=9(X+4)2=9
(X−4+8)2=9(X−4+8)2=9
let X-4 = A
(A+8)2=9(A+8)2=9
Now, sub answer choices in A
A) (−11+8)2=(−3)2=9(−11+8)2=(−3)2=9
A is your answer
Answer: (A) -11
Question: what is the smallest number should be added to 5377 so that the sum is completely divisible by 7?
(A) 5
(B) 4
(C) 6
(D) 2
(E) 1
Rationale: Solution: Divide 5377 with 7 we get remainder as 1. so, add 6 to the given number so that it will divisible by 7.
Answer C
Answer: (C) 6
Question: Amy has to visit towns B and C in any order. The roads connecting these towns with her home are shown on the diagram. How many different routes can she take starting from A and returning to A, going through both B and C (but not more than once through each) and not travelling any road twice on the same trip?
(A) 1
(B) 8
(C) 9
(D) 2
(E) 7
Rationale: Explanation:
Amy can travel clockwise or anticlockwise on the diagram.
Clockwise, she has no choice of route from A to B, a choice of one out of two routes from B to C, and a choice of one out of two routes from C back to A. This gives four possible routes.
Similarly, anticlockwise sh
Answer: B) 8
Answer: (B) 8
Question: if each of its sides of a rectangle is increased by 18%, what is the percentage increase in the area of the rectangle, ?
(A) 39.24%
(B) 38.24%
(C) 36.24%
(D) 37.24%
(E) 38.24%
Rationale: Assume original length = 100m by 50m
original area = 100*50= 5000
18% increase on each side
l = 100 + 18= 118
w = 50 + 9 = 59
new area = 118*59= 6962
increase in area = 6962 - 5000 = 1962
%increase =39.24%
Answer A
Answer: (A) 39.24%
Question: If 4 : 6 :: x : 36, then find the value of x
(A) 24
(B) 22
(C) 28
(D) 30
(E) 18
Rationale: Explanation:Treat 4:6 as 4/6 and x:36 as x/36, treat :: as = So we get 4/6 = x/36=> 6x = 144=> x = 24 Option A
Answer: (A) 24
Question: One-third of Rahul's savings in National Savings Certificate is equal to one-half of his savings in Public Provident Fund. If he has Rs. 1,50,000 as total savings, how much has he saved in Public Provident Fund ?
(A) Rs. 30,000
(B) Rs. 50,000
(C) Rs. 60,000
(D) Rs. 90,000
(E) Rs. 70,000
Rationale: N/3=P/2
N+P=150000
60000
ANSWER:C
Answer: (C) Rs. 60,000
Question: A is thrice as good as workman as B and therefore is able to finish a job in 60 days less than B. Working together, they can do it in?
(A) 22 1/2
(B) 22 1/3
(C) 23
(D) 23 1/2
(E) 23 1/3
Rationale: Ratio of times taken by A and B = 1 : 3.
The time difference is (3 - 1) 2 days while B take 3 days and A takes 1 day.
If difference of time is 2 days, B takes 3 days.
If difference of time is 60 days, B takes 3	x 60 = 90 days.
2
So, A takes 30 days to do the work.
A's 1 day's work =	1
30
B's 1 day's work =	1
90
(A + B)'s 1 day's work = 1	+	1 =	4	=	2
30	90	90	45
A and B together can do the work in	45	= 22	1	days.
2	2
Answer is A
Answer: (A) 22 1/2
Question: Ten circular coins are thrown on the street so that no two of them
overlap or touch, and no three of them have a tangent line in common.
What is the total number of lines which are tangent to two of the coins?
(A) 60
(B) 100
(C) 180
(D) 240
(E) 360
Rationale: There are n(n-1)=2 different ways
of choosing 2 objects from a given collection
of n objects. Thus, there are 10*9/2 = 45
different ways of choosing 2 of the 10 coins.
For each selection of two coins, one can form 4
tangent lines as shown at the right. Therefore,
the answer is 4*45 = 180.
correct answer C
Answer: (C) 180
Question: The diameter of a wheel of cycle is 21 cm. It moves slowly along a road. How far will it go in 500 revolutions?
