mathewhe/aqua_rat huggingface dataset:
Question: Tea worth Rs. 126 per kg and Rs. 135 per kg are mixed with a third variety in the ratio 1 : 1 : 2. If the mixture is worth Rs. 153 per kg, the price of the third variety per kg will be:
(A) Rs. 169.50
(B) Rs. 170
(C) Rs. 175.50
(D) Rs. 175.50
(E) None
Rationale: EXPLANATION
Since first and second varieties are mixed in equal proportions.
So, their average price = Rs. (126 + 135 / 2)= Rs. 130.50
So, the mixture is formed by mixing two varieties, one at Rs. 130.50 per kg and the other at say, Rs. x per kg in the ratio 2 : 2, i.e., 1 : 1. We have to find x.
By the rule of alligation, we have:
x-153/ 22.50 =1
x – 153 = 22.50
x = 175.50
Answer C
Answer: (C) Rs. 175.50
Question: John was thrice as old as Tom 6 yrs back. He will be 5/3 times as old as Tom 6 years hence. How old is Tom today?
(A) 10
(B) 11
(C) 12
(D) 19
(E) 21
Rationale: Sol. RMBflSk -6 = 3 (Ravi - 6) ...(j)
and Rupesh + 6 = | (Ravi + 6) ...(ii)
Solving both the equations we get,
Ravi = 12 years.
C
Answer: (C) 12
Question: The General Hospital is comprised of, 3/5 Pediatricians, 1/4 Surgeons, and the rest are GP doctors. If 1/4 of the Surgeons are Heart Surgeons, and the hospital doubles the number of GP doctors, what proportion of the hospital are now Heart Surgeons?
(A) 2/5
(B) 1/4
(C) 1/2
(D) 1/24
(E) 1/25
Rationale: Ped = 3/5 = 12/20
Sur = 1/4 = 4/20
GP = 1 - (12/20 + 4/20) = 1 - 16/20 = 4/20
HSur = (1/4)(4/20) = 1/20
If GP doubled => (2)(4) = 8; then, total = 12 + 4 + 8 = 24,
and 1 is HSur => proportion = 1/24.
Answer: D
Answer: (D) 1/24
Question: A lent Rs. 5000 to B for 2 years and Rs. 3000 to C for 4 years on simple interest at the same rate of interest and received Rs. 1980 in all from both of them as interest. The rate of interest per annum is?
(A) 16%
(B) 12%
(C) 9%
(D) 10%
(E) 45%
Rationale: Let the rate be R% p.a. Then,
(5000 * R * 2)/100 + (3000 * R * 4)/100 = 1980
100 R + 120 R = 1980
R = 9%
Answer:C
Answer: (C) 9%
Question: On a test average (arithmetic mean) test score for 4 students is 85. What must be 5th student's score that average score for 5 students to be 86?
(A) 70
(B) 80
(C) 90
(D) 100
(E) 110
Rationale: (4*85+x)/5=86
x=(5*86)-(4*85)
x= 430 - 340
total score required 430 - 340=90
Correct answer is C
Answer: (C) 90
Question: How many ounces of a 60% salt solution must be added to 50 ounces of a 20 percent salt solution so that the resulting mixture is 50% salt?
(A) 16.67
(B) 30
(C) 50
(D) 60.33
(E) 150
Rationale: let x=ounces of 60% salt solution to be added
.2*50+.6x=.5(50+x)
x=150
Answer E
Answer: (E) 150
Question: In how many ways can 4 boys and three girls sit in a row such that all boys sit together?
(A) A)670
(B) B)484
(C) C)720
(D) D)576
(E) E)398
Rationale: Treat all boys as one unit. Now there are four students and they can be arranged in 4! ways. Again four boys can be arranged among themselves in 4! ways.
Required number of arrangements
= 4! * 4! = 24 * 24
= 576.
Answer:D
Answer: (D) D)576
Question: Find a a prime number the options below.
