mathewhe/aqua_rat huggingface dataset:
Question: A can do a work in 6 days , B can do a work in 8 days and C can do it in 12 days. B left work after 6 days. For how many number of days should A and C should work together to complete the remaining work ?
(A) 1
(B) 2
(C) 3
(D) 4
(E) 5
Rationale: b work 1/8 * 6=3/4
remaining work =1-3/4=1/4
a and c work together =1/6+1/12=3/12=1/4
take reciprocial 4 * remaining work =4 *1/4=1
ANSWER:A
Answer: (A) 1
Question: David invested certain amount in three different schemes A, B and C with the rate of interest 10% p.a., 12% p.a. and 15% p.a. respectively. If the total interest accrued in one year was Rs. 3200 and the amount invested in Scheme C was 150% of the amount invested in Scheme A and 240% of the amount invested in Scheme B, what was the amount invested in Scheme B?
(A) Rs.5000
(B) Rs.2000
(C) Rs.6000
(D) Rs.3000
(E) Rs.4000
Rationale: Explanation :
Let x , y and x be his investments in A, B and C respectively. Then
Then, Interest on x at 10% for 1 year
+ Interest on y at 12% for 1 year
+ Interest on z at 15% for 1 year
= 3200
x×10×1/100+y×12×1/100+z×15×1/100=3200
⇒10x+12y+15z=320000−−−(1)
Amount invested in Scheme C was 240% of the amount invested in Scheme B
=>z=240y/100=60y/25=12/y5−−−(2)
Amount invested in Scheme C was 150% of the amount invested in Scheme A
=>z=150x/100=3x/2
=>x=2z/3=2/3×12y/5=8y/5−−−(3)
From(1),(2) and (3),
10x + 12y + 15z = 320000
10(8y/5)+12y+15(12y/5)=320000
16y+12y+36y=320000
64y=320000
y=320000/64=10000/2=5000
i.e.,Amount invested in Scheme B = Rs.5000
Answer : Option A
Answer: (A) Rs.5000
Question: What is the greatest value of n such that 4^n is a factor of 23! ?
(A) 8
(B) 4
(C) 7
(D) 5
(E) 9
Rationale: Pretty simple, really.
If m = 9, then 4m = 36, which is 18x2, both of which are included in 23!
Since 9 is the largest number here, its the answer.
Answer is E
Answer: (E) 9
Question: In what ratio should a variety of rice costing $6 per kg be mixed with another variety of rice costing $8.75 per kg to obtain a mixture costing $7.50 per kg?
(A) 4/7
(B) 5/6
(C) 5/9
(D) 4/8
(E) 3/8
Rationale: B
5/6
Let us say the ratio of the quantities of cheaper and dearer varieties = x : y
By the rule of allegation, x/y = (87.5 - 7.50) / (7.50 - 6) = 5/6
Answer: (B) 5/6
Question: Pipe A can fill a tank in 6 hours, pipe B in 12 hours and pipe C in 36 hours. If all the pipes are open,in how many hours will the tank be filled ?
(A) 3.2
(B) 3
(C) 3.3
(D) 3.5
(E) 3.6
Rationale: 1/6+1/12+1/36=10/36=1/3.6. so 3.6 hrs
ANSWER:E
Answer: (E) 3.6
Question: A tank is filled by three pipes with uniform flow. The first two pipes operating simultaneously fill the tank in the same time during which the tank is filled by the third pipe alone. The second pipe fills the tank 5 hours faster than the first pipe and 4 hours slower than the third pipe. Time required by the first pipe to fill the tank is
(A) 30 hours
(B) 15 hours
(C) 10 hours
(D) 6 hours
(E) 7 hours
Rationale: Explanation:
Suppose the first pipe alone can fill the tank in x hours. Then,
second pipe alone can fill the tank in (X-5)hours,
third pipe alone can fill the tank in(xâˆ’5)-4=(xâˆ’9)hours.
Part filled by first pipe and second pipe together in 1 hr= Part filled by third pipe in 1 hr
We can not take the value (xâˆ’3)because,(xâˆ’9)becomes negative which is not possible, because the third pipe can fill the tank in(xâˆ’9) hours.
