mathewhe/aqua_rat huggingface dataset:
Question: Which of the following are/is prime?
I. 145
II. 147
III. 149
(A)  II only
(B)  III only
(C)  III
(D)  IIII
(E)  I, II,III
Rationale: 1) 143 = 13*11 so we know it is not prime quickly eliminate all options having 1 as a choice
which leaves us with 2 ) and 3) as possible answers
From here on we find 147 = 3* 49 so we eliminate 147 which leaves us with 149 as the only possible solution
C
Answer: (C)  III
Question: A football coach must choose 4 freshers from a team of 12players. How many different ways can the coach choose the freshers?
(A) 495
(B) 650
(C) 729
(D) 800
(E) 890
Rationale: Choose 4 starters from a team of 12 players. Order is not important.
\inline {\color{Black} 12C_{4}}= 495
A
Answer: (A) 495
Question: The average height of 35 boys in a class was calculated as 180cm. It has later found that the height of one of the boys in the class was wrongly written as 166 cm whereas his actual height was 106 cm. Find the actual average height of the boys in the class (Round off your answer to two decimal places?
(A) 187.89 cm
(B) 178.29 cm
(C) 123.98 cm
(D) 149.98 cm
(E) 146.89 cm
Rationale: Calculated average height of 35 boys = 180 cm.
Wrong total height of 35 boys = 180 * 35 cm. This was as a result of an actual height of 106 cm being wrongly written as 166 cm. Correct total height of 35 boys = 180 * 35 cm - 166 cm + 106 cm
= 180 * 35 cm - 166 cm + 106 cm/35 = 180 cm - 60 /35 cm
= 180 cm - 1.71 cm = 178.29 cm.
Answer: B
Answer: (B) 178.29 cm
Question: Rs.1170 is divided so that 4 times the first share, thrice the 2nd share and twice the third share amount to the same. What is the value of the third share?
(A) 177
(B) 169
(C) 199
(D) 540
(E) 123
Rationale: A+B+C = 1170
4A = 3B = 2C = x
A:B:C = 1/4:1/3:1/2 = 3:4:6
6/13 * 1170 = Rs.540
Answer: D
Answer: (D) 540
Question: Mahesh visited his cousin Akash during the summer vacation. In the mornings, they both would go for swimming. In the evenings, they would play tennis. They would engage in at most one activity per day, i.e. either they went swimming or played tennis each day. There were days when they took rest and stayed home all day long. There were 32 mornings when they did nothing, 18 evenings when they stayed at home, and a total of 28 days when they swam or played tennis. What duration of the summer vacation did Mahesh stay with Akash?
(A) 46 days
(B) 36 days
(C) 39 days
(D) 58 days
(E) None
Rationale: Explanation :
Let, the duration of Mahesh's vacation be 'n' days.
Acording to the question, he was free on 32 mornings and on 18 evenings and on total 28 days they either went for swimming or tennis together.
Thus, they were together on (n−32) mornings and (n−18) evenings.
=>(n−32)+(n−18)=28.
=>x=39.
Hence, the require number of days is 39.
Answer : C
Answer: (C) 39 days
Question: ACME’s manufacturing costs for sets of horseshoes include a $11,450 initial outlay, and $19.75 per set. They can sell the sets $51.50. If profit is revenue from sales minus manufacturing costs, and the company producessells 987 sets of horseshoes, what was their profit?
(A) $19,887.25
(B) $30,943.25
(C) $41,308.50
(D) $51,817.50
(E) $53,624.25
Rationale: its A
since options are not so close we can solve this by uniting calculation and guessing
total sales will be bit lower than 51500
from that initial outlay will get deducted 11500 so we left with 40000
variable cost say 20 X 1000 = 20000 will be deducted so finally we left with 20000
since we have considered the price greater than it actually is, the correct answer will certainly not cross the threshold of 20000.
Answer: (A) $19,887.25
Question: Ravi purchased a T.V. and a mobile phone for Rs. 30000 and Rs. 10000 respectively. He sold the refrigerator at a loss of 5 percent and the mobile phone at a profit of 10 percent. Overall he make a.