(A) 220
(B) 330
(C) 360
(D) 390
(E) 410
Rationale: In revolution, distance that wheel covers = circumference of wheel Diameter of wheel = 21 cm
Therefore, circumference of wheel = πd
= 22/7 × 21
= 66 cm
So, in 1 revolution distance covered = 66 cm
In 500 revolution distance covered = 66 × 500 cm
= 33000 cm
= 33000/100 m
= 330 m
ANSWER B
Answer: (B) 330
Question: A metallic sheet is of rectangular shape with dimensions 40m x 30 m. From each of its corners, a square is cut off so as to make an open box. If the length of the square is 8 m, the volume of the box (in m cube) is:
(A) 3220 m cube
(B) 4140 m cube
(C) 2688 m cube
(D) 4000 m cube
(E) None of these
Rationale: Explanation:
l = (40 - 16)m = 24 m, [because 8+8 = 16]
b = (30 -16)m = 14 m,
h = 8 m.
Volume of the box = (24 x 14 x 8) m cube
= 2688 m cube.
Option C
Answer: (C) 2688 m cube
Question: A work can be finished in 13 days by ten women. The same work can be finished in fifteen days by ten men. The ratio between the capacity of a man and a woman is
(A) 14:13
(B) 13:15
(C) 12:13
(D) 13:12
(E) 14:15
Rationale: Work done by 10 women in 1 day = 1/13
Work done by 1 woman in 1 day = 1/(13Ã—10)
Work done by 16 men in 1 day = 1/15
Work done by 1 man in 1 day = 1/(15Ã—10)
Ratio of the capacity of a man and woman =1/(15Ã—10) : 1/(13Ã—10) = 1/15 : 1/13
= 1/15 :1/13 = 13 : 15
Answer is B.
Answer: (B) 13:15
Question: A 3% stock produces 10%. The market value of the stock is:
(A) Rs. 15
(B) Rs. 25
(C) Rs. 20
(D) Rs. 30
(E) Rs. 40
Rationale: Let the face value of the product is Rs.100
It stock Rs.3
Market value of the stock=(3/10)*100=Rs.30
ANSWER:D
Answer: (D) Rs. 30
Question: In how many different ways can the letters of the word ‘ARMOUM’ be arranged?
(A) 240
(B) 260
(C) 370
(D) 409
(E) 360
Rationale: ARMOUR = 6 letter whereas R repeated twice 6! 6xSx4x3x2x1 => 360
E
Answer: (E) 360
Question: There are 20 poles with a constant distance between each pole. A car takes 20 second to reach the 12th pole. How much will it take to reach the last pole.
(A) 34.4543
(B) 34.5455
(C) 34.45128
(D) 34.51288
(E) 34.41222
Rationale: Assuming the car starts at the first pole.
To reach the 12th pole, the car need to travel 11 poles (the first pole doesn't count, as the car is already there).
11 poles 20 seconds
1 pole (20/11) seconds
To reach the last (20th) pole, the car needs to travel 19 poles.
19 pole 19 x (20/11) seconds
= 34.5455 seconds
Answer:B
Answer: (B) 34.5455
Question: Murali travelled from city A to city B at a speed of 40 kmph and from city B to city C at 60 kmph. What is the average speed of Murali from A to C given that the ratio of distances between A to B and B to C is 10 : 5?
(A) 16
(B) 45
(C) 277
(D) 92
(E) 11
Rationale: Let the distances between city A to B and B to C be 10x km and 5x km respectively.
Total time taken to cover from A to C
= (10x)/40 + (5x)/60 = (30x + 10x)/120 = 40x/120 = x/3 Average speed = (10x + 5x)/(x/3) = 45 kmph.
Answer:B
Answer: (B) 45
Question: An outlet pipe can empty 2/3 rd of a cistern in 12 minutes. In 8 minutes, what part of the cistern will be emptied?
