mathewhe/aqua_rat huggingface dataset:
Question: If x is the product of three consecutive positive integers, which of the following must be true?
I. x is an integer multiple of 4.
II. x is an integer multiple of 3
III. x is an integer multiple of 6
(A) a) I only
(B) b) II only
(C) c) I and II only
(D) d) I and III only
(E) e)II and III only
Rationale: The answer should be D i.e. X will be an integer and multiple of 3 and 6.
Let us take example n, n+1, n+2 as 3 three consecutive positive integers.
In a sequence of consecutive integers a number is multiple of 3 after every interval of 2 numbers i.e 3,4,5,6 Or 8,9,10,11,12
Hence in a product of 3 consecutive integers, the product is always divisible by 3.
Now, in a consecutive sequence every alternate is an even number, and when an even number is multiplied by 3 we will have 6 as one of the multiple also.
Now for a number to be a multiple of 4 we need at least 2 2's. this is only possible if the first number of three consecutive positive integers is an even number so that 3 is also even and we have 2 2's. But incase the sequence starts with odd we will have one 2 hence, the divisibility by 4 depends on the first number to be even
Answer E
Answer: (E) e)II and III only
Question: In a pond 100 fish were caught and examined for levels of mercury. Of this sample, 25 fish were found to have unhealthy levels of mercury. If we use this sample as an estimate, and we know the population of the pond to be 5,000 fish, what is the approximate number of fish in the pond that have healthy levels of mercury?
(A) 2,150
(B) 750
(C) 1,250
(D) 3,750
(E) 2,500
Rationale: Let D = fish population of the pond = 5,000,
B = fish population of the sample = 100,
A = fish sample with healthy level of mercury = 100 - 25 = 75, and
C = fish population with healthy level of mercury, then:
Proportion: A/B = C/D
Proportion: 75/100 = C/5,000
C = 3,750. There are approximately 3,750 healthy fish in the pond.
Answer is D
Answer: (D) 3,750
Question: In a group of ducks and cows, the total number of legs are 12 more than twice the no. of heads. Find the total no.of buffaloes.
(A) 6
(B) 8
(C) 10
(D) 4
(E) 12
Rationale: Let the number of buffaloes be x and the number of ducks be y
=> 4x + 2y = 2 (x + y) + 12
=> 2x = 12=> x = 6
A
Answer: (A) 6
Question: A shop owner sells 40 Pencils and gains SP of 15 pencils. Find the gain %?
(A) 55%
(B) 40%
(C) 50%
(D) 60%
(E) 78%
Rationale: Gain=15 orangesTotal 40 orangesCP 40-15=25(15/25)*100=60%Ans D
Answer: (D) 60%
Question: Peter read C books last year, and Nikki read N books last year. If Peter read 35 more books than Nikki last year, which of the following reflects this relationship?
(A) C > 35N
(B) C < N − 35
(C) C > N + 35
(D) C = N − 35
(E) C = N + 35
Rationale: Peter read C books last year, and Nikki read N books last year. If Peter read 35 more books than Nikki last year, which of the following reflects this relationship?
A. C > 35N
B. C < N − 35
C. C > N + 35
D. C = N − 35
E. C = N + 35
Since Peter read more books than Nikki we have C>N. Moreover since Peter reads 35 more books than Nikki easily we can have C=N+35.
So the answer is (E).
Answer: (E) C = N + 35
Question: How much did Rohit get as profit at the year-end in the business done by Nitin, Rohit and Kunal?
I.Kunal invested Rs. 8000 for nine months, his profit was times that of Rohit’s and his investment was four times that of Nitin.
II.Nitin and Rohit invested for one year in the proportion 1 : 2 respectively.
III.The three together got Rs. 1000 as profit at the year end.
(A) Only I and II
(B) Only I and III
(C) Question cannot be answered even with the information in all the three statements.
(D) All I, II and III
(E) None of these
Rationale: Explanation:
I and II give:
K = Rs. (8000 x 9) for 1 month = Rs. 72000 for 1 month.