(A) loss of Rs. 500
(B) loss of Rs. 100
(C) profit of Rs. 100
(D) profit of Rs. 200
(E) None of these
Rationale: Total C.P. = 30000+10000 = 40000
S.P. of TV = 30000/100*95= 28500
S.P. of Mobile = 10000/100*110 = 11000
Total S.P. = 28500 + 11000 = 39500
Tota. C.P. - Total S.P. = 40000 - 39500 = 500
Answer : A
Answer: (A) loss of Rs. 500
Question: If the average (arithmetic mean) of a and b is 35 and the average of b and c is 80, what is the value of c − a?
(A) 25
(B) 50
(C) 90
(D) 140
(E) It cannot be determined from the information given.
Rationale: -(a + b = 70)
b + c=160
c-a=90
C. 90
Answer: (C) 90
Question: If P(A) = 2/15, P(B) = 4/15, and P(A âˆª B) = 12/15 Find P(B|A)
(A) 1/2
(B) 2/3
(C) 3/2
(D) 4/5
(E) 6
Rationale: P(B|A) = P(A âˆª B)/P(A)
P(B|A) = (12/15)/(2/15) = 6.
E
Answer: (E) 6
Question: Two pipes can fill the cistern in 10hr and 12 hr respectively, while the third empty it in 20hr. If all pipes are opened simultaneously, then the cistern will be filled in
(A) 7.5 hr
(B) 8 hr
(C) 8.5 hr
(D) 10 hr
(E) None of these
Rationale: Solution:
Work done by all the tanks working together in 1 hour.
1/10+1/12−1/20=2/15
Hence, tank will be filled in 15/2=7.5 hour
Option(A)
Answer: (A) 7.5 hr
Question: If a fair coin is flipped four times in a row, what is the probability that there will be at least one head and one tail?
(A) 3/4
(B) 7/8
(C) 15/16
(D) 31/32
(E) 63/64
Rationale: The number of possible outcomes is 2^4 = 16
There is one way to get no heads and one way to get no tails.
Thus there are 14 outcomes with at least one head and one tail.
P(at least one head and one tail) = 14/16 = 7/8
The answer is B.
Answer: (B) 7/8
Question: If two numbers x, a perfect square and y, a perfect cube are added results a two digit number, whose digits if reversed, difference is 27, Find x and y ?
(A) x=4,y=8
(B) x=4,y=9
(C) x=4,y=7
(D) x=4,y=9
(E) x=9,y=27
Rationale: 9+27=36
when reversed 63
63-36=27
x=9,y=27
ANSWER:E
Answer: (E) x=9,y=27
Question: A thief goes away with a SANTRO car at a speed of 40 kmph. The theft has been discovered after half an hour and the owner sets off in a bike at 50 kmph when will the owner over take the thief from the start?
(A) 2 hours
(B) 7 hours
(C) 9 hours
(D) 5 hours
(E) 3 hours
Rationale: |-----------20--------------------|
50 40
D = 20
RS = 50 – 40 = 10
T = 20/10 = 2 hours
Answer: A
Answer: (A) 2 hours
Question: If f(x) = 2x^2 + y, and f(2) = 100, what is the value of f(5)?
(A) 104
(B) 60
(C) 52
(D) 50
(E) 142
Rationale: f(x) = 2x^2 + y
f(2) = 100
=> 2*(2)^2 + y = 100
=> 8 + y = 100
=> y = 92
f(5)= 2*(5)^2 + 92
= 142
Answer E
Answer: (E) 142
Question: In a certain state, the ratio of registered Republicans to registered Democrats is 3 to 2, and every registered voter is either a Republican or a Democrat. If 70 percent of the Republicans and 25 percent of the Democrats are expected to vote for Candidate X, and everyone else is expected to vote for Candidate Y, by what percent is Candidate X expected to win the election?
