mathewhe/aqua_rat huggingface dataset:
Question: In a certain mathematical activity, we have five cards with five different prime numbers on them. We will distribute these five cards among three envelope: all could go in any envelope, or they could be broken up in any way among the envelopes. Then in each envelop, we find the product of all the cards in that envelope: that is the “number” of the envelope. An envelope containing no cards has the number 1. We then put the three envelope numbers in order, from lowest to highest, and that is our set. How many different Q sets can be produced by this process?
(A)  41
(B)  89
(C)  125
(D)  243
(E)  512
Rationale: Case 1: 1 used envelope => 1 way
Case 2: 2 used envelopes
- 4-1-0: Choose 4 from 5 cards: 5 ways
- 3-2-0: Choose 3 from 5 cards: 10 ways
Case 3: All envelopes used
- 3-1-1: Choose 3 from 5 andno need to choose 1 from 2: 10 ways
- 2-2-1: Choose 2 from 5 and choose 2 from 3, but two groups are the same => (10X3):2 = 15
Total Q: 1+5+10+10+15=41 => Answer: A
Answer: (A)  41
Question: It takes Avery 3 hours to build a brick wall while Tom can do it in 2.5 hours. If the two start working together and after an hour Avery leaves, how much time will it take Tom to complete the wall on his own?
(A) 25 minutes.
(B) 30 minutes.
(C) 40 minutes.
(D) 55 minutes
(E) 1 hour and 20 minutes
Rationale: Avery's efficiency is 100/3 = 33%
tom's = 100/2.5= 40%
they worked together for 1 hour and finished 73% of the job
remaining = 27 %
tom will complete 40% in 60 minutes , 20% in 30 minutes and ,
7% in 60*7/40 minutes = 10.5 minutes
time taken by tom to finish the remaining on his own = 30+10.5 = 40.5 minutes (adjusting for the 0.333) ~ 40 minutes
ANSWER:C
Answer: (C) 40 minutes.
Question: A and B together have $1210. If 4/15 of A's amount is equal to 2/5 of B's amount, how much amount does B have?
(A) $310
(B) $395
(C) $484
(D) $512
(E) $542
Rationale: 4/15 A = 2/5 B
A = 2/5 * 15/4 B
A = 3/2 B
A/B = 3/2
A:B = 3:2
B's share = 1210*2/5 = $484
Answer is C
Answer: (C) $484
Question: The average age of husband, wife and their child 3 years ago was 27 years and that of wife and the child 5 years ago was 20 years. The present age of the husband is:
(A) 44 years
(B) 40 years
(C) 50 years
(D) 60 years
(E) None of these
Rationale: Lets assume fathers,mothers and child's age before 3 years is x,y,z respe.
therefore (x+y+z)/3=27
now x+y+z=27*3=81
and (y-2+z-2)/2=20
y+z=40
on calculating both equations x=37
hence present age x+3=40
ANSWER:B
Answer: (B) 40 years
Question: Tough and Tricky questions: Word Problems.
AC Car Company wants to manufacture a new car known as Model X, and it is trying to determine how many cars it needs to sell in order to make an annual profit of $30,500,000. The annual fixed costs for Model X total $50,200,000. In addition, each Model X car has an average cost of $5,000 per vehicle to manufacture. If the Company forecasts it will sell 20,000 Model X cars this year, at what price must the Company sell the car to achieve the desired annual profit?
(A) $4,035
(B) $4,036
(C) $9,035
(D) $16,140
(E) $36,140
Rationale: The AC company plans to make a profit of $30,500,000 and it needs to earn the fixed costs of $50,200,000, so it needs to earn $80,700,000 on top of the costs for the production of the 20,000 cars.
Therefore, price of each car needs to be the unit costs plus $80,700,000/20,000. After removing the 0's, we end with the unit costs plus $8,070/2, which is $5,000 plus $4,035. Therefore, Answer C is correct.
Answer: (C) $9,035
Question: A goods train leaves a station at a certain time and at a fixed speed. After 6 hours, an express train leaves the same station and moves in the same direction at a uniform speed of 90 kmph. This train catches up the goods train in 4 hours. Find the speed of the goods train.