Hence, x=15
ANSWER IS B
Answer: (B) 15 hours
Question: The average of 10 numbers is calculated as 16. It is discovered later on that while calculating the average, the number 55 was incorrectly read as 25, and this incorrect number was used in the calculation. What is the correct average?
(A) 17
(B) 19
(C) 25
(D) 31
(E) 46
Rationale: The total sum of the numbers should be increased by 30.
Then the average will increase by 30/10 = 3.
The correct average is 19.
The answer is B.
Answer: (B) 19
Question: The factorial expression 10!/5! is divisible by which of the following integers?
(A) 5
(B) 31
(C) 21
(D) 11
(E) 19
Rationale: 10!/5! => 10 x 9 x 8 x 7 x 6
(A) 5 Can divide 10
(B) 31 None of the Multiplicands present
(C) 21 None of the Multiplicands present
(D) 11 None of the Multiplicands present
(E) 19 None of the Multiplicands present
Hence answer will be (A)
Answer: (A) 5
Question: If from a group of 5 people, an old member is replaced by a new one, the average age is same as it was 3 years ago. What is the difference between the ages of the old member and the new one?
(A) 12
(B) 15
(C) 11
(D) 18
(E) 16
Rationale: Explanation:
The present average age is (x + 3) when the old member is present and it equals to x when an old member is replaced by a new one.
The difference in the ages of the old member and the new one is equal to the difference in the total age before and after the replacement = 15 years.
ANSWER: B
Answer: (B) 15
Question: The ratio of the present ages of Sunitha and Vinitha is 4:5. Six years hence the ratio of their ages will be 14:17. What will be the ratio of their ages 12 years hence ?
(A) 15:19
(B) 13:15
(C) 16:19
(D) 17:19
(E) 14: 16
Rationale: Suppose the present ages of sunitha and vinitha be 4x and 5x years respectively.
six years hence
4x + 6 / 5x + 6 = 14/17
or 68x + 102 = 70x + 84
or x= 9
Ratio of ages of sunita and vinita after 12 years
4x + 12 : 5x + 12 = 48 : 57 = 16 : 19 ANSWER :C
Answer: (C) 16:19
Question: A total of 324 coins of 20 paise and 25 paise make a sum of Rs. 71. The number of 25-paise coins is
(A) 120
(B) 124
(C) 144
(D) 200
(E) 220
Rationale: Explanation:
Let the number of 20-paise coins be x. Then, number of 25-paise coins = (324 - x).
Therefore 0.20 x x + 0.25 (324 - x) = 71 20x + 25 (324 - x) = 7100
5x= 1000 x = 200. Hence, number of 25-paise coins = (324 - x) - 124.
Answer:B
Answer: (B) 124
Question: There are 600 students in a school. The ratio of boys and girls in this school is 3:5. Find the total of girls & boys are there in this school?
(A) 225
(B) 257
(C) 375
(D) 380
(E) 390
Rationale: In order to obtain a ratio of boys to girls equal to 3:5, the number of boys has to be written as 3 x and the number of girls as 5 x where x is a common factor to the number of girls and the number of boys. The total number of boys and girls is 600. Hence
3x + 5x = 600
Solve for x
8x = 600
x = 75
Number of boys
3x = 3 × 75 = 225
Number of girls
5x = 5 × 75 = 375
C
Answer: (C) 375
Question: If a person walks at 15 km/hr instead of 9 km/hr, he would have walked 20 km more. The time traveled by him is?
(A) 8 hours
(B) 9/5 hours
(C) 10/3 hours
(D) 6 hours
(E) 11/3 hours
Rationale: Let the actual distance traveled be x km. Then,
x/9 = (x + 20)/15
5x - 3x = 60 =>x = 30 km.
travel time is = 30/9 hours = 10/3 hours
Answer :C
Answer: (C) 10/3 hours
Question: A, B, C subscribe Rs. 50,000 for a business. A subscribes Rs. 4000 more than B and B Rs. 5000 more than C. Out of a total profit of Rs. 35,000, C receives:
(A) s. 14,000
(B) s. 14,200
(C) s. 4,400
(D) s. 8,400
(E) s. 4,800
Rationale: Let C = x.
Then, B = x + 5000 and A = x + 5000 + 4000 = x + 9000.