(A) 2%
(B) 4%
(C) 8%
(D) 10%
(E) 15%
Rationale: Since we were expected to find a percentage figure - It thought that it might be easier to pick a 'smart number' to represent the total number of voters (republicans and democrats). Therefore, I picked 100 (as the total number of voters) and thus 60:40 represents the number ratio of Republicans:Democrats. If 70% of Republicans (which is (60*0.7) = 42) and 25% of Democrats (40*0.25 = 10) voted for candidate X, means that out of total of 100 voters; 52 (42 +10) voters voted for candidate X and 48 voted for candidate Y. Thus we can infer that candidate X is expected to win the election by 4 (52-48) votes. Therefore candidate X is expected to win the election by (4/100) votes which is equivalent to 4%.
I think the answer is B.
Answer: (B) 4%
Question: What Is The Next Number
12 13 15 17 111 113 117 119 123 129 ?
(A) 154
(B) 220
(C) 129
(D) 131
(E) 224
Rationale: 131.
These are the first 10 prime numbers (2, 3, 5...) prefixed with a 1
Answer : D
Answer: (D) 131
Question: A number when successively divided by 3,5 and 8 leaves remainders 1,4 and 7 respectively. Find the respective remainders T when the order of the divisors is reversed.
(A) 8,5,3
(B) 4,2,1
(C) T=3,2,1
(D) T=6,4,2
(E) None of above
Rationale: My approach would be
Three Divisors: 3, 5, 8
Three Remain: 1, 4, 7
Start from the bottom of the last column i.e. from the third remainder:
Go up diagonally and multiply by the second divisor: 5*7 = 35
Go down and add the second remainder: 35 + 4 = 39
Go up diagonally and multiply by the first divisor: 39* 3 = 117
Go down and add the first remainder: 117 + 1 = 118
Divide 118 by 8, 5, 3
118/8 gives quotient = 14 and remainder = 6
14/5 gives quotient = 2 and remainder = 4
2/3 gives quotient = 0 and remainder = 2
Ans is D i.e. 6,4,2
Answer: (D) T=6,4,2
Question: On a partly cloudy day, john decides to walk back from work. When it is sunny, he walks at a speed of s miles/hr (s is an integer) and when it gets cloudy, he increases his speed to (s + 1) miles/hr. If his average speed for the entire distance is 2.8 miles/hr, what fraction of the total distance did he cover while the sun was shining on him?
(A) 1/8
(B) 1/7
(C) 1/6
(D) 1/5
(E) 1/4
Rationale: If s is an integer and we know that the average speed is 2.8, s must be = 2. That meanss+1= 3. This implies that the ratio of time for s=2 is 1/4 of the total time. The formula for distance/rate is D=Rt...so the distance travelled when s=2 is 2t. The distance travelled for s+1=3 is 3*4t or 12t. Therefore, total distance covered while the sun was shining over him is 2/14 = 1/7. Answer: B
Answer: (B) 1/7
Question: The ratio of the volumes of two cubes is 729 : 1331. What is the ratio of their total surface areas?
(A) 81:121
(B) 81:126
(C) 81:221
(D) 86:121
(E) 81:131
Rationale: Ratio of the sides = ³√729 : ³√1331
= 9:11
Ratio of surface areas = 92 : 112
= 81:121
Answer: A
Answer: (A) 81:121
Question: In a certain state, gasoline stations compute the price per gallon p, in dollars, charged at the pump by adding a 5 percent sales tax to the dealer's price per gallon d, in dollars, and then adding a gasoline tax of $0.18 per gallon. Which of the following gives the dealer's price per gallon d in terms of the price per gallon p charged at the pump?
(A) d= (p-0.18)/1.05
(B) d = (p-0.05)/1.18
(C) d = p/1.23
(D) d = p-0.23
(E) d = p/1.05 - 0.18
Rationale: Let dealers price (d) be 1. so adding 5% to dealers price is d+ 5% of d. i.e. 1 + 5% of 1 which is1 + 0.05. then add 0.18 to the value.