(A) 36 kmph
(B) 40 kmph
(C) 30 kmph
(D) 42 kmph
(E) None of these
Rationale: Let the speed of the goods train be x kmph.
Distance covered by goods train in 10 hours
= Distance covered by express train in 4 hours.
∴ 10x = 4 × 90 or x = 36.
So, speed of goods train = 36 kmph.
Answer A
Answer: (A) 36 kmph
Question: What percentage of numbers from 1 to 70 have 1 or 9 in the unit's digit?
(A) 4%
(B) 13%
(C) 20%
(D) 23%
(E) 26%
Rationale: Clearly, the numbers which have 1 or 9 in the unit's digit, have squares that end in the digit 1. Such numbers from 1 to 70 are 1, 9, 11, 19, 21, 29, 31, 39, 41, 49, 51, 59, 61, 69.
Number of such number =14
Required % = (14/70)x100 % =20%
answer :C
Answer: (C) 20%
Question: Find the value of X: 2a^2-7a+10 = 14
(A) 7
(B) 5
(C) 6
(D) 4
(E) 2
Rationale: Using the elimination method substitute options for x and find the correct option.
Answer: D
Answer: (D) 4
Question: If one type of tobacco costs Re.1/- per kg and other type costs Rs. 5/- per kg. What quantity of first type and second type are mixed so that 100 kg of mixture costs Rs. 100/-?
(A) 50 kg
(B) 100 kg
(C) 150 kg
(D) 200 kg
(E) 250 kg
Rationale: 100 kg of first type.
ANSWER:B
Answer: (B) 100 kg
Question: The moon revolves around the earth at a speed of approximately 0.2 kilometers per second. This approximate speed is how many kilometers per hour?
(A) 60
(B) 720
(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 3600seconds.
so one hour, speed= 0.2*3600=720kilometers per hour.
Option B is correct
Answer: (B) 720
Question: Find the odd man out. 1, 16, 81, 255, 625, 1296
(A) 255
(B) 1296
(C) 81
(D) 1
(E) 625
Rationale: Explanation :
The pattern is 1^4, 2^4, 3^4, 4^4, 5^4, 6^4
Hence, in place of 255, the right digit is 44 = 256
Answer : Option A
Answer: (A) 255
Question: Two trains for Delhi leave Jaipur at 8:30 am and 9:00 am and travel at 60 km/hr and 75 km/hr respectively. How many km from Jaipur will the two trains meet?
(A) 150 km
(B) 127 km
(C) 1717 km
(D) 166 km
(E) 177 km
Rationale: ANSWER: A
Answer: (A) 150 km
Question: How many 4 digit numbers are there, if it is known that the first digit is even, the second is odd, the third is prime, the fourth (units digit) is divisible by 3, and the digit 2 can be used only once?
(A) 20
(B) 150
(C) 225
(D) 300
(E) 320
Rationale: 4 options for the first digit: 2, 4, 6, 8;
5 options for the second digit: 1, 3, 5, 7, 9;
4 options for the third digit: 2, 3, 5, 7;
4 options for the fourth digit: 0, 3, 6, 9.
Four digit # possible without the restriction (about the digit 2): 4*5*4*4=320
Numbers with two 2-s, 2X2X 1*5*1*4=20.
Thus there are 320-20=300 such numbers.
Answer: D.
Answer: (D) 300
Question: There are two positive numbers in the ratio 3:11. If the larger number exceeds the smaller by 32, then what is the smaller number?
(A) 8
(B) 11
(C) 12
(D) 15
(E) 17
Rationale: Let the two positive numbers be 3x and 11x respectively.
11x - 3x = 32
8x = 32 => x = 4
Thus, the smaller number = 3x = 12.
Answer: C
Answer: (C) 12
Question: If two dice are thrown together, the probability of getting an even prime number on the dice is
(A) 1/36
(B) 1/18
(C) 1/13
(D) 1/9
(E) 5/36
Rationale: The number of exhaustive outcomes is 36.
Let E be the event of getting an even number prime number on the dice.
P(E) = 1/36
A)
Answer: (A) 1/36
Question: A trader mixes 80 kg of tea at 15 per kg with 20 kg of tea at cost price of 20 per kg. In order to earn a profit of 30%, what should be the sale price of the mixed tea?