N = Rs. ( 1/4 x 8000 x12 ) for 1 month = Rs. 24000 for 1 month.
R = Rs. 48000 for 1 month.
K : N : R = 72000 : 24000 : 48000 = 3 : 1 : 2.
III gives, total profit = Rs. 1000.
Rohit’s share = Rs. (1000 x 2/6 )= Rs. 333 1/3
answer is (D).
Answer: (D) All I, II and III
Question: A man can row his boat with the stream at 6 km/h and against the stream in 4 km/h. The man's rate is?
(A) 1 kmph
(B) 5 kmph
(C) 8 kmph
(D) 3 kmph
(E) 4 kmph
Rationale: DS = 6
US = 4
S = ?
S = (6 - 4)/2 = 1 kmph
ANSWER:A
Answer: (A) 1 kmph
Question: How many different 6 letter combinations can be created from the letters A,B,C,D,E and F?
(A) 216
(B) 36
(C) 46656
(D) 1296
(E) 7776
Rationale: This is a case of number of arrangements possible with repetition.
Thus you have 6 options each for the 1st,2nd,3rd,4th,5th and 6th letter giving you a total of 6*6*6*6*6*6 = 46656 number of possible combinations.
Answer : C
Answer: (C) 46656
Question: man is 21 years older than his son. In two years, his age will be twice the age of his son. The present age of his son is:
(A) 14years
(B) 26 years
(C) 19 years
(D) 18 years
(E) 22 years
Rationale: Let the son's present age be x years. Then, man's present age = (x + 20) years.
(x + 21) + 2 = 2(x + 2)
x + 23 = 2x + 4
x = 19.
answer :C
Answer: (C) 19 years
Question: Salaries of Ravi and Sumit are in the ratio 2 : 3. If the salary of each is increased by Rs. 4000, the new ratio becomes 40 : 57. What is Sumit's salary?
(A) Rs. 17,000
(B) Rs. 20,000
(C) Rs. 25,500
(D) Rs. 38,000
(E) Rs. 35,000
Rationale: Explanation:
Let the original salaries of Ravi and Sumit be Rs. 2x and Rs. 3x respectively.
Then,	2x + 4000/	3x + 4000=40/57
57(2x + 4000) = 40(3x + 4000)
6x = 68,000
3x = 34,000
Sumit's present salary = (3x + 4000) = Rs.(34000 + 4000) = Rs. 38,000.
ANSWER IS D
Answer: (D) Rs. 38,000
Question: A certain rectangular crate measures 12 feet by 16 feet by 18 feet. A cylindrical gas tank is to be made for shipment in the crate and will stand upright when the crate is placed on one of its six faces. What should the radius of the tank be if it is to be of the largest possible volume?
(A) 4
(B) 5
(C) 6
(D) 8
(E) 10
Rationale: For max volume of cylinder (pi*r^2*h) we need to max out r^2*h. We don't know what the dimensions of the crate refer to. . Therefore for max vol base should be 18x16 i.e. of radius 16/2 = 8
D
Answer: (D) 8
Question: The probability that event M will not occur is 0.8 and the probability that event R will not occur is 0.9. If events M and R cannot both occur, which of the following is the probability that either event M or event R will occur?
(A) 1/5
(B) 2/5
(C) 3/10
(D) 4/5
(E) 12/25
Rationale: p(m) =0.2
p(r) =0.1
p(m intersection r) = 0 (If events M and R cannot both occur)
p(m or r) = 0.2+0.1 =0.3
Corrected !!
Answer C
Answer: (C) 3/10
Question: Shekhar started a business investing Rs.25,000 in 1999.In 2000,he invested an additional amount of Rs.10,000 and Rajeev joined him with an amount of Rs.35,000.In 2001,Shekhar invested another additional amount of Rs.10,000 and Jatin joined them with an amount of Rs.35,000.What will be Rajeev’s share in the profit of Rs.1,20,000 earned at the end of 3 years from the start of the business in 1999 ?