So, x + x + 5000 + x + 9000 = 50000
3x = 36000
x = 12000
A : B : C = 21000 : 17000 : 12000 = 21 : 17 : 12.
C's share = Rs. (35000 x 12/50) = Rs. 8,400.
D
Answer: (D) s. 8,400
Question: The value of ((x – y)³ + (y - z)³ + (z – x)³)/(21 (x – y) (y – z) (z – x))
is equal to :
(A) 0
(B) 1/12
(C) 1/7
(D) 1/4
(E) 1/3
Rationale: Since (x – y) + (y – z) + (z – x) = 0,
so (x – y)³ + (y – z)³ + (z – x)³= 3 (x – y) (y – z) (z – x).
(3 (x – y) (y – z) (z – x))/(21(x – y) (y – z) (z – x)) = 1/7.
ANSWER:C
Answer: (C) 1/7
Question: A box contains 1 red balls and 5 black balls. One by one, every ball is selected at random without replacement. What is the probability that the fourth ball selected is black?
(A) 1/4
(B) 1/2
(C) 1/2
(D) 5/8
(E) 2/3
Rationale: My complicated version of your simple approach
Let the 5 black balls be BBBBB and 1 Red Balls be R
They can be arranged in 6 slots _ _ _ _ _ _ _ _
in (6!)/ (5!x1!)
If the fourth slot is Black ball then the arrangement will be to fill
_ _ _ B _ _ _ _
we have 5 slots and 4 Black (BBBB) and 1 Red (R)
They can be arranged in (5!)/ (4!x1!)
Hence required probability = [(6!)/ (5!x1!)]/[(5!)/ (4!x1!)]
=6/5
C
Answer: (C) 1/2
Question: How many different ways can a group of 8 people be divided into 4 teams of 2 people each?
(A) 56
(B) 105
(C) 75
(D) 120
(E) 112
Rationale: The required answer is = 8!/(4!*2!*2!*2!*2!) = 105
Answer is B
Answer: (B) 105
Question: As part of her MBA program, Karen applied for three different Spring Break outreach projects, each of which selects its students by a random lottery of its applicants. If the probability of her being accepted to each individual project is 60%, what is the probability that Karen will be accepted to at least one project?
(A) 4/5
(B) 19/25
(C) 37/50
(D) 98/125
(E) 117/125
Rationale: Since the probability of Karen's being accepted to each individual project is 60%, the probability of her not being accepted to each project is 40%. The probability that she will be accepted to none is, therefore, (2/5)*(2/5)*(2/5)=8/125.
P(Karen will be accepted to at least one project) = 1 - (8/125) = 117/125.
The answer is E.
Answer: (E) 117/125
Question: Ratio between Rahul and Deepak is 4:3, After 6 Years Rahul age will be 22 years. What is Deepak present age?
(A) 22
(B) 15
(C) 77
(D) 266
(E) 12
Rationale: Present age is 4x and 3x,
=> 4x + 6 = 22 => x = 4
So Deepak age is = 3(4) = 12
Answer: E
Answer: (E) 12
Question: An urn contains 4 white 6 black and 8 red balls .Three balls are drawn at random from the bag.the probability that all of them are white are????
(A) 4/24
(B) 8/24
(C) 7/24
(D) 1/24
(E) 6/24
Rationale: 4c3/18c3=4/816=1/24
ANSWER:D
Answer: (D) 1/24
Question: If a, b, c, d, e and f are integers and (ab + cdef) < 0, then what is the maximum number A of integers that can be negative?
(A) 2
(B) 3
(C) 4
(D) 5
(E) 6
Rationale: Minimuum should be 1
Maximum should be 4:
1 out of a or b to make the multiplication negative
3 out of c, d, e or f to make the multiplication negative.
Negative+Negative<0
Answer:C
maximum will be 5..
you dont require both the multiplicatin to be negative for entire equation to be negative...
any one a or b can be negative to make ab negative and it can still be more(away from 0) than the multiplication of 4 other -ve numbers...
actually by writing minimum required as 1 out of 6,you are actually meaning 5 out of 6 also possible as you will see A=5 or 1 will give you same equation..
ans D
Answer: (D) 5
Question: In how many ways the letters of the word MAXICABE be arranged?