(A) 4/9
(B) 4/3
(C) 4/2
(D) 4/8
(E) 4/1
Rationale: 2/3 ---- 12
? ----- 8 ==> 4/9
Answer: A
Answer: (A) 4/9
Question: From a pack of 52 cards, 1 card is drawn at random. Find the probability of a face card drawn
(A) 4/13
(B) 1/52
(C) 1/4
(D) 1/5
(E) None of above
Rationale: Explanation:
Total number of cases = 52
Total face cards = 16 [favourable cases]
So probability = 16/52 = 4/13
Answer: A
Answer: (A) 4/13
Question: A sells a bicycle to B at a profit of 70% and B sells it to C at a loss of 40%. Find the resultant profit or loss.
(A) -4%
(B) 2%
(C) -5%
(D) 6%
(E) -7%
Rationale: The resultant profit or loss = 70 - 40 - (70*40)/100 = +2%
Profit = 2%
Answer is B
Answer: (B) 2%
Question: Consider the sequence of numbers beginning 23, 27, 28, 32, 33... It continues in such a way that by adding 5 to the nth term, one obtains the (n + 2)th term. What is the sum of the first 15 members of this sequence?
(A) 618
(B) 900
(C) 788
(D) 928
(E) 1022
Rationale: I would split them up like this.
23 28 33 and so on (8 terms)....the 8th term = 23+7*5 = 58
27 32 37 and so on (7 terms)......the 7th term = 27+6*5 = 57
Since the distance between any two numbers is the same we can use arithmetics
first+last/2 times no of numbers = the sum
(23+58)/2 * 8= 324
(27+57)/2 * 7 = 294
= 618
A
Answer: (A) 618
Question: An empty pool being filled with water at a constant rate takes 5 hours to fill to 3/5 of its capacity. How much more time will it take to finish filling the pool?
(A) 5 hr 30 min
(B) 5 hr 20 min
(C) 4 hr 48 min
(D) 3 hr 20 min
(E) 2 hr 40 min
Rationale: (3/5) of a pool/ 5 hours = 3/25 (the rate)
(3 pools/25 hours) = (2/5* pool)/ x hours
Cross multiply 3x = (2/5) 25
x = 3 1/3
1/3 of an hour = 20 minutes
D
Answer: (D) 3 hr 20 min
Question: If 5x + y = 15, 5y + z = 25 and 2z + x = 2, what is the value of x ?
(A) 2
(B) 7
(C) 9
(D) 12
(E) None of these
Rationale: Explanation:
5x + y = 15 –-------I * 5
5y + z = 25 –------ II
2z + x = 2 -------- III
Subtract (I) and (II)
25x + 5y + 0 = 75
- 0 + 5y + z = 25
-------------------------------
25x + 0 – z = 50 ….......... IV
Multiply (IV)*2, we get 50x – 2z = 100
Adding (III) and (IV) we get,
50x – 2z = 100
+ x + 2z = 2
------------------------
51 x = 102
x = 2
The value of x = 2
ANSWER A
Answer: (A) 2
Question: 7^8 is equal to which of the following?
(A) 5,764,787
(B) 5,764,788
(C) 5,764,799
(D) 5,764,800
(E) 5,764,801
Rationale: Units digit spotting can be fun
Cyclicity of 7 to the power of anything
7^1= 7
7^2= 9
7^3= 3
7^4= 1
7^5= 7
--- pattern formed --
So the cycle of this is 4. The fifth power will start the cycle again. Therefore, 7 to the power of 8 will give a units digit of 1. Answer E
Answer: (E) 5,764,801
Question: If a company allocates 15 percent of its budget to advertising, 10 percent to capital improvements, and 55 percent to salaries, what fraction of its budget remains for other allocations?
(A) 4/5
(B) 3/5
(C) 3/10
(D) 1/5
(E) 1/10
Rationale: 100%-(15%+10%+55%)=20% remains for other allocations --> 20% = 20/100 = 1/5.
Answer: D.