(A) Rs.40,000
(B) Rs.50,000
(C) Rs.70,000
(D) Rs.75,000
(E) None of these
Rationale: Solution
Shekhar : Rajeev : Jatin
= (25000x12+35000x12+45000x12) :(35000x24) : (35000x12)
= 1260000 : 840000 : 420000 = 3 : 2 : 1.
∴ Rajeev’s share = Rs.(12000x2/6) = Rs. 40,000. Answer A
Answer: (A) Rs.40,000
Question: The slant height of a cone is 22 cm and radius of the base is 7cm, find the curved surface of the cone?
(A) 426
(B) 284
(C) 483
(D) 256
(E) 428
Rationale: π * 22 * 7
= 483
Answer:C
Answer: (C) 483
Question: Set #1 = {A, B, C, D, E, F}
Set #2 = {K, L, M, N, O, P}
There are these two sets of letters, and you are going to pick exactly one letter from each set. What is the probability of picking at least one vowel?
(A) 1/6
(B) 1/3
(C) 1/2
(D) 2/3
(E) 4/9
Rationale: So Not a vowel in Set-1 : 4/6
And not a vowel in Ser-2:5/6
Now,
4/6∗5/6=5/9
This is for not a vowel.
Then for at least one vowel will be = 1−5/9=4/9
Answer will be E.
Answer: (E) 4/9
Question: 99,998^2 - 2^2 =
(A) 10^10 - 2
(B) (10^5 – 2)^2
(C) 10^4(10^5 – 2)
(D) 10^5(10^4 – 2)
(E) 10^5(10^5 – 4)
Rationale: (99,998)^2 - (2)^2 = (100,000 -2)^2 - (1)^2 = (100,000)^2 - 2*2*100,000 + 2^2-2^2=(10^5)^2 - 4*(10^5) = 10^10 - 4*(10^5)=10^5(10^5 - 4) Answer E
Answer: (E) 10^5(10^5 – 4)
Question: If Leo gains 10 pounds, he will weigh 50% more than his sister Kendra. Currently their combined weight is 170 pounds. What is Leo's current weight?
(A) 80
(B) 86
(C) 92
(D) 98
(E) 104
Rationale: L+K = 170 and so K = 170-L
L+10 = 1.5K = 1.5(170-L)
2.5L = 245
L = 98
The answer is D.
Answer: (D) 98
Question: In a certain boys camp, 20% of the total boys are from school A and 30% of those study science. If there are 56 boys in the camp that are from school A but do not study science then what is the total number of boys in the camp?
(A) 70
(B) 400
(C) 150
(D) 35
(E) 350
Rationale: Since 30% of the boys from school A study science, then 70% of the boys from school A do NOT study science and since 20% of the total number of boys are from school A, then 0.2*0.7 = 0.14, or 14% of the boys in the camp are from school A and do not study science.
We are told that this number equals to 56, so 0.14*{total} = 56 --> {total} = 400.
Answer: B.
Answer: (B) 400
Question: In six successive games, a baseball team scored 3 runs once, 6 runs twice, and 7 runs three times.
What was the average (arithmetic mean) number of runs the team scored per game over the six-game period?
(A) 8
(B) 7
(C) 6
(D) 5
(E) 4
Rationale: 3 runs once (one game)
6 runs twice (two game)
7 runs three times (three games)
SO we have (3*1 + 6*2 + 7*3)/6 = 36/6 = 6.
ANS: C.
Answer: (C) 6
Question: If the cost price of 50 articles is equal to the selling price of 40 articles, then the gain or loss percent is?
(A) 28%
(B) 65%
(C) 23%
(D) 78%
(E) 25%
Rationale: Given that, cost price of 50 article is equal to selling price of 40 articles.
Let cost price of one article = Rs. 1
Selling price of 40 articles = Rs. 50
But Cost price of 40 articles = Rs. 40
Therefore, the trader made profit.\Percentage of profit = 10/40 * 100 = 25%
Answer: E
Answer: (E) 25%
Question: I purchases perfume from a store and gave him a thousand rupee note.
The perfume cost Rs.300.
Since the store person have no change, he gets the change from next shop and return me 800 rupees.