(A) 32,230 ways.
(B) 20,320 ways.
(C) 30,320 ways.
(D) 40,320 ways.
(E) 42,320 ways.
Rationale: Total ways of arranging the letters = 8! = 40,320 ways.
D)
Answer: (D) 40,320 ways.
Question: Bill has a small deck of 10 playing cards made up of only 2 suits of 5 cards each. Each of the 5 cards within a suit has a different value from 1 to 5; thus, there are 2 cards in the deck that have the same value. Bill likes to play a game in which he shuffles the deck, turns over 4 cards, and looks for pairs of cards that have the same value. What is the chance that Bill finds at least one pair of cards that have the same value?
(A) 7/15
(B) 9/16
(C) 11/18
(D) 13/21
(E) 16/25
Rationale: P(no pairs) = 8/9*6/8*4/7 = 8/21
P(at least one pair) = 1 - 8/21 = 13/21
The answer is D.
Answer: (D) 13/21
Question: (935421 x 625) = ?
(A) 583038125
(B) 583538125
(C) 583738125
(D) 584038125
(E) 584638125
Rationale: 935421 x 625 = 935421 x 54 = 935421 x 10 4
2
=	935421 x 104	=	9354210000
24	16
= 584638125
E)
Answer: (E) 584638125
Question: Six dots are evenly spaced on the circumference of a circle. How many combinations of three dots can we make from these 6 dots that do not form an equilateral triangle?
(A) 18
(B) 17
(C) 16
(D) 15
(E) 14
Rationale: The total number of ways we can choose three dots is 6C3=20.
We can form two equilateral triangles from these six dots.
There are 20 - 2 = 18 combinations which do not form an equilateral triangle.
The answer is A.
Answer: (A) 18
Question: How many seconds will it take for a car that is traveling at a constant rate of 120 miles per hour to travel a distance of 77 yards?	(1 mile = 1,160 yards)
(A) 1.25
(B) 1.31
(C) 1.58
(D) 1.87
(E) 2.3
Rationale: speed = 120 miles/hr = 58.67 yard/s
distance = 77 yards
time = distance/speed
=77/58.67
=1.31 sec
ans - B
Answer: (B) 1.31
Question: A team of 6 cooks is chosen from 7 men and 5 women. The team must have at least 2 men and at least 3 women. How many ways can this team be created?
(A) 140
(B) 320
(C) 560
(D) 455
(E) 840
Rationale: Only possible combinations are a team of 2M, 4 W or 3M,3W.
Possible ways to make a team of 2M,4W = 7C2 * 5C4 =21*5 =105
Possible ways to make a team of 3M,3W = 7C3* 5C3 = 35*10 = 350
Total possible ways = 105+350 = 455
Ans D it is.
Answer: (D) 455
Question: The average of 7 consecutive numbers is 20. The largest of these numbers is :
(A) 22
(B) 20
(C) 23
(D) 21
(E) 92
Rationale: Explanation:
Let the numbers be x, x + 1, x + 2, x + 3, x + 4, x + 5 and x + 6,
Then (x + (x + 1) + (x + 2) + (x + 3) + (x + 4) + (x + 5) + (x + 6)) / 7 = 20.
or 7x + 21 = 140 or 7x = 119 or x =17.
Latest number = x + 6 = 23.
Answer: C
Answer: (C) 23
Question: mixture contains alcohol and water in the ratio 4 : 3. If 7 liters of water is added to the mixture, the ratio becomes 4: 5. Find the quantity of alcohol in the given mixture.
(A) 10
(B) 99
(C) 5
(D) 22
(E) 29
Rationale: Let the quantity of alcohol and water be 4x litres and 3x litres respectively
28x = 4(3x+5)
16x = 20
x = 1.25
Quantity of alcohol = (4 x 1.25) litres = 5 litres.
Answer: C
Answer: (C) 5
Question: Aman can row 1km upstream in 20 min and back to his starting point in 12 min.How long would he take to row 1km in still water?.
