mathewhe/aqua_rat huggingface dataset:
Question: Pipe A can fill a tank in 3 hours, pipe B in 15 hours and pipe C in 24 hours. If all the pipes are open, in how many hours will the tank be filled ?
(A) 2.5 hours
(B) 2 hours
(C) 3.5 hours
(D) 3 hours
(E) None of these
Rationale: Explanation:
Part filled by A in 1 hour = 1/3
Part filled by B in 1 hour = 1/15
Part filled by C in 1 hour = 1/24
Part filled by (A+B+C) in 1 hour =
1/3+1/15+1/24=93/120
So all pipes will fill the tank in 1.3 hours.
Option E
Answer: (E) None of these
Question: Find the value of X, Y by solving the below equations
X + Y = 5
X - Y = -3
(A) 4, 1
(B) 3, 2
(C) 1, 4
(D) 4, 6
(E) 5, 4
Rationale: X + Y = 5 ---(I)
X - Y = -3 -----(II) by adding (I) and (II)
------------
2X = 2 ==> X = 2/2 = 1
By Replacing the value of X in (I) we get 1 + Y = 5 ==>
Y = 5 -1 = 4.
So, X = 1, Y = 4
Answer C) 1, 4
Answer: (C) 1, 4
Question: A pupil's marks were wrongly entered as 85 instead of 45. Due to that the average marks for the class got increased by half. The number of pupils in the class is :
(A) 30
(B) 80
(C) 20
(D) 25
(E) 26
Rationale: Let there be x pupils in the class.
Total increase in marks = (X*1/2) = X/2.
X/2 = (85 - 45)
=> X/2 = 40
=> X = 80.
ANSWER:B
Answer: (B) 80
Question: A batch of widgets costs p + 15 dollars for a company to produce and each batch sells for p(10 – p) dollars. For which of the following values of p does the company make a profit?
(A) 10
(B) 9
(C) 8
(D) 6
(E) 7
Rationale: to make profit, selling price should be greater than cost price
p(10-p) - p-15 >0
=> p^2-9*p+15<0
hence p=6
D
Answer: (D) 6
Question: Two quarts containing 2⁄5 water and 4⁄5 formula are mixed with three quarts containing 3⁄10 water and 2⁄10 formula. Approximately what percent of the combined five-quart mixture is water?
(A) 34%
(B) 36%
(C) 38%
(D) 40%
(E) 45%
Rationale: 2/5 of 2 quarts = 4/5 quarts of water
3/10of 3 quarts = 9/10 quarts of water
4/5 = 0.8
9/10 = 0.9
Total water = 0.8 + 0.9= 1.7
Total quarts = 5
1.7/5 = 34%
Answer : A
Answer: (A) 34%
Question: A bus started its journey from Mumbai and reached Pune in 44min with its average speed of 50 km/hr. If the average speed of the bus is increased by 5km/hr, how much time will it take to cover the same distance?
(A) 38 min
(B) 36 min
(C) 31 min
(D) 40 min
(E) 49 min
Rationale: Sol. Distance between Ramgarh and Devgarh =(50*44)/60=110/3
Average speed of the bus is increased by 5 km/hr then the
speed of the bus = 55 km/hr
Required time = 110/3*60/55 = 40 min
D
Answer: (D) 40 min
Question: How many positive integers less than 100 have a remainder of 3 when divided by 13?
(A) 6
(B) 7
(C) 8
(D) 9
(E) 3
Rationale: We have to include 3 also.As 13*0 + 3 =3
If somebody says to divide 3 by 13 ,we will be telling we have 0 quotient and remainder as 3.
Answer is E
Answer: (E) 3
Question: If k and s are positive integers such that (2^k)(4^s) = 16, then 2k + s =
(A)  2
(B)  3
(C)  4
(D)  5
(E)  6
Rationale: lets get the eq into simplest orm..
(2^k)(4^s) = 16..
(2^k)(2^2s) = 2^4..
or k+2s=4..
since k and s are positive integers, only k as 2 and s as 1 satisfy the Equation..
so 2k+s=2*2+1=5..
D
Answer: (D)  5
Question: A train 250 m long is running at a speed of 68 kmph. How long does it take to pass a man who is running at 8 kmph in the same direction as the train?