(A) 78
(B) 80
(C) 81
(D) 82
(E) 83
Rationale: Clearly, 83 is a prime number.
E
Answer: (E) 83
Question: A man misses a bus by 40 minutes if he travels at 30 kmph. If he travels at 40 kmph, then also he misses the bus by 10 minutes. What is the minimum speed required to catch the bus on time?
(A) 58.75 kmph
(B) 68.75 kmph
(C) 78.75 kmph
(D) 79.75 kmph
(E) 48.75 kmph
Rationale: Let the distance to be travelled to catch the bus be x km
x/30 - x/35 = 30/60 => (7x - 6x)/210 = 1/2 => x = 105 km
By traavelling 30 kmph time taken = 60/30 = 2 hours
By taking 2 hours, he is late by 40 min. So, he has to cover 105 km in at most speed = 60/(4/3) = 78.75 kmph.
ANSWER:C
Answer: (C) 78.75 kmph
Question: Sum of two numbers is 40 and their difference is 4. The ratio of the numbers is
(A) 10:3
(B) 5:9
(C) 11:9
(D) 13:9
(E) None of these
Rationale: Explanation:
=>(x+y)/(x−y)=40/4
=>(x+y)=10(x−y)
=>9x=11y=>x/y=11/9
Option C
Answer: (C) 11:9
Question: The average height of 20 students in a class was calculated as 175 cm. It has later found that the height of one of the students in the class was incorrectly written as 151 cm whereas the actual height was 136 cm. What was the actual average height of the students in the class?
(A) 174.75 cm
(B) 174.25 cm
(C) 173.75 cm
(D) 173.25 cm
(E) 172.75 cm
Rationale: The total height was 15 cm too much.
The average height should be reduced by 15 cm/20 = 0.75 cm
The answer is B.
Answer: (B) 174.25 cm
Question: Local kennel has cats and dogs in the ratio of 2:3. If there are 6 fewer cats than dogs, how many dogs are in the kennel?
(A) 24
(B) 18
(C) 30
(D) 15
(E) 12
Rationale: Lets work with the data given to us. We know that there ratio of cats to dogs is 2:3 or
cats 2
dogs 3
we can write number of cats as 2x and number of dogs as 3x and we know that 3x-2x= 6 (therefore x = 6)
Then # of dogs = 3x6= 18
Answer is B
Answer: (B) 18
Question: An even positive integer 'x' has 'y' positive integral factors including '1' and the number itself. How many positive integral factors E does the number 4x have?
(A) 4y
(B) 3y
(C) 16y
(D) 5y
(E) Cannot be determined
Rationale: I tried for x=2,4 and 6. The integral factors E for x and 4x did not have any specific relation.
My answer is E.
Answer: (E) Cannot be determined
Question: Find the odd man out
2880, 490, 96, 24, 8, 4, 4
(A) 96
(B) 8
(C) 24
(D) 490
(E) 4
Rationale: from the right side
4*1=4,
4*2=8
8*3=24
24*4=96
96*5=490 but here given 480 so it's not.
480*6=2880
ANSWER:D
Answer: (D) 490
Question: A man's speed with the current is 18 km/hr and the speed of the current is 2.5 km/hr. The man's speed against the current is?
(A) 10
(B) 18
(C) 50
(D) 30
(E) 40
Rationale: Man's speed with the current = 18 km/hr
=> speed of the man + speed of the current = 18 km/hr
speed of the current is 2.5 km/hr
Hence, speed of the man = 18 - 2.5 = 20.5 km/hr
man's speed against the current = speed of the man - speed of the current
= 20.5 - 2.5 = 18 km/hr
Answer is B.
Answer: (B) 18
Question: In a recent election, Ms. Robbins received 6,000 votes cast by independent voters, that is, voters not registered with a specific political party. She also received 10 percent of the votes cast by those voters registered with a political party. If N is the total number of votes cast in the election and 40 percent of the votes cast were cast by independent voters, which of the following represents the number of votes that Ms. Robbins received?
