mathewhe/aqua_rat huggingface dataset:
Question: (112 x 54) = ?
(A) 70000
(B) 71000
(C) 72000
(D) 73000
(E) 74000
Rationale: (112 x 54) = 112 x 10 4	=	112 x 104	=	1120000	= 70000
2	24	16
A)
Answer: (A) 70000
Question: A man can swim in still water at 4.5 km/h, but takes twice as long to swim upstream than downstream. The speed of the stream is?
(A) 1.8
(B) 1.6
(C) 1.3
(D) 1.5
(E) 1.1
Rationale: M = 4.5
S = x
DS = 4.5 + x
US = 4.5 + x
4.5 + x = (4.5 - x)2
4.5 + x = 9 -2x
3x = 4.5
x = 1.5
Answer: D
Answer: (D) 1.5
Question: The probability that A speaks truth is 3/5 and that of B speaking truth is 2/7. What is the probability that they agree in stating the same fact?
(A) 16/35
(B) 16/37
(C) 16/39
(D) 16/33
(E) 16/31
Rationale: If both agree stating the same fact, either both of them speak truth of both speak false.
Probability = 3/5 * 2/7 + 2/5 * 5/7
= 16/35
Answer:A
Answer: (A) 16/35
Question: p:q = 7:6 , q:r = 4 : 7 , p:q:r = ?
(A) 28 : 24 : 42
(B) 28 : 24 : 40
(C) 28 : 24 : 52
(D) 28 : 24 : 41
(E) 28 : 24 : 48
Rationale: p:q = 7:6 ,
q:r = 4 : 7
p:q:r =28 : 24 : 42
Answer : A
Answer: (A) 28 : 24 : 42
Question: Two partners (Moses and Norris) invested Rs 5000 and Rs.12000 in a business. Moses runs the business while Norris is a sleeping partner in the business. Moses receives 4% of the profit for managing the business the rest is divided in proportion of their capitals. Out of a total profit of Rs.5500, how much did Moses receive?
(A) 1772.95
(B) 1537.6
(C) 1877.6
(D) 1937.6
(E) 1857.6
Rationale: ratio of their investments Rs.5000:12000=5:12
4% of the profit for managing the business =4/100*5500=220
remaining profit=5500-220=5280
share profit in ratio of investment 5280/17 =310.59
Moses's ratio share=5*310.59=1552.95
total money Moses collects=1552.95+220=1772.95
Answer: A
Answer: (A) 1772.95
Question: A person buys an article at $500. At what price should he sell the article so as to make a profit of 20%?
(A) 560
(B) 449
(C) 600
(D) 740
(E) 460
Rationale: C
600
Cost price = $500
profit = 20% of 500 = $100
Selling price = Cost price + Profit
= 500 + 100 = 600
Answer: (C) 600
Question: The average age of husband, wife and their child 3 years ago was 27 years and that of wife and the child 5 years ago was 20 years. What is the present age of the husband?
(A) 30
(B) 40 years
(C) 20
(D) 50
(E) 25
Rationale: Let the present age of the husband = h
Present age of the wife = w
Present age of the child = c
3 years ago, average age of husband, wife and their child = 27
=> Sum of age of husband, wife and their child before 3 years = 3 × 27 = 81
=> (h-3) + (w-3) + (c-3) = 81
=> h + w + c = 81 + 9 = 90 --- equation(1)
5 years ago, average age of wife and child = 20
=> Sum of age of wife and child before 5 years = 2 × 20 = 40
=> (w-5) + (c-5) = 40
=> w + c = 40 + 10 = 50 --- equation(2)
Substituting equation(2) in equation(1)
=> h + 50 = 90
=> h = 90 - 50 = 40
i.e., Present age of the husband = 40
Answer is B.
Answer: (B) 40 years
Question: A man divides $6800 Among 4 Sons, 4 Daughters and 2 Nephews. If each daughter receives four times as much as each nephews and each son receives five times as much as each nephews, how much does each daughter receive?
(A) A)$200
(B) B)$1000
(C) C)$800
(D) D)$1200
(E) E)$400
Rationale: Let the share of each nephews be $X.
Then, share of each daughter=$4X, share of each son= $5X.
So, 4*4X+4*4X+2*X=6800
16X+16X+2X=8600
34X=6800, X=200.