(A) 15 sec
(B) 9 sec
(C) 12 sec
(D) 15 sec
(E) 18 sec
Rationale: Speed of the train relative to man = (68 - 8) kmph
= (60* 5/18) m/sec = (50/3)m/sec
Time taken by the train to cross the man
= Time taken by It to cover 250 m at 50/3 m / sec = 250 *3/ 50 sec = 15 sec
Answer : A.
Answer: (A) 15 sec
Question: Two whole numbers whose sum is 36 cannot be in the ratio
(A) 2:4
(B) 3:4
(C) 3:6
(D) 1:3
(E) 3:36
Rationale: B) 3:4
Answer: (B) 3:4
Question: What is 3/4 of 4/5 of 2/3?
(A) 1/4
(B) 2/5
(C) 9/16
(D) 5/8
(E) 16/9
Rationale: 3/4 * 4/5 * 2/3= 2/5
Answer: B
Answer: (B) 2/5
Question: The sale price of an article including the sales tax is Rs. 616. The rate of sales tax is 10%. If the shopkeeper has made a profit of 12%, then the cost price of the article is?
(A) 500
(B) 277
(C) 266
(D) 188
(E) 123
Rationale: 110% of S.P. = 616
S.P. = (616 * 100)/110 = Rs. 560
C.P = (110 * 560)/112 = Rs. 500
Answer: A
Answer: (A) 500
Question: By selling a watch for Rs.720/-, a man loses 20% what is that watch cost price
(A) s. 700/-
(B) s. 800/-
(C) s. 880/-
(D) s. 900/-
(E) s. 990/-
Rationale: 80 % ------> 720 (80 * 9 = 720)
100 % ------>900 (100 * 9 = 900)
Cost price = Rs. 900/-
D
Answer: (D) s. 900/-
Question: A girl was asked to state his age in years. Her reply was , "Take my age 5 years hence, multiply it by 5 and subtract 5 times my age 5 years ago and you will know how old I am." What was the age of the person ?
(A) 50
(B) 92
(C) 27
(D) 26
(E) 19
Rationale: Explanation:
Let the present age of girl be x years.
Then, 5(x + 5) - 5(x - 5 ) = x <=> (5x + 25) - (5x - 25) = x <=> x = 50..
Answer: A
Answer: (A) 50
Question: A man purchases 2 watches for $ 580. He sells one at 15% profit and the other at a loss of 10%. He neither gains nor loses on the whole. Thus, the cost price of two watches are :
(A) $ 260 and $ 300
(B) $210 and $ 350
(C) $224 and $336
(D) $560 and $560
(E) $232 and $ 348
Rationale: x + y = 580 --- (1)
1.15x + 0.9y = 580 --- (2)
(2) - (1) --> 0.15x - 0.1y = 0
15x = 10y
x/y = 2/3 = (2*116)/(3*116) = 232/348
Answer: E
Answer: (E) $232 and $ 348
Question: A team of 30 men is supposed to do a work in 38 days. After 25 days, 5 more men were employed and the work finished one day earlier. How many days would it have been delayed if 5 more men were not employed?
(A) 1
(B) 2
(C) 3
(D) 4
(E) 5
Rationale: 35 men do the rest of the job in 12days (38-25-1 = 12days)
30 men can do the rest of the job in 12*35/30 = 14 days
Thus the work would have been finished in 25+14 = 39daya that is 39-38 = 1 day after the scheduled time
Answer is A
Answer: (A) 1
Question: If y exceeds x by 10%, then x is less than y by?
(A) 1/3%
(B) 1/5%
(C) 1/7%
(D) 1/9%
(E) 1/11%
Rationale: X=100	y=110
110------10
100-------? => 9 1/11%
Answer:E
Answer: (E) 1/11%
Question: 150 ml of 30% sulphuric acid was added to approximate 400 ml of 12% sulphuric acid solution. Find the approximate concentration E of the acid in the mixture?
(A) 1/2
(B) 1/3
(C) 1/4
(D) 1/6
(E) 1/5
Rationale: Do not need any computation
30%-----------21%---------12%
if volume of both sol. were equal the concentration E would be 21%=1/5, but 12% is more than 3 times
only possibility is 1/6
D
Answer: (D) 1/6
Question: David walks to a viewpoint and returns to the starting point by his car and thus takes a total time of 4 hours 20 minutes. He would have gained 2 hours by driving both ways. How long would it have taken for him to walk both ways.
