mathewhe/aqua_rat huggingface dataset:
Question: A box contains 4 red chips and 5 blue chips. If two chips are selected at random without replacement, what is the probability that the chips are different colors?
(A) 1/2
(B) 5/9
(C) 7/12
(D) 2/3
(E) 7/10
Rationale: Total selection ways: 9C2=9!/5!4!=36
Selecting one blue chip out of two: 5C1=5!/4!1!=5
Selecting one red chip out of four: 4C1=4!/1!3!=4
Thus, (5C1*4C1)/9C2=(5*4)/36=20/36=5/9=B
Answer: (B) 5/9
Question: Walking at 8KMPH From Point R to Point railway station, mike will miss the train by 5 minutes. If he walks at 10KMPH he will reach the station by 5 minutes early.What is the distance between Point R to Railway station?
(A) A)9KM
(B) B)6.66KM
(C) C)7.25KM
(D) D)12.40KM
(E) E)13KM
Rationale: Since time differences given are in minutes so let's convert speed in Km per minute
8 kmph = 8/60 km per minute = (2/15) km per minute
10 kmph = 10/60 km per minute = (1/6) km per minute
Let, Time of train to depart from station = t minutes
Distance between Point R and Railway Station = Speed*Time = (2/15)*(t+5)
Distance between Point R and Railway Station = Speed*Time = (1/6)*(t-5)
i.e. (2/15)*(t+5) = (1/6)*(t-5)
i.e. 12t+60 = 15t - 75
i.e. 3t = 135
i.e. t = 45 minutes
i.e. Distance = (1/6)*(t-5) = (1/6)*(45-5) = 40/6 = 20/3 Km = 6.66 Km
Answer: Option B
Answer: (B) B)6.66KM
Question: A shop sells bicycles and tricycles. In total there are 10 cycles (cycles include both bicycles and tricycles) and 23 wheels. Determine how many of each there are, if a bicycle has two wheels and a tricycle has three wheels.
(A) b=7,t=3
(B) b=5,t=3
(C) b=8,t=2
(D) b=2,t=5
(E) b=6,t=4
Rationale: Let b be the number of bicycles and let t be the number of tricycles.
Set up the equations
b+t=10............(1)
2b+3t=23............(2)
Let b be the number of bicycles and let t be the number of tricycles.
Set up the equations
b+t=8............(1)
2b+3t=19............(2)
Rearrange equation (1) and substitute into equation (2)
2b+30-3b=23
-b=-7
b=7
Calculate the number of tricycles t
t=10−b
=10−7
=3
There are 3 tricycles and 7 bicycles.
Answer is A.
Answer: (A) b=7,t=3
Question: 12 buckets of water fill a tank when the capacity of each tank is 13.5 litres. How many buckets will be needed to fill the same tank, if the capacity of each bucket is 9 litres?
(A) 8
(B) 15
(C) 16
(D) 18
(E) None
Rationale: Solution
Capacity of the tank	= (12×13.5) litres
= 162 litres.
Capacity of each bucket	= 9 litres.
Number of buckets needed	= (162/9)
‹=› 18.
Answer D
Answer: (D) 18
Question: On average, the boys in the class have 20 pencils and the girls have 38 pencils. If the overall class average is 30 pencils, what is the ratio of boys to girls in the class?
(A) 1/2
(B) 2/3
(C) 3/4
(D) 4/5
(E) 5/6
Rationale: (38G + 20B) / (G+B) = 30
38G + 20B = 30(G+B)
8G=10B
B/G = 4/5
The answer is D.
Answer: (D) 4/5
Question: What is the ratio of 12 minute to 1 hour ?
(A) 1/4
(B) 3/4
(C) 1/5
(D) 2/2
(E) 3/1
Rationale: C
1/5
Answer: (C) 1/5
Question: Tough and Tricky questions: Work/Rate Problems.
If it takes 70 workers 3 hours to disassemble the exhibition rides at a small amusement park, how many hours would it take 20 workers to do this same job?
(A) 40/3
(B) 10.5
(C) 7
(D) 7/3
(E) 9/7
Rationale: 70 Workers = 3 hours then,
1 Worker = 3*70 Hours
20 Workers = (3*70) /(20) = 10.5 Answer. B
Answer: (B) 10.5
Question: The moon revolves around the earth at a speed of approximately 1.02 kilometers per second. This approximate speed is how many kilometers per hour?
