mathewhe/aqua_rat huggingface dataset:
Question: A company has two types of machines, type R and type S. Operating at a constant rate, a machine of type R does a certain job in 24 hrs and a machine of type S does the same job in 12 hours. If the company used the same number of each type of machine to do the job in 4 hours, how many machines of type R were used?
(A) 2
(B) 4
(C) 6
(D) 9
(E) 12
Rationale: Rate of machine R = 1/24
Rate of machine S = 1/12
Rate of R+S = 1/8
To finish the work in 4 hrs, the combined rate needs to be 1/4.
x * 1/8 = 1/4
x = 2
The answer is A.
Answer: (A) 2
Question: A 160 meter long train crosses a man standing on the platform in 16 sec. What is the speed of the train?
(A) 36 kmph
(B) 54 kmph
(C) 92 kmph
(D) 86 kmph
(E) 76 kmph
Rationale: S = 160/16 * 18/5 = 36 kmph
ANSWER:A
Answer: (A) 36 kmph
Question: There are 32 people in a party. If everyone is to shake hands with one another, how many hand shakes are possible?
(A) 496
(B) 367
(C) 361
(D) 297
(E) 261
Rationale: Explanation:
Total number of persons = n = 32
Shake hands involve only 2 persons = r = 2
Number of shake hands = nCr = 32C2
32C2 = (32 * 31) /(2 * 1) = 496
ANSWER:A
Answer: (A) 496
Question: 40% of the population of a village is 23040. The total population of the village is ?
(A) 57600
(B) 44000
(C) 34936
(D) 25640
(E) None
Rationale: Answer
∵ 40% of P = 23040
∴ P = (23040 x 100) / 40 = 57600
Correct Option: A
Answer: (A) 57600
Question: One side of a rectangular field is 15 m and one of its diagonals is 17 m. Find the area of the field.
(A) 111 m^2
(B) 120 m^2
(C) 130 m^2
(D) 124 m^2
(E) 131 m^2
Rationale: Other side = ((17) 2- (15)2)(1/2) = (289- 225)(1/2) = (64)(1/2) = 8 m.
Area = (15 x 8) m2 = 120 m2.
ANSWER B 120 m^2
Answer: (B) 120 m^2
Question: Three friends are buying a gift for a friend. Declan contributes 3 dollars more than 1/4 the cost of the gift, Ed contributes 1 dollar less than 1/3 the cost of the gift, and Frank contributes the remaining 22 dollars. What is the cost of the gift?
(A) 48
(B) 57.6
(C) 60
(D) 66
(E) 72
Rationale: Declan = D, Ed = E, Frank = F
t = total
D + E + F = t
(t/4 + 3) + (t/3 - 1) + 22 = t
t = 24 + (7t/12)
12t = 24(12) + 7t
5t = 24(12)
t = 57.6
The correct answer is B.
Answer: (B) 57.6
Question: The present ages of three persons in proportions 4 : 7 : 9. Eight years ago, the sum of their ages was 56. Find their present ages (in years).
(A) 8, 20, 28
(B) 16, 28, 36
(C) 16, 28, 35
(D) 16, 28, 34
(E) 16, 28, 33
Rationale: Let their present ages be 4x, 7x and 9x years respectively.
Then, (4x - 8) + (7x - 8) + (9x - 8) = 56
20x = 80
x = 4.
Their present ages are 4x = 16 years, 7x = 28 years and 9x = 36 years respectively.
Answer:B
Answer: (B) 16, 28, 36
Question: Find the value of 658217 x 99999 = m?
(A) 65842158943
(B) 65839570421
(C) 65821141683
(D) 66821785904
(E) 65821041783
Rationale: 658217 x 99999 = 658217 x (100000 - 1)
= 658217 x 100000 - 658217 x 1
= 65821700000 - 658217
= 65821041783
E
Answer: (E) 65821041783
Question: The largest 4 digit number exactly divisible by 88 is?
(A) 9930
(B) 9936
(C) 9944
(D) 9952
(E) 9960
Rationale: Largest 4-digit number = 9999
88) 9999 (113
88
----
119
88
----
319
264
---
55
---
Required number = (9999 - 55)
= 9944.