Now 1.05 + 0.18. this is now 1.23. you have the gasoline stations price (p) as 1.23 dollars.
Now sub 1.23 in the options to know which option gave you d = 1. d must equal 1 because you earlier picked 1 as the value of d in the question.
PS: always remember to start from E upwards.
Answer : A
Answer: (A) d= (p-0.18)/1.05
Question: Seven people are planning to share equally the cost of a rental car. If one person withdraws from the arrangement and the others share equally the entire cost of the car, then the share of each of the remaining persons increased by:
(A) 1/6
(B) 2/7
(C) 3/7
(D) 4/6
(E) None of them
Rationale: Original share of 1 person = 1/7
New share of 1 person = 1/6
Increase = (1/6 - 1/7	= 1/42)
Therefore, Required fraction = (1/42)/(1/7)	= (1/42)x (7/1)	= 1/6
Answer is A.
Answer: (A) 1/6
Question: A couple decides to have 4 children. If they succeed in having 4 children and each child is equally likely to be a boy or a girl, what is the probability that they will have exactly 2 girls and 2 boys?
(A) 3/8
(B) 1/4
(C) 3/16
(D) 1/8
(E) 1/16
Rationale: no of ways of getting P(GGBB) is 4!/2!*2!;
Total no of ways is 2^n =2^4 =16;
6/16 = 3/8;
We can consider this question to a coin that is flipped for 4 times . what is the probability of getting exactly two heads .
P(all out comes) = 1/2 *1/2 *1/2 *1/2 =1/16;
P(favorable outcomes) = 4!/(2! * 2!) = 6/16 =3/8;
ANSWER:A
Answer: (A) 3/8
Question: At a small company, 58 percent of the employees are women, and 60 percent of the employees are married. If 2/3 of the men are single, what fraction of the women are married?
(A) 5/16
(B) 1/3
(C) 9/20
(D) 7/10
(E) 41/58
Rationale: Lets take total employees are 100.
Given that,Total Women= 58 and Total Married = 60.
Total Men = 100 - 58 = 42 and Single men = 2/3*42 = 28.
Married men = total men - single men = 47 - 28 = 19.
Married women= Total married - Married men = 60 - 19 = 41.
Fraction of women are married = Married women / Total Women = 41 / 58 = 5/7. ANS E
Answer: (E) 41/58
Question: here are 6 periods in each working day of a school. In how many ways can one organize 5 subjects such that each subject is allowed at least one period?
(A) 1235
(B) 4510
(C) 1203
(D) 1800
(E) 4512
Rationale: 5 subjects can be arranged in 6 periods in 6P5 ways.
Any of the 5 subjects can be organized in the remaining period (5C1 ways).
Two subjects are alike in each of the arrangement. So we need to divide by 2! to avoid overcounting.
Total number of arrangements
= 6P5× 5C1 /2!=1800
Ans: D
Answer: (D) 1800
Question: During a certain season, a team won 60 percent of its first 100 games and 50 percent of its remaining games. If the team won 70 percent of its games for the entire season, what was the total number of games that the team played?
(A) 80
(B) 70
(C) 56
(D) 50
(E) 105
Rationale: We are first given that a team won 60 percent of its first 100 games. This means the team won 0.6 x 100 = 60 games out of its first 100 games.
We are next given that the team won 50 percent of its remaining games. If we use variable T to represent the total number of games in the season, then we can say T – 100 equals the number of remaining games in the season. Thus we can say:
0.5(T – 100) = number of wins for remaining games
0.5T – 50 = number of wins for remaining games
Lastly, we are given that team won 70 percent of all games played in the season. That is, they won 0.7T games in the entire season. With this we can set up the equation:
Number of first 100 games won + Number of games won for remaining games = Total Number of games won in the entire season
60 + 0.5T – 50 = 0.7T
10 = 0.2T
100 = 2T
50 = T
Answer is D.
Answer: (D) 50
Question: Two trains A and B are 225 m and 150 m long and are moving at one another at 54 Km/hr and 36 Km/hr respectively. Arun is sitting on coach B1 of train A. Calculate the time taken by Arun to completely cross Train B.