Daughter receives four times of nephew so 4 * 200 = 800.
So Each Daughter receives $800. answer is option C) $800.
Answer: (C) C)$800
Question: A , B , and C started a partnership business by investing $45,000 , $63,000 , and $72,000 respectively. At the end of the year, the profit was distributed among them. If C's share of profit is $16,000, what is the total profit?
(A) $28,000
(B) $32,000
(C) $36,000
(D) $40,000
(E) $44,000
Rationale: A:B:C = 45000:63000:72000 which is a ratio of 5:7:8.
Let the total profit be x.
x * 8/20 = 16000
x = 16000*20/8 = 40,000.
The answer is D.
Answer: (D) $40,000
Question: A and B finish the job in 15 days.while A,B and C can finish it in 11 days . C alone will finish the job in
(A) 41.25 days
(B) 30.25 days
(C) 60.25 days
(D) 71.25 days
(E) 51.25 days
Rationale: Explanation:
11= (15 * x)/(15 + x)
165+11x=15x
4x=165
X=41.25
Answer: Option A
Answer: (A) 41.25 days
Question: Kim purchased n items from a catalog for $8 each. Postage and handling charges consisted of $2 for the first item and $1 for each additional item. Which of the following gives the total dollar amount for Kim’s purchase, including postage and handling, in terms of n ?
(A) 8n + 2
(B) 9n + 1
(C) 9n + 2
(D) 9n + 3
(E) 9n + 4
Rationale: its C
n items for $8 each
total price $8n
postage and handling of $3 for 1st item and $1 for the rest
total postage and handling = $ [2+ (n-1)]
= $ n+1
total cost
8n+n+1 = 9n+1
B
Answer: (B) 9n + 1
Question: Which of the following is satisfied with |x-4|+|x-3|<7?
(A) 0<x<7
(B) 2<x<5
(C) 2.5<x<4.5
(D) 2.5<x<4
(E) 3<x<4
Rationale: --> If there is addition when there are 2 absolute values, you can just ignore the middle. That is, |x-4|+|x-3|<7 -> |x-4+x-3|<7 -> |2x-7|<7, -7<2x-7<7, 0<2x<14, 0<x<7
Therefore, the answer is A.
Answer: (A) 0<x<7
Question: A certain restaurant offers 5 different salads, 4 different main courses, and 7 different desserts. If customers choose one salad, one main course, and two different desserts for their meal, how many different meals are possible?
(A) 300
(B) 340
(C) 380
(D) 420
(E) 460
Rationale: The number of possible choices for desserts is 7C2 = 21
The number of possible meals is 5*4*21 = 420
The answer is D.
Answer: (D) 420
Question: find last digits of (1023^3923)+(3081^3921)
(A) 8
(B) 9
(C) 10
(D) 11
(E) 12
Rationale: we have (1023^3923)+(3081^3921)
(3923/4)=4n+3 (3921/4)=4n+1 where n can be any integer
now through cyclicity we can obtain or you can learn the chart from arun sharma
number ending in 4n+1 4n+2 4n+3 4n
1 1 1 1 1
2 2 4 8 6
3 3 9 7 1
in this way 7+1=8 is the unit's place digit
ANSWER:A
Answer: (A) 8
Question: A person walking at 4 Kmph reaches his office 8 minutes late. If he walks at 6 Kmph, he reaches there 8 minutes earlier. How far is the office from his house?
(A) 3 1/5 Kilometre
(B) 2 1/5 Km
(C) 3 Km
(D) 4 Km
(E) 4 1/3 Km
Rationale: Formula = S1*S2/ S2-S1 * T1+T2/60
= 4*6/2 * 16/6
= 24/2 * 16/60
= 8 * 2/5
= 16/5 = 3 1/5 Km
A)
Answer: (A) 3 1/5 Kilometre
Question: A rectangular photograph is surrounded by a border that is 1 inch wide on each side. The total area of the photograph and the border is M square inches. If the border had been 6 inches wide on each side, the total area would have been (M + 200) square inches. What is the perimeter of the photograph, in inches?
(A) 8
(B) 12
(C) 16
(D) 20
(E) 24
Rationale: Let x and y be the width and length of the photograph.
(x+2)(y+2)=M and so (1) xy + 2x + 2y + 4 = M
(x+12)(y+12)=M and so (2) xy + 12x + 12y + 144 = M+200
Let's subtract equation (1) from equation (2).