C)
Answer: (C) 9944
Question: A, B, C together started a business. A invested Rs.6000 for 5 months B invested Rs.3600 for 6 months and C Rs.7500 for 3 months. If they get a total profit of Rs.7410. Find the share of A?
(A) 3002
(B) 3000
(C) 3018
(D) 3019
(E) 3012
Rationale: 60*5:36*6:75*3
100: 72: 75
100/247 * 7410 = 3000
Answer: B
Answer: (B) 3000
Question: Four men and three women can do a job in 6 days. When five men and six women work on the same job, the work gets completed in 4 days. How long will a woman take to do the job, if she works alone on it?
(A) 54 days
(B) 53 days
(C) 52 days
(D) 44 days
(E) 50 days
Rationale: 24m+18w=20m+24w
=>1m=3/2w
3(1/3w)+3w=1/6=
>w=54 days
ANSWER:A
Answer: (A) 54 days
Question: Given 2 negative numbers, the lesser is 5 less than twice the greater number. What is the greater number if the product of both numbers is 228?
(A) -11
(B) -14
(C) -12
(D) -18
(E) -11
Rationale: Test the options. The options give you the greater number. Start from the middle option.
(C) - 12
Twice of -12 is -24 and 5 less is -19.
-19 * -12 = 228 (Correct)
Answer (C)
Answer: (C) -12
Question: The tax on a commodity is diminished by 10% and its consumption increases by 10%. Find the effects on revenue ?
(A) 1% decrease
(B) 2% increase
(C) 3% decrease
(D) 4% decrease
(E) none of these
Rationale: Since tax consumption = revenue .
Therefore, Net % change in revenue
= ( x + y + xy/100) %
= [ - 10 + 10 + ( - 10 x 10)/100]% or -1% .
Therefore, revenue decreased by 1%.
ANSWER:A
Answer: (A) 1% decrease
Question: A person purchased a TV set for Rs. 16000 and a DVD player for Rs. 6250. He sold both the items together for Rs. 33820. What percentage of profit did he make?
(A) 80%
(B) 49%
(C) 40%
(D) 52%
(E) 90%
Rationale: The total CP = Rs. 16000 + Rs. 6250
= Rs. 22250 and SP = Rs. 33820
Profit(%) = (33820 - 22250)/22250 * 100
= 52%
Answer:D
Answer: (D) 52%
Question: If 0.75 : x :: 5 : 8, then x is equal to:
(A) 1.34
(B) 1.43
(C) 1.2
(D) 1.45
(E) 1.56
Rationale: C
1.20
(x x 5) = (0.75 x 8) x = 6/5 = 1.20
Answer: (C) 1.2
Question: The average age of three boys is 40 years and their ages are in proportion 8:10:22. What is the age in years of the youngest boy?
(A) 8
(B) 9
(C) 7
(D) 6
(E) 5
Rationale: 8x + 10x + 22x = 40
x =1
8x = 8
Answer:A
Answer: (A) 8
Question: From 5 positive numbers and 5 negative numbers, how many groups of 4 numbers, yielding a positive product, can be formed?
(A) 720
(B) 110
(C) 30
(D) 960
(E) 255
Rationale: The number of ways to choose 4 positive numbers is 5C4 = 5.
The number of ways to choose 4 negative numbers is 5C4 = 5.
The number of ways to choose 2 positive and 2 negative is 5C2*5C2 = 10*10 = 100.
The total number of groups is 5+5+100 = 110.
The answer is B.
Answer: (B) 110
Question: X and Y are both integers. If X/Y = 59.60, then what is the sum of all the possible two digit remainders of X/Y?
(A) 560
(B) 315
(C) 672
(D) 900
(E) 1024
Rationale: Remainder = 0.60 --> 60/100 --> Can be written as (60/4) / (100/4) = 15/25
So remainders can be 15, 30, 45, 60, ..... 90.