(A) 10 s
(B) 15 s
(C) 4 s
(D) 8 s
(E) 12 s
Rationale: DETAILED SOLUTION
Speed of A = 54∗1000/60∗60 = 15 m/s
Speed of B = 36∗1000/60∗60 = 10 m/s
Relative speed = S1 + S2 = 15 + 10 m/s = 25 m/s
The length that needs to be crossed = length of train B = 150 m. Therefore time taken = 150/25 = 6s.
What is the time taken for trains to completely cross each other? The length that needs to be crossed = 225 + 150 = 375 m. Time taken = 375/25 = 15 s.
CORRECT ANSWER B.
Answer: (B) 15 s
Question: What is the normal price of an article sold at $72 after two successive discounts of 10% and 20%?
(A) $92
(B) $96
(C) $100
(D) $104
(E) $108
Rationale: 0.8*0.9*cost price = $72
cost price = $100
The answer is C.
Answer: (C) $100
Question: Of the 600 residents of Clermontville, 35% watch the television show Island Survival, 40% watch Lovelost Lawyers and 50% watch Medical Emergency. If all residents watch at least one of these three shows and 18% watch exactly 2 of these shows, then how many Clermontville residents V watch all of the shows?
(A)  150
(B)  108
(C)  42
(D)  21
(E)  -21
Rationale: OA is D.
100= A+B+C-AB-AC-BC+ABC, which is the same as the following formula
100= A+B+C+(-AB-AC-BC+ABC+ABC+ABC)-2ABC.
The term between parantheses value 18% so the equation to resolve is
100=35+40+50-18-2ABC
therefore the value of ABC is 3.5% of 600,V is 21. D is the correct answer
Answer: (D)  21
Question: Look at this series: 70, 71, 76, __, 81, 86, 70, 91, ... What number should fill the blank?
(A) 70
(B) 71
(C) 80
(D) 96
(E) None
Rationale: Explanation: In this series, 5 is added to the previous number; the number 70 is inserted as every third number.
Answer: Option A
Answer: (A) 70
Question: We bought a total of 90 books at the store. Math books cost $4 and history books cost $5. The total price was $390. How many math books did we buy?
(A) 57
(B) 60
(C) 63
(D) 66
(E) 69
Rationale: M + H = 90
H = 90 - M
4M + 5H = 390
4M + 5*(90 - M) = 390
M = 60
The answer is B.
Answer: (B) 60
Question: Thabo owns exactly 220 books, and each book is either paperback fiction, paperback nonfiction, or hardcover nonfiction. If he owns 20 more paperback nonfiction books than hardcover nonfiction books, and twice as many paperback fiction books as paperback nonfiction books, how many hardcover books nonfiction books does Thabo own?
(A) 10
(B) 20
(C) 30
(D) 40
(E) 50
Rationale: I think we can use double-matrix method and solve using only one variable.
Our goal is to find the number of hardcover nonfiction books. Let that number be x. We are given that all 140 books are either paperback fiction, paperback nonfiction, or hardcover nonfiction. This implies that number of hardcover fiction books is 0.
Double-matrix: P = paperback; H = hardcover; F = fiction; NF = nonfiction
P H Total
F 2x+40 0
NF x+20 x
Total 3x+60 x 220
3x + 60 + x = 220
x = 40
Answer (D.)
Answer: (D) 40
Question: In an examination, a student scores 4 marks for every correct answer and loses 1 mark for every wrong answer. If he attempts all 60 questions and secures 130 marks, the no of questions he attempts correctly is :
(A) 35
(B) 38
(C) 40
(D) 42
(E) 44
Rationale: Explanation:
Let the number of correct answers be X.
Number of incorrect answers = (60 – X).
4x – (60 – x) = 130
=> 5x = 190
=> x = 38
Answer: B
Answer: (B) 38
Question: The average (arithmetic mean) of eight numbers is 43.2. If the sum of half of these numbers is 154.4, what is the average of the other half?