After a while, the next shopkeeper comes and told the 1st shopkeeper that the note is a fraud and takes his money back.
How much loss does the 1st shopkeeper have to bear ?
(A) 4400
(B) 1300
(C) 1800
(D) 2500
(E) 1000
Rationale: E
Rupees 1000
Answer: (E) 1000
Question: A man divides $8600 Among 5 Sons, 3 Daughters and 2 Nephews. If each daughter receives four times as much as each nephews and each son receives five times as much as each nephews, how much does each daughter receive?
(A) A)$200
(B) B)$716.67
(C) C)$800
(D) D)$1200
(E) E)$400
Rationale: Let the share of each nephews be $X.
Then, share of each daughter=$4X, share of each son= $5X.
So, 5*5X+3*3X+2*X=8600
25X+9X+2X=8600
36X=8600, X=238.89
Daughter receives four times of nephew so 3 *238.89 = 716.67.
So Each Daughter receives $800. answer is option B) $716.67.
Answer: (B) B)$716.67
Question: If x+y=300, x-y=200, for integers of x and y, y=?
(A) 200
(B) 250
(C) 50
(D) 115
(E) 150
Rationale: x+y = 300
x-y = 200
2x = 100
x = 50
y = 250
Answer is B
Answer: (B) 250
Question: The sale price sarees listed for Rs.550 after successive discount is 18% and 12% is?
(A) 298
(B) 237
(C) 342
(D) 396
(E) 291
Rationale: 550*(88/100)*(82/100)
= 396
Answer: D
Answer: (D) 396
Question: In a school 10% of the boys are same in number as 1/6th of the girls. what is the ratio of boys to the girls in the school?
(A) 5:3
(B) 2:3
(C) 1:4
(D) 3:7
(E) 2:5
Rationale: 10% of B = 1/6 G
10B/100 = G/6
B = 5G/3
B/G = 5/3
B:G = 5:3
Answer is A
Answer: (A) 5:3
Question: A taxi charges u dollars for the first two miles and c cents per quarter mile for every mile after the first two. Which equation describes cost of a taxi ride of n miles in dollars.
(A) un – c/8(100)
(B) cu + 4n-8/200
(C) u + (4cn-8c)/100
(D) u + 100cn/4
(E) 4cu(n-2) – 100
Rationale: This is about as complicated as these types of problems come, but it is essentially the same as any problem which has an initial cost which is added to a dependent additional cost. Looking at the problem, we notice that the cost u is added to the mile dependent cost, which is some combination of the other terms listed in the problem. With just that knowledge we can eliminate all but two of the answer choices! Choices (A), (B), and (E) either do some strange calculation with the initial cost u, or subtract the additional cost from u. Both of these circumstances would be next to impossible if there is an initial cost being added to another cost. Thus, we only have to choose between choice (C) and choice (D). We can easily find the right answer by plugging in real numbers and checking which choice yields a correct answer. We can also see that answer choice (D) seems to be multiplying the cost in cents by 100, which, if the trip was 6 miles and the charge per mile was 25 cents, would make the taxi cost an additional $3750! This seems impossible, and leaves only the correct answer choice, (C).
Answer: (C) u + (4cn-8c)/100
Question: If the selling price of 10 articles is same as the cost price of 12 articles. Find the gain or loss percentage?
(A) 10%
(B) 20%
(C) 30%
(D) 32%
(E) None
Rationale: Let the C.P of each article be Re 1. Then,
S.P of 10 articles = C.P of 12 articles = Rs. 12
Now, C.P of 10 articles = Rs. 10, S.p of 10 articles = Rs 12
Gain = Rs ( 12 - 10 ) = Rs 2.
Gain% = ( 2/10 × 100 ) % = 20%
B)
Answer: (B) 20%
Question: Three numbers are in the ratio 2 : 3 : 7. The sum of its longest and smallest numbers equals the sum of the third number and 48. Find the third number?
(A) A)24
(B) B)75
(C) C)48
(D) D)46
(E) E)63
Rationale: Let the numbers be 2x, 3x, 7x.
Largest number = 7x.