10x + 10y + 140 = 200
2x + 2y = 12, which is the perimeter of the photograph.
The answer is B.
Answer: (B) 12
Question: Find the one which does not belong to that group ?
(A) 16
(B) 28
(C) 36
(D) 64
(E) 4
Rationale: Explanation:
16, 36, 64 and 4 are perfect squares but not 28.
ANSWER IS C
Answer: (C) 36
Question: The average of 25 results is 18. The average of first 12 of those is 14 and the average of last 12 is 17. What is the 13th result?
(A) 74
(B) 75
(C) 69
(D) 78
(E) 45
Rationale: Solution: Sum of 1st 12 results = 12*14
Sum of last 12 results = 12*17
13th result = x (let)
Now,
12*14+12*17+x = 25*18
Or, x = 78.
Answer: Option D
Answer: (D) 78
Question: The probability of a lottery ticket being a prized ticket is 0.2. When 4 tickets are purchased, the probability of winning a prize on atleast one ticket is -.
(A) 0.4869
(B) 0.5904
(C) 0.6234
(D) 0.5834
(E) 0.2952
Rationale: Explanation:
P(winning prize atleast on one ticket)
= 1 - P("Losing on all tickets")
= 1 - (0.8)4 = (1 + (0.8)2)(1 - (0.8)2)
= (1.64)(0.36) = 0.5904
ANSWER IS B
Answer: (B) 0.5904
Question: Wendy begins sanding a kitchen floor by herself and works for 8 hours. She is then joined by Bruce, and together the two of them finish sanding the floor in 2 hours. If Bruce can sand the floor by himself in 20 hours, how long would it take Wendy to sand the floor by herself?
(A) 544/49 hours
(B) 3/20 hours
(C) 20/3 hours
(D) 80/9 hours
(E) 10 hours
Rationale: Let Wendy finishes sanding the floor alone in W hours while B be the hours for Bruce.
Thus in 1 hour Wendy finishes 1/w of the work while Bruce finishes 1/B of the work.
If wendy works for 8 hours and is then joined by Bruce to finish the work in 2 more hours,
8/W + 2/W+2/B = 1 (1 denotes the total amount of work)
10/W + 2/B =1 and given B =20 hours.
Thus W = 544/49 hours , A is the correct answer.
Answer: (A) 544/49 hours
Question: In what time a sum of money double itself at 6% per annum simple interest?
(A) 33 1/8%
(B) 16 2/3%
(C) 33 7/3%
(D) 32 1/3%
(E) 23 1/3%
Rationale: P = (P*6*R)/100
R = 16 2/3%
Answer: B
Answer: (B) 16 2/3%
Question: In an election only two candidates contested. A candidate secured 70% of the valid votes and won by a majority of 172 votes. Find the total number of valid votes?
(A) 430
(B) 437
(C) 435
(D) 431
(E) 433
Rationale: Let the total number of valid votes be x.
70% of x = 70/100 * x = 7x/10
Number of votes secured by the other candidate = x - 7x/100 = 3x/10
Given, 7x/10 - 3x/10 = 172 => 4x/10 = 172
=> 4x = 1720 => x = 430.
Answer: A
Answer: (A) 430
Question: Two MBA admissions committees are to be formed randomly from 6 second year MBAs with 3 members each. What is the probability that Jane will be on the same committee as Albert?
(A) 12%
(B) 20%
(C) 33%
(D) 40%
(E) 50%
Rationale: Total number of ways to choose 3 member committee - 6C3=(6!/3!3!)=20
No. of ways Albert n Jane are in same committee:- (4C1 * 2)= 8
Probability= (8/20) *100 =40%.
ANS::D
Answer: (D) 40%
Question: 6 men and 2 boys working together can do four times as much work as a man and a boy. Working capacity of man and boy is in the ratio
(A) 1:1
(B) 1:3
(C) 2:1
(D) 2:3
(E) None of these
Rationale: Explanation:
Let 1 man 1 day work = x
1 boy 1 day work = y
then 6x + 2y = 4(x+y)
=> 2x = 2y
=> x/y = 1/1
=> x:y = 1:1
Option A
Answer: (A) 1:1
Question: What is the least integer greater than –3+0.5?