(A) 60
(B) 61.2
(C) 62.5
(D) 3,600
(E) 3,672
Rationale: moon revolves around the earth at a speed of 1.02kilometers per second.
one hour equal to 60 minutes.
one minute equals to 60 seconds. so one hour equals to 3600 seconds.
so one hour, speed= 1.02*3600=3672 kilometers per hour.
Option E is correct
Answer: (E) 3,672
Question: Monica planned her birthday party. She prepared 5 muffins for each of her guests and kept aside two additional muffins in case someone will want extra. After the party, it turned out that one of the guests didn't come but every one of the guests that did come ate six muffins and 7 muffins remained. How many guests did Monica plan on?
(A) 3.
(B) 4.
(C) 1.
(D) 6.
(E) 7.
Rationale: 5N +2 = 7 + 6(N-1)
Solving N= 1
Hence C
Answer: (C) 1.
Question: A man rows his boat 72 km downstream and 30 km upstream, taking 3 hours each time. Find the speed of the stream?
(A) 6 kmph
(B) 5 kmph
(C) 2 kmph
(D) 8 kmph
(E) 7 kmph
Rationale: Speed downstream = d/t = 72/(3) = 24 kmph
Speed upstream = d/t = 30/(3) = 10 kmph
The speed of the stream = (24 - 10)/2 = 7 kmph
Answer:E
Answer: (E) 7 kmph
Question: A and B enter into a partnership with respective capitals of Rs. 20,000 and Rs. 40,000. At the end of the year, the total profit is Rs. 39,000. If A receives Rs. 15,000 as both his salary and profit, then what is his salary?
(A) Rs. 2000
(B) Rs. 4000
(C) Rs. 3500
(D) Rs. 3000
(E) None of these
Rationale: Explanation:
A's capital : B 's capital
20000 : 40000 = 1 : 2
Since, the time period is fixed, the profit is distributed in the ratio of capital 1 : 2
Profit of A = (1/3) * 39,000 = Rs. 13,000
Salary of A = Rs. (15000 – 13000) = Rs. 2000
ANSWER: A
Answer: (A) Rs. 2000
Question: Jack and Jill work at a hospital with 4 other workers. For an internal review, 2 of the 6 workers will be randomly chosen to be interviewed. What is the probability that Jack and Jill will both be chosen?
(A) 1/3
(B) 1/4
(C) 1/15
(D) 3/8
(E) 2/3
Rationale: Total number of ways to choose 2 out of 6 workers= 6!/2!4!= 15
Number of ways to choose both jack and jill= 1
probability= 1/15
C should be the answer
Answer: (C) 1/15
Question: A man can row 6 kmph in still water. When the river is running at 1.2 kmph, it takes him 1 hour to row to a place and black. What is the total distance traveled by the man?
(A) 5.77 km
(B) 5.98 km
(C) 5.76 km
(D) 5.96 km
(E) 5.12 km
Rationale: Explanation:
M = 6
S = 1.2
DS = 7.2
US = 4.8
x/7.2 + x/4.8 = 1
x = 2.88
D = 2.88 * 2 = 5.76
Answer: Option C
Answer: (C) 5.76 km
Question: How long does a train 110 m long running at the speed of 72 km/hr takes to cross a bridge 132 m length?
(A) 120
(B) 121.1
(C) 13
(D) 156
(E) 148
Rationale: Speed = 72 * 5/18 = 20 m/sec
Total distance covered = 110 + 132 = 242 m.
Required time = 242/20 = 12.1 sec.
Answer: Option B
Answer: (B) 121.1
Question: The sum of ages of 5 children born 2 years different each is 50 yrs. What is the age of the Elder child?
(A) 8
(B) 14
(C) 16
(D) 17
(E) 18
Rationale: Let the ages of children be x, (x + 2), (x + 4), (x + 6) and (x + 8) years.
Then, x + (x + 2) + (x + 4) + (x + 6) + (x + 8) = 50
5x = 30
x = 6
x+8= 6+8= 14
Answer : B
Answer: (B) 14
Question: If x and y are prime numbers, which of the following CANNOT be ( x + Y )?
(A) 5
(B) 23
(C) 13
(D) 16
(E) 3
Rationale: All answer choices but B are odd. In order odd number to be the sum of two prime numbers one must be even, so 2, and another odd.