(A) 23.75
(B) 22
(C) 20.8
(D) 19.2
(E) None of these
Rationale: C.P. of mixture = 80×15+20×20 /80+20=16
∴ S.P. = (100+30)/100×16=20.8
Answer C
Answer: (C) 20.8
Question: A train crosses a platform of 120 m in 15 sec, same train crosses another platform of length 180 m in 18 sec. then find the length of the train?
(A) 298
(B) 180
(C) 289
(D) 177
(E) 123
Rationale: Length of the train be ‘X’
X + 120/15 = X + 180/18
6X + 720 = 5X + 900
X = 180m
Answer: B
Answer: (B) 180
Question: In how many ways 4 boys and 3 girls can be seated in a row so that they are alternate.
(A) 144
(B) 288
(C) 12
(D) 256
(E) None
Rationale: Solution: Let the Arrangement be,
B G B G B G B
4 boys can be seated in 4! Ways.
Girl can be seated in 3! Ways.
Required number of ways,
= 4!*3! = 144.
Answer: Option A
Answer: (A) 144
Question: What is the remainder when 43^89 is divided by 5?
(A) 0
(B) 1
(C) 2
(D) 3
(E) 4
Rationale: The units digit of the exponents of 3 cycle in a group of 4: {3, 9, 7, 1}
89 has the form 4k+1 so the units digit of 43^89 is 3.
The remainder when dividing by 5 is 3.
The answer is D.
Answer: (D) 3
Question: The average (arithmetic mean) of the even integers from 0 to 40 inclusive is how much greater than the average (arithmetic mean) of the even integers from 0 to 20 inclusive?
(A) 5
(B) 8
(C) 10
(D) 15
(E) 20
Rationale: The sum of even numbers from 0 to N is 2 + 4 +...+ N
= 2(1 + 2 + ...+ N/2)
= 2(N/2)(N/2+1)/2 = (N/2)(N/2+1)
The average is (N/2)(N/2+1)/(N/2+1) = N/2
The average of the even numbers from 0 to 40 is 40/2 = 20
The average of the even numbers from 0 to 20 is 20/2 = 10
The answer is C.
Answer: (C) 10
Question: The HCF and LCM of two numbers m and n are respectively 5 and 210. If m + n = 75, then 1/m + 1/n is equal to
(A) 1/14
(B) 3/35
(C) 5/37
(D) 2/35
(E) None
Rationale: Answer
We have, m x n = 5 x 210 = 1050
âˆ´ 1/m + 1/n = (m + n)/mn = 75/1050 = 1/14
Correct Option: A
Answer: (A) 1/14
Question: If x^2 − 2x − 15 = (x + r)( x + s) for all values of x, and if r and s are constants, then which of the following is a possible value of (r + s)^2?
(A) 8
(B) 2
(C) − 2
(D) − 3
(E) 4
Rationale: We know that given ax^2 + bx + c = 0, Sum of the roots = -b/a and product of the roots = c/a.
The roots here are -r and -s.
-r - s = -(-2)/1 = r + s = -2
(-r)*(-s) = -15/1 = rs
So one of r and s is -5 and the other is 3. So (r + s)^2 could be 4.
Answer (E)
Answer: (E) 4
Question: There are 3 income earning members in a family namely X,Y&Z. .Total monthly income of the family is $12200.Ratio of their income 12:15:16.Find out the income of Z?
(A) $5681.45
(B) $4539.54
(C) $3556.25
(D) $6528.98
(E) $2926.38
Rationale: Ratio of their income 12+15+16=43. Income of Z = 16/43 *12200=$4539.54 Answer: B
Answer: (B) $4539.54
Question: Out of 20 students studying in a class, 7 are from Maharashtra, 5 are from Karnataka and 3 are from Goa. Four students are to be selected at random. What are the chances that at least one is from Karnataka?