(A) –2
(B) –1
(C) 0
(D) 1
(E) 2
Rationale: This question is just about doing careful Arithmetic and remembering what makes a numberbiggerorsmallercompared to another number.
First, let's take care of the Arithmetic:
(-3) + (0.5) = -2.5
On a number line, since we're ADDING +.5 to a number, the total moves to the RIGHT (so we're moving from -3 to -2.5).
Next, the question asks for the LEAST integer that is GREATER than -2.5
Again, we can use a number line. Numbers become greater as you move to the RIGHT. The first INTEGER to the right of -2.5 is -2.
Final Answer:
A
Answer: (A) –2
Question: A certain mixture of nuts consists of 5 parts almonds to 2 parts walnuts, by weight. What is the number of pounds of almonds in 280 pounds of the mixture ?
(A)  200
(B)  84
(C)  40
(D)  28
(E)  20
Rationale: Almonds : Walnuts = 5 : 2
Total mixture has 7 parts
In a 280 pound mixture, Almonds are 5/7 (total mixture)
= 5/7 * 280 = 200 pounds
Answer (A)
Answer: (A)  200
Question: If A speaks the truth 65% of the times, B speaks the truth 60% of the times. What is the probability that they tell the truth at the same time
(A) 0.39
(B) 0.48
(C) 0.41
(D) 0.482
(E) 0.411
Rationale: Explanation:
Probability that A speaks truth is 65/100 = 0.65
Probability that B speaks truth is 60/100 = 0.6
Since both A and B are independent of each other
So probability of A intersection B is P(A) × P(B) =0.65 × 0.6 = 0.39
Answer: A
Answer: (A) 0.39
Question: The average (arithmetic mean)Q of the four distinct positive integers p, q, s and t is x. If p and q are odd, and s and t are even, which of the following must be true?
I. x is an integer
II. (x−0.5) is an integer.
III. 2x is an odd integer.
(A) I only
(B) II only
(C) III only
(D) II and III only
(E) None of the above
Rationale: Given :
p + q = EVEN (odd + odd =even)
p + q + s + t = EVEN (even + even = even) nothing more....
(p + q + s + t) / 4 = x
I.
x may or may not be integer, we only know sum of 4 variables is even not necessarily multiple of 4. I is out.
II.
Similarly, x an integer if sum of 4 variables is multiple of 4 but not an integer if it is not multiple of 4, we only know it is even. II is out.
III.
As in II, if X is integer 2x is Even, if X has decimal part (a.5), 2x is odd. III is out.
Answer E, None.
Answer: (E) None of the above
Question: A trader mixes 80 kg of tea at 15 per kg with 20 kg of tea at cost price of 20 per kg. In order to earn a profit of 25%, what should be the sale price of the mixed tea?
(A) 23.75
(B) 22
(C) 20
(D) 19.2
(E) None of these
Rationale: C.P. of mixture = 80×15+20×20 /80+20=16
∴ S.P. = (100+25)/100×16=20
Answer C
Answer: (C) 20
Question: During a certain two-week period, 58 percent of the movies rented from a video store were comedies, and of the remaining movies rented, there were 5 times as many dramas as action movies. If no other movies were rented during that two-week period and there were A action movies rented, then how many comedies, in terms of A, were rented during that two-week period?
(A) 10A
(B) 9A
(C) 8 2/3A
(D) 11A
(E) 12A
Rationale: Total movies = 100.
Comedies = 58.
Action + Drama = 42. Since there were 5 times as many dramas as action movies, then Action + 5*Action = 42 --> Action = A = 7.
Comedies = = 8 2/3A
Answer: C.
Answer: (C) 8 2/3A
Question: If a 3-member subcommittee is to be formed from a certain 8-member committee, how many different such subcommittee are possible?
(A) 6
(B) 18
(C) 40
(D) 108
(E) 216
Rationale: Another way:
1st member can be selected in 8 ways
2nd can be selected in 6 ways
3rd can be selected in 5 ways
So total ways : 240
But to avoid the similar scenarios 240/3!=40
C
Answer: (C) 40
Question: For an integer n greater than 1, n* denotes the product of all the integers from 1 to n inclusive. How many prime numbers are there between 7*+4 and 7*+7, inclusive ?
(A) 1
(B) 0
(C) 2
(D) 3
(E) 4
Rationale: Given that n* denotes the product of all the integers from 1 to n, inclusive so, 7* + 4 = 7! + 4 and 7* + 7 = 7! + 7.
