mathewhe/aqua_rat huggingface dataset:
Question: Speed of boat in water is 12km/hr. and the speed of the stream is 3km/hr. Find the time taken by the boat to go upstream a distance of 45km.
(A) 3
(B) 4
(C) 5 hrs.
(D) 6
(E) 2
Rationale: US =speed of the boat - speed of the stream 12-3 =9km/hr. Time taken to cover 45km =45/9 = 5hrs. Answer : C
Answer: (C) 5 hrs.
Question: An error 6% in excess is made while measuring the side of a square. The percentage of error in the calculated area of the square is:
(A) 12.36
(B) 8.36
(C) 9.36
(D) 10.36
(E) 11.36
Rationale: Explanation:
100 cm is read as 106 cm.
A1 =(100 × 100)cm2 = 10000
and A2= (106 × 106)cm2= 11236
(A2 - A1) = 11236-10000 = 1236
=> 1236/10000*100 =12.36
Answer : A
Answer: (A) 12.36
Question: A pharmaceutical company uses 900 gm in place of 1 kg to sell the drug. Find the actual % profit or loss, when the company sells the product on 10% gain on cost price?
(A) 20
(B) 25
(C) 30
(D) 35
(E) 40
Rationale: Selling price of 900gm = 100+10 = $110
Profit = 110-90 = $20
% of profit = 20*100/80 =25 %
Answer is B
Answer: (B) 25
Question: A certain cricket team played seven games and scored an average of 180 runs per game. If, in the team’s first five games, it scored 175, 169, 181, 190, and 173 points, what was the average (arithmetic mean) number of points scored over the last two games?
(A) 165
(B) 181
(C) 182
(D) 186
(E) Cannot be determined from the information given.
Rationale: Avg runs for total of 7 games = 50
So A+B+C+D+E+F+G/7=180
and A+B+C+D+E+F+G = 1260
Given A+B+C+D+E = 888
So F+G = 372
So average (arithmetic mean) number of runs scored over the last two games is 372/2 = 186
Correct answer is D) 186
Answer: (D) 186
Question: A train 280 m long, running with a speed of 72 km / hr will pass a tree in
(A) 14 sec
(B) 15 sec
(C) 16 sec
(D) 20 sec
(E) None
Rationale: Sol.
Speed = (72 x 5/18) m/sec.
= 20 m / sec.
Time taken = (280 x 1/20) sec = 14 sec
Answer A
Answer: (A) 14 sec
Question: At what rate of compound interest per annum will a sum of Rs.1200 become Rs.1348.32 in 2 years?
(A) 6%
(B) 6.5%
(C) 7%
(D) 7.5%
(E) 8%
Rationale: Let the rate be R% p.a. (1+ R )2 = 1348.32. Then, 1200* (1+ (R/100))2 = 1348.32
(1+R/100)2 = 134832/120000 = 11236/10000 :. (1 + R/100) 2 = (106/100)2
1 + R/100 = 106/100. So R = 6%
ANSWER:A
Answer: (A) 6%
Question: The average weight of 8 person's increases by 2.5 kg when a new person comes in place of one of them weighing 65 kg. What might be the weight of the new person?
(A) 80 kg
(B) 85 kg
(C) 90 kg
(D) 100 kg
(E) 110 kg
Rationale: Total weight increased = (8 x 2.5) kg = 20 kg.
Weight of new person = (65 + 20) kg = 85 kg.
B)
Answer: (B) 85 kg
Question: The sum of a certain number and its reciprocal is equal to 2,9. What is the absolute value of the difference of this number and its reciprocal ?
(A) 2,2
(B) 1,2
(C) 0,3
(D) 0,4
(E) 2,1
Rationale: x + 1/x = 2.9
x-1/x = y
Add two equations
2x = 2.9 + y
So when 2.9 and correct answer choice are added, the final digit should be even
So eliminate A, B and D
Substitute y=0.3
x=1.6
1.6+1/1.6 is not equal to 2.9
Substitute y = 2.1
So x=2.5
2.5+1/2.5 =2.9
ANSWER:E
Answer: (E) 2,1
Question: In what time will a railway train 70 m long moving at the rate of 36 kmph pass a telegraph post on its way?