(A) 12 mins
(B) 13 mins
(C) 14 mins
(D) 15 mins
(E) 16 mins
Rationale: If his speed is x mtr/min in still water and w mtr/minis speed of water, then
x-w= 1000/20=50
x+w= 1000/12= 250/3
adding
2x= 50 + 250/3= 400/3
x=200/3 mtrs/min
time taken to row 1 kms in still water = 1000/(200/3)= 15 mins.
ANSWER:D
Answer: (D) 15 mins
Question: The length of a rectangle is two - fifths of the radius of a circle. The radius of the circle is equal to the side of the square, whose area is 1600 sq.units. What is the area (in sq.units) of the rectangle if the rectangle if the breadth is 10 units?
(A) 140
(B) 150
(C) 160
(D) 170
(E) 180
Rationale: Given that the area of the square = 1600 sq.units
=> Side of square = √1600 = 40 units
The radius of the circle = side of the square = 40 units
Length of the rectangle = 2/5 * 40 = 16 units
Given that breadth = 10 units
Area of the rectangle = lb = 16 * 10 = 160 sq.units
Answer: Option C
Answer: (C) 160
Question: The length of a rectangular floor is more than its breadth by 200%. If Rs.361 is required to paint the floor at the rate of Rs.3/sq m, what would be the length of the floor?
(A) 18
(B) 19
(C) 20
(D) 22
(E) 24
Rationale: Let the length and the breadth of the floor be l m and b m respectively.
l = b + 200% of b = l + 2b = 3b
Area of the floor = 361/3 = 120.33 sq m
l b = 120.33 i.e., l * l/3 = 120.33
l^2 = 361 => l = 19.
B
Answer: (B) 19
Question: For the set {2, 2, 3, 3, 4, 4, x}, which of the following values of x will most increase the standard deviation?
(A) 1
(B) 2
(C) 3
(D) 4
(E) (2)^2
Rationale: Standard Deviation Step 1, as pointed out by others, is to find out the mean = 3
Step 2, For each number: subtract the Mean and square the result =
(1-3)^2=(-2)^2
(2-3)^2=(-1)^2
(3-3)^2 =(0)^2
(4-3)^2=(1)^2
(5-3)^2=(2)^2
Clearly (1-3)^2=(-2)^2 will give you the greatest value among all the other options.
Hence E
Answer: (E) (2)^2
Question: A salesman sold twice as much pears in the afternoon than in the morning. If he sold 360 kilograms of pears that day, how many kilograms did he sell in the morning and how many in the afternoon?
(A) 240
(B) 377
(C) 269
(D) 277
(E) 768
Rationale: Let xx be the number of kilograms he sold in the morning.Then in the afternoon he sold 2x2x kilograms. So, the total is x+2x=3xx+2x=3x. This must be equal to 360.
3x=3603x=360
x=3603x=3603
x=120x=120
Therefore, the salesman sold 120 kg in the morning and 2⋅120=2402⋅120=240 kg in the afternoon.
Answer:A
Answer: (A) 240
Question: A certain number of persons can finish a piece of work in 100 days. If there were 10 persons less, it would take 10 more days finish the work. How many persons were there originally?
(A) 90
(B) 100
(C) 110
(D) 120
(E) None of these
Rationale: Explanation :
Assume that x persons can finish a piece of work in 100 days
Also it is given that (x-10) persons can finish a piece of work in 110 days (∵ 100 + 10 = 110)
More persons, less days(indirect proportion)
Hence we can write as
personsx:(x−10)}:: 110 : 100
⇒ 100x = 110(x − 10)
⇒ 100x = 110x − 1100
⇒ 10x = 1100
⇒ x = 1100/10 = 110. Answer : Option C
Answer: (C) 110
Question: A, B, C enter into a partnership investing Rs. 35,000, Rs. 45,000 and Rs. 55,000 respectively. The respective shares of A, B, C in annual profit of Rs. 40,500 ?