We need the sum of only 2 digit remainders --> 15 + 30 + 45 + 60 + 75 + 90 = 315
Answer: B
Answer: (B) 315
Question: Which of the following numbers is the biggest => [-1/7 , -7/8 , -9/10 , -12/13 , -34/35]
(A) A)-1/7
(B) B)-7/8
(C) C)-9/10
(D) D)-12/13
(E) E)-34/35
Rationale: If we observe all the fractions just differ by one i.e denominator vs numerate.. in such case the biggest will be with large values... here all values are with -ve value...the least value is biggest. i.e. -1/7..
Hence A is correct answer...
Answer: (A) A)-1/7
Question: If a two-digit positive integer has its digits reversed, the resulting integer differs from the original by 54. By how much do the two digits differ?
(A) 3
(B) 4
(C) 5
(D) 6
(E) 7
Rationale: Let’s first label the original two-digit integer as N. We can then say that N = 10A + B, where A is the tens digit and B is the units digit of N.
If this is hard to see let’s try it with a sample number, say 24. We can say the following:
24 = (2 x 10) + 4
24 = 20 + 4
24 = 24
Getting back to the problem, we are given that if the integer N has its digits reversed the resulting integer differs from the original by 54. First let’s express the reversed number in a similar fashion to the way in which we expressed the original integer.
10B + A = reversed integer
Since we know the resulting integer differs from the original by 54 we can say:
10B + A – (10A + B) = 54
10B + A – 10A – B = 54
9B – 9A = 54
B – A = 6
Since B is the tens digit and A is the units digit, we can say that the digits differ by 6.
The answer is D.
Answer: (D) 6
Question: In how many ways can four members be selected from a group of eight members?
(A) 10C6
(B) 10C8
(C) 8C4
(D) 8C3
(E) 10C1
Rationale: Four members can be selected from eight members in
10C6
= 8C4 ways.
Answer: C
Answer: (C) 8C4
Question: There were 36,000 hardback copies of a certain novel sold before the paperback version was issued. From the time the first paperback copy was sold until the last copy of the novel was sold 9 times as many paperback copies as hardback copies were sold. If a total of 439,000 copies of the novel were sold in all, how many paperback copies were sold?
(A) 45,000
(B) 360,000
(C) 362,700
(D) 392,000
(E) 396,900
Rationale: Say x was the # of hardback copies sold from the time the first paperback copy was sold.
Then the total # of paperback copies sold was 9x;
Hence the total # of copies sold was (hardback)+(paperback)=(36+x)+(9x)=439 --> x=40.3.
So, the total # of paperback copies sold was 9x=9*40.3=362.7 or 362,700.
Answer: C.
Answer: (C) 362,700
Question: To furnish a room in a model home an interior decorator is to select 2 chairs and 2 tables from the collection of chairs and tables in a warehouse that are all different from each other. If there are 5 chairs in the warehouse and if 150 different combinations are possible, how many tables y are there in the warehouse?
(A) 6
(B) 8
(C) 10
(D) 15
(E) 30
Rationale: Total number of ways to choose 2 chairs from 5 y= 5C2=10
Total number of combination=150
That means we need get 15 combinations from the selection of tables....
Screening through the answers.... 6C2=15..... 15*10=150
Answer is 6... A
Answer: (A) 6
Question: What least number must be added to 1049, so that the sum is completely divisible by 25 ?
(A) 2
(B) 4
(C) 6
(D) 8
(E) 1
Rationale: If we divide 1049 by 25 remainder is 24
25-24 =1
Answer : E
Answer: (E) 1
Question: A is a working partner and B is a sleeping partner in the business. A puts in Rs.2000 and B Rs.3000, A receives 10% of the profit for managing the business the rest being divided in proportion of their capitals. Out of a total profit of Rs.9600, money received by A is?
(A) 1978
(B) 2707
(C) 7728
(D) 4416
(E) 7291
Rationale: 2:3 => 2:3
9600*10/100 = 960
9600 - 960 = 8640
8640*2/5 = 3456 + 960
= 4416
Answer: D
Answer: (D) 4416
Question: The radius of a wheel is 22.4 cm. What is the distance covered by the wheel in making 3000 resolutions?