Now, notice that , we can factor out 4 our of 7! + 4 so it cannot be a prime number, ... The same way for all numbers between 7! + 4 and 7! +7, inclusive. Which means that there are no primes in this range.
Answer: B
Answer: (B) 0
Question: There are 5 burglars and once went to a bakery to rob it obviously. The first guy ate 1/2 of the total bread and 1/2 of the bread. The second guy ate 1/2 of the remaining and 1/2 of the bread. The third guy ,fourth guy and fifth guy did the same. After fifth guy there is no bread left out. How many bread are there?
(A) 30
(B) 31
(C) 32
(D) 33
(E) 34
Rationale: (1/2 + 1/2) = 1
2(1 + 1/2) = 3
2(3 + 1/2) = 7
2(7 + 1/2) = 15
2(15 + 1/2) = 31
ANSWER:B
Answer: (B) 31
Question: If I walk at 3 kmph, I miss the train by 2 min, if however, I walk at 4 kmph. I reach the station 2 min before the arrival of the train. How far do I walk to reach the station?
(A) 4/5 km
(B) 4/8 km
(C) 2/5 km
(D) 4/6 km
(E) 3/5 km
Rationale: x/3 – x/4 = 4/60
x = 4/5 km
Answer: A
Answer: (A) 4/5 km
Question: A and B started a business in partnership investing Rs.20,000 and Rs.15,000 respectively. After 6months, C joined them with Rs.20,000. Whatwill be B's share in total profit of Rs.21,000 earned at the end of 2years from the startingof the business?
(A) s. 5,000
(B) s. 5,500
(C) s. 5,700
(D) s. 6,300
(E) s. 7,500
Rationale: A : B : C = (20,000 x 24) : (15,000 x 24) : (20,000 x 18) = 4 : 3 : 3.
B's share = Rs. 21000 x	3/10	= Rs. 6,300.
D
Answer: (D) s. 6,300
Question: In a group of dogs and people, the number of legs was 28 more than twice the number of
heads. How many dogs were there? [Assume none of the people or dogs is missing a leg.]
(A) 4
(B) 7
(C) 12
(D) 14
(E) 28
Rationale: If there were only people, there would be exactly twice the number of legs as
heads. Each dog contributes two extra legs over and above this number. So 28 extra legs
means 14 dogs.
correct answer D
Answer: (D) 14
Question: what smallest no. should subtracted from 5000,so that remainder completely divisible from 19?
(A) 3
(B) 4
(C) 5
(D) 6
(E) 9
Rationale: if 5000 is divided by 19 then remainder is 3.
no. should subtracted is 3.
answer A
Answer: (A) 3
Question: At what price must an Book costing $47.50 be marked in order that after deducting 10% from the list price. It may be sold at a profit of 25% on the cost price?
(A) 72.5
(B) 55.5
(C) 62.5
(D) 82.5
(E) 65.9
Rationale: E
$62.50
CP = 47.50
SP = 47.50*(125/100) = 59.375
MP*(90/100) = 59.375
MP = 65.9
E
Answer: (E) 65.9
Question: A and B start from Opladen and Cologne respectively at the same time and travel towards each other at constant speeds along the same route. After meeting at a point between Opladen and Cologne, A and B proceed to their destinations of Cologne and Opladen respectively. A reaches Cologne 40 minutes after the two meet and B reaches Opladen 60 minutes after their meeting. How long did A take to cover the distance between Opladen and Cologne?
(A) 1 hour
(B) 1 hour 20 minutes
(C) 2 hours 30 minutes
(D) 1 hour 40 minutes
(E) 2 hours 10 minutes
Rationale: v1 and V2 are speeds.
v1.t /60 = v2
v2.t/40 = v1
v1/v2 = 3/2
which train A would 60. 2/3 mins to cover the same distance
40 + 40 = 80 mins (ANS B)
Answer: (B) 1 hour 20 minutes
Question: If a mixture is 1⁄7 alcohol by volume and 2⁄7 water by volume, what is the ratio of the volume of alcohol to the volume of water in this mixture?