(A) 5 h 20 min
(B) 4 h 15 min
(C) 6 h
(D) 7 h
(E) 6 h 20 min
Rationale: 1.Walking to to a viewpoint+Driving back=4 hours 20 minutes
2.Driving to a viewpoint+Driving back=4 hours 20 minutes - 2 hours=2 hours 20 minutes, thereforeone way driving=2 hours 20 minutes/2 =1 hours 10 minutes.
3. From 1.one way driving=4 hours 20 minutes-1 hours 10 minutes=3 hours 10 minutes.
4.Walking to to a viewpoint+Walking back=3 hours 10 minutes+3 hours 10 minutes=6 hours 20 minutes.
Answer: E
Answer: (E) 6 h 20 min
Question: Two trains each 150 m in length are running on the same parallel lines in opposite directions with the speed of 80 kmph and 70 kmph respectively. In what time will they cross each other completely?
(A) 7.8 sec
(B) 7.2 sec
(C) 8.2 sec
(D) 6.2 sec
(E) 9.2 sec
Rationale: D = 150 m + 150 m = 300 m
RS = 80 + 70 = 150 * 5/18 = 125/3
T = 300 * 3/125 = 7.2 sec
ANSWER:B
Answer: (B) 7.2 sec
Question: A bag contains 4 white balls, 4 black balls, and 2 red balls. One by one, three balls are drawn out without replacement. What is the probability that the third ball is red?
(A) 1/2
(B) 1/5
(C) 3/8
(D) 5/11
(E) 2/7
Rationale: The probability for each ball to be drawn third is equal.
Then the probability a red ball is drawn third is 2/10 = 1/5.
The answer is B.
Answer: (B) 1/5
Question: If x/y =3/2, then (x-y)/x?
(A) -1/2
(B) -1/3
(C) 1/3
(D) 1/2
(E) 5/2
Rationale: we have this law of fraction:
a/b=c/d= (a-c)/(b-d)
x/y=3/2 ---> x/3=y/2= (x-y)/(3-2)=(x-y)/(1) ---> (x-y)/x= 1/3
Answer: C
Answer: (C) 1/3
Question: If a particular is never chosen, in how many ways can a cricketbe chosen out of 15 players?
(A) 245
(B) 278
(C) 364
(D) 378
(E) 389
Rationale: A particular players is never chosen, it means that 11 players are selected out of 14 players.
=> Required number of ways = 14C11
= 14!/11!x3! = 364
C
Answer: (C) 364
Question: Tim and Tom are workers in a department that has a total of 5 employees. Their boss decides that two workers from the department will be picked at random to participate in a company interview. What is the probability that both Jim and John are chosen?
(A) 3/10
(B) 1/10
(C) 7/10
(D) 4/11
(E) 2/11
Rationale: Probability = 2c2/5c2
= 1/10
Answer B
Answer: (B) 1/10
Question: The population of a town increases 25% and 40% respectively in two consecutive years. After the growth the present population of the town is 1750. Then what is the population of the town 2 years ago?
(A) A)750
(B) B)800
(C) C)850
(D) D)900
(E) E)950
Rationale: Explanation:
Formula: (After =100 denominator
Ago = 100 numerator)
1750 * 100/125 * 100/140 = 1000
Answer: Option B
Answer: (B) B)800
Question: Ramesh purchased a refrigerator for Rs. 12500 after getting a discount of 20% on the labelled price. He spent Rs. 125 on transport and Rs. 250 on installation. At what price should it be sold so that the profit earned would be 15% if no discount was offered?
(A) 17608
(B) 17606
(C) 17604
(D) 18400
(E) 117601
Rationale: Price at which the TV set is bought = Rs. 12,500
Discount offered = 20%
Marked Price = 12500 * 100/80 = Rs. 15625
The total amount spent on transport and installation = 125 + 250 = Rs. 375\Total price of TV set = 15625 + 375 = Rs. 16000
The price at which the TV should be sold to get a profit of 15% if no discount was offered = 16000 * 115/100 = Rs. 18400.Answer: D
Answer: (D) 18400
Question: A certain number when divided by 899 leaves the remainder 63. Find the remainder when the same number is divided by 29.