Now, 23=2+21. Since 21 is not a prime then 23 cannot be written as the sum of two prime numbers.
Answer: B
Answer: (B) 23
Question: Two goods trains each 500 m long are running in opposite directions on parallel tracks. Their speeds are 45 km/hr and 30 km/hr respectively. Find the time taken by the slower train to pass the driver of the faster one?
(A) 22
(B) 66
(C) 48
(D) 77
(E) 21
Rationale: Relative speed = 45 + 30 = 75 km/hr.
75 * 5/18 = 125/6 m/sec.
Distance covered = 500 + 500 = 1000 m.
Required time = 1000 * 6/125 = 48 sec.
Answer:C
Answer: (C) 48
Question: In a division sum, the divisor is ten times the quotient and five times the remainder. If the remainder is 50, the dividend is:
(A) A)5322
(B) B)5330
(C) C)6300
(D) D)5340
(E) E)5342
Rationale: Divisor = (5 * 50) = 250
= 10 * Quotient = Divisor
=> Quotient = 250/10 = 25
Dividend = (Divisor * Quotient) + Remainder
Dividend = (250 * 25) + 50 = 6300.
C
Answer: (C) C)6300
Question: Which of the following is equal to (x+1)!/x!
(A) x-1
(B) 1+(1/x)
(C) x+1
(D) 1
(E) x
Rationale: (x + 1)! = (x + 1) * x!
(x + 1)!/x! = x + 1
Answer: C
Answer: (C) x+1
Question: There are 47 distinct numbers in set M, there are 28 distinct numbers in set N, and there are 12 distinct numbers that are in both sets M and N. Set H is the set containing the elements that are in at least one of sets M and N. How many elements are in set H?
(A) 39
(B) 40
(C) 51
(D) 58
(E) 63
Rationale: {Total} = {M} + {N} - {Both}
{Total} = 47 + 28 - 12 = 63.
Answer: E.
Answer: (E) 63
Question: which of the following will not give an integer on taking square root?
(A) 64
(B) 529
(C) 441
(D) 484
(E) 450
Rationale: square root(64)=8
square root(529)=23
square root(441)=21
square root(484)=22
square root(450) is not an integer
so the answer is E
Answer: (E) 450
Question: In how many different number of ways 4 boys and 2 girls can sit on a bench?
(A) 700
(B) 710
(C) 720
(D) 800
(E) 820
Rationale: npn = n!
6p6 = 6 × 5 × 4 × 3 × 2 × 1 = 720
C)
Answer: (C) 720
Question: A car gets 40 kilometers per gallon of gasoline. How many gallons of gasoline would the car need to travel 140 kilometers?
(A) 4.5
(B) 5.5
(C) 6.5
(D) 7.5
(E) 3.5
Rationale: Each 40 kilometers, 1 gallon is needed. We need to know how many 40 kilometers are there in 140 kilometers?
140 ÷ 40 = 3.5 × 1 gallon = 3.5 gallons
correct answer E
Answer: (E) 3.5
Question: Charlie's lawn service fills up all their gas cans every Friday at Zeb's store. They have to get enough gas for 10 lawn mowers and 10 weed-eaters. The weed-eaters use 5 liters of gas each. The mowers us 60% more than the weedeaters.
Zeb charges .75 cents service per item. Fuel is .40 cents per liter. How much will it cost to fill all mowers and weed-eaters?
(A) $77
(B) $60
(C) $67
(D) $62
(E) $55
Rationale: Lots of calculations.
.75*20 + 10*.40*5+ 5*(8/5)*10*.40
Answer=$67
The correct option is C
Answer: (C) $67
Question: A tin of oil was 4/5full.when 6 bottles of oil were taken out and four bottles of oil were poured into it, it was ¾ full. how many bottles of oil can the tin contain?
(A) 40
(B) 30
(C) 20
(D) 50
(E) 60
Rationale: Suppose x bottles can fill the tin completely
Then4/5x-3/4x=6-4
X/20=2
X=40
Therefore required no of bottles =40
Answer is A.
Answer: (A) 40
Question: A goods train runs at a speed of 72 kmph and crosses a 270 m long platform in 26 seconds.What is the length of the goods train?