(A) 5 sec
(B) 4 sec
(C) 3 sec
(D) 7 sec
(E) 1 sec
Rationale: T = 70/36 * 18/5 = 7 sec
Answer: D
Answer: (D) 7 sec
Question: In a box of 6 pencils, a total of 2 are defective. If a customer buys 3 pencils selected at random from the box, what is the probability that neither pencils will be defective?
(A) 1/2
(B) 1/5
(C) 2/3
(D) 2/5
(E) 1/7
Rationale: First, there are 4C3 ways you can select 3 good pencils from 4 good ones.
Second, there are 6C3 ways you select 3 pencils from 6 ones in the box.
Then, the probability that neither pen will be defective is: 4C3/6C3=4/20 = 1/5
Answer is B
Answer: (B) 1/5
Question: In a pet shop there are 120 eyes and 172 legs. How many birds are included in these?
(A) 33
(B) 34
(C) 35
(D) 36
(E) 37
Rationale: Let there are x birds and y puppies.
Each bird and puppy has 2 eyes. Each bird has 2 legs and each puppy has 4 legs.
Then 2x+2y = 120 => x+y = 60 (i)
2x+4y = 172 => x+2y = 86 (ii)
Solving (i) and (ii) we get
y = 26 & x = 34
So birds are 34
ANSWER:B
Answer: (B) 34
Question: On dividing 109 by a number, the quotient is 9 and the remainder is 1. Find the divisor?
(A) 10
(B) 12
(C) 14
(D) 16
(E) 18
Rationale: d = (D-R)/Q
= (109 - 1)/9
= 108/9 = 12
B)
Answer: (B) 12
Question: The sum of the present ages of two persons A and B is 60. If the age of A is twice that of B, find the sum of their ages 4 years hence?
(A) 22
(B) 77
(C) 70
(D) 68
(E) 71
Rationale: A + B = 60, A = 2B
2B + B = 60 => B = 20 then A = 40.
4 years, their ages will be 44 and 24.
Sum of their ages = 44 + 24 = 68.
Answer: D
Answer: (D) 68
Question: If circles x and y have the same area and circle x has a circumference of 18π, half of the radius of circle y is:
(A) 16
(B) 4.5
(C) 4
(D) 2
(E) 1
Rationale: x be radius of circle x
y be radius of circle y
given:
pi*x^2 = pi*y^2
also,
2*pi*x = 18*pi
x = 9
thus y =9
y/2 = 4.5
Ans: B
Answer: (B) 4.5
Question: . In digging a pond 18 m * 8 m * 6 m the volumes of the soil extracted will be?
(A) 889
(B) 1000
(C) 864
(D) 989
(E) 678
Rationale: 20 * 10 * 5 = 864
Answer: C
Answer: (C) 864
Question: The digits of a three-digit number A are written in the reverse order to form another three-digit number B. If B>A and B-A is perfectly divisible by 7, then which of the following is necessarily true?
(A) 100<A<299
(B) 106<A<305
(C) 112<A<311
(D) 118<A<317
(E) None
Rationale: Explanation:
Let A = abc the B = cba
Given, B – A is exactly divisible by 7.
Therefore, 100c + 10b + a – (100a + 10b + c) = 99c – 99a = 99(c – a)
So 99(c – a) should be divisible by 7.
We know that 99 is not divisible by 7. So (c – a) should be divisible by 7 which implies c – a is 0, 7, 14...
c – a = 0 is not possible as c = a implies A = B but given that B > A
c – a = 14 is not possible as the maximum difference between c and a = 9 – 1 = 8 only.
So c – a = 7.
If c = 9, a = 2
c = 8, a = 1
b can take any value from 0 to 9
Therefore, minimum value of abc = 109, maximum value = 299
From the given options, option B satisfies this.
Correct option: B
Answer: (B) 106<A<305
Question: A number x is multiplied with itself and then added to the product of 4 and x. If the result of these two operations is -8, what is the value of x?
(A) -4
(B) -2
(C) 2
(D) 4
(E) Cannot be determined.
Rationale: A number x is multiplied with itself --> X^2
added to the product of 4 and x --> X^2+4X
If the result of these two operations is -4 --> X^2+4X=-8
i.e X^2+4X+8=0 is the Quadratic equation which needs to be solved.
no solution
IMO E
Answer: (E) Cannot be determined.