Answer: (D) 1/5
Question: A can finish a work in 8 days and B can do same work in half the time taken by A. then working together, what part of same work they can finish in a day?
(A) 3/5
(B) 3/6
(C) 3/7
(D) 3/8
(E) None of these
Rationale: Explanation:
Please note in this question, we need to answer part of work for a day rather than complete work. It was worth mentioning here because many do mistake at this point in hurry to solve the question
So lets solve now,
A's 1 day work = 1/8
B's 1 day work = 1/4 [because B take half the time than A]
(A+B)'s one day work =
(1/8+1/4)=3/8
So in one day 3/8 work will be done
Answer: D
Answer: (D) 3/8
Question: A pharmaceutical company received $2 million in royalties on the first $15 million in sales of generic equivalent of one of its products and then $6 million in royalties on the next $72 million in sales. By approximately what percent did the ratio of royalties to sales decrease from the first $15 million in sales to the next $72 million in sales?
(A) 25%
(B) 30%
(C) 32.5%
(D) 37.5%
(E) 40%
Rationale: change in ratio of royalties to sales = 2/15 -6/72 = 1/20
% decrease = (1/20)/(2/15) *100 = 37.5%
Answer: D)
Answer: (D) 37.5%
Question: The workforce of Company X is 60% female. The company hired 22 additional male workers, and as a result, the percent of female workers dropped to 55%.How many employees did the company have after hiring the additional male workers?
(A) 160
(B) 220
(C) 264
(D) 360
(E) 420
Rationale: Let's xx be total quantity of employees
0.6x=females before adding men
0.55(x+22)=females after adding men
as quantity of women doesn't change we can make an equation:
0.6x=0.55(x+22)
0.05x=12.1
x=242 - this is quantity of employees before adding 22 men
So after adding it will be 264
Answer is C
Answer: (C) 264
Question: If each side of the square is increased by 25% find the percentage change in its area?
(A) 89.45%
(B) 56.25%
(C) 89.98%
(D) 54.48%
(E) 45.0%
Rationale: let each side of the square be a. then area =a^2
new side=125a/100=5a/4
new area=(5a/4)^2=25a^2/16
increase in area=(25a^2/16-a^2)=9a^2/16
increased %=(9a^2/16*1/a^2*100)=56.25%
Answer is(B)
Answer: (B) 56.25%
Question: A circular mat with diameter 16 inches is placed on a square tabletop, each of whose sides is 24 inches long. Which of the following is closest to the fraction of the tabletop covered by the mat?
(A) 5/12
(B) 2/5
(C) 1/3
(D) 3/4
(E) 5/6
Rationale: SO we are looking for the area of the cloth over the area of the table
Area of the Cloth = (pi)(r)^2 which is about (3)(8)(8)
Area of the Table = (24)(24)
So the quick way to estimate is looking at the fraction like this: (3/24)(64/24)
I hope this is easy to follow, so with some simplification i get (1/8)(8/3) = (1/3) Answer is C
Answer: (C) 1/3
Question: A AND B CAN DO A WORK IN 12 DAYS, B AND C IN 15 DAYS, C AND A IN 20 DAYS. IF A, B AND C WORK TOGETHER, THEY WILL COMPLETE THE WORK IN:
(A) 5 DAYS
(B) 7 5/6 DAYS
(C) 10 DAYS
(D) 15 2/3 DAYS
(E) NONE OF THESE
Rationale: (A+B)'S 1 DAY'S WORK=1/12, (B+C)'S 1 DAY'S WORK = 1/15;
(A+C)'S 1 DAY'S WORK = 1/20
ADDING, WE GET : 2(A+B+C)'S 1 DAY'S WORK =(1/12+1/15+1/20)=12/60=1/5
(A+B+C)'S 1 DAY'S WORK = 1/10
SO, A, B AND C TOGETHER CAN COMPLETE THE WORK IN 10 DAYS.
CORRECT OPTION: C
Answer: (C) 10 DAYS
Question: A student scored an average of 85 marks in 3 subjects: Physics, Chemistry and Mathematics. If the average marks in Physics and Mathematics is 90 and that in Physics and Chemistry is 70, what are the marks in Physics?