(A) 0.06N + 6,000
(B) 0.1N + 7,200
(C) 0.4N + 7,200
(D) 0.1N + 8,000
(E) 0.06N + 8,000
Rationale: total vote = N
vote cast by independent voters = 0.4 N
vote cast by registered voters = 0.6 N
vote received by Ms. Robbins = 6000 + 10% of vote be registered voters = 6000 + 0.06 N
Answer choice A
Answer: (A) 0.06N + 6,000
Question: How many Kilograms of Pure water is to be added to 100 Kilograms of a 30% saline solution to make it a 10% saline solution.
(A) 100
(B) 200
(C) 300
(D) 400
(E) 500
Rationale: Let x be the weights, in Kilograms, of pure water to be added. Let y be the weight, in Kilograms, of the 10% solution. Hence
x + 100 = y
x = 200 Kilograms.
Answer B
Answer: (B) 200
Question: If we know that a positive integer is a multiple of 4, how many (distinct) possibilities are there for the last digit of the integer?
(A) 3
(B) 4
(C) 5
(D) 6
(E) 7
Rationale: the last digit of the integer may be any of (0,2,4,6,8)
so, 1/5
ANSWER:C
Answer: (C) 5
Question: Two mechanics were working on your car. One can complete the given job in 4 hours, but the new guy takes eight hours. They worked together for the first two hours, but then the first guy left to help another mechanic on a different job. How long will it take the new guy to finish your car?
(A) 2
(B) 4/3
(C) 15/4
(D) 10/3
(E) 17/5
Rationale: Rate(1)=1/4
Rate(2)=1/8
Combined = 3/8
Work done in 2 days=3/4
Work left = 1/4
Rate * Time = Work left
1/8 * Time = 1/4
Time=2
A
Answer: (A) 2
Question: The water level in a rectangular swimming pool measuring 20 feet by 25 feet is to be lowered by 6 inches. How many gallons of water must be removed? (1 cu ft = 7.5 gallons)
(A) 100
(B) 250
(C) 1875
(D) 1200
(E) 5625
Rationale: 6 inches = 1/2 feet (there are 12 inches in a foot.), so 20*25*1/2=250 feet^3 of water must be removed, which equals to 250*7.5=1875 gallons.
Answer: C.
Answer: (C) 1875
Question: (?)-19657-33994=9999
(A) 63650
(B) 53760
(C) 59640
(D) 61560
(E) None of them
Rationale: Let x-53651=9999
Then x=53651+9999
=63650
Answer is A
Answer: (A) 63650
Question: By selling 12 pencils for a rupee a man loses 20%. How many for a rupee should he sell in order to gain 20%?
(A) 8
(B) 9
(C) 6
(D) 4
(E) 1
Rationale: 80% --- 12
120% --- ?
80/120 * 12 = 8
Answer: A
Answer: (A) 8
Question: In a kilometer race, A beats B by 52 meters or 18 seconds. What time does A take to complete the race?
(A) 277 sec
(B) 190 sec
(C) 328 sec
(D) 367 sec
(E) 376 sec
Rationale: Time taken by B run 1000 meters = (1000 * 18)/52 = 346 sec.
Time taken by A = 346 - 18 = 328 sec.Answer: C
Answer: (C) 328 sec
Question: x is what percent of y percent of z, in terms of x, y and z?
(A) 100xy/z
(B) 100yz/x
(C) 100yz/x
(D) 10000x/yz
(E) 10000yz/x
Rationale: Soln:-
y% of z is just (y/100)*z, or yz/100. So we want to answer the question: x is what percent of yz/100? Say x is equal to m% of yz/100; then we have:
x = (m/100)*(yz/100)
10,000x/yz = m
and since m is what we were asked to find, the answer is 10,000x/yz
ANSWER:B
Answer: (B) 100yz/x
Question: How much water must be added to 68 litres of milk at 1 1⁄2 litres for 20 so as to have a mixture worth 10 2⁄3 a litre?