Question: Thirty men can do a work in 24 days. In how many days can 20 men can do the work, given that the time spent per day is increased by one-third of the previous time?
(A) 27
(B) 88
(C) 26
(D) 55
(E) 12
Rationale: Let the number of hours working per day initially be x. we have M1 D1 H1= M2 D2 H2
30 * 24 * x = 20 * d2 * (4x)/3 => d2 = (30 * 24 * 3)/(24 * 4) = 27 days.
Answer:A
Answer: (A) 27
Question: What is the smallest positive integer K such that the product of 450 x K is a perfect square?
(A) 3
(B) 9
(C) 15
(D) 25
(E) 63
Rationale: A perfect square, is just an integer that can be written as the square of some other integer. For example 16=4^2, is a perfect square.
Now, 450 = 3^2 * 5^2 *3 , so if k=3 then 450k = (3 * 5 * 3)^2, which is a perfect square (basically the least positive value of k must complete only the power of 7 to even power as powers of other primes are already even).
Answer: A.
Answer: (A) 3
Question: A train 210 m long, running with a speed of 63 km/hr will pass a tree in?
(A) 15 sec
(B) 16 sec
(C) 18 sec
(D) 12 sec
(E) 25 sec
Rationale: Speed = 63 * 5/18 = 35/2 m/sec
Time taken = 210 * 2/35 = 12 sec
ANSWER: D
Answer: (D) 12 sec
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) 278
(B) 29
(C) 12
(D) 17
(E) 10
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: What is the area of square field whose side of length 16 m?
(A) 225
(B) 777
(C) 256
(D) 288
(E) 261
Rationale: 16 * 16 = 256 sq m
Answer: C
Answer: (C) 256
Question: Einstein walks on an escalator at a rate of 5steps per second and reaches the other end in 10 sec. while coming back, walking at the same speed he reaches the starting point in 40secs. What is the number of steps on the escalator?
(A) 40
(B) 60
(C) 120
(D) 80
(E) data insufficient
Rationale: Let the speed of escaltor be X steps per sec.
And length of escalator be Y.
Einstein's speed = 5 step/ sec
Then,
During upward movement
5-X=Y/10
During downward movement
5+X=Y/40
By solving equations we get Y=80.
ANSWER:D
Answer: (D) 80
Question: In a shop, shirts are usually sold at 40% above the cost price. During a sale, the shopkeeper offers a discount of 10% off the usual selling price. If he manages to sell 72 shirts for Rs 13.608, then his cost price per shirt, in Rs, is
(A) 120
(B) 130
(C) 140
(D) 150
(E) 160
Rationale: suppose cost price is x
so selling price is 14x/10
now after 10% discount selling price is 126x/100
total selling price is 72*126x/100
72*126x/100=13608
x=150
so the cost price per shirt is 150.
ANSWER:D
Answer: (D) 150
Question: The speed of a train is 80 kmph. What is the distance covered by it in 6 minutes?
(A) 15 kmph
(B) 11 kmph
(C) 18 kmph
(D) 8 kmph
(E) 12 kmph
Rationale: 80 * 6/60
= 8 kmph
Answer:D
Answer: (D) 8 kmph
Question: A train consists of 12 boggies, each boggy 15 metres long. The train crosses a telegraph post in 18 seconds. Due to some problem, two boggies were detached. The train now crosses a telegraph post in
(A) 18 sec
(B) 12 sec
(C) 15 sec
(D) 20 sec
(E) None of these
Rationale: Length of train = 12 × 15 = 180 m.
Then, speed of train = 180⁄18 = 10 m/s
Now, length of train = 10 × 15 = 150m
∴ Required time = 150⁄10 = 15 sec.
Answer C
Answer: (C) 15 sec
Question: How many inches are in 2000 millimeters? (round your answer to the nearest hundredth of of an inch).
(A) 51.45 inches
(B) 86.09 inches
(C) 67.34 inches
(D) 34.98 inches
(E) 78.74 inches
Rationale: One inch is the same as 25.4 mm. Let x inches be the same as 1000 mm
x = 1 inch * 2000 mm / 25.4 mm = 78.74 inches
correct answer E
Answer: (E) 78.74 inches
Question: Simran started a software business by investing Rs. 50,000. After six months, Nanda joined her with a capital of Rs. 80,000. After 3 years, they earned a profit of Rs. 24,500. What was Simran's share in the profit ?