(A) 2187 m
(B) 3704 m
(C) 4179 m
(D) 4224 m
(E) 4297 m
Rationale: In one resolution, the distance covered by the wheel is its own circumference. Distance covered in 3000 resolutions.
= 3000 * 2 * 22/7 * 22.4
= 422400 cm
= 4224 m
Answer:D
Answer: (D) 4224 m
Question: In a maths test, students were asked to find 5/16 of a certain number. One of the students by mistake found 5/6th of that number and his answer was 200 more than the correct answer. Find the number.
(A) 384
(B) 76
(C) 26
(D) 28
(E) 11
Rationale: Explanation:
Let the number be x.
5*x/6 = 5*x/16 + 200
25*x/48 = 200
x = 384
ANSWER: A
Answer: (A) 384
Question: Two men, 3 women working full time and 3 part times can complete a job in 20 days. Four men and 9 women working full time can complete the same job in 10 days. Find the ratio of the times taken by a woman (full-timer) and a part timer to complete the job.
(A) 1:2
(B) 2:1
(C) 1:3
(D) 3:1
(E) 1:4
Rationale: let X=single man one day work
y=single woman one day work
so single woman's part tym work will be y/2
so 1st equation is,
2x+3y+3(y/2)=1/20 (as they are completing in 20 days)
2nd equation wil be,
4x+9y=1/10 (as they are completing in 10 days)
solving both equations we will get,
y=1/90 (this is the single woman's full timer 1 day work)
so now taking the ratio of full-timer and a part timer we will get
90:45=2:1
ANSWER:B
Answer: (B) 2:1
Question: Griffin has a bag of marbles that contains 7 black marbles and 4 red marbles. If he removes 3 marbles at random without replacing any of the marbles, what is the probability that all 3 marbles selected will be black?
(A) 4/11
(B) 5/22
(C) 7/33
(D) 8/55
(E) 9/77
Rationale: P(3 black marbles) = 7/11*6/10*5/9 = 7/33
The answer is C.
Answer: (C) 7/33
Question: How many two-digit numbers are there whose remainder when divided by 12 is 1, and whose remainder when divided by 6 is 5?
(A) 3
(B) 4
(C) 5
(D) 6
(E) 7
Rationale: 2 digit numbers whose remainder when divided by 10 is 1 are
11 , 21 , 31 , 41 , 51 , 61 , 71 , 81 , 91
Out of above , numbers whose remainder when divided by 6 is 5 are
11 , 41 and 71
Answer C
Answer: (C) 5
Question: A and B invest money in the ratio 5:4 and they has loss of Rs.7200 at the end of year. what is the share of loss of B?
(A) Rs.3200
(B) Rs.3100
(C) Rs.3000
(D) Rs.2900
(E) None of the above
Rationale: et ratio of A and B be 5x & 4x
so net loss = 5x+4x= 7200
x=800
A=5x=5(800)=4000
B= 4x=4(800)=3200
so, B= 3200
ANSWER:A
Answer: (A) Rs.3200
Question: If 3d + 1 < 2d < 9 - d, which of the following must be true?
I. -1 < d < 3
II. d < -1
III. d < 3
(A)  II only
(B)  III only
(C)  I and II only
(D)  II and III only
(E)  I, II and III
Rationale: Just try plugging d in a number like 0 or 1, and you'll quickly find that the inequality doesn't hold.
So you can immediately cross out any answers with I or III, leaving just (A) II only.
Answer: (A)  II only
Question: A child must place 2 different toys in 4 different bins. If any of the toys can go in any of the bins, in how many ways can the child place the toys into the bins?
(A) 6^6
(B) 6^4
(C) 4^6
(D) 4^4
(E) 4^2
Rationale: there are 4 different bins and each of the toy can go to any of these bins..
so answer 4âˆ—4=4^2
ANSWER:E
Answer: (E) 4^2
Question: The market value of a 10.5% stock, in which an income of Rs. 756 is derived by investing Rs. 6500, brokerage being 1/4%, is:
(A) 90.03
(B) 114
(C) 114.75
(D) 124
(E) 124.75
Rationale: Face Value = Rs. 6500.