(A) Rs. 10,500, Rs. 13,500, Rs. 16,500
(B) Rs. 10,500, Rs. 13,500, Rs. 16,509
(C) Rs. 10,500, Rs. 13,500, Rs. 16,506
(D) Rs. 10,500, Rs. 13,500, Rs. 16,5065
(E) Rs. 10,500, Rs. 13,500, Rs. 16,5012
Rationale: A:B:C = 35000 : 45000 : 55000 = 7:9:11
A's share = 40500 * 7/27 = Rs. 10500
B's share = 40500 * 9/27 = Rs. 13500
C's share = 40500 * 11/27 = Rs. 16500
Answer: A
Answer: (A) Rs. 10,500, Rs. 13,500, Rs. 16,500
Question: A number consists of two digits. If the digits interchange places and the new number is added to the original number, then the resulting number will be divisible by:
(A) 11
(B) 5
(C) 2
(D) 8
(E) 4
Rationale: Let the ten's digit be x and unit's digit be y.
Then, number 10x + y.
Number obtained by interchanging the digits = 10y + x.
(10x + y) + (10y + x) = 11(x + y)
which is divisible by 11.
ANSWER A
Answer: (A) 11
Question: If x^2 is divisible by 240 what is the least possible value of integer x?
(A) 120
(B) 30
(C) 90
(D) 60
(E) 12
Rationale: 240 can be written as (2^4)*3*5.
For x^2 to be divisible by 240 it should contain at least 2^4 and 3 and 5 in its factors. We can leave out option E because 12 doesnt have 5 as one of its factor. Now if we check for option B, 30 can be written as 2*3*5, hence 30^ 2 will have 2 as the maximum power of 2, so we can leave out this option too.
Option D is the right answer if we follow the same method as we followed for other two previous options.
60 = (2^2)*3*5; 60^2 = (2^4)*(3^2)*(5^2). So it shows that 60^2 is divisible by 240 and hence the answer.
Answer : D
Answer: (D) 60
Question: Rs.1210 were divided among 3 person P, Q, R so that P:Q=5:4 and Q: R=9:10. Then R gets the amount.
(A) Rs. 300
(B) Rs. 400
(C) Rs. 480
(D) Rs. 490
(E) Rs. 500
Rationale: P : Q = 5 : 4, Q : R = 9 : 10 = ( 9 x 4 / 9 ) : ( 10 x 4 / 9 ) = 4 : 40 / 9.
So, P : Q : R = 5 : 4 : 40 /9 = 45 : 36 : 40
Sum of ratio terms is = ( 45 + 36 + 40 ) =121.
R share of amount is Rs (1210 x 40 / 121) = Rs. 400.
B
Answer: (B) Rs. 400
Question: If $10,000 is invested at x percent simple annual interest for n years, which of the following represents the total amount of interest, in dollars, that will be earned by this investment in the n years?
(A) 10,000(x^n)
(B) 10,000(x/100)^n
(C) 10,000n(x/100)
(D) 10,000(1+x/100)^n
(E) 10,000n(1+x/100)
Rationale: The reasoning is from the following:
The formula for simple rate of interest is F = P(1+rt) where
F = future value
P = present value
r = rate
t = time
We can substitute x for r
n for t
and 10,000 in for P
F = 10,000(1+xn)
This formula will tell you the principal (original amount invested) + interest, but we only want interest, so the "1+" portion of the formula in unnecessary. -->
F = 10,000(xn)
Now, we need to get the x into terms of a percentage, so we divide x by 100 -->
F = 10,000(n * x/100)
If we move the n outside the brackets, we get -->
F = 10,000n(x/100)
ANSWER:C
Answer: (C) 10,000n(x/100)
Question: A, B, C, D and E are 5 consecutive points on a straight line. If BC = 3CD, DE = 8, AB = 5 and AC = 11, what is the length of AE?
(A) 15
(B) 17
(C) 19
(D) 21
(E) 23
Rationale: AC = 11 and AB = 5, so BC = 6.
BC = 3CD so CD = 2.
The length of AE is AB+BC+CD+DE = 5+6+2+8 = 21
The answer is D.
Answer: (D) 21
Question: A sum of money is to be distributed among A, B, C, D in the proportion of 5 : 2 : 4 : 3. If C gets $500 more than D, what is D's share?
(A) $1000
(B) $1200
(C) $1500
(D) $1800
(E) $2000
Rationale: Let the shares of A, B, C and D be 5x, 2x, 4x and 3x respectively.
Then, 4x - 3x = 500
x = $500
D's share = 3x = 3*$500 = $1500
The answer is C.