Smallest number = 3x.
Third number = 6x.
7x + 2x = 3x + 48
6x = 48 =>x=8
3x=24=> third number is 24.
Answer:A
Answer: (A) A)24
Question: A money lender finds that due to a fall in the annual rate of interest from 8% to 7 2/7 % his yearly income diminishes by Rs.61.50. his capital is
(A) 22.378
(B) 87.86
(C) 246.0
(D) 78.88
(E) 127.71
Rationale: Explanation:
Capital = Rs.x , then
5/7x = 61.5
x = 87.86
Answer: B) Rs.87.86
Answer: (B) 87.86
Question: Find the least number of five digits which is exactly divisible by 12, 15 and 18?
(A) 1080
(B) 10080
(C) 10025
(D) 11080
(E) 12080
Rationale: LCM = 180
180) 10000 (55
9900
---------
100
10000 + 180 - 100 = 10080
ANSWER:B
Answer: (B) 10080
Question: For any integer n greater than 1, n* denotes the product of all the integers from 1 to n, inclusive. How many prime numbers W are there between 6* + 2 and 6* + 6, inclusive?
(A) None
(B) One
(C) Two
(D) Three
(E) Four
Rationale: Given that n* denotes the product of all the integers from 1 to n, inclusive so, 6*+2=6!+2 and 6*+6=6!+6.
Now, notice that we can factor out 2 our of 6!+2 so it cannot be a prime number, we can factor out 3 our of 6!+3 so it cannot be a prime number, we can factor out 4 our of 6!+4 so it cannot be a prime number, ... The same way for all numbers between 6*+2=6!+2 and 6*+6=6!+6, inclusive. Which means that there are no primes W in this range.
Answer: A.
Answer: (A) None
Question: A person buys an article at Rs.500. At what price should he sell the article so as to make a profit of 20%?
(A) 600
(B) 277
(C) 269
(D) 261
(E) 281
Rationale: Cost price = Rs.500
profit = 20% of 500 = Rs.100
Selling price = Cost price + Profit
= 500 + 100 = 600.Answer: A
Answer: (A) 600
Question: On his first 4 tests, John received an average score of X points. If on his fifth test, he exceeds his previous average score by 30 points, what is his average score for his first 5 tests?
(A) X +6
(B) X +5
(C) X +4
(D) X
(E) X +10
Rationale: Total of 1st 4 tests= 4X
5th test score = X + 30
Total of all 5 tests = 5X + 30
Average = X +6
Answer : A
Answer: (A) X +6
Question: A certain family has 3 sons: Richard is 6 years older than David, and David is 8 years older than Scott. If in 8 years, Richard will be twice as old as Scott, then how old was David 3 years ago?
(A) 11
(B) 10
(C) 12
(D) 14
(E) 16
Rationale: Let's say
Age of Richard is "R"
Age of David is "D"
Age of Scott is "S"
Now
Richard is 6 years older than David,
i.e. R = D +6
David is 8 years older than Scott
i.e. D = S +8
If in 8 years, Richard will be twice as old as Scott
i.e. R+8 = 2x(S+8)
i.e. R+8 = 2S + 16
i.e. R = 2S+8
But R = D+6 = (S+8)+6 = S+14
therefore, 2S + 8 = S +14
i.e. S = 6
i.e. R = 20
i.e. D = 14
Now,
how old was David 3 years ago?
i.e. D-4 = 14-3 = 11 years
ANSWER:A
Answer: (A) 11
Question: What is the ratio of Arun's monthly income in the year 2006, Suman's monthly income in the year 2007 and Jyothi's monthly income in the year 2005?
(A) 22
(B) 67
(C) 26
(D) 18
(E) 16
Rationale: Answer:	A
Answer: (A) 22
Question: The sum of two numbers is 80. Their difference is 10. The bigger number is
(A) 20
(B) 25
(C) 30
(D) 35
(E) 45
Rationale: X + Y = 80
X - Y = 10
Adding 2X = 90 ==> X = 45 and Y = 80 - 45 = 35
Bigger number is X = 45
Answer E.