(A) 5
(B) 4
(C) 1
(D) 0
(E) Can not be determined
Rationale: Sol.(a) Number = 899Q + 63, where Q is quotient
= 31 × 29 Q + (58 + 5) = 29 [ 31Q + 2] + 5
∴ Remainder = 5 Answer A
Answer: (A) 5
Question: If 2 cards are selected (with replacement) at random from the deck of 52 cards then what is the probability that one of the selected cards will be a king or a queen, and the other card will be a jack? A deck of cards has a total of 52 cards, consisting of 4 suits: spades (black), hearts (red), diamonds (red), and clubs (black). In each suit, there are 13 cards including 1 king, 1 queen, and 1 jack.
(A) 3/16
(B) 3/32
(C) 3/64
(D) 4/169
(E) 8/169
Rationale: P(1 king or queen, and 1 jack) = 2(8/52*4/52) = 2(2/169) = 4/169
The answer is D.
Answer: (D) 4/169
Question: A fruit seller sells mangoes at the rate of Rs.16 per kg and thereby loses 12%. At what price per kg, he should have sold them to make a profit of 20%?
(A) Rs.21.81
(B) Rs.12
(C) Rs.12.25
(D) Rs.12.31
(E) None
Rationale: Solution
88 : 16 = 120 : x
x= (16Ã—120/88)
= Rs.21.81
Hence, S.p per Kg	= Rs.21.81
Answer A
Answer: (A) Rs.21.81
Question: If 90% of A = 30% of B and B = C% of A,then the value of C is ?
(A) 900
(B) 800
(C) 600
(D) 300
(E) None
Rationale: Answer
∵ 90A/100 = 30B/100 = (30/100) x AC/100
∴ C = 100 x (100/30) x (90/100) = 300
Correct Option: D
Answer: (D) 300
Question: The sum of three consecutive numbers is 63. The greatest among these three number is:
(A) 26
(B) 28
(C) 29
(D) 22
(E) 31
Rationale: Let the numbers be x, x + 1 and x + 2
Then,
x + (x + 1) + (x + 2) = 63
3x =60
x = 20
Greatest number, (x + 2) = 22.
ANSWER:D
Answer: (D) 22
Question: There is 60% increase in an amount in 6 years at S.I. What will be the C.I. of Rs. 12,000 after 3 years at the same rate?
(A) Rs.3928
(B) Rs.3920
(C) Rs.3972
(D) Rs.3979
(E) Rs.3962
Rationale: Let P = Rs. 100. Then, S.I. Rs. 60 and T
= 6 years.
R = (100 * 60)/(100 * 6) = 10% p.a.
Now, P = Rs. 12000, T = 3 years and R
= 10% p.a.
C.I. = [12000 * {(1 + 10/100)3 - 1}]
= 12000 * 331/1000
= Rs.3972
Answer:C
Answer: (C) Rs.3972
Question: Total dinning bill for 9 people was $211.00.If they add 15% tip and divided the bill evenly ,approximate.What was each persons find share
(A) $30.14
(B) 45.14
(C) 34.66
(D) 26.96
(E) 33.16
Rationale: 211*15=3165/100=31.65
211+31.65=242.65
242.65/9=26.96
ANSWER:D
Answer: (D) 26.96
Question: Find the fourth proportional to 2.8 , 3.4 and 5.2?
(A) 5.98
(B) 6.14
(C) 6.29
(D) 6.31
(E) 5.64
Rationale: Formula = fourth proportion =(b x c)/a
a=2.8 , b=3.4 and c=5.2
(3.4 x 5.2)/2.8=6.31
D
Answer: (D) 6.31
Question: Johnny bought six peanut butter cans at an average price (arithmetic mean) of 37.5¢. If Johnny returned two cans to the retailer, and the average price of the remaining cans was 31¢, then what is the average price, in cents, of the two returned peanut butter cans?
(A) 5.5
(B) 11
(C) 47.5
(D) 50.5
(E) 67.5
Rationale: Total price of six cans = 6*37.5 = 225
Total price of 4 cans = 4*31 = 124
Total rice of two cans = 225 - 124 = 101
Average price of two cans = 101/2 = 50.5 c
Another way to do it is this:
Assume that the four leftover cans were of 31c each. The avg was 37.5c initially because the two cans were 36.5c each and were providing another 6.5c of cost to other 4 cans.