(A) 44.2
(B) 47.8
(C) 50.5
(D) 53.6
(E) 56.9
Rationale: The average of this half is 154.4/4 = 38.6
This is 4.6 below the overall average, thus the average of the other half of the numbers must be 4.6 above the overall age, that is 43.2+4.6 = 47.8
The answer is B.
Answer: (B) 47.8
Question: Express a speed of 108 kmph in meters per second?
(A) 10 mps
(B) 05 mps
(C) 09 mps
(D) 30 mps
(E) 11 mps
Rationale: D
30 mps
108 * 5/18 = 30 mps
Answer: (D) 30 mps
Question: A brick measures 20 cm * 10 cm * 7.5 cm how many bricks will be required for a wall 24 m * 2 m * 0.75 m?
(A) 22377
(B) 27782
(C) 27891
(D) 24000
(E) 18771
Rationale: 24 * 2 * 0.75 = 20/100 * 10/100 * 7.5/100 * x
24 = 1/100 * x => x = 24000
Answer: D
Answer: (D) 24000
Question: If 1 is added to the denominator of fraction, the fraction becomes 1/2. If 1 is added to the numerator, the fraction becomes 1. The fraction is ?
(A) 4/7
(B) 5/9
(C) 2/3
(D) 10/11
(E) None
Rationale: Answer
Let the required fraction be x/y
Then, x/(y + 1) = 1/2
⇒ 2x - y = 1 ...(1)
(x + 1) / y = 1
⇒ x - y = -1 ...(2)
Solving Eq. (1) and (2)
We get x = 2, y = 3
∴ The fraction is 2/3
Correct Option: C
Answer: (C) 2/3
Question: The ratio of length to width of a rectangular showroom window is 3.3 to 2. If the width of the window is 8 feet, what is the approximate length of the display in feet?
(A) 7
(B) 11
(C) 13
(D) 16
(E) 26
Rationale: Explanation:
Letting L be the length of the window, the proportion for the ratio of the length to the width can be expressed in the following equation:
3.3/2=L/8
26.4=2L
13.2=L
Answer: Option C
Answer: (C) 13
Question: Suresh started a business, investing Rs.18000. After 3 months and 4 months respectively, Rohan and Sudhir joined him with capitals of 12000 and 9000. At the end of the year the total profit was Rs.3982. What is the difference between Rohan’s and Sudhir’s share in the profit?
(A) 350
(B) 360
(C) 362
(D) 375
(E) 380
Rationale: Suresh : Rohan : Sudhir
Ratio of their investments = 18000 × 12 : 12000 × 9 : 9000 × 8
= 6 : 3: 2
The difference between Rohan’s and Sudhir’s share = 1 share
:.i.e. = Rs. 3982 × 1/11 = Rs.362.
Option 'C'
Answer: (C) 362
Question: What is the greatest prime factor of 4^15 - 2^28?
(A) 2
(B) 3
(C) 5
(D) 7
(E) 11
Rationale: I'm happy to help with this.
We know 4 = 2^2, so 4^15 = (2^2)^15 = 2^(2*15) = 2^30
That takes advantage of a law of exponents that says (a^n)^m = a^(n*m)
So, 4^15 - 2^28 = 2^30 - 2^28 = 2^(28 + 2) - 2^28 = (2^28)*(2*2) - 2^28 = (2^2 - 1) *(2^28)
= (4 - 1)*(2^28) = 3*(2^28)
The prime factors of 63 are 3, so the largest prime factor is 7, answer choice D.
Here's a blog you may find helpful.
http://magoosh.com/gmat/2012/gmat-math-factors/
Does all that make sense? Please let me know if you have any further questions.
Mike
Wow. I am floored by how great of an explanation you provided. Posts like that make me really think that doing thousands of practice problems with good explanations beats out reading books on math every day of the week.
B
Answer: (B) 3
Question: A number of 44 marbles is to be divided and contain with boxes. If each box is to contain 3, 4, or 5 marbles, what is the largest possible number of boxes?