(A) 230 m
(B) 250 m
(C) 260 m
(D) 270 m
(E) 240 m
Rationale: s=270+x/t
72*5/18=270+x/26
x=250
ANSWER:B
Answer: (B) 250 m
Question: The cost price of 20 books is the same as the selling price of ’X’ books. If the profit is 25%, then the value of X is ?
(A) 25
(B) 18
(C) 16
(D) 15
(E) 14
Rationale: let S.P. of X books = Rs 100 = C.P. of 20 books
Therefore, C.P. of one book = Rs 5
Profit = 25 %
Therefore, S.P of one book = 6.25
S.P of X articles = 6.25 X
6.25 X = 100 => X = 16
ANSWER:C
Answer: (C) 16
Question: he average of 10 numbers is zero. Of them, at the most, how many may be greater than zero?
(A) 0
(B) 1
(C) 10
(D) 9
(E) 8
Rationale: Average of 10 numbers = 0.
Sum of 10 numbers (0 x 10) = 0.
It is quite possible that 9 of these numbers may be positive and if their sum is a the 10th number is (-a).
Answer: Option D
Answer: (D) 9
Question: Divide Rs. 1500 among A, B and C so that A receives 1/3 as much as B and C together and B receives 2/3 as A and C together. A's share is?
(A) 378
(B) 277
(C) 375
(D) 287
(E) 279
Rationale: A+B+C = 1500
A = 1/3(B+C); B = 2/3(A+C)
A/(B+C) = 1/3
A = 1/4 * 1500 => 375
Answer: C
Answer: (C) 375
Question: Consider two statements
Statement 1 => If X is an integer and X=2p+1 where p is not an integer.
Statement 2 => If Y is an integer and Y=2q where q is not an integer
Which of the following correctly specifies the Even/Odd nature of X and Y respectively
(A) Odd,Even
(B) Odd,Odd
(C) Even,Odd
(D) Even,Even
(E) Cannot be determined
Rationale: x = integer
x = 2p+1 = integer here p can be any n/2 and n can be even or odd , matters alot 2 get cancelled out
if n were even x would odd
if n odd x would be even
Similarly other
answer will be E
Answer: (E) Cannot be determined
Question: Martin has a business washing cars. Last year he washed 20 cars a
week. This year, he wants to increase his business to 1,200 cars a year.
How many cars will he have to wash each month on average?
(A) 200 cars
(B) 500 cars
(C) 300 cars
(D) 100 cars
(E) 400 cars
Rationale: The last year part is extra information. 1200÷12 (months in a year)= 100
He will have to wash 100 cars each month.
correct answer D
Answer: (D) 100 cars
Question: A train speeds past a pole in 23 seconds and a platform 125 m long in 33 seconds. Its length is?
(A) 275
(B) 287.5
(C) 288
(D) 233.5
(E) 245.6
Rationale: Let the length of the train be x meters and its speed be y m/sec.
They, x / y = 23 => y = x/23
x + 125 / 33 = x / 23
x = 287.5 m.
Answer:B
Answer: (B) 287.5
Question: A vending machine randomly dispenses four different types of fruit candy. There are twice as many apple candies as orange candies, twice as many strawberry candies as grape candies, and twice as many apple candies as strawberry candies. If each candy cost $0.2, and there are exactly 90 candies, what is the minimum amount of money required to guarantee that you would buy at least three of each type of candy?
(A) $16.60
(B) $20.75
(C) $22.50
(D) $42.75
(E) $45.00
Rationale: Let number of Apple , Orange , strawberry and grape candies be A, O ,S and G respectively .
A= 2O
S= 2G
A= 2S
A= 4G
A+O+S+G = 90
=>A + A/2 + A/2 +A/4 = 90
=> 9A/4 = 90
=> A = 40
O = 20
S = 20
G = 10
Cost of each candy = .2 $
Mininum amount of money required to guarantee that you would buy at least three of each type of candy
We can buy 40 Apple candies , 20 orange candies , 20 strawberry candies and 3 grape candies to ensure atleast 3 of each type of candies .
Total = 83 candies
Amount required = 83 * .2 = 16.60 $
Answer A
Answer: (A) $16.60
Question: What is the remainder when 14,451 × 15,654 × 16,783 is divided by 5?
(A) 1
(B) 3
(C) 2
(D) 4
(E) 5
Rationale: Only the unit's digit of the product will decide the remainder when divided by 5.