So cost of the two cans = 2*37.5 + 4*6.5 = 101
Avg cost of the two cans = 101/2 = 50.5c
Answer (D)
Answer: (D) 50.5
Question: The age of a man is three times the sum of the ages of his two sons. Five years hence, his age will be double of the some of the ages of his sons. The father’s present age is :
(A) 29 years
(B) 36 years
(C) 42 years
(D) 45 years
(E) None
Rationale: Sol.
Let the sum of present ages of the two sons be x years.
Then, faher’s present age = 3x years.
∴ (3x + 5) = 2 (x + 10) ⇔ 3x + 5 = 2x + 20 ⇔ x = 15.
Hence, father’s present age = 45 years.
Answer D
Answer: (D) 45 years
Question: The temperature in Winnipeg, Manitoba was 4 degrees Fahrenheit. At 8 pm the temperature was was -10 degrees Fahrenheit. What is the difference between the temperatures?
(A) 6
(B) -14
(C) 14
(D) -6
(E) 0
Rationale: Addition of positive and negative integers
4+-10=
answer is D)-6
Answer: (D) -6
Question: A man's age is 125% of what it was 10 years ago, but 83 X 1/3% of what it will be after 10years. What is his present age?
(A) 20
(B) 60
(C) 50
(D) 70
(E) 80
Rationale: C
50
Let the age before 10 years =x Then,
125x/100=x+10
⇒125x=100x+1000
⇒x=1000/25=40
Present age =x+10=40+10=50
Answer: (C) 50
Question: A, B and C started a business A's investment is 2 times of B's investment is 5 times of C's investment. Find the profit of B in the total profit of Rs. 25600.
(A) Rs. 25600
(B) Rs. 8500
(C) Rs. 7200
(D) Rs. 8000
(E) None of these
Rationale: Explanation:
A = 2B and B = 5C
=> A : B = 2 and B : C = 5 : 1
=> A : B : C = 10 : 5 : 1
Ratio of capitals of A, B and C = 10 : 5 : 1
B's share = Rs.[(5/16) × 25600] = Rs. 8000
Answer: Option D
Answer: (D) Rs. 8000
Question: A caterer ordered 225 ice-cream bars and 125 sundaes. If the total price was $200.00 and the price of each ice-cream bar was $0.60, what was the price of each sundae?
(A) $0.52
(B) $0.80
(C) $1.00
(D) $1.20
(E) $1.60
Rationale: Let price of a sundae = S
Price of ice cream bar = .6 $
225 * .6 + 125*S = 200
=> 125*S = 65
=> S = 0.52
Answer A
Answer: (A) $0.52
Question: The average of the two-digit numbers, which remain the same when the digits interchange their positions, is?
(A) 76
(B) 88
(C) 55
(D) 86
(E) 26
Rationale: Average = (11 + 22 + 33 + 44 + 55 + 66 + 77 + 88 + 99)/9
= [(11 + 99) + (22 + 88) + (33 + 77) + (44 + 66) + 55]/9
= [(4 * 110) + 55]/9 = 495/9 = 55.
Answer: C
Answer: (C) 55
Question: Two trains are moving in the same direction at 72 kmph and 36 kmph. The faster train crosses a man in the slower train in 27 seconds. Find the length of the faster train?
(A) 270 m
(B) 189 m
(C) 278 m
(D) 279 m
(E) 917 m
Rationale: Relative speed = (72 - 36) * 5/18 = 2 * 5
= 10 mps.
Distance covered in 27 sec
= 27 * 10
= 270 m.
The length of the faster train
= 270 m.
Answer:A
Answer: (A) 270 m
Question: If the positive integer x is divisible by 3, 8, and 12, then which of the following must x be divisible by?
I. 24
II. 26
III. 48
(A) IIonly
(B) I only
(C) I and II only
(D) II and III only
(E) I, II, and III
Rationale: LCM of 3, 8, 12 = 24
Answer = 24
Answer : B
Answer: (B) I only
Question: Three unbiased coins are tossed. What is the probability of getting at most two heads?
(A) 9/7
(B) 7/8
(C) 1/2
(D) 5/4
(E) 3/8
Rationale: Explanation:
Here S = {TTT, TTH, THT, HTT, THH, HTH, HHT, HHH}
Let E = event of getting at most two heads.
Then E = {TTT, TTH, THT, HTT, THH, HTH, HHT}.