(A) 4/2
(B) 3/2
(C) 1/2
(D) 5/2
(E) 7/2
Rationale: Should be a sub-600 level Q..
volume= {1/7}/{2/7}=1/2
C
Answer: (C) 1/2
Question: If 1 + x^4 + x^3 + x^2 + x = 80, then the average (arithmetic mean)R of x, x^2, x^3, x^4 and x^5 is equal to which of the following?
(A) 12x
(B) 13x
(C) 14x
(D) 16x
(E) 20x
Rationale: 1 + x^4 + x^3 + x^2 + x = 81
i.e. 1 +x+ x^2+ x^3+ x^4 = 81
x+ x^2+ x^3+ x^4 = 80
x(1 +x+ x^2+ x^3) = 80
x(81-x^4) = 80
81x - x^5 = 80
x^5 = 81x -80
Now x+ x^2+ x^3+ x^4+ x^5 = 80 + 81x -80 = 81x
Average of R{x, x^2, x^3, x^4, x^5} = 81x/5 ~ 16x
AnswerD
Answer: (D) 16x
Question: In how many ways can a group of 5 men and 2 women be made out of a total of 7 men and 3 women?
(A) 53
(B) 57
(C) 63
(D) 65
(E) 67
Rationale: Explanation:
We need to select 5 men from 7 men and 2 women from 3 women.
Number of ways to do this
= 7C5 × 3C2
= 7C2 × 3C1 [∵ nCr = nC(n-r)]
=
7
×
6
2
×
1
×
3
=
21
×
3
=63
C)
Answer: (C) 63
Question: John invests $x at the semi-annual constant compounded rate of 2 percent and also does $5,000 at the quarterly constant compounded rate of 4 percent. If the interests are the same after 1 year, what is the value of x??
(A) 10000
(B) 10100.5
(C) 20000
(D) 15000
(E) 19000
Rationale: A = P(1+r/n)^nt
A= total amount accrued
P = principal deposited
r = rate of interest in decimal form
n = number of times per year, interest compounded
t = time in number of years.
.
x(1+0.02/2)^2 - x = 5,000(1+0.04/4)^4 - 5,000 [ when the principal is subtracted from the total amount accrued , the resulting difference is the interest portion and question states interests are equal)
=> x[(1.01)^2 - 1] = 5,000[(1.01)^4 - 1]
=> x[(1.01)^2 - 1] = 5,000[(1.01)^2+1][(1.01)^2-1] --> Using a^2-b^2 = a+b X a-b formula and cancel common expression on both sides
=> x = 5,000(1.0201+1) =10,100.5
Hence answer is B.
Answer: (B) 10100.5
Question: An design manager has 10patterns of chairs & 8patterns of tables. In how many ways can he make a pair of table & chair?
(A) 20
(B) 40
(C) 80
(D) 90
(E) 100
Rationale: He has has ten patterns of chairs and eight patterns of tables
Hence, A chair can be arranged in 10 ways and
A table can be arranged in 8 ways
Hence one chair and one table can be arranged in 10 x 8 ways = 80 ways
C
Answer: (C) 80
Question: The salaries A, B, C are in the ratio 2 : 3 : 5. If the increments of 15%, 10% and 20% are allowed respectively in their salaries, then what will be new ratio of their salaries?
(A) 40
(B) 60
(C) 20
(D) 10
(E) 50
Rationale: Let A = 2k, B = 3k and C = 5k.
A's new salary = 115/100 of 2k = (115/100) 2k = 23k/10
B's new salary = 110/100 of 3k = (110/100) 3k = 33k/10
C's new salary = 120/100 of 5k = (120/100) 5k = 6k
Therefore, New ratio	(23k/10) : (33k/10): 6k)
= 23 : 33 : 60
Answer is B.
Answer: (B) 60
Question: If 9 engines consume 24 metric tonnes of coal, when each is working 8 hoursa day, how much coal will be required for 8 engines, each running 13 hours a day, it is being given that 3 engines of former type consume as much as 4 engines of latter type?
(A) 23
(B) 25
(C) 26
(D) 28
(E) 30
Rationale: Explanation :
Let 3 engines of former type consume 1 unit in 1 hour.
Then, 4 engines of latter type consume 1 unit in 1 hour.
Therefore 1 engine of former type consumes(1/3) unit in 1 hour.
1 engine of latter type consumes(1/4) unit in 1 hour.
Let the required consumption of coal be x units.