Hence, 1*4*3= will give units digit as 2
So, whatever be the number, if it ends in 2, the remainder after dividing with 5 will be 2.
Option C
Answer: (C) 2
Question: In a public show 75 % of the seats were filled. If there were 600 seats in the hall, how many seats were vacant?
(A) 100
(B) 110
(C) 120
(D) 140
(E) 150
Rationale: 75 % of 600
= 75/100 × 600
= 450
Therefore, the number of vacant seats = 600 - 450 = 150.
Answer:E
Answer: (E) 150
Question: In a group of 120 people, 90 have an age of more 30 years, and the others have an age of less than 20 years. If a person is selected at random from this group, what is the probability the person's age is less than 20?
(A) 60/ 120
(B) 15 / 120
(C) 30 / 120
(D) 80 / 120
(E) 40/ 120
Rationale: Number of people whose age is less than 20 is given by
120 - 90 = 30
Probability P that a person selected at random from the group is less than 20 is gieven by
30 / 120 = 0.25
correct answer C
Answer: (C) 30 / 120
Question: 0.99999+0.11112=?
(A) 1
(B) 1.0001
(C) 1.0021
(D) 1.111
(E) 1.11111
Rationale: 0.99999 + 0.11112
= 0.99999 + 0.11111 + 0.00001
= (0.99999 + 0.00001) + 0.11111
= 1 + 0.11111
= 1.11111
E
Answer: (E) 1.11111
Question: Find the one which does not belong to that group?
(A) 16
(B) 36
(C) 77
(D) 64
(E) 4
Rationale: Explanation:
16, 36, 64 and 4 are perfect squares but not 77.
Answer:C
Answer: (C) 77
Question: If one positive integer is greater than another positive integer by 4, and the difference of their cubes is 316, what is their sum?
(A) 6
(B) 8
(C) 10
(D) 12
(E) 14
Rationale: 1^3 = 1
2^3 = 8
3^3 = 27
4^3 = 64
5^3 = 125
6^3 = 216
7^3 = 343
The two numbers are 3 and 7.
The answer is C.
Answer: (C) 10
Question: A car X takes 3 hours more than a bus Y in covering 40 km. If the car triples its speed it takes 1 hour less than bus. What is the speed of the car?
(A) 6 km/hr
(B) 6.25 km/hr
(C) 6.67 km/hr
(D) 7 km/hr
(E) None of these
Rationale: Explanation :
Let the car's speed be x km/hr.
=> 40/x-40/(3x)=4
=> 80/3x=4
=> 12x=80
=> x=6.67 km/hr
Answer : C
Answer: (C) 6.67 km/hr
Question: A can finish a piece of work in 4 days. B can do it in 12 days. They work together for two days and then A goes away. In how many days will B finish the work?
(A) 6 days
(B) 5 days
(C) 7 days
(D) 4 days
(E) 3 days
Rationale: 2/4 + (2 + x)/12= 1 => x =6 days
Answer: A
Answer: (A) 6 days
Question: If k is the greatest positive integer such that 4^k is a divisor of 32! then k =
(A) 3
(B) 4
(C) 5
(D) 6
(E) 10
Rationale: 32/4=8
32/16=2
8+2 =10=k
Answer:E
Answer: (E) 10
Question: A local bank that has 9 branches uses a two-digit code to represent each of its branches. The same integer can be used for both digits of a code, and a pair of two-digit numbers that are the reverse of each other (such as 17 and 71) are considered as two separate codes. What is the fewest number of different integers required for the 9 codes?
(A) 9 codes 3 integers
(B) 4
(C) 5
(D) 6
(E) 7
Rationale: Pick any two integer.
Integers: 12
Code: 11, 12, 21, 22 = 4 Codes
Add one more integer: 3
13, 31, 33, 23, 32 = 5 Codes
Total = 9 Codes.. Answer: A
Answer: (A) 9 codes 3 integers
Question: If the number 481 * 673 is completely divisible by 9, then the smallest whole number in place of * will be
(A) 7
(B) 9
(C) 12
(D) 14
(E) 15
Rationale: Sum of digits = (4 + 8 + 1 + x + 6 + 7 + 3) = (29 + x), which must be divisible by 9.
x = 7.
A)
Answer: (A) 7
Question: If the number 5 * 2 is divisible by 6, then * = ?