Dividend = 10.5%.
Annual Income = Rs. 756.
Brokerage per Rs. 100 = Rs. 0.25.
Dividend is always paid on the face value of a share.
Face Value * Dividend / (Market Value + Brokerage per Rs. 100) = Annual income.
= 6500 * 10.5 / 756 = Market Value of Rs. 100 stock + Brokerage per Rs. 100.
= Market Value of Rs. 100 stock + Brokerage per Rs. 100 = Rs. 90.27.
= Market Value of Rs. 100 stock = Rs. 90.27 - Re. 0.25.
= Market Value of Rs. 100 stock = Rs. 90.03.
answer : A
Answer: (A) 90.03
Question: In how many different ways can the letters of the word "CLAIM" be rearrangement?
(A) 120
(B) 130
(C) 140
(D) 145
(E) 150
Rationale: Option 'A'
The total number of arrangements is
5P5 = 5! = 120
Answer: (A) 120
Question: In one day, Juan sends Keith three times as many messages as he sends Laurence, and Laurence sends Missy 2 times as many messages as he receives from Juan. If Missy received 18 messages from Laurence, how many messages does Keith receive from Juan?
(A) 3
(B) 12
(C) 16
(D) 27
(E) 56
Rationale: Juan --> Laurence = x messages;
Juan --> Keith = 3x messages (Juan sends Keith three times as many messages as he sends Laurence);
Laurence --> Missy = 2x =18 (Laurence sends Missy 2 times as many messages as he receives from Juan).
2x =18 --> x = 9 --> 3x = 27.
Answer: D.
Answer: (D) 27
Question: A metallic sphere of radius 12 cm is melted and drawn into a wire, whose radius of cross section is 12 cm. What is the length of the wire?
(A) 6 cm
(B) 14 cm
(C) 16 cm
(D) 23 cm
(E) 29 cm
Rationale: Volume of the wire (in Cylindrical shape) is equal to the volume of the sphere.
π(12)^2 * h = (4/3)π (12)^3 => h
= 16 cm
Answer:C
Answer: (C) 16 cm
Question: In a six-sided polygon ZQRSTV ∠Z measures 48° less than the average (arithmetic mean) of the remaining five angles. What does ∠Z equal to, in degrees?
(A)  72
(B)  80
(C)  88
(D)  96
(E)  104
Rationale: The sum of interior angle in a polygon is (n-2)*180
so for a six sided figure, (6-2)*180 = 720
let the A.M of the other 5 angles be 'm'
--> m*5 + ∠Z = 720, we know ∠Z=m-48
--> m*5 + m - 48 = 720, solving we get m=128
hence ∠Z= 128-48 = 80
Ans B.
Answer: (B)  80
Question: 45 girls and 60 boys are present at a party. There are 17 girl-boy are in relationship among them. If a girl and a boy is selected at random, what is the probability that they will be a couple?
(A) 1/200
(B) 1/100
(C) 90/2900
(D) 17/2700
(E) 1/20
Rationale: In how many ways we can select a girl and a boy from 45 lady and 60 gentlemen? In 45*60 = 2,700 ways.
We have a total of 17 couples so, the probability of selecting a couple is 17/2,700 = 17/2700.
Ans- D
Answer: (D) 17/2700
Question: In the equation 2x â€“ cy = 18, c is a constant. If the value of y is 2 when x is 6, what is the value of x when y is 7 ?
(A) âˆ’9/2
(B) -4
(C) -3/2
(D) 4
(E) 9/2
Rationale: 2x - cy = 18
x=6, y=2;
12-2c=18
c=-3
2x-cy=18
when y=7, c=-3, x=
x=-3/2
ANSWER:C
Answer: (C) -3/2
Question: Janice has divided her department of 12 employees into 4 teams of 3 employees each to work on a new project. Four new employees are to be added to Janice’s department, but the number of teams is to remain the same. If every employee must be on exactly 1 team, then the total number of different teams into which Janice can divide the enlarged department is approximately how many times the number of different teams into which Janice could have divided the original department?