(A) 13500
(B) 10500
(C) 9423
(D) 8500
(E) None of these
Rationale: Explanation:
Simran : Nanda =(50000Ã—36):(80000Ã—30)=(50000Ã—36):(80000Ã—30) =3:4=3:4.
Simran's share = Rs. (24500Ã—37)(24500Ã—37) = Rs. 10500.
ANSWER IS B
Answer: (B) 10500
Question: A man can do a job in 20 days. His father takes 20 days and his son finishes it in 25 days. How long will they take to complete the job if they all work together?
(A) 6.3
(B) 6.9
(C) 7.1
(D) 6.1
(E) 6.2
Rationale: 1 day work of the three persons = (1/20 + 1/20 + 1/25) = 7/50
So, all three together will complete the work in 300/47 = 7.1 days.
Answer:C
Answer: (C) 7.1
Question: If x is an integer, then x(x – 1)(x – k) must be evenly divisible by five when k is any of the following values EXCEPT
(A) -4
(B) -2
(C) 2
(D) -1
(E) 5
Rationale: We have the product of 3 integers: (x-1)x(x-k).
Note that the product of 3 integers is divisible by 5 if at least one multiple is divisible by 5. Now, to guarantee that at least one integer out of x, (x – 1), and (x – k) is divisible by 5 these numbers must have different remainders upon division by 5, meaning that one of them should have remainder of 1, another reminder of 2 and the last one remainder of 0, so be divisible by 5.
Next, if k=2 then we'll have (x-1)x(x-k)=(x-1)x(x-2) --> which means that (x-1) and (x-2) will have the same remainder upon division by 5. Thus for k=2 we won't be sure whether (x-1)x(x-k) is divisible by 5.
Answer: C.
Answer: (C) 2
Question: A hen leaps 3 leaps for every 2 leaps of a duck, but 4 leaps of the duck are equal to 3 leaps of the hen. What is the ratio of the speed of the hen to that of the duck?
(A) 2:1
(B) 3:4
(C) 4:3
(D) 1:4
(E) 5:6
Rationale: Given;
4 duck = 3 hen;
Or, duck/hen = 3/4;
Let hen's 1 leap = 4 meter and ducks 1 leap = 3 meter.
Then, ratio of speed of hen and duck = 4*3/3*2 = 2:1''Answer: 2:1;
Answer: (A) 2:1
Question: What is the fraction in the simplest form of the terminating decimal 0.0325?
(A) 31/40
(B) 41/30
(C) 13/40
(D) 1/30
(E) 1/40
Rationale: The fraction of the decimal 0.0325 is 325/10000. Simplifying by dividing the top and bottom by 25 to get 13/40.
Option C
Answer: (C) 13/40
Question: How many multiples of 4 are there between 12 and 104, inclusive?
(A) 21
(B) 22
(C) 23
(D) 24
(E) 25
Rationale: The multiples of 4 are from 4*3 up to 4*26.
26-3+1 = 24.
The answer is D.
Answer: (D) 24
Question: How many integers from 101 to 800, inclusive, remains the value unchanged when the digits were reversed?
(A) 50
(B) 60
(C) 70
(D) 80
(E) 90
Rationale: first digit possibilities - 1 through 7 = 7
8 is not possible here because it would result in a number greater than 8 (i.e 808 , 818..)
second digit possibilities - 0 though 9 = 10
third digit is same as first digit
=>total possible number meeting the given conditions = 7 *10 = 70
Answer is C.
Answer: (C) 70
Question: For which of the following functions f is f(a) = f(1-a) for all a?
(A) f (x) = 1 - x
(B) f (a) = 1 - a^2
(C) f (a) = a^2 - (1 - a)^2
(D) f (a) = a^2*(1 - a)^2
(E) f (x) = x/(1 - x)
Rationale: I remember seeing this problem in a GMATprep test. I think choice D should be F(a)=(a^2) (1-a)^2. If that is true then substituting (1-a) for will give us the same function back and the answer choice is D, where the function is multiplicative
Answer: (D) f (a) = a^2*(1 - a)^2
Question: The ratio of a to b to c is 2 to 3 to 4, and a, b, c are positive integers. If the average (arithmetic mean) of the three numbers is 36, what is the value of a?