P(E)=n(E)/n(S)=7/8
Answer:B
Answer: (B) 7/8
Question: The division of a whole number N by 10 gives a quotient of 15 and a remainder of 2. Find N.
(A) 152
(B) 197
(C) 597
(D) 997
(E) 297
Rationale: According to the division process of whole numbers, N can be written, using multiplication, as follows
N = quotient *divisor + remainder = 15* 10 + 2 = 152 correc answer A
Answer: (A) 152
Question: A salesman sold twice as much pears in the afternoon than in the morning. If he sold $510 kilograms of pears that day, how many kilograms did he sell in the afternoon?
(A) 120
(B) 180
(C) 340
(D) 280
(E) 320
Rationale: 3x=510
x=170
Therefore, the salesman sold 170kg in the morning and 2⋅170=340 kg in the afternoon. So answer is C.
Answer: (C) 340
Question: A box contains nine bulbs out of which 4 are defective. If four bulbs are chosen at random, find the probability that atleast one bulb is good.
(A) 125/128
(B) 115/122
(C) 125/126
(D) 125/122
(E) 125/112
Rationale: Required probability = 1 - 1/126
= 125/126
Answer:C
Answer: (C) 125/126
Question: A goods train runs at the speed of 72 km/hr and crosses a 250 m long platform in 26 sec. What is the length of the goods train?
(A) 772
(B) 369
(C) 277
(D) 270
(E) 782
Rationale: Speed = 72 * 5/18 = 20 m/sec.
Time = 26 sec.
Let the length of the train be x meters.
Then, (x + 250)/26 = 20
x = 270 m.
Answer: D
Answer: (D) 270
Question: Every Monday, Marina eats one croissant and every Tuesday she eats two croissants. On each subsequent day of the week, she eats a number of croissants equal to the sum of the croissants eaten on the two previous days, with the exception that if she eats more than four croissants on any particular day, the next day she will eat only one croissant. At the end of the week (which runs from Monday through Sunday), the cycle resets, and Marina goes back to eating one croissant on Monday, two on Tuesday, and so forth. If a particular month begins on a Saturday, how many croissants will Marina eat on the 30th of that month?
(A) 1
(B) 2
(C) 3
(D) 5
(E) 6
Rationale: She eat as follow
Mon - 1
Tue - 2
Wed - 3
Thr - 5
Fri - 1(since she had more than 4 previous day)
sat - 6
sunday - 1 (since she had more than 4 previous day)
so 30th day of month she will have 1.
Answer is A
Answer: (A) 1
Question: The price of an article has been reduced by 25%. In order to restore the original price the new price must be increased by?
(A) 33 1/3%
(B) 33 1/9%
(C) 33 1/3%
(D) 32 1/3%
(E) 33 1/2%
Rationale: 100
75
-------
75 ------- 25
100 ------ ? => 33 1/3%
Answer:A
Answer: (A) 33 1/3%
Question: In 1995, the Johnsons spent $800 on the family’s water bills. Anticipating that water rates would increase in 1996 by 50%, the Johnsons cut back their water usage. By how much must the Johnsons have reduced their 1996 water usage to pay exactly the same amount Q in 1996 as they paid in 1995?
(A) 33 1⁄3%
(B) 40%
(C) 50%
(D) 66 2⁄3%
(E) 100%
Rationale: water rate increases by 50 % in 1996 means 150% of rate in 1995. to pay exactly the same amount in 1996 as they paid in 1995, water use should decrease in the same ratio
Q=150-> 100 means 1/3 rd= 33(1/3) %=A
Answer: (A) 33 1⁄3%
Question: If 2x + y = 7 and x + 2y = 5, then 7xy/3 =?
(A) A) 1
(B) B) 2
(C) C) 7
(D) D) 18/5
(E) E) 4
Rationale: 2*(x+2y = 5) equals 2x+4y=10
2x+4y=10
- 2x + y= 7
= 3y=3
Therefore Y = 1
Plug and solve...
2x + 1 = 7
2x=6
x=3
(7*3*1)/3
= 21/3
=7
C
Answer: (C) C) 7
Question: Sonika deposited Rs.8000 which amounted to Rs.9200 after 3 years at simple interest. Had the interest been 2% more. She would get how much?