(A) 10
(B) 14
(C) 15
(D) 16
(E) 17
Rationale: To maximize # of boxes we should minimize marbles per box: 13*3+1*5=44 --> 13+1=14.
Answer B
Answer: (B) 14
Question: A batsman makes a score of 82 runs in the 17th inning and thus increases his averages by 3. What is his average after 17th inning?
(A) 25
(B) 31
(C) 27
(D) 29
(E) 34
Rationale: Let the average after 17 innings = x
Total runs scored in 17 innings = 17x
Average after 16 innings = (x-3)
Total runs scored in 16 innings = 16(x-3)
Total runs scored in 16 innings + 82 = Total runs scored in 17 innings
=> 16(x-3) + 82 = 17x
=> 16x - 48 + 82 = 17x
=> x = 34
Answer is E.
Answer: (E) 34
Question: Which of the following describes all values of x for which 1–x^2 >0?
(A)  x >= 1
(B)  x <= –1
(C)  0 <= x <= 1
(D)  x <= –1 or x >= 1
(E)  –1 < x < 1
Rationale: Which of the following describes all values of x for which 1–x^2 >= 0?
(A) x >= 1
Plugged in 2. 1–(2)^2 >= 0 -3>=0? NO. Wrong
(B) x <= –1
Plugged in -2. 1–(-2)^2 >= 0 -3>=0? NO. Wrong
(C) 0 <= x <= 1
Plugged in 0, 1, and 1/2. All of them work. But E is better because it describes all the values of x
(D) x <= –1 or x >= 1
A and B answer this. Wrong.
(E) –1 < x < 1
X is a positive or negative fraction.
x = -1/2 x = 1/2 x = 0
Plug all of them. They work.
Answer is E.
Answer: (E)  –1 < x < 1
Question: The sum of ages of 5 children born 1.5 years different each is 50 years. What is the age of the Elder child?
(A) 8
(B) 9
(C) 10
(D) 16
(E) 13
Rationale: Let the ages of children be x, (x + 1.5), (x + 3), (x + 4.5) and (x + 6) years.
Then, x + (x + 1.5) + (x + 3) + (x + 4.5) + (x + 6) = 50
5x = 35
x = 7.
x+6= 7+6= 13
Answer : E
Answer: (E) 13
Question: Two wheels are connected via a conveyor belt. The larger wheel has a 48cm diameter and the smaller wheel has a 32cm diameter. In order for the conveyor belt to work smoothly, each wheel must rotate the exact same number of centimetres per minute. If the larger wheel makes r revolution per minute, how many revolutions does the smaller wheel make per hour in terms of r?
(A) 90r
(B) 75r
(C) 48r
(D) 24r
(E) (64π)/3
Rationale: Interesting to note that the larger wheel has a diameter of 48 (8*6) while the smaller one has a diameter of 32 (8*4)...
If the large wheel has a diameter of 40 and the small wheel, 32, then their circumferences are 48pi and 32pi respectively. In order for them to move the conveyor belt at the same rate, the smaller wheel would need to rotate 1.5 times as fast as the larger wheel. Lets say the large wheel makes 10 revolutions per minute, the smaller wheel would need to make 10*1.5 = 15 revolutions per minute. If the large wheel makes 10 revolutions per minute it makes 600 per hour. Therefore, the smaller wheel would need to make 600*1.5 = 900 revolutions per hour.
If r = 10, then the answer choice must be b.
A. 90r
Answer: (A) 90r
Question: A and B can do a piece of work in 18 and 9 days respectively. A does the work for a few days and left, then B continued for 6 days. How many days did A and B work together?
(A) 1
(B) 2
(C) 3
(D) 4
(E) 5
Rationale: A and B work together for 2days.
A 1day work 1/18
B 1day work 1/9
Let A work x days.
Then equation form is
(x/18) + ((x+6)/9) = 1
From this equation x value is 2.
ANSWER:B
Answer: (B) 2