Less engines, Less coal consumed (direct proportion)
More working hours, More coal consumed (direct proportion)
Less rate of consumption, Less coal consumed(direct proportion)
Number of engines 9: 8
Working hours 8 : 13 } :: 24 : x
Rate of consumption (1/3):(1/4)
( 9 * 8 * (1/3) * x) = (8 * 13 * (1/4) * 24 ) <=> 24x = 624 <=> x = 26.
Answer : C
Answer: (C) 26
Question: Two cards are drawn together from a pack of 52 cards. The probability that one is a spade and one is a heart, is:
(A) 3/20
(B) 1/20
(C) 13/102
(D) 11/20
(E) 2/20
Rationale: Let S be the sample space.
Then, n(S) = 52C2
= (52*51)/(2*1)
= 1326
Let E = event of getting 1 spade and 1 heart.
n(E)	= number of ways of choosing 1 spade out of 13 and 1 heart out of 13
= (13C1 * 13C1)
= (13 * 13)
= 169
P(E) = n(E)/n(S)
= 169/1326
= 13/102
Answer should be C
Answer: (C) 13/102
Question: Sam invested Rs. 15000 @ 10% per annum for one year. If the interest is compounded half-yearly, then the amount received by Sam at the end of the year will be?
(A) Rs. 16537.52
(B) Rs. 16137.11
(C) Rs. 16537.50
(D) Rs. 16237.52
(E) Rs. 16537.11
Rationale: Explanation:
P = Rs. 15000; R = 10% p.a. = 5% per half-year; T = 1 year = 2 half-year
Amount = [15000 * (1 + 5/100)2]
= (15000 * 21/20 * 21/20) = Rs. 16537.50
Answer:C
Answer: (C) Rs. 16537.50
Question: What is the greater of the two numbers whose product is 2688, given that the sum of the two numbers exceeds their difference by 64?
(A) A)84
(B) B)104
(C) C)110
(D) D)72
(E) of these
Rationale: Let the greater and the smaller number be g and s respectively.
gs = 2560
g + s exceeds g - s by 64 i.e., g + s - (g - s) = 64
i.e., 2s = 64 => s = 32.
g = 2688/s = 84.
ANSWER:A
Answer: (A) A)84
Question: For any numbers a and b, a#b = ab(6 − b). If a and a#b both represent positive numbers, which of the following could be a value of b?
(A) 5
(B) 5,4
(C) 5,4,3
(D) 5,4,3,2,1
(E) 5,4,3,2
Rationale: a#b positive then b may be positive or negative. if positive then b< 6 may be 5,4,3,2 or 1 and if negative then it is more than or equal to - 1 negative . ab will be -ve which is not possible as a and a#b should be positive.
ans 5,4,3,2 and 1
D
Answer: (D) 5,4,3,2,1
Question: If each side of a square is increased by 25%, find the percentage change in its area?
(A) 54%
(B) 56%
(C) 56.25%
(D) 58.25%
(E) 59%
Rationale: let each side of the square be a , then area = a x a
New side = 125a / 100 = 5a / 4
New area =(5a x 5a) / (4 x 4) = (25a²/16)
increased area== (25a²/16) - a²
Increase %= [(9a²/16 ) x (1/a² ) x 100]% = 56.25%
answer :C
Answer: (C) 56.25%
Question: Rs.600 amounts to Rs.900 in 3 years at simple interest. If the interest is increased by 4%, it would amount to how much?
(A) 672
(B) 246
(C) 258
(D) 856
(E) 653
Rationale: (600*3*4)/100 = 72
600 + 72 = 672
Answer: A
Answer: (A) 672
Question: Alan buys 4 TVs, a 26 inch, a 28 inch, a 30 inch, and a 32 inch, for his new house. Each TV costs $200 more than the size below it. Alan spends a total of $3,800. How much would he have spent if he had bought only the 28 inch and 30 inch TVs?
(A) 850
(B) 1,100
(C) 1,900
(D) 2,550
(E) 3,400
Rationale: Assume the cost of the least sized (26 Inch) TV = x
Cost of 28 inches TV = x + 200
Cost of 30 inches TV = x + 400
Cost of 32 inches TV = x + 600
Total cost = 4x + 1200 = 3800
Therefore x = 2600/4 = 650
Price of 28inch + 30 inch = 850 + 1050 = 1900
Option C
Answer: (C) 1,900