(A) 10 litres
(B) 17 litres
(C) 15 litres
(D) 18 litres
(E) None of these
Rationale: C.P. of 1 litre of milk = (20 × 2⁄3) = 40⁄3
∴ Ratio of water and milk = 8⁄3 : 32⁄3 = 8 : 32 = 1 : 4
∴ Quantity of water to be added to 68 litres of milk
= (1⁄4 × 68) litres = 17 litres.
Answer B
Answer: (B) 17 litres
Question: Sravan travelled for 15 hours. He covered the first half of the distance at 45 kmph and remaining half of the distance at 30 kmph. Find the distance travelled by Sravan?
(A) 520
(B) 540
(C) 550
(D) 560
(E) 440
Rationale: Let the distance travelled be x km.
Total time = (x/2)/45 + (x/2)/30 = 15 => x/90+ x/60 = 15 => (2x + 3x)/180 = 15
=> x = 540 km
Answer:B
Answer: (B) 540
Question: A reindeer chased by a Cheetah passed a certain tree at a constant speed of 50 miles per hour while being chased by a Cheetah. Then, 2 minutes later, the Cheetah passed the same tree at a constant speed of 60 miles per hour. If both animals maintained their speeds, how long after the Cheetah passed the tree did the Cheetah catch up with the reindeer?
(A) 30 min
(B) 45 min
(C) 1 hr
(D) 3 min
(E) 1 min
Rationale: When the Cheetah is at the tree, the reindeer is 50/30 miles ahead on the highway. (the distance covered in 2 min)
every hour, Cheetah runs 10miles more than the deer. how many hours will it takes it to cover 50/30 miles more? the answer is (50/30)/10 = 1/60=1 min
Answer E
Answer: (D) 3 min
Question: The ratio of incomes of two person P1 and P2 is 5 : 4 and the ratio of their expenditures is 3 : 2. If at the end of the year, each saves Rs.1600, then what is the income of P1?
(A) Rs.800
(B) Rs.2400
(C) Rs.4000
(D) Rs.3200
(E) Rs.4200
Rationale: Let the income of P1 and P2 be Rs. 5x and Rs.4x respectively and let their
expenditures be Rs.3y and 2y respectively.
Then, 5x – 3y = 1600 …(i) and 4x – 2y = 1600 ……..(ii)
On multiplying (i) by 2, (ii) by 3 and subtracting, we get : 2x = 1600 -> x = 800
P1’s income = Rs 5*800 = Rs.4000
ANSWER:C
Answer: (C) Rs.4000
Question: A person purchased a TV set for Rs. 2000 and a DVD player for Rs. 2000 . He sold both the items together for Rs. 5000. What percentage of profit did he make?
(A) 80%
(B) 80%
(C) 40%
(D) 48%
(E) 25%
Rationale: The total CP = Rs. 2000 + Rs. 2000
= Rs. 4000 and SP = Rs. 5000
Profit(%) = (5000 - 4000)/4000 * 100
= 25%
Answer: E
Answer: (E) 25%
Question: Kim has 6 pairs of shoes; each pair is a different color. If Kim randomly selects 2 shoes without replacement from the 12 shoes, what is the probability that she will select 2 shoes of the same color?
(A) 2/5
(B) 1/5
(C) 1/9
(D) 1/11
(E) 1/25
Rationale: Total pairs = 12C2 = 66; Same Color Pairs= 6C1*1C1=6; Prob = 1/11
Ans D
Answer: (D) 1/11
Question: 5+5
(A) 9
(B) 12
(C) 20
(D) 10
(E) 0
Rationale: D
Answer: (D) 10
Question: The price for a loaf of bread in April was $1.20, in May the price was $1.27, and in June the price was $1.08. If 2/3 as much bread was sold in April as in May, and twice as much was sold in June as in April, what was the average price for a loaf of bread sold during the three-month period?