Answer: (C) $1500
Question: A particular library has 75 books in a special collection, all of which were in the library at the beginning of the month. These book are occasionally loaned out through an inter-library program. If, by the end of the month, 65 percent of books that were loaned out are returned and there are 54 books in the special collection at that time, how many books of the special collection were loaned out during that month?
(A) 20
(B) 30
(C) 35
(D) 40
(E) 60
Rationale: The total number of books is 75.
Let x be the number of books which were loaned out.
65% of books that were loaned out are returned.
35% of books that were loaned out are NOT returned.
Now, there are 54 books, thus the number of un-returned books is 75-54 = 21 books.
0.35x = 21
x = 60
The answer is E.
Answer: (E) 60
Question: The difference between a two-digit number and the number obtained by interchanging the positions of its digits is 36. What is the difference between the two digits of that number?
(A) 3
(B) 4
(C) 9
(D) Cannot be determined
(E) None of these
Rationale: Let the ten's digit be x and unit's digit be y.
Then, (10x + y) - (10y + x) = 36
9(x - y) = 36
x - y = 4.
Answer:B
Answer: (B) 4
Question: A number exceeds by 30 from its 3/8 part. Then the number is?
(A) A)32
(B) B)35
(C) C)39
(D) D)40
(E) E)48
Rationale: x – 3/8 x = 30
x = 48
ANSWER:E
Answer: (E) E)48
Question: How many of the positive factors of 15 , 45 and how many common factors are there in numbers?
(A) 1
(B) 2
(C) 3
(D) 4
(E) 5
Rationale: factors of 15 - 1, 3, 5, and 15
factors of 45 - 1, 3, 9, 15 and 45
Comparing both, we have three common factors of 45,16-3
Answer C
Answer: (C) 3
Question: What number has a 5:1 ratio to the number 10?
(A) 22
(B) 50
(C) 99
(D) 72
(E) 12
Rationale: 5:1 = x: 10
x = 50
Answer: B
Answer: (B) 50
Question: The tax on a commodity is diminished by 27% and its consumption increased by 16%. The effect on revenue is?
(A) 18
(B) 16
(C) 5
(D) 15
(E) 4
Rationale: 100 * 100 = 10000
73 * 116 = 8468
-----------
10000-----------1532
100-----------? => 15% decrease
Answer:D
Answer: (D) 15
Question: Three business people who wish to invest in a new company. Each person is willing to pay one third of the total investment. . After careful calculation, they realize that each of them would pay $ 7600 less if they could find two more equal investors. How much is the total investment in the new business.
(A) a)	$ 64,000
(B) b)	$ 54,000
(C) c)	$ 21,000
(D) d)	$ 5,400
(E) e)	$57,000
Rationale: Initially each invest in x. Hence total investment is 3x.
Total investment is also 5(x-7600).
3x = 5(x-7600)
x= 5*7600/2 = 19000
3x = 57000 and the answer is E.
Answer: (E) e)	$57,000
Question: In how many different number of ways 5 men and 2 women can sit on a shopa which can accommodate persons
(A) A)160
(B) B)170
(C) C)210
(D) D)190
(E) E)230
Rationale: 7p3 = 7 × 6 × 5 = 210
Option 'C'
Answer: (C) C)210
Question: The Chennai Express of 200 m runs at a speed of 62 km/hr and a person runs on the platform at a speed of 20 km/hr in the direction opposite to that of train. Find the time taken by the train to cross the running person?
(A) 8.77 sec
(B) 9.77 sec
(C) 12.77 sec
(D) 13.00 sec
(E) None of these
Rationale: EXPLANATION:
Given: Length of train = 200 m, speed of train = 62 km/hr, speed of person = 20 km/hr
1) Convert km/hr into m/s
- 62 km/hr = 62 x	5/18= 17.22 m/s
- 20 km/hr = 20 x	5/18=5.55 m/s
As the train and the running person move in opposite directions, their speed values are added to find the relative speed.
Relative speed (Speed of train relative to man) = 17.22 + 5.55 = 22.77 m/s
We know,
Speed =	Distance/Time
Therefore, time taken by the train to cross the running person = Time taken by the train to cover 200 m at a relative of 22.77 m/s
=	200/22.78
= 8.77 sec
ANSWER IS A
Answer: (A) 8.77 sec