(A) 16
(B) 170
(C) 340
(D) 1820
(E) 43,680
Rationale: we assume the four teams must always be of equal size, then when we pick the four teams in the 12-person department, we can pick the first team in 12C3 ways, the second in 9C3 ways, the third in 6C3 ways, and the fourth in 3C3 ways. So if we assume we're picking teams in order, we can pick them in:
12C3 * 9C3 * 6C3 * 3C3 = 12! / (3!)^4
ways. The order of the 4 teams presumably doesn't matter, so we'd divide this by 4! if this were a counting problem, but we'll also divide by 4! when we count how many teams we can make in the larger department, and those two 4!'s will cancel in the end anyway, so I'll just omit that term.
When we have 16 employees, and divide them into four teams of four, we can similarly do that in
16C4 * 12C4 * 8C4 * 4C4 = 16! / (4!)^4
ways if the order of the teams matters. We need to divide this by the result above, so we get:
16!(4!)4/12!(3!)^4=(16!)(3!)4/(12!)(4!)^4=(16)(15)(14)(13)/4^4=(15)(14)(13)/4^2
which is roughly equal to 170.
ANS:B
Answer: (B) 170
Question: In how many different number of ways a Committee of 4person of can be selected from 4boys and 4girls such that at least 1 girl is included in the committe
(A) 70
(B) 69
(C) 67
(D) 68
(E) 65
Rationale: 1G 3B 2G 2B 3G 1B 4G
=(4C1*4C3)+(4C2*4C2)+(4C3*4C1)+4C4
= (4*4)+(6*6)+(4*4)+1
= 16+36+16+1=69
Total 4M 4W
8C4=70
4C4=1
At least one girl = total - with out girl
At least one girl =70-1=69
B)
Answer: (B) 69
Question: If r and k are integers whose product is 400, which of the following statements must be true?
(A) n + k > 0
(B) n is not equal to k.
(C) Either n or k is a multiple of 10.
(D) If n is even, then k is odd.
(E) If r is odd, then k is even.
Rationale: If r and k are integers whose product is 400, which of the following statements must be true?
A.n + k > 0n and k should have the same sign, but that means that they can also both be negative
B.n is not equal to k.20 x 20 = 400[i]
C.Either n or k is a multiple of 10. [i]25 x 16 = 400
D.If n is even, then k is odd.k can also be even since even x even will be even
E. If r is odd, then k is even.k must be even since odd x even = even
Answer: (E) If r is odd, then k is even.
Question: The area of a sector of a circle of radius 4 cm formed by an arc of length 3.5 cm is?
(A) 7
(B) 7.67
(C) 8.75
(D) 8.98
(E) 8.28
Rationale: (4 * 3.5)/2
= 7
Answer:A
Answer: (A) 7
Question: What is the smallest no. which must be added to 53403977 so as to obtain a sum which is divisible by 11?
(A) 5
(B) 4
(C) 0
(D) 1
(E) 2
Rationale: For divisibility by 11, the difference of sums of digits at even and odd places must be either zero or divisible by 11.
For 53403977 , Difference =(5+4+3+7) -(3+0+9+7)=19-19=0.
=> 53403977 is also divisible by 11
C
Answer: (C) 0
Question: A, B and C start swimming in a pool simultaneously from the same end. To complete 10 laps, A takes 10 minutes, B takes 8 minutes and C takes 9 minutes. What is the ratio of speeds A:B:C?
(A) 3:4:5
(B) 12:15:20
(C) 5:4:3
(D) 4:6:5
(E) 36:45:40
Rationale: The slowest one is A, then comes B and the fastest one is C. So, the the ratio of speeds A:B:C must be in ascending order. Eliminate options C, D, and E.
A's speed (distance)/(time) = 10/10 = 1 lap per minute = 36 laps in 36 minute;
B's speed (distance)/(time) = 10/8 = 5/4 lap per minute = 45 laps in 36 minutes;
C's speed (distance)/(time) = 10/9 = 10/9 lap per minute = 40 laps in 36 minutes/
Therefore, the the ratio of speeds A:B:C is 36:45:40.