(A) $1.18
(B) $1.17
(C) $1.16
(D) $1.15
(E) $1.14
Rationale: Let x be the number of loaves sold in May.
Then 2x/3 loaves were sold in April and 4x/3 loaves were sold in June.
The average price was (2x/3)(120) + 127x + (4x/3)(108) / (2x/3 + x + 4x/3) =
(80 + 127 + 144) / (3) = 351/3 = $1.17
The answer is B.
Answer: (B) $1.17
Question: Two employees M and N are paid a total of Rs. 550 per week by their employer. If M is paid 120 percent of the sum paid to N, how much is N paid per week?
(A) Rs.230
(B) Rs.240
(C) Rs.250
(D) Rs.300
(E) Rs.320
Rationale: Let the amount paid to M per week = x
and the amount paid to N per week = y
Then x + y = 550
But x = 120% of y = 120y/100 = 12y/10
∴12y/10 + y = 550
⇒ y[12/10 + 1] = 550
⇒ 22y/10 = 550
⇒ 22y = 5500
⇒ y = 5500/22 = 500/2 = Rs.250
C)
Answer: (C) Rs.250
Question: What number times (1⁄7)^2 will give the value of 7^3?
(A) 7
(B) 49
(C) 343
(D) 2401
(E) 16,807
Rationale: x*(1/7)^2 = 7^3
x = 7^2*7^3 = 7^5 = 16,807
The answer is E.
Answer: (E) 16,807
Question: If a boy sells a book for Rs. 450 he gets a loss of 10 %, then find cost price. To gain 10 %, what should be the selling price?
(A) 400, 500
(B) 550, 600
(C) 500, 550
(D) 475, 525
(E) 520, 450
Rationale: 1) Find cost price
Let C.P. of book = x and S.P. = Rs. 450
S.P. of book = C.P. – (10% of C.P.)
S.P. = x – (0.10x)
450 = 0.9 x
x i.e cost price = Rs. 500
2) Find Selling Price to gain 10 %.
Now, we are asked to find selling price to gain 10% profit.
Hint:
Selling Price =	(100 + Gain%)	/100*C.P.
Selling Price =	(100 + 10)/100*500
Selling Price =	(110/100)*500
Therefore, selling Price = Rs. 550
ANSWER IS C
Answer: (C) 500, 550
Question: A certain bridge is 4,024 feet long. Approximately how many minutes does it take to cross this bridge at a constant speed of 11 miles per hour? (1 mile = 5,280 feet)
(A)  1
(B)  2
(C)  4
(D)  6
(E)  7
Rationale: Distance: 4024 feet. This is (4024/5280) miles = 0.76 miles
Speed: 11 miles per hour
Time: (Distance / Speed) (0.76/11) {This will come in Hours}. Multiply by 60 to get answer in minutes. It is 4.15 minutes.
Answer to be 4 minutes.
ANS C
Answer: (C)  4
Question: If (-7)^(8x) = 7^(12 - 5x) and x is an integer, what is the value of x ?
(A) 5
(B) -4
(C) 1
(D) 2
(E) 3
Rationale: Since x is an integer, (-7)^(8x) is always positive.
So, 7^8x = 7^(13 - 5x)
8x = 12 - 5x
12x = 12
x = 1
Answer: C
Answer: (C) 1
Question: How many shots of 1cm radius can be prepared from a sphere of 5cm radius?
(A) 33
(B) 88
(C) 27
(D) 125
(E) 199
Rationale: 4/3 Ï€ * 5 * 5 * 5 = 4/3 Ï€ * 1 * 1 * 1 * x
x = 125
Answer: D
Answer: (D) 125
Question: if N is a prime number bigger than 5. Which of the following expressions must be even?
(A) 72
(B) (b) N^2+2.
(C) (c) N(N+2).