(A) 12â„13
(B) 11â„13
(C) 10â„15
(D) 1â„15
(E) 51/71
Rationale: Total possible ways of selecting 4 students out of 20 students =20C4 =4845
The no. of ways of selecting 4 students in which no student belongs to Karnataka = 15C4=1365
âˆ´ Hence no. of ways of selecting at least one student from Karnataka = 20C4 â€“ 15C4 =3480
âˆ´ Probability = 3480â„4845 = 51/71
Answer E
Answer: (E) 51/71
Question: A corporation that had $2 billion in profits for the year paid out $100 million in employee benefits. Approximately what percent of the profits were the employee benefits? (Note: 1 billion = 10^9)
(A) 50%
(B) 20%
(C) 5%
(D) 2%
(E) 0.2%
Rationale: required answer = [employee benefit/profit] *100
=[(100 million)/(2 billion)]*100
=[(100*10^6)/(2*10^9)]*100
=(50/1000)*100
=5%
So answer is (C)
Answer: (C) 5%
Question: The difference between the compound interest compounded annually and simple interest for 2 years at 20% per annum is Rs.72. Find the principal?
(A) 2277
(B) 2667
(C) 3600
(D) 2766
(E) 1800
Rationale: P = 72(100/5)^2 => P = 1800
Answer: E
Answer: (E) 1800
Question: How many odd numbers between 10 and 1,300 are the squares of integers?
(A) 12
(B) 13
(C) 14
(D) 15
(E) 17
Rationale: The square of an odd number is an odd number:
10 < odd < 1,000
10 < odd^2 < 1,000
3.something < odd < 31.something (by taking the square root).
So, that odd number could be any odd number from 5 to 31, inclusive: 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25, 27, 29, and 31.
17 numbers.
Answer: E.
Answer: (E) 17
Question: What is the present worth of Rs. 132 due in 2 years at 5% simple interest per annum?
(A) 288
(B) 266
(C) 120
(D) 277
(E) 6123
Rationale: Let the present worth be Rs. x. Then,
S.I. = (132 - x)
(x * 5 * 2) / 100 = (132 - x)
10x = 13200 - 100x
110x = 13200 => x = 120.
Answer: C
Answer: (C) 120
Question: In an examination, 35% of the students passed and 455 failed. How many students appeared for the examiantion?
(A) 490
(B) 620
(C) 700
(D) 845
(E) None
Rationale: Solution
Let the number of students appeared be x.
Then, 65% of x = 455
‹=›65 / 100 x = 455
‹=› x= [455 x 100 / 65]
= 700.
Answer C
Answer: (C) 700
Question: The average age of a class of 32 students is 16 yrs. if the teacher’s age is also included, the average increases by one year. Find the age of the teacher
(A) 48
(B) 49
(C) 47
(D) 44
(E) 40
Rationale: Explanation:
Total age of students is 32X16 = 512 Years
Total age inclusive of teacher = 33X (16+1) = 561
So, Teacher’s age is 561-512 = 49 Yrs
There is a shortcut for these type of problems
Teacher’s age is 16+(33X1) = 49 Years
Answer: B
Answer: (B) 49
Question: A polling company surveyed a certain country, and it found that 35% of that country’s registered voters had an unfavorable impression of both of that state’s major political parties and that 20% had a favorable impression only of Party R. If one registered voter has a favorable impression of both parties for every two registered voters who have a favorable impression only of Party B, then what percentage of the country’s registered voters have a favorable impression of both parties (assuming that respondents to the poll were given a choice between favorable and unfavorable impressions only)?
(A) 15
(B) 20
(C) 30
(D) 35
(E) 45
Rationale: S=100
not( R and B ) =35
only R=20
(R and B)/B=1/2
let ( R and B ) =x
only B =2x
so now, 20+35+x+2x=100
x= 15
A ans
Answer: (A) 15
Question: The average of five numbers id 27. If one number is excluded, the average becomes 25. The excluded number is
(A) 25
(B) 27
(C) 30
(D) 35
(E) None
Rationale: Solution
Excluded number	= (27 x 5 ) - ( 25 x 4)
= 135 - 100
= 35.
Answer D
Answer: (D) 35
Question: If Daniel is 18 years old in December and is 10 years younger than his sister, which of the following could be true?
I. Daniel's Sister will be 28 years in December.
II. When Daniel is 20 years, his sister will be 25 years.
III. Daniel is older than his sister.
(A)  I only
(B)  I and II only
(C)  I and III only
(D)  II and III only
(E)  I, II and III
Rationale: Let’s check each statement.