(A) 86
(B) 16
(C) 76
(D) 65
(E) 26
Rationale: Given M + P + C = 85 * 3 = 255--- (1)
M + P = 90 * 2 = 180 --- (2)
P + C = 70 * 2 = 140 --- (3)
Where M, P and C are marks obtained by the student in Mathematics, Physics and Chemistry.
P = (2) + (3) - (1) = 180 + 140 - 255
= 65
Answer:D
Answer: (D) 65
Question: The distance from City A to City B is 30 miles. While driving from City A to City B, Bob drives at a constant speed of 40 miles per hour. Alice leaves City A 30 minutes after Bob. What is the minimum constant speed in miles per hour that Alice must exceed in order to arrive in City B before Bob?
(A) 45
(B) 88
(C) 120
(D) 152
(E) 154
Rationale: The time it takes Bob to drive to City B is 30 / 40 =0.75 hours.
Alice needs to take less than 0.25 hours for the trip.
Alice needs to exceed a constant speed of 30 /0.25 = 120 miles per hour.
The answer is C.
Answer: (C) 120
Question: Sreenivas sells a table to Shiva at 10% profit and Shiva sells it to Mahesh at 10% loss. At what price did Sreenivas purchase the table if Mahesh paid Rs. 2178?
(A) Rs. 2100
(B) Rs. 2150
(C) Rs. 2200
(D) Rs. 2250
(E) None of these
Rationale: Let the cost price of table for Sreenivas be Rs. x and given that, cost price of table for Mahesh = Rs. 2178.
=> (90%) of (110%) of x = Rs. 2178.
=> (90/100)(110/100)x = 2178
=> x = (2178 * 100)/(9 * 11)
=> x = Rs. 2200
ANSWER:C
Answer: (C) Rs. 2200
Question: If 1/a^2 + a^2 represents the diameter of circle O and 1/a + a = 4, which of the following best approximates the circumference of circle O?
(A) 28
(B) 22
(C) 20
(D) 16
(E) 12
Rationale: Given that (1/a)+a =3
Square both sides of the equation:
We get,
[(1/a)^2 + a^2 + 2*(1/a)*a] = 9
=> (1/a)^2 + a^2 + 2 = 9
=> (1/a)^2 + a^2 = 7 ----------------- (1)
Diameter D = (1/a)^2 + a^2
= 7 (From (1))
So Radius = D/2 = 7/2
Circumference = 2*Pi*r
= 2*(22/7)*(7/2)
=20
So the answer should be C
Answer: (C) 20
Question: The difference between simple and compound interest on Rs. 1500 for one year at 10% per annum reckoned half-yearly is?
(A) 8.0
(B) 3.0
(C) 9.5
(D) 3.75
(E) 2.15
Rationale: S.I. = (1500 * 10 * 1)/100 = Rs. 150
C.I. = [1500 * (1 + 5/100)2 - 1500]
= Rs. 153.75 Difference = (153.75 - 150)
= Rs.3.75
Answer:D
Answer: (D) 3.75
Question: If -3x+2y=28 and 3x+6y=84, what is the product of x and y?
(A) 264.
(B) 428
(C) 0
(D) 462
(E) 642
Rationale: Given -3x+2y=28 ---Eq 1
3x + 6y =84 -- Eq 2
Sum both eqns we get 8Y = 112 => Y = 14
Sum 2Y in eq 1 => -3X - 28 = 28.
=> X = 0
Now XY = 0 * 14 = 0.
Option C is correct answer.
Answer: (C) 0
Question: A vessel contains 20 liters of a mixture of milk and water in the ratio 3:2. 10 liters of the mixture are removed and replaced with an equal quantity of pure milk. If the process is repeated once more, find the ratio of milk and water in the final mixture obtained?
(A) 9:1
(B) 4:7
(C) 7:1
(D) 2:5
(E) None of these
Rationale: Explanation:
Milk = 3/5 * 20 = 12 liters, water = 8 liters
If 10 liters of mixture are removed, amount of milk removed = 6 liters and amount of water removed = 4 liters.