(D) (d) (N+1)(N+2)
(E) (e) (N-2)^2
Rationale: N =7
a=81 odd
b =51 odd
c = 63 odd
d = 72 even
e =25 odd
A
Answer: (A) 72
Question: A train passes a station platform in 27 seconds and a man standing on the platform in 16 seconds. If the speed of the train is 54 km/hr, what is the length of the platform?
(A) 299
(B) 165
(C) 170
(D) 185
(E) 112
Rationale: Speed = [54 * 5/18] m/sec = 15 m/sec.
Length of the train = (15 * 16) m = 240 m.
Let the length of the platform be x meters.
Then, x + 240 / 27 = 15
x + 240 = 405
x = 165 m.
Answer:B
Answer: (B) 165
Question: 39 persons can repair a road in 12 days, working 5 hours a day. In how many days will 30 persons, working 6 hours a day, complete the work?
(A) 10
(B) 15
(C) 12
(D) 14
(E) 13
Rationale: Let the required number of days be x.
Less persons, More days (Indirect Proportion)
More working hours per day, Less days (Indirect Proportion)
Persons	30:39 :: 12 : x
Working hours/day	6:5
:. 30 x 6 * x = 39 * 5 * 12
x =	(39 * 5 * 12)/(30 * 6)
x = 13.
Answer is E
Answer: (E) 13
Question: How many multiples of 4 are there between 8 and 160 ?
(A) 28
(B) 37
(C) 32
(D) 35
(E) 39
Rationale: It should be mentioned whether 8 and 160 are inclusive.
If 8 and 160 are inclusive, then the answer is (160-8)/4+1=39.
If 8 and 160 are NOT inclusive, then the answer is (156-12)/4+1=37.
Since OA is B, then we have NOT inclusive case.
Answer: (B) 37
Question: A 270 metres long train running at the speed of 120 kmph crosses another train running in opposite direction at the speed of 80 kmph in 9 seconds. What is the length of the other train?
(A) 190
(B) 200
(C) 225
(D) 230
(E) none
Rationale: Sol.
Relative speed = (120 + 80) km/hr [200 * 5/18] m/sec = [500/9] m/sec.
Let the length of the other tain be x metres.
Then, x + 270 / 9 = 500/9 ⇔ x + 270 = 500 ⇔ x = 230.
Answer D
Answer: (D) 230
Question: If 4 men can colour 48 m long cloth in 2 days, then 8 men can colour 36 m long cloth in
(A) 0.75 day
(B) 2 days
(C) 1.2 days
(D) 4 days
(E) 5 days
Rationale: The length of cloth painted by one man in one day = 48 / 4 × 2 = 6 m
No. of days required to paint 36 m cloth by 6 men = 36/ 6 × 8 = 0.75 day.
A
Answer: (A) 0.75 day
Question: 377 ÷ 13 ÷ 29 × 1/4 ÷ 2 = ?
(A) 1/6
(B) 1/8
(C) 1/10
(D) 1/12
(E) 1/15
Rationale: Explanation:
377 ÷ 13 ÷ 29 × 1/4 ÷ 2 = ?
=> ? = (337/(13 × 29 × 4 × 2)) = 1/8
Answer: Option B
Answer: (B) 1/8
Question: Two numbers are less than third number by 20% and 37% respectively. How much percent is the second number less than by the first
(A) 5%
(B) 10%
(C) 9%
(D) 11%
(E) 12%
Rationale: Let the third number is x.
then first number = (100-20)% of x
= 80% of x = 80x/100
Second number is (63x/100)
Difference = 80x/100 - 63x/100 = 17x/100
So required percentage is, difference is what percent of first number
(17x/100 * 100/80x * 100 )% = 5% ANSWER :A
Answer: (A) 5%
Question: What is the smallest positive integer x such that 180-x is the cube of a positive integer
(A) 50
(B) 52
(C) 60
(D) 55
(E) 12
Rationale: Given 180-x is a perfect cube
so we will take 125= 5*5*5
180-x = 125
x =180-125 = 55
correct option is D
Answer: (D) 55
Question: A dealer offers a cash discount of 15% and still makes a profit of 36% when he further allows 25 articles to be sold at the cost price of 20 articles to a particular sticky bargainer. How much percent above the cost price were his articles listed?