Statement I: Daniel's Sister will be 28 years in December. There is 10 years difference in their ages so the sister's age will be 20 + 8 = 28, in which case Statement I is TRUE.
Statement II: When Daniel is 20 years, his sister will be 25 years. There is 10 years difference in their ages so the sister's age will be 20 + 8 = 28, in which case Statement II can NEVER be TRUE.
Statement III: Daniel is older than his sister. When Daniel is 10 the sister will be 28, in which case Statement III can NEVER BE TRUE
Only Statement I is TRUE
So, the Correct answer is A
Answer: (A)  I only
Question: Tom opened a shop investing Rs.30000. Jose joined him 2 months later, investing Rs.45000. They earned a profit of Rs.54000 after completion of one year. What will be Jose's share of profit?
(A) 10000
(B) 14000
(C) 15000
(D) 16000
(E) 30000
Rationale: SoL = ~s- So Anju’s share = [5/9] x 54000 = 30000
E
Answer: (E) 30000
Question: Let A, B, and C be three points on circle O such that AC is a diameter of O. Extend line AC
to a point D such that DB is tangent to O at B, and suppose that \ADB = 20o. Compute
\ACB.
(A) 32o
(B) 47o
(C) 55o
(D) 68o
(E) 71o
Rationale: Since we did not specify in which direction to extend the line AC, we also accepted
35 as an acceptable answer.
Let O be the center of the circle. Through angle chasing, we can determine that
\BOD = 90o - \ADB = 70o
\ACB =
180o - \BOD/2= 55o
correct answer C
Answer: (C) 55o
Question: The average (arithmetic mean) of 20, 40, and 60 is 5 more than the average of 10, 80, and what number?
(A) 35
(B) 30
(C) 25
(D) 20
(E) 15
Rationale: a1 = 120/3 = 40
a2 = a1 -5 = 35
sum of second list = 35*3 = 105
therefore the number = 105 -90 = 15
E
Answer: (E) 15
Question: Amanda goes to the toy store to buy 1 ball and 3 different board games. If the toy store is stocked with 3 types of balls and 6 types of board games, how many different selections T of the 4 items can Amanda make?
(A) 9
(B) 12
(C) 14
(D) 15
(E) 60
Rationale: Amanda goes to the toy store to buy 1 ball and 3 different board games. If the toy store is stocked with 3 types of balls and 6 types of board games, how many different selections of the 4 items can Amanda make?
3! / 1!2! * 6! / 3!3!
T=3*20=60
E. 60
Answer: (E) 60
Question: Let the function E(n) represent the product of the first n prime numbers, where n > 0. If x = E(n) + 1, which of the following must be true?
(i) x is always odd
(ii) x is always prime
(iii) x is never the square of an integer
(A) ii only
(B) iii only
(C) i and ii only
(D) i and iii only
(E) ii and iii only
Rationale: E(n) is always even, because the first prime is 2 and no matter what n is, 2 always will be a divisor of E(n). Thus, E(n) + 1 = even + 1 = odd. So, (i) is always true.
Now, use logic:
If (ii) is true (so if x is always prime), then (iii) must automatically be true: no prime is the square of an integer. So, the correct answer must be i only; i, ii, and iii only; or i and iii only. since onlyi and iii onlyis among the options, then it must be true.
Or, since (i) is always true, then from options the answer must be either C or D. C cannot be correct because if (ii) is true, then so must be (iii). Thus only D remains.
Answer: D.
Answer: (D) i and iii only
Question: 35 liters of a mixture is created by mixing Liquid P and Liquid Q in the ratio 4:3. How many liters of Liquid Q must be added to make the ratio 5:7?
(A) 10
(B) 11
(C) 12
(D) 13
(E) 14
Rationale: Let x be the amount of liquid Q to be added.
(3/7)*35 + x = (7/12)*(35+x)
1260 + 84x = 1715 + 49x
35x = 455
x = 13
The answer is D.