(A) 8
(B) 6
(C) 2
(D) 1
(E) 5
Rationale: C
2
6 = 3 x 2. Clearly, 5 * 2 is divisible by 2. Replace * by x.
Then, (5 + x + 2) must be divisible by 3. So, x = 2.
Answer: (C) 2
Question: In a regular week, there are 5 working days and for each day, the working hours are 8. A man gets Rs. 2.40 per hour for regular work and Rs. 3.20 per hours for overtime. If he earns Rs. 432 in 4 weeks, then how many hours does he work for ?
(A) 160
(B) 175
(C) 180
(D) 195
(E) 166
Rationale: Explanation:
Suppose the man works overtime for x hours.
Now, working hours in 4 weeks = (5 x 8 x 4) = 160.
=160 x 2.40 + x x 3.20 = 432
=> 3.20x = 432 - 384 = 48
=> x = 15.
Hence, total hours of work = (160 + 15) = 175.
Answer: B
Answer: (B) 175
Question: How many litres of pure acid are there in 8 litres of a 20% solution?
(A) 2 litres
(B) 1.4 litres
(C) 1 litres
(D) 1.6 litres
(E) None of these
Rationale: Explanation :
Quantity of pure acid = 8 × (20/100) = 1.6
Answer : Option D
Answer: (D) 1.6 litres
Question: The radius of a cylinder is 8 m, height 14 m. The volume of the cylinder is:
(A) 2816
(B) 5500
(C) 3300
(D) 1100
(E) 4400
Rationale: Cylinder volume = Ï€r(power2)h
= 22/7 Ã— 8 Ã— 8 Ã— 14
= 2816 m(power3)
Answer is A.
Answer: (A) 2816
Question: The ratio of the number of ladies to gents at a party was 1:2 but when 2 ladies and 2 gents left, the ratio became 1:3. How many people were at the party originally?
(A) 11
(B) 77
(C) 12
(D) 99
(E) 887
Rationale: x, 2x
(x-2):(2x-2) = 1:3
3x-6 = 2x-2
x = 4
x+2x = 3x
=> 3*4 = 12
Answer: C
Answer: (C) 12
Question: If n is an integer and n^4 is divisible by 20, which of the following could be the remainder when n is divided by 20?
(A) 5
(B) 10
(C) 12
(D) 16
(E) 18
Rationale: option 1
Remainder 5 means 20+5=25
n^4= 25^4= 25*25*25*25/20 is not an integer
option 2
Remainder 10 means 20+10=30
n^4= 30*30*30*30/20 is an integer means n^4 is divisible by 20 if we take n=10
so B is correct
Answer: (B) 10
Question: The profit earned after selling an article for Rs.675 is twice the loss incurred after selling the article for Rs.435. What is the cost price of the article?
(A) Rs.450
(B) Rs.595
(C) Rs.400
(D) Rs.395
(E) None of these
Rationale: Explanation:
Let ‘x’ be the CP of the article.
i.e. Rs.675-x = 2(x-435)
675-x = 2x-870
675+870 = 3x, therefore, x=1545/3 =Rs.515
Answer: Option E
Answer: (E) None of these
Question: At what rate percent per annum will the simple interest on a sum of money be 7/5 of the amount in 10 years?
(A) 4%
(B) 7%
(C) 9%
(D) 3%
(E) 14%
Rationale: Let sum = x. Then, S.I. = 7x/5, Time
= 10 years.
Rate = (100 * 7x) / (x * 5 * 10)
= 14%
Answer: E
Answer: (E) 14%
Question: A race course is 400 m long. A and B run a race and A wins by 5m. B and C run over the same course and B win by 4m. C and D run over it and D wins by 16m. If A and D run over it, then who would win and by how much?
(A) D by 7.2 m
(B) A by 7.2 m
(C) A by 8.4 m
(D) D by 8.4 m
(E) None of these
Rationale: Explanation :
If A covers 400m, B covers 395 mIf B covers 400m, C covers 396 mIf D covers 400m, C covers 384 mNow if B covers 395 m, then C will cover(396/400)×395=391.05 mIf C covers 391.05 m, then D will cover(400/384)×391.05=407.24If A and D run over 400 m, then D win by 7.2 m (approx.)