Answer: (E) 45
Question: A square with sides of 15 units each. What would be the area of the square. Consider a square as a combination of two right angled triangles.
(A) 100
(B) 256
(C) 225
(D) 81
(E) 144
Rationale: A square can be considered as a set of two right angled triangles joined from the hypotenuse.
Since the sides are 10 units each. The height and base of both the triangles is 10 each.
Area of a right angled triangle is 1/2 * base * height
Area of both the triangles is 2 * 1/2 * base * height. Since both triangles are similar.
= base * height
= 15*15 =225
Ans: C
Answer: (C) 225
Question: 4 men can check exam papers in 8 days working 5 hours regularly. What is the total hours when 2 men will check the double of the papers in 20 days?
(A) 8
(B) 9
(C) 6
(D) 1
(E) 5
Rationale: Let a man can do 1 unit of work in 1 hour.
Total units of work = 4 x 8 x 5 = 160 units.
Now work = 2 x 160 = 320 units.
Now 2 men work for 20 days. Let in x hours they have to work per day.
Now total work = 2×x×20 = 40 x
40x = 320 So x = 320/40 = 8 hours.
Answer:A
Answer: (A) 8
Question: A, B and C play a cricket match. The ratio of the runs scored by them in the match is A:B = 2:3 and B:C = 2:5. If the total runs scored by all of them are 75, the runs scored by B are?
(A) 10
(B) 18
(C) 16
(D) 14
(E) 15
Rationale: A:B = 2:3
B:C = 2:5
A:B:C = 4:6:15
6/25 * 75 = 18
Answer: B
Answer: (B) 18
Question: Which is the least number that must be subtracted from 1100 so that the remainder when divided by 7, 12, 16 is 4?
(A) 58
(B) 68
(C) 78
(D) 88
(E) 90
Rationale: First we need to figure out what numbers are exactly divisible by 7,12,16. This will be the set {LCM,LCMx2,LCMx3,...}
LCM(7,12,16) = 48*7 = 336
The numbers which will leave remainder 4 will be {336+4, 336x2 +4, 336x3 +4,...}
The largest such number less than or equal to 1100 is 336x3+4 or 1012
To obtain this you need to subtract 88
D
Answer: (D) 88
Question: In how many different ways can the letters of the word 'OPTICAL' be arranged so that the vowels always come together?
(A) 680
(B) 700
(C) 720
(D) 800
(E) 820
Rationale: The word 'OPTICAL' contains 7 different letters.
When the vowels OIA are always together, they can be supposed to form one letter.
Then, we have to arrange the letters PTCL (OIA).
Now, 5 letters can be arranged in 5! = 120 ways.
The vowels (OIA) can be arranged among themselves in 3! = 6 ways.
Required number of ways = (120 x 6) = 720.
ANSWER : C
Answer: (C) 720
Question: On average, Machine A will produce a completed item once every six minutes, and Machine B will produce a completed item once every ten minutes. The number of items Machine A produces in a 24-hour period is approximately what percent greater than the number of items Machine B would produce in that same period?
(A) 100%%
(B) 67%
(C) 25%
(D) 125%
(E) 20%
Rationale: Machine A: 1 item in 6 minutes --> 1/6 items in 1 minute;
Machine B: 1 item in 10 minutes --> 1/10 items in 1 minute.
In the same time period, Machine A produces (1/6-1/10)/(1/10)*100=~67% more items than machine B.
Answer: B.
Answer: (B) 67%
Question: What inequality represents the condition 1<x<8?
(A) |x|<3
(B) |x+5|<4
(C) |x-9/2|<7/2
(D) |-5+x|<4
(E) |3+x|<5
Rationale: 1<x<8 represents segment with
length: 8-1 = 7
center: (8+1)/2 = 9/2
For any |x-a|<b a is a center and b is a half of length. So, |x-9/2|<7/2 represents our inequality (answer C)
Answer: (C) |x-9/2|<7/2
Question: . In a certain city, 60 percent of the registered voters are Democrats and the rest are Republicans. In a mayoral race, if 55 percent of the registered voters who are Democrats and 20 percent of the registered voters who are Republicans are expected to vote for Candidate A, what percent of the registered voters are expected to vote for Candidate A ?