Answer: (D) 13
Question: 12,31,?,129,220,347,516
(A) 129
(B) 220
(C) 347
(D) 68
(E) 520
Rationale: 2*2*2 + 4 = 12
3*3*3 +4 = 31
5*5*5 + 4 = 129
6*6*6 + 4 = 220
7 *7 *7 + 4 = 347
8 *8 *8 + 4 = 516.
4*4*4 + 4 = 68
ANSWER : D
Answer: (D) 68
Question: If the sum of two numbers is 24 and the sum of their squares is 404, then the product of the numbers is
(A) 40
(B) 44
(C) 80
(D) 86
(E) 90
Rationale: Sol.
Let the numbers be x and y.
Then, (x+y) = 24 and x2 + y2 = 404.
Now, 2xy = (x+y)2 - (x2 + y2)
= (24)2 - 404 = 576- 404 = 172
xy = 86.
Answer D
Answer: (D) 86
Question: If a=2 and b=3,then 2^(a+1)+2^(b+1)=?
(A) 2^b(3)
(B) 2^(a + b)
(C) 2^a
(D) 2a^(b + 1)
(E) 3(2^b)
Rationale: If a=2 and b=3 then 2^3+2^4
=2^3(1+2^1)=2^3(3)
=2^b(3){b=3}
Answer is option A
Answer: (A) 2^b(3)
Question: A student has to obtain 33% of the total marks to pass. He got 92 marks and failed by 40 marks. The maximum marks are?
(A) 400
(B) 300
(C) 500
(D) 610
(E) 175
Rationale: Let the maximum marks be x
Then, 33% of x = 92+40
33x/100 = 132
x = 400
Answer is A
Answer: (A) 400
Question: The line y = 5x/3 + b goes through the point (7, –1). What is the value of b?
(A) 3
(B) –5/3
(C) –7/5
(D) 16/3
(E) –38/3
Rationale: “finding the equation” procedure. Plug (x, y) = (7, –1) into this equation:
{-1} = {{5(7)}/3} + b = {35/3} + b
b = {-35/3} - 1 = {-35/3} - {3/3} = -{38/3}
Answer = E
Answer: (E) –38/3
Question: Which number is the odd one out ?
9654 4832 5945 7642 7963 8216 3648
(A) 3648
(B) 9654
(C) 5945
(D) 7963
(E) 8216
Rationale: The product of first two digits in a number equals the last two digits, except in 3648. Hence, it is the odd one.
The answer is 3648.
ANSWER:A
Answer: (A) 3648
Question: A single discount equivalent to the discount series of 20%, 10% and 5% is?
(A) 31.6
(B) 31.9
(C) 31.6
(D) 31.4
(E) 31.1
Rationale: 100*(80/100)*(90/100)*(95/100) = 68.4
100 - 68.4 = 31.6
Answer: A
Answer: (A) 31.6
Question: What day of the week does May 28 2006 fall on
(A) Saturday
(B) Monday
(C) Sunday
(D) Thursday
(E) Wednesday
Rationale: 28th May 2006 = (2005 years + period from 1-Jan-2006 to 28-May-2006)
We know that number of odd days in 400 years = 0
Hence the number of odd days in 2000 years = 0 (Since 2000 is a perfect multiple of 400)
Number of odd days in the period 2001-2005
= 4 normal years + 1 leap year
= 4 x 1 + 1 x 2 = 6
Days from 1-Jan-2006 to 28-May-2006 = 31 (Jan) + 28 (Feb) + 31 (Mar) + 30 (Apr) + 28(may)
= 148
148 days = 21 weeks + 1 day = 1 odd day
Total number of odd days = (0 + 6 + 1) = 7 odd days = 0 odd day
0 odd day = Sunday
Hence May 28 2006 is Sunday.
Answer is C
Answer: (C) Sunday
Question: Two alloys A and B are composed of two basic elements. The ratios of the compositions of the two basic elements in the two alloys are 5:3 and 1:2, respectively. A new alloy X is formed by mixing the two alloys A and B in the ratio 4:3. What is the ratio of the composition of the two basic elements in alloy X?
(A) 1:1
(B) 2:3
(C) 5:2
(D) 4:3
(E) None of these
Rationale: Explanation :
Let,the actual amount of A and B be 4x and 3x respectively.
Amount of 1st basic element in the new alloy T is (5/8)*4x + (1/3)*3x = (7x)/2.