(A) 21
(B) 24
(C) 25
(D) 27
(E) 30
Rationale: Let a=2k, b=3k, and c=4k.
a+b+c = 2k+3k+4k = 9k
Since the average is 36:
9k/3 = 36
3k = 36
k=12
Then a=24.
The answer is B.
Answer: (B) 24
Question: A student has to obtain 50% of the total marks to pass. He got 200 marks and failed by 20 marks. The maximum marks are?
(A) 510
(B) 520
(C) 530
(D) 540
(E) 440
Rationale: Let the maximum marks be x
Then, 50% of x = 200+20
50x/100 = 220
50x= 220*100= 22000
x = 440
Answer is E
Answer: (E) 440
Question: Three medical experts, working together at the same constant rate, can write an anatomy textbook in 18 days. How many additional experts, working together at this same constant rate, are needed to write the textbook in 9 days?
(A) 2
(B) 3
(C) 5
(D) 8
(E) 15
Rationale: Each expert can write 1/54 of the book per day.
To complete the book in 9 days, we need 54/9 = 6 experts, thus 3 more experts are needed.
The answer is B.
Answer: (B) 3
Question: A watch was sold at a loss of 10%. If it was sold for Rs.140 more, there would have been a gain of 4%. What is the cost price?
(A) Rs.1000
(B) Rs.1009
(C) Rs.1007
(D) Rs.1006
(E) Rs.1002
Rationale: Explanation:
90%
104%
--------
14% ---- 140
100% ---- ? => Rs.1000
Answer:A
Answer: (A) Rs.1000
Question: How many words can be formed by using all letters of the word ‘BIHAR’ ?
(A) 110
(B) 120
(C) 130
(D) 140
(E) None of these
Rationale: Solution
The word BIHAR contains 5 different letters.
Required number of words = 5P5 = 5 ! = (5 x 4 x 3 x 2 x 1) = 120, Answer B
Answer: (B) 120
Question: Two discounts of 40% and 20% equal to a single discount of?
(A) 52%
(B) 48%
(C) 60%
(D) 80%
(E) 70%
Rationale: {[(100-40)/100]*[(100-20)/100]}%=(60*80)/(100*100)%
=48%
single discount is equal to (100-48)%=52%
ANSWER A 52%
Answer: (A) 52%
Question: In a recent election, James received 5 percent of the 2,000 votes cast. To win the election, a candidate needed to receive more than 50 percent of the vote. How many additional votes would James have needed to win the election?
(A) 901
(B) 989
(C) 990
(D) 991
(E) 1,001
Rationale: James = (5/100)*2000 = 100
Votes to win = (50/100)*Total Votes +1 = (50/100)*2000 +1 = 1001
Remaining Voted needed to win election = 1001 - 100 = 901
Answer: option A
Answer: (A) 901
Question: In a certain pond, 70 fish were caught, tagged, and returned to the pond. A few days later, 50 fish were caught again, of which 2 were found to have been tagged. If the percent of tagged fish in the second catch approximates the percent of tagged fish in the pond, what is the approximate number of fish in the pond?
(A) 400
(B) 625
(C) 1,750
(D) 2,500
(E) 10,000
Rationale: This is a rather straight forward ratio problem.
1. 70 fish tagged
2. 2 out of the 50 fish caught were tagged thus 2/50
2/50=70/x
thus, x=1750
Think of the analogy: 2 fish is to 50 Fish as 50 fish is to ...?
You've tagged 50 fish and you need to find what that comprises as a percentage of the total fish population - we have that information with the ratio of the second catch.
C
Answer: (C) 1,750
Question: Three unbased coins are tossed. the probability of getting at most three head is ?
(A) 1/2
(B) 7/8
(C) 3/4
(D) 1/5
(E) 1/8
Rationale: S={TTT,TTH,THT,HTT,THH,HTH,HHT,HHH}
E be the event of getting at least two head is {HHH}
P(E)=n(E)/n(S)=1/8
Answer(E)
Answer: (E) 1/8
Question: If pqr = 1, the value of the expression (1 / ( 1 + p + q-1)) + (1 / ( 1 + p + r-1)) + (1 / ( 1 + p + p-1))
(A) p + q + r
(B) 1/ (p + q + r )
(C) 1
(D) p ^ (-1) + q ^ (-1) + r ^ (-1)
(E) None
Rationale: Explanation :
If p = q = r = 1, then expression = 1
Check the choice only, one choice gives the value of expression = 1.
