mathewhe/aqua_rat huggingface dataset:
Question: A tank is filled in 5 hours by three pipes A,B and C. The pipe C is twice as fast as B and B is twice as fast as A. How much time will pipe A alone take to fill the tank?
(A) 35 hours
(B) 25 hours
(C) 20 Hours
(D) Cannot be determined
(E) None of these
Rationale: Let pipe A alone takes to fill the tank = x hours.
Then, pipes B take twice fast as A = x/2
And pipes C take twice fast as B = x/4
Therefore, Tank filled in 5 hours by A,B,C pipes => 1/x + 2/x + 4/x = 1/5
==> 7/x = 1/5
==> x = 5*7
x= 35 hours
x = 35 hrs.
ANSWER:A
Answer: (A) 35 hours
Question: A family consists of two grandparents, two parents and three grandchildren. The average age of the grandparents is 67 years, that of the parents is 35 years and that of the grandchildren is 6 years. What is the average age of family?
(A) 31 5/7years
(B) 31
(C) 30
(D) 33
(E) 35
Rationale: Required average
= (67 x 2 + 35 x 2 + 6 x 3 )/(2 + 2 + 3)
= (134 + 70 + 18)/7
= 222/7
= 31 5/7years.
Answer is A
Answer: (A) 31 5/7years
Question: A car covers a certain distance at aspeed of 55 kmph in 6 hours. To cover the same distance in 2 hrs, it must travel at a speed of?
(A) 567 km/hr
(B) 678 km/hr
(C) 165 km/hr
(D) 789 km/hr
(E) 720 km/hr
Rationale: Distance = (55 x 6) = 330 km.
Speed = Distance/Time
Speed = 330/2 = 165 kmph
Answer : C
Answer: (C) 165 km/hr
Question: If m and n are positive integers of J such that m is a factor of n, how many positive multiples of m are less than or equal to 2n ?
(A) 2m/n + 1
(B) 2n/m + 1
(C) 2n/(m+1)
(D) 2m/n
(E) 2n/m
Rationale: Lets say N=10, M=5
2N=20. so the answer should be 4 (20/5)
lets try to plug in the answers:
A-not an integer
B-not an integer
C-not an integer
D-1 (not the answer)
E-4 - the answer. (the only one).
I would choose E.
Method 2
N=M*A (A is an integer)
So - A=N/M
therefore in 2N A will be 2N/M
Again - Answer is E.
Answer: (E) 2n/m
Question: A 300 m long train crosses a platform in 45 sec while it crosses a signal pole in 18 sec. What is the length of the platform?
(A) 287
(B) 350
(C) 828
(D) 450
(E) 122
Rationale: Speed = 300/18 = 50/3 m/sec.
Let the length of the platform be x meters.
Then, (x + 300)/45 = 50/3
3x + 900 = 2250 => x = 450 m.
Answer: D
Answer: (D) 450
Question: How many different subset of the set {A, B, C, D, E. F, G) do not contain G.
(A) 79
(B) 78
(C) 75
(D) 80
(E) 74
Rationale: This is a Combination Solution
Since we have 6 different letters other than the letter G we can take any letter from the set of 6 to make a subset.
6C1 +6C2 + 6C3 + 6C4 + 6C5 + 6C6 = 78
Plus the one set that is null that is the Set having no element in it which is 6C0 =1
= 78 + 1 = 16
A = 79
Answer: (A) 79
Question: The value of a machine depreciates at 20% per annum. If its present value is Rs. 1,50,000, at what price should it be sold after two years such that a profit of Rs. 24,000 is made?
(A) Rs. 120,002
(B) Rs. 1,20,000
(C) Rs. 1,20,00
(D) Rs. 1,20,028
(E) Rs. 1,20,011
Rationale: Explanation:
The value of the machine after two years = 0.8 * 0.8 * 1,50,000 = Rs. 96,000
SP such that a profit of Rs. 24,000 is made = 96,000 + 24,000 = Rs. 1,20,000
Answer: B
Answer: (B) Rs. 1,20,000
Question: A box contains 80 balls, numbered from 1 to 80. If three balls are selected at random and with replacement from the box, what is the probability that the sum of the three numbers on the balls selected from the box will be odd?
(A) 1/4
(B) 3/8
(C) 1/2
(D) 5/8
(E) 3/4
Rationale: I don't think order matters in this case, because 2 + 2 + 1 = 2 + 1 + 2
My answer is: 1/4
A
Answer: (A) 1/4
Question: Two pipes A and B can fill a tank in 30 and 60 minutes respectively. If both the pipes are used together, then how long will it take to fill the tank?
(A) 10
(B) 20
(C) 30
(D) 24
(E) 25
Rationale: Part filled by A in 1 min. = 1/30
Part filled by B in 1 min. = 1/60
part filled by (A + B) in 1 min. = 1/30 + 1/60 = 1/20.
Both the pipes can fill the tank in 20 minutes.
Answer: B
Answer: (B) 20
Question: If x is a positive odd integer and y is a negative even integer, which of the following must be true?
(A) x^3 + y is a positive odd integer
(B) x^2 + y^2 is a negative odd integer
(C) x^0 + y^11 is a negative odd integer
(D) x + y is a positive odd integer
(E) x + y is a negative odd integer
Rationale: Anything power 0 is always 1 and given that Y is even and negative, then
1 + (-2) will be negative with odd power values for Y.
Answer: C
Answer: (C) x^0 + y^11 is a negative odd integer
Question: In what time will a train 100 metres long cross an electric pole, if its speed be 144 km/hr?