Answer: E.
Answer: (E) 36:45:40
Question: Of 67 players on a cricket team, 37 are throwers. The rest of the team is divided so one third are left- handed and the rest are right handed. Assuming that all throwers are right handed, how many right- handed players are there total?
(A) 54
(B) 55
(C) 57
(D) 71
(E) 92
Rationale: Total = 67
Thrower = 37
Rest = 67 - 37 = 30
Left Handed = 30/3 = 10
Right handed = 20
If all Thrower are right handed then total right handed is 30 + 20 = 57
so C. 57 is the right answer
Answer: (C) 57
Question: Average of 17 results is 71. If the average of first eight results is 72 and average of last eight results is 69 Then find the ninth result?
(A) 79
(B) 81
(C) 77
(D) 72
(E) 85
Rationale: Option 'A'
Answer: (A) 79
Question: In a group of buffaloes and ducks, the number of legs are 24 more than twice the number of heads. What is the number of buffaloes in the group?
(A) 6
(B) 8
(C) 10
(D) 12
(E) 14
Rationale: Let the number of buffaloes be x and the number of ducks be y.
Then 4x+2y=2(x+y)+24
=>x=12
ANSWER D 12
Answer: (D) 12
Question: A and B started a business investing Rs. 50,000 and Rs 20,000 respectively. In what ratio the profit earned after 2 years be divided between A and B respectively?
(A) 5:2
(B) 9:2
(C) 18:20
(D) 1:4
(E) 18:4
Rationale: A: B = 50000 : 20000 = 5 : 2
ANSWER:A
Answer: (A) 5:2
Question: There are two numbers. If 40% of the first number is added to the second number, then the second number increases to its five-fourth. Find the ratio of the first number to the second number?
(A) 5/9
(B) 5/7
(C) 5/3
(D) 5/8
(E) 5/1
Rationale: Let the two numbers be x and y.
40/100 * x + y = 5/4y
=> 2/5 x = 1/4 y => x/y
= 5/8
Answer: D
Answer: (D) 5/8
Question: The average of 13 numbers is 60. Average of the first 7 of them is 57 and that of the last 7 is 61. Find the 8th number?
(A) 46
(B) 87
(C) 265
(D) 276
(E) 256
Rationale: Sum of all the 13 numbers = 13 * 60 = 780
Sum of the first 7 of them = 7 * 57 = 399
Sum of the last 7 of them = 7 * 61 = 427
So, the 8th number = 427 + 399 - 780
= 46.
Answer: A
Answer: (A) 46
Question: __2A
x__B
____
CC
In the multiplication problem above, A, B, and C represent distinct digits. If the sum of A and B is equal to 2, what is the value of C?
(A) 6
(B) 5
(C) 0
(D) 3
(E) 2
Rationale: If A+B=2
assuming A and B are positive then A*B<10 (they could be either 1)
therefore
A*B=C
2*B=C
A+B=2
Three simple equations - divide the 1st/2nd --> A=2 plug it the 3rd --> B=0 --> C=0 (ANSWER C)
Answer: (C) 0
Question: The positive value of x that satisfies the equation (1 + 2x)^5 = (1 + 3x)^6 is between
Bunuel, can you please explain this one?
(A) 0 and 0.5
(B) 0.5 and 1
(C) 1 and 1.5
(D) 1.5 and 2
(E) 2 and 2.5
Rationale: Trial and error would probably be the easiest way to solve this problem. When x is large enough positive number, then because of the exponents (5>4), LHS will be more than RHS (as you increase the positive value of x the distance between the values of LHS and RHS will increase).
Try x=1 --> LHS=3^5=81*3=243 and RHS=4^4=64*4=256, so (1 + 2x)^5 < (1 + 3x)^4. As you can see LHS is still slightly less than than RHS. So, the value of x for which (1 + 2x)^5 = (1 + 3x)^4 is slightly more than 1.
Answer: E.
Answer: (E) 2 and 2.5