Answer : C
Answer: (C) 1
Question: How many different numbers can we have by changing the position of the digits of the number 718844?
(A) 15
(B) 90
(C) 180
(D) 360
(E) 720
Rationale: Permutation in a group where there are repeated elements = n!/(p! * p2! *...*pn!); where p1, p2, .., pn are the number of times the element is repeated.
So, here required numbers = 6!/(2! * 2!) since we have 6 digits and 8 and 4 are each repeated twice.
= 180
Hence option C
Answer: (C) 180
Question: A and B invest in a business in the ratio 3: 2. Assume that 5% of the total profit goes to charity. If A's share is Rs. 855, what is the total profit?
(A) 1400
(B) 1500
(C) 1600
(D) 1200
(E) 1800
Rationale: Explanation:
Assume that the total profit is xx
since 5% goes for charity, 95% of xx will be divided between A and B in the ratio 3:2
Therefore, A's profit =95x 100×35
Given that A's share is Rs. 855. Therefore,
95 x 100×35=855
⇒95x100=855×53=285×5=1425
⇒x=1425×10095=285×10019=1500
Hence the total profit = 1500
Answer: Option B
Answer: (B) 1500
Question: A,B,C can complete a piece of work in 16,6,12 days. Working together, they complete the same work in how many days?
(A) 2
(B) 48/15
(C) 7/9
(D) 10
(E) 24/7
Rationale: A+B+C 1day work = 1/16 + 1/6 + 1/12 = 15/48
A,B,C together will complete the job in 48/15 days
Answer is B
Answer: (B) 48/15
Question: The diameters of two spheres are in the ratio 1:2 what is the ratio of their volumes?
(A) 1:9
(B) 1:2
(C) 1:8
(D) 1:1
(E) 1:6
Rationale: 1:8
Answer:C
Answer: (C) 1:8
Question: A train 700 m long can cross an electric pole in 20 sec and then find the speed of the train?
(A) 117 Kmph
(B) 178 Kmph
(C) 126 Kmph
(D) 118 Kmph
(E) 119 Kmph
Rationale: Length = Speed * time
Speed = L/T
S = 700/20
S = 35 M/Sec
Speed= 35*18/5 (To convert M/Sec in to Kmph multiply by 18/5)
Speed = 126 Kmph
Answer: C
Answer: (C) 126 Kmph
Question: If 20 gallons of grape juice are added to 40 gallons of a mixture, which contains 10 percent grape juice then what percent of the resulting mixture is grape juice?
(A) 14%
(B) 25%
(C) 28%
(D) 34%
(E) 40%
Rationale: OFFICIAL SOLUTION:
If we start with 40 gallons of a mixture that is 10% grape juice, then we have:
40 × 0.10 = 4 gallons of grape juice.
40 × 0.90 = 36 gallons of other components.
If we add 20 gallons of grape juice, we will end up with 24 gallons of grape juice and 36 gallons of other components, and we will have a total of 60 gallons of the mixture.
So 24/60 of the new mixture is grape juice. Now we convert this to a percent:Percent Grape Juice = 40/100 =40%.
The correct answer is choice (E)
Answer: (E) 40%
Question: A can finish a work in 24 days, B n 9 days and C in 12 days. B&C start the
work but are forced to leave after 3 days. The remaining work done by A in:
(A) 15
(B) 12
(C) 10
(D) 16
(E) 18
Rationale: (B+C)'s one day's work=1/9+1/12=7/36
Work done by B & C in 3 days=3*7/36=7/12
Remaining work=1-(7/12)=5/12
Now , 1/24 work is done by A in 1 day.
So, 5/12 work is done by A in 24*5/12=10 days
ANSWER C
Answer: (C) 10
Question: A boy writes all the numbers from 100 to 999. The number of zeroes that he uses is 'a', the number of 5's that he uses is 'b' and the number of 8's he uses is 'c'.