Similarly, the amount of 2nd basic element in the new alloy T is (3/8)*4x + (2/3)*3x= (7x)/2.
So, the ratio of 1st basic element to 2nd basic element is [(7x)/2 ] / [ 7x/2] = 1/1 = 1:1.
Answer : A
Answer: (A) 1:1
Question: After working for 8 days, Anil finds that only 1⁄3 of the work has been done. He employs Rakesh who is 60 % efficient as Anil. How many more days will Anil take to complete the job?
(A) 15 days
(B) 12 days
(C) 10 days
(D) 8 days
(E) None of these
Rationale: In 8 days, Anil does = 1⁄3 rd work
∴ in 1 day, he does = 1⁄24 th work.
∴ Rakesh’s one day’s work
= 60% of 1⁄24 = 1⁄40 th work.
Remaining work = 1 - 1⁄3 = 2⁄3
(Anil and Rakesh)’s one day’s work
= 1⁄24 + 1⁄40 = 1⁄15 th work.
Now, 1⁄15 th work is done by them in one day.
∴ 2⁄3 rd work is done by them in 15 × 2⁄3 = 10 days
Answer C
Answer: (C) 10 days
Question: If Rs.420 amount to Rs.540 in 4 years, what will it amount to in 6 years at the same rate % per annum?
(A) s.575
(B) s.595
(C) s.590
(D) s.600
(E) s.585
Rationale: 80 = (420*4*R)/100
R = 7.14%
I = (420*6*7.14)/100 = 180
420 + 180 = 600
ANSWER:D
Answer: (D) s.600
Question: A and B can finish a work together in 12 days, and B and C together in 16 days. If A alone works for 5 days and then B alone continues for 7 days, then remaining work is done by C in 13 days. In how many days can C alone finish the complete work?
(A) 22 days
(B) 21 days
(C) 25 days
(D) 24 days
(E) 23 days
Rationale: Here LCM of 12 and 16 is taken as total work. ( becomes easy to solve)
Assume total work =48 units
Then workdone by (A+B) in one day = 48/12 = 4 units
Similarly, by (B+C) in one day = 48/16 = 3 units
Now according to question,
A works 5 days , B for 7 days and C for 13 days to complete total work
So, 5A + 7B + 13C = 48 units
5(A+B) + 2(B+C) + 11C = 48 units
5*4 + 2*3 +11C =48 units
11C = 22 units
C = 2 units ( C does 2 units of work daily)
Therefore, 48/2 = 24 days
C requires 24 days to complete the work alone.
Answer D
Answer: (D) 24 days
Question: If 20 typists can type 42 letters in 20 minutes, then how many letters will 30 typists working at the same rate complete in 1 hour?
(A) 189
(B) 72
(C) 144
(D) 216
(E) 400
Rationale: 20 typists can type 42 letters, so 30 typists can type = 42*30/20
42*30/20 letters can be typed in 20 mins. In 60 mins typist can type= 42*30*60/20*20= 189
A is the answer
Answer: (A) 189
Question: A bag contains equal number of Rs.5, Rs.2 and Re.1 coins. If the total amount in the bag is Rs.1152, find the number of coins of each kind?
(A) 337
(B) 268
(C) 144
(D) 772
(E) 997
Rationale: Let the number of coins of each kind be x.
=> 5x + 2x + 1x = 1152
=> 8x = 1152 => x = 144
Answer:C
Answer: (C) 144
Question: What is the rate percent when the simple interest on Rs.800 amount to Rs.160 in 4 Years?
(A) 5%
(B) 8%
(C) 3%
(D) 9%
(E) 1%
Rationale: 160 = (180*4*R)/100
R = 5%
Answer: A
Answer: (A) 5%
Question: When positive integer X is divided by positive integer Y, the remainder is 9. If X/Y = 96.12, what is the value of Y?
(A) 96
(B) 75
(C) 48
(D) 25
(E) 12
Rationale: x = qy+9 , where q is the quotient
x/y = (q y+9) /y = q + (9/y) = 96.12 = 96 + 0.12
=> q =96
9/y = 0.12 = > y = 75
Answer is B.
Answer: (B) 75