(A) 60%
(B) 80%
(C) 100%
(D) 120%
(E) 150%
Rationale: Given
Cash Discount - 15%
Profit - 36%
Items Sold - 25
Price Sold at = List Price of 20
Assume List price = $10
Total Invoice = $200
-15% Cash Discount = $170
Let cost price of 25 items be x
So total cost = 25*x
Given the shopkeeper had a profit of 36%
25 * x * 136/100 = 170
or x = $5
Which means his products were listed at $10 which is a 100% markup over $5
Answer C
Answer: (C) 100%
Question: A bag contains 12 white and 18 black balls. 2balls are drawn in succession. What is the probability that first is white and second is black?
(A) 31/111
(B) 36/145
(C) 21/115
(D) 11/153
(E) None
Rationale: The probability that first ball is white:
=12C130C1=12C130C1
=1230=1230
=25=25
Since, the ball is not replaced; hence the number of balls left in bag is 29.
Hence, the probability the second ball is black:
=18C129C1=18C129C1
=1829=1829
Required probability,
=(25)×(1829)=(25)×(1829)
=36/145
B
Answer: (B) 36/145
Question: What will come in place of the x in the following Number series? 5,28,57,88,125, x
(A) 120
(B) 143
(C) 166
(D) 170
(E) 180
Rationale: 28=23+5
57=29+28
88=31+57
125=37+88
166=41+125
=166
C
Answer: (C) 166
Question: Praveen starts business with Rs.3640 and after 5 months, Hari joins with Praveen as his partner. After a year, the profit is divided in the ratio 2 : 3. What is Hari’s contribution in the capital?
(A) s.7500
(B) s.8000
(C) s.8500
(D) s.9000
(E) s.9360
Rationale: Let Hari’s capital be Rs. x. Then, 3640 * 12/7x = 2/3
=> 14x = 131040
=> x = 9360.
ANSWER:E
Answer: (E) s.9360
Question: A man goes down stream with a boat to some destination and returns upstream to his original place in 5 hours. If the speed of the boat in still water and the strean are 10km/hr and 14km/hr respectively, the distance of the destination from the string place is
(A) 11 km
(B) 71 km
(C) 21 km
(D) 41 km
(E) 91 km
Rationale: Explanation:
Let the distance covered be D km.
\inline \frac{D}{10+4}+\frac{D}{10-4}=5
\Rightarrow \frac{D}{14}+\frac{D}{6}=5
\inline \Rightarrow 10D= 42\times 5=210
\inline \Rightarrow D= 21 km
Answer: C
Answer: (C) 21 km
Question: If the difference between the length and breadth of a rectangle is 23 m and its perimeter is 226 m, what is its area?
(A) 2510
(B) 2535
(C) 3060
(D) 2515
(E) 2520
Rationale: length = breadth +23. Therefore,
4× breadth +2×23=226 m
⇒ breadth =45 m
length =45+23=68 m
Area =68×45=3060 m2
Answer is C.
Answer: (C) 3060
Question: The true discount on Rs. 2562 due 4 months hence is Rs. 122. The rate percent is:
(A) 12%
(B) 40/3%
(C) 15%
(D) 14%
(E) 24%
Rationale: si of 4 month ie of 1/3 years=122
so p=2562-122=2440
now R=(si*100)/p*time
so R=122*100*3/2440*1=15
ANSWER:C
Answer: (C) 15%
Question: How many 3-letter words with or without meaning, can be formed out of the letters of the word, 'LOGARITHMS', if repetition of letters is not allowed?
(A) 720
(B) 420
(C) None of these
(D) 5040
(E) Cannot be determined
Rationale: Explanation :
The word 'LOGARITHMS' has 10 different letters.