Remaining milk = 12 - 6 = 6 liters
Remaining water = 8 - 4 = 4 liters
10 liters of pure milk are added, therefore total milk = (6 + 10) = 16 liters.
The ratio of milk and water in the new mixture = 16:4 = 4:1
If the process is repeated one more time and 10 liters of the mixture are removed, then amount of milk removed = 4/5 * 10 = 8 liters.
Amount of water removed = 2 liters.
Remaining milk = (16 - 8) = 8 liters.
Remaining water = (4 -2) = 2 liters.
The required ratio of milk and water in the final mixture obtained = (8 + 10):2 = 18:2 = 9:1.
ANSWER IS A
Answer: (A) 9:1
Question: 0.03 x 0.5 = ?
(A) 0.0001
(B) 0.001
(C) 0.015
(D) 0.1
(E) NONE OF THESE
Rationale: Explanation:
3 x 5 = 15.
Sum of decimal places = 3
0.02 x 0.5 = 0.015
Answer- C
Answer: (C) 0.015
Question: A train 100 meters long takes 6 seconds to cross a man walking at 5 kmph in the direction opposite to that of the train. Find the speed of the train.
(A) 45 kmph
(B) 50 kmph
(C) 55 kmph
(D) 60 kmph
(E) 70 kmph
Rationale: Explanation:
Let the speed of the train be x kmph.
Speed of the train relative to man = (x + 5) kmph = (x + 5) ×5/18 m/sec.
Therefore 100/((x+5)×5/18)=6 <=> 30 (x + 5) = 1800 <=> x = 55
Speed of the train is 55 kmph.
Answer: Option C
Answer: (C) 55 kmph
Question: A present value of a machine is $2000. Its value depletiation rate is 20% per annum then find the machine value before 2 years?
(A) $3125
(B) $2945
(C) $3012
(D) $2545
(E) $3150
Rationale: P= $2000
R = 20%
T = 2 years
Machine value before 2 years = P/[(1-R/100)^T]
=2000*5/4 * 5/4
=$3125
Answer is A
Answer: (A) $3125
Question: Calculate the cost of p meters of rope given that the cost of m meters of said rope is q rupees?
(A) Rs.(q*m)
(B) Rs.(pq/m)
(C) Rs.(q/m)
(D) Rs.(p/m)
(E) Rs.(p*m)
Rationale: Cost of m metres = Rs. q.
Cost of 1 metre = Rs.	q/m
Cost of p metres = Rs.(q/m)* p= Rs.(pq/m)
Answer is B.
Answer: (B) Rs.(pq/m)
Question: Amit and Ian paint a wall in alternating shifts. First Amit paints alone, then Ian paints alone, then Amit paints alone, etc. During each of his shifts, Amit paints 1/2 of the remaining unpainted area of the wall, while Ian paints 1/3 of the remaining unpainted area of the wall during each of his shifts. If Amit goes first, what fraction of the wall's area will remain unpainted after Amit has completed his 2th shift?
(A) 1/27
(B) 1/54
(C) 1/81
(D) 1/6
(E) 1/216
Rationale: Fraction of area unpainted after FIRST shift of Amit = 1-(1/2) = 1/2
Fraction of area unpainted after FIRST shift of Ian = (1/2)-(1/3)(1/2) = (2/3)(1/2)
Fraction of area unpainted after SECOND shift of Amit = (1/2)(2/3)(1/2)=1/6
Answer: option D
Answer: (D) 1/6
Question: If two letters are taken at random from the word HOME, what is the probability that none of the letters would be vowels?
(A) 1/3
(B) 1/2
(C) 1/6
(D) 1/8
(E) 1/9
Rationale: Explanation :
P(first letter is not vowel)=2/4P(second letter is not vowel)=1/3So,probability that none of letters would be vowels is =(2/4)x(1/3)=1/6
Answer : C
Answer: (C) 1/6