Answer : A
Answer: (A) D by 7.2 m
Question: I have a few sweets to be distributed. If I keep 2, 3 or 4 in a pack, I am left with one sweet. If I keep 5 in a pack, I am left with none. What is the minimum number of sweets I have to pack and distribute ?
(A) 25
(B) 37
(C) 54
(D) 65
(E) 75
Rationale: when divided 2,3,4 leaves remainder 1 and leaves remainder 0 while dividing 5
ANSWER:A
Answer: (A) 25
Question: If A : B= 2 : 4 and B : C = 6 : 8, then A : B : C is:
(A) 11:2:3
(B) 22:44:66
(C) 12:24:32
(D) 6:9:12
(E) 4:8:10
Rationale: A:B=2:4, B:C=6:8, A:B:C=2Ã—6:6Ã—4:4Ã—8
â‡’ 12:24:32
Answer: C.
Answer: (C) 12:24:32
Question: Gauri went to the stationers and bought things worth Rs. 25, out of which 30 paise went on sales tax on taxable purchases. If the tax rate was 6%. then what was the cost of the tax free items?
(A) Rs.15
(B) Rs.15.70
(C) Rs.19.70
(D) Rs.20
(E) None
Rationale: Solution
Let the amount of taxable purchases be Rs.x.
Then, 6% of x	= 30/100
x ‹=› (30/100×100/6)
= 5.
Cost of tax free items	= Rs.[25 - (5 + 0.30)]
= Rs. 19.70
Answer C
Answer: (C) Rs.19.70
Question: If 75 percent of a class answered the first question on a certain test correctly, 45 percent answered the second question on the test correctly, and 20 percent answered neither of the questions correctly, what percent answered both correctly?
(A)  40%
(B) (8) 20%
(C)  30%
(D)  50%
(E)  65%
Rationale: {Total} = {First} + {Second} - {Both} + {Neither}
100% = 75% + 45% - {Both} + 20% --> {Both} = 40%.
Answer: A
Answer: (A)  40%
Question: There has been successive increases of 25% and then 15% in the price of gas from the previous month. By what percentage should a driver reduce gas consumption so that the expenditure does not change?
(A) 30%
(B) 50%
(C) 66.66%
(D) 15%
(E) 75%
Rationale: Let P be the original price per unit of gas.
Let x be the original gas consumption.
Let y be the reduced gas consumption.
y*1.15*1.25*P = x*P
y = x / (1.15*1.25) which is about 0.7x which is a decrease of about 30%.
The answer is A.
Answer: (A) 30%
Question: A batch of cookies was divided amomg 3 tins: 2/3 of all the cookies were placed in either the blue or the green tin, and the rest were placed in the red tin. If 1/5 of all the cookies were placed in the blue tin, what fraction of the cookies that were placed in the other tins were placed in the green tin
(A) 21/31
(B) 9/4
(C) 5/9
(D) 7/5
(E) 9/7
Rationale: This will help reduce the number of variables you have to deal with:
G + B = 2/3
R = 1/3
B = 1/5
We can solve for G which is 7/10
What fraction (let it equal X) of the cookies that were placed in the other tins were placed in the green tin?
So..
X*(G+R)=G
X*(7/10 + 1/3) = 7/10
X = 21/31
ANSWER: A
Answer: (A) 21/31
Question: The sum of the ages of a father and son is 45 years. Five years ago, the product of their ages was four times the fathers age at that time. The present age of father and son
(A) 34,11
(B) 35,10
(C) 36,9
(D) 40,5
(E) None of these
Rationale: Explanation:
Let sons age = x years. Then fathers age = (45 - x)years.
(x—5)(45—x—5) = 4(45- x - 5) hence (x—5) = 4 so x = 9
Their ages are 36 years and 9 years.
Option C
Answer: (C) 36,9
Question: Find 96 ×× 98
(A) 92/8
(B) 92/12
(C) 92/13
(D) 92/10
(E) 92/11
Rationale: Here both numbers are less than 100. So they are deficient of - 4 and - 2 compared with 100. So
Answer:	A
Answer: (A) 92/8
Question: a man owns 1/3 of market reserch beauro buzness,and sells 3/5 of his shares for 15000rs,what is the value of buzness?
(A) 55000
(B) 75000
(C) 65000
(D) 190000
(E) 250000
Rationale: If value of business=x
Total sell (2x/3)(3/4)=15000
->x=75000
ANSWER:B
Answer: (B) 75000