Hence, the number of 3-letter words(with or without meaning) formed by using these letters
= 10P3
= 10 x 9 x 8
= 720. Answer : Option A
Answer: (A) 720
Question: X and Y invested in a business. They earned some profit which they divided in the ratio of 2 : 3. If X invested Rs.40,000. the amount invested by Y is
(A) Rs.45,000
(B) Rs.50,000
(C) Rs.60,000
(D) Rs.80,000
(E) None
Rationale: Solution
Suppose Y invested Rs.y
Then,	40000 /y = 2 / 3
‹=› y=(40000×3 / 2).
‹=› y=60000.
Answer C
Answer: (C) Rs.60,000
Question: Ramu bought an old car for Rs. 42000. He spent Rs. 13000 on repairs and sold it for Rs. 64900. What is his profit percent?
(A) 11
(B) 12
(C) 18
(D) 17
(E) 19
Rationale: Explanation:
Total CP = Rs. 42000 + Rs. 13000 = Rs. 55000 and SP = Rs. 64900
Profit(%) = (64900 - 55000)/55000 * 100 = 18%
Answer:C
Answer: (C) 18
Question: What is the sum of the first 25 natural numbers (starting from 1)?
(A) 325
(B) 350
(C) 375
(D) 400
(E) 425
Rationale: The sum of n natural numbers = n*(n+1) / 2 = 25*26/2 = 325
The answer is A.
Answer: (A) 325
Question: Excluding stoppages, the speed of a bus is 50 kmph and including stoppages, it is 42 kmph. For how many minutes does the bus stop per hour?
(A) 10 min
(B) 7 min
(C) 8.2 min
(D) 9.6 min
(E) 40 min
Rationale: D
9.6 min
Due to stoppages, it covers 8 km less.
Time taken to cover 9 km = (8/50 x 60) min = 9.6 min
Answer: (D) 9.6 min
Question: (1.00001)(0.99999) - (1.00003)(0.99997) =
(A) 0
(B) 10^-10
(C) 8(10^-10)
(D) 10^-5
(E) 3(10^-5)
Rationale: (1.00001*0.99999)-(1.00003*0.99997)
= (1+0.00001)(1-0.00001) - (1+0.00003)(1-0.00003)
= 1 - (0.00001)^2 - 1 + (0.00003)^2
= -(0.0000000001) + (0.0000000009)
= 0.0000000008=8(10^-10)
Answer C
Answer: (C) 8(10^-10)
Question: If (m-8) is a factor of m^2-km-24, then k=
(A) 3
(B) 5
(C) 6
(D) 11
(E) 16
Rationale: (m-8)(m-a)=m^2-km-24
A=-3
k=8+a=5=B
Answer: (B) 5
Question: The number of diagonals of a polygon of n sides is given by the formula f=n(n-3)/2. If a polygon has twice as many diagonals as sides, how many sides does it have?
(A)  3
(B)  5
(C)  6
(D)  7
(E)  8
Rationale: f=n(n-3)
f=2*n
2n=n(n-3)
=>2=n-3
=>n=5
Answer B
Answer: (B)  5
Question: The area of a triangle will be when a = 1m, b = 1m, c = 2m, a, b, c being lengths of respective sides?
(A) 2
(B) 7
(C) 5
(D) 3
(E) 4
Rationale: S = (1 + 1 + 2)/2
= 2
Answer: A
Answer: (A) 2
Question: Find large number from below question The difference of two numbers is 1345. On dividing the larger number by the smaller, we get 6 as quotient and the 15 as remainder
(A) 1234
(B) 1596
(C) 1350
(D) 1467
(E) 1635
Rationale: Let the smaller number be x. Then larger number = (x + 1345).
x + 1345 = 6x + 15
5x = 1330
x = 266
Large number = 266+1330 = 1596
B
Answer: (B) 1596