What is the value of b+c−a?
(A) 280
(B) 380
(C) 180
(D) 80
(E) 90
Rationale: We can see by symmetry b=c and hence all we need to calculate b and a
b=280 and a=180
⇒ 2b−a= 380
Option(B)
Answer: (B) 380
Question: A man purchased 3 blankets @ Rs.100 each, 5 blankets @ Rs.150 each and two blankets at a certain rate which is now slipped off from his memory. But he remembers that the average price of the blankets was Rs.150. Find the unknown rate of two blankets?
(A) 288
(B) 2778
(C) 279
(D) 450
(E) 278
Rationale: 10 * 150 = 1500
3 * 100 + 5 * 150 = 1050
1500 – 1050 = 450
Answer:D
Answer: (D) 450
Question: How long does a train 165 meters long running at the rate of 54 kmph take to cross a bridge 720 meters in length?
(A) 28
(B) 27
(C) 55
(D) 59
(E) 12
Rationale: T = (720 + 165)/54 * 18/5
T = 59
Answer: D
Answer: (D) 59
Question: Which number should replace both the asterisks in (* /18) x (*/162) = 1 ?
(A) 27
(B) 36
(C) 54
(D) 72
(E) 90
Rationale: Let (y/18) x (y/162) = 1
y^2 = 18 x 162 = 18 x 18 x 9
y = (18 x 3) = 54
The answer is C.
Answer: (C) 54
Question: If 3<x<6<y<11, then what is the greatest possible positive integer difference of x and y?
(A) 3
(B) 4
(C) 5
(D) 6
(E) 7
Rationale: 3 < x < 6 < y < 11;
3 < x
y < 11
3 + y < x + 11
y - x < 8.
Positive integer difference is 7 (for example y = 10.5 and x = 3.5)
Answer: E.
Answer: (E) 7
Question: Of all the homes on Gotham Street, 2/3 are termite-ridden, and 1/5 of these are collapsing. What fraction of the homes are termite-ridden, but NOT collapsing?
(A) a) 2/15
(B) b) 8/15
(C) c) 4/5
(D) d) 2/5
(E) e)1/5
Rationale: let total homes be 15
termite ridden= 2/3(15)= 10
termite ridden and collapsing = 1/5(10)=2
thus homes that are termite ridden, but not collapsing = 10-2=8
thus required ratio = 8/15
Answer B
Answer: (B) b) 8/15
Question: How many of the following numbers are divisible by 3 but not by 9?
2133, 2343, 3474, 4131, 5286, 5340, 6336, 7347, 8115, 9276
(A) 5
(B) 6
(C) 7
(D) 8
(E) 9
Rationale: Taking the sum of the digits, we have:
S1=9, S2=12, S3=18, S4= 9, S5=21, S6= 12, S7=18, S8=21, S9=15, S10=24.
Clearly S2, S5, S6, S8, S9, S10 are all divisible by 3 but not by 9. So, the number of required numbers= 6.
ANSWER:B
Answer: (B) 6
Question: How many W ways are there of placing 6 marbles in 4 bowls, if any number of them can be placed in each bowl?
(A) 6C4
(B) 6P4
(C) 4^6
(D) 6^4
(E) 6!
Rationale: Each marble has 4 options, so there are total of W=4*4*4*4*4*4=4^6 ways.
Answer: C.
The total number of ways of dividing n identical items among r persons, each one of whom, can receive 0,1,2 or more items is (n+r -1)C(r-1).
Answer: (C) 4^6
Question: A and B start a business jointly. A invests Rs.16000 for 8 months and B remains in the business for 4 months. Out of the total profit B claims 2/7th share. How much money is contributed by B?
(A) 27782
(B) 12800
(C) 28892
(D) 26702
(E) 27902
Rationale: 16*8: x*4 = 5:2
x = 12.8 => Rs.12800
Answer: B
Answer: (B) 12800
Question: A 15% stock yielding 12% is quoted at:
(A) s. 83.33
(B) s. 110
(C) s. 112
(D) s. 125
(E) s. 140
Rationale: Income of Rs 12 on investment of Rs 100
Income of Rs 15 on investment of ?
= (15*100)/12=125
ANSWER:D
Answer: (D) s. 125