(A) 9680
(B) 4280
(C) 2789
(D) 7892
(E) 2792
Rationale: (8000*3*2)/100 = 480
9200
--------
9680
Answer:A
Answer: (A) 9680
Question: The ages of two person differ by 20 years. If 10 years ago, the elder one be 5 times as old as the younger one, their present ages(in years) are respectively
(A) 30, 10
(B) 25, 5
(C) 29, 9
(D) 35, 15
(E) 20,10
Rationale: Let their ages be x and (x + 20) years.
Then, 5(x - 10) = (x + 20 - 10)
=> 4x = 60
=>x =15
Their present ages are 35 years and 15 year.
ANSWER:D
Answer: (D) 35, 15
Question: Sum of ages of two friends is 28 while difference is 4 then their ages are
(A) 20 years, 8 years
(B) 10 years, 18 years
(C) 24 years, 4 years
(D) 18 years, 16 years
(E) None
Rationale: 24,4
ANSWER:C
Answer: (C) 24 years, 4 years
Question: 2^3,5^2,6^1 Find largest Value?
(A) 2
(B) 3
(C) 1
(D) 10
(E) 25
Rationale: Explanation:
2^3=2*2*2=8
5^2=5*5=25
6^1=6*1=6
Hence 5^2 is the largest one
Answer:E
Answer: (E) 25
Question: WHEN A PERSON SELLS TWO ITEMS $900 each, ONE AT A GAIN OF 20% AND OTHER AT A LOSS OF 20%.THEN THE SELLER INCURES A LOSS OR GAIN OF:
(A) 4% loss
(B) no loss no gain
(C) 1% loss
(D) 2% gain
(E) 5% gain
Rationale: When two items are sold at the same price, one at a profit of a% and other at a loss of a% (which means the cost price of one item was lower than the selling price and the cost price of the other item was higher than the selling price), there will always be a loss of (a^2)/100 %. e.g. Here a = 20, so loss % = (20)^2/100 % = 4%.
Answer : A
Answer: (A) 4% loss
Question: A bag contains 3 blue and 5 white marbles. One by one, marbles are drawn out randomly until only two are left in the bag. What is the probability that out of the two, one is white and one is blue?
(A) 15/56
(B) 41/56
(C) 13/28
(D) 15/28
(E) 5/14
Rationale: The required probability = probability of choosing 6 balls out of the total 8 in such a way that we remove 4 out of 5 white and 2 out of 3 blue balls.
Ways to select 6 out of total 8 = 8C6
Ways to select 4 out of 5 white balls = 5C4
Ways to select 2 out of 3 blue balls = 3C2
Thus the required probability = (5C4*3C2)/8C6 = 15/28.
D is thus the correct answer.
Answer: (D) 15/28
Question: There are 3 teams each with 7 basket players. How many combinations are there if we were to pick 2 players from the 3 teams such that no team was picked twice?
(A) 50
(B) 23
(C) 147
(D) 28
(E) 45
Rationale: There are altogether three arrangements, which are we can select two members each from team A and B, each from team A and C, and each from team B and C. For each arrangement, there are altogether 49 possibilities (7*7) since each team has 7 players. So there are a total of 147 possibilities (49*3). I hope this method is easier for you to understand.
Answer: (C) 147
Question: If the cost price of 50 articles is equal to the selling price of 40 articles, then the gain or loss percent is?
(A) 16
(B) 127
(C) 12
(D) 18
(E) 25
Rationale: Given that, cost price of 50 article is equal to selling price of 40 articles.
Let cost price of one article = Rs. 1
Selling price of 40 articles = Rs. 50
But Cost price of 40 articles = Rs. 40
Therefore, the trader made profit.\Percentage of profit = 10/40 * 100 = 25%
Answer: E
Answer: (E) 25
Question: A farmer is planting a row consisting of 4 unique apple trees and 3 unique orange trees. How many ways are there for the farmer to plant the trees such that no apple tree is adjacent to another apple tree and no orange tree is adjacent to another orange tree?
(A) 512
(B) 576
(C) 1,024
(D) 288
(E) 10,080
Rationale: 2 possible arrangements are possible
AOAOAOAO
OAOAOAOA
2 unique type of trees are present consisting of 4 trees each
4 apple trees can be arranged in 4! ways
3 orange trees can be arranged in 4! ways
as 2 arrangements are possible
total arrangements = 2 *4! * 3! = 288
correct answer option D
Answer: (D) 288