(A)  50%
(B)  53%
(C)  54%
(D)  41%
(E)  57%
Rationale: Registered voters = 100
D = 60
R = 40
55% of D ( 60) = 33
20% of R ( 40 ) = 8
Total voter% of registered voters = 41 / 100
41% Ans D
Answer: (D)  41%
Question: A meal cost $ 37.25 adn there was no tax. If the tip was more than 10 pc but less than 15pc of the price, then the total amount paid should be:
(A) 42-45
(B) 41-43
(C) 39-41
(D) 37-39
(E) 36-37
Rationale: 10%(37.25) = 3.725
15%(37.25) = 5.5875
total amount could have been 37.25+3.725 and 37.25+5.5875
=> could have been between 40.975 and 42.8375
=> approximately between 41 and 43
Answer is B.
Answer: (B) 41-43
Question: sue has 3 apples. Billy has 5 apples. If billy steals all of sues apples and eats 2 how many does he have left?
(A) 2
(B) 5
(C) 6
(D) 4
(E) 8
Rationale: 6 C
Answer: (C) 6
Question: If n + 15 is a positive odd integer, which of the following must be true about the sum of the next four integers?
(A) It is a multiple of 3
(B) It is a multiple of 4
(C) It is a prime number
(D) It is a multiple of 5
(E) It is a multiple of 2
Rationale: n+15 is a positive odd integer. This means n will be an odd integer
The next 4 integers would be: n + 15, n + 16, n + 17, n + 18
Sum = 4n + 56
This sum will always be even.
Option B
Answer: (B) It is a multiple of 4
Question: In a certain game of dice, the player’s score is determined as a sum of three throws of a single die. The player with the highest score wins the round. If more than one player has the highest score, the winnings of the round are divided equally among these players. If Jim plays this game against 24 other players, what is the probability of the minimum score that will guarantee Jim some monetary payoff?
(A) 1/216
(B) 1/221
(C) 1/212
(D) 1/84
(E) 1/42
Rationale: Toguaranteethat Jim will get some monetary payoff he must score the maximum score of 6+6+6=18, because if he gets even one less than that so 17, someone can get 18 and Jim will get nothing.
P(18)=1/6^3=1/216.
Answer: A.
Answer: (A) 1/216
Question: A full stationary oil tank that is a right circular cylinder has a radius of 100 feet and a height of 25 feet. Oil is pumped from the stationary tank to an oil truck that has a tank that is a right circular cylinder until the truck's tank is completely filled. If the truck's tank has a radius of 6 feet and a height of 10 feet, how far (in feet) did the oil level drop in the stationary tank?
(A) 0.036
(B) 0.36
(C) 0.6
(D) 6
(E) 3.6
Rationale: The volume of oil pumped to the tank = The volume of oil taken away from stationary cylinder.
pi*36*10 = pi*h*100*100 (h is distance that the oil level dropped)
h = 360/10,000 = 36/1000 = 0.036 ft
The answer is A.
Answer: (A) 0.036
Question: Working simultaneously at their respective constant rates, Machines A and B produce 800 nails in x hours. Working alone at its constant rate, Machine A produces 800 nails in t hours. In terms of x and t, how many hours does it take Machine B, working alone at its constant rate, to produce 800 nails?
(A) x/(x+y)
(B) y/(x+y)
(C) xy/(x+y)
(D) xy/(x-y)
(E) xt/(t-x)
Rationale: Pick some smart numbers for x and t.
Say x=1 hour and t=2 hours (notice that t must be greater than x, since the time for machine A to do the job, which is t hours, must be more than the time for machines A and B working together to do the same job, which is x hours).
In this case, the time needed for machine B to do the job must also be 2 hours: 1/2+1/2=1.
Now, plug x=1 and t=2 in the options to see which one yields 2. Only option E fits.
Answer: E.
Answer: (E) xt/(t-x)