(A) 2.5 sec
(B) 4.25 Sec
(C) 5 sec
(D) 12.5 sec
(E) None
Rationale: Solution
Speed	= (144 x 5 /18) m/sec
= 40 m / sec
Time taken	= (100 /40) sec
= 2.5 sec.
Answer A
Answer: (A) 2.5 sec
Question: A delegation of 5 members has to be formed from 3 ladies and 5 gentlemen. In how many ways the delegation can be formed, if 2 particular ladies are always included in the delegation?
(A) 20
(B) 27
(C) 24
(D) 25
(E) 12
Rationale: There are three ladies and five gentlemen and a committee of 5 members to be formed.
Number of ways such that two ladies are always included in the committee
= 6C3 = (6 * 5 * 4)/6
= 20.
Answer:A
Answer: (A) 20
Question: Five 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) 1/4
(B) 2/7
(C) 3/4
(D) 4/7
(E) None of them
Rationale: Original share of 1 person = 1/5
New share of 1 person = 1/4
Increase = (1/4- 1/5	= 1/20)
Therefore, Required fraction = (1/20)/(1/5)	= (1/20)x (5/1)	= 1/4
Answer is A.
Answer: (A) 1/4
Question: What will come in place of the x in the following Number series? 5,28,57,88,125,166
(A) 209
(B) 159
(C) 166
(D) 170
(E) 180
Rationale: 28=23+5
57=29+28
88=31+57
125=37+88
166=41+125
209=43+166
=209
A
Answer: (A) 209
Question: If x is the sum of p and q, then which one of the following must equal p – q?
(A) x+2q
(B) x-2q
(C) x+q
(D) x-q
(E) xq
Rationale: Given x= p+q if you subtracts both side with -2q
x-2q = p-q
Answer : A
Answer: (A) x+2q
Question: Two trains running in opposite directions cross a man standing on the platform in 27 seconds and 17 seconds respectively and they cross each other in 23 seconds. The ratio of their speeds is:
(A) 3 : 1
(B) 3 : 2
(C) 3 : 8
(D) 3 : 25
(E) 3 : 4
Rationale: Let the speeds of the two trains be x m/sec and y m/sec respectively. Then, length of the first train = 27 x meters, and length of the second train = 17 y meters. (27 x + 17 y) / (x + y) = 23 ==> 27 x + 17 y = 23 x + 23 y ==> 4 x = 6 y ==> x/y = 3/2.
Answer: Option B
Answer: (B) 3 : 2
Question: A certain roller coaster has 5 cars, and a passenger is equally likely to ride in any 1 of the 5 cars each time that passenger rides the roller coaster. If a certain passenger is to ride the roller coaster 5 times, what is the probability that the passenger will ride in each of the 5 cars?
(A) 0
(B) 24/625
(C) 2/9
(D) 1/3
(E) 1
Rationale: If he is to ride 5 times and since he can choose any of the 5 cars each time, total number of ways is
= 5 * 5 * 5 *5 * 5
= 3125
Now the number of ways if he is to choose a different car each time is
= 5 * 4 * 3 * 2 * 1
= 120
So the probability is
= 120/3125 = 24/625
Answer : B
Answer: (B) 24/625
Question: The cost of an article is decreased by 20%. If the original cost is $40, find the decrease cost.
(A) 33
(B) 32
(C) 68
(D) 36
(E) 38
Rationale: Original cost = $40
Decrease in it = 20% of $40
= 20/100 Ã— 40
= 800/100
= $8
Therefore, decrease cost = $40 - $8 = $32
Answer:B
Answer: (B) 32
Question: The average age of 15 students of a class is 15 years. Out of these, the average age of 5 students is 14 years and that of the other 9 students is 16 years, The age of the 15th student is
(A) 11 years
(B) 12 years
(C) 13 years
(D) 18 years
(E) 10 years
Rationale: Age of the 15th student = [15 * 15 - (14 * 5 + 16 * 9)] = (225-214)
= 11 years.
Answer: A
Answer: (A) 11 years
Question: If the selling price of 6 toys is same as the cost price of 12 toys . Find the gain or loss percentage?
(A) 65%
(B) 75%
(C) 85%
(D) 68%
(E) 100%
Rationale: Let the C.P of each toys be Re 1. Then,
S.P of 6 toys = C.P of 12 toys= Rs. 12
Now, C.P of 6 toys= Rs.6, S.p of 6 toys = Rs 12
Gain = Rs ( 12 -6 ) = Rs 6.
Gain% = ( 6/6× 100 ) % = 100%
Answer : E
Answer: (E) 100%
Question: If $0.30 is the commission for sales of $1,000, what percent of the sales amount is the commission?
(A) 3%
(B) 0.3%
(C) 0.03%
(D) 0.003%
(E) 0.0003%
Rationale: % of sales amount of commission
= (Commission/Total Value) *100
= (0.3/1000) * 100
= 0.03%
The answer is C.
Answer: (C) 0.03%
Question: A trader bought a car at 50% discount on its original price. He sold it at a 80% increase on the price he bought it. What percent of profit did he make on the original price?
(A) 17%
(B) 62%
(C) 12%
(D) 19%
(E) 71%
Rationale: Original price = 100
CP = 95
S = 95*(180/100) = 112
100 - 171= 71%
Answer: E
Answer: (E) 71%
Question: A train running at the speed of 90 km/hr crosses a pole in 9 sec. What is the length of the train?
(A) 225 m
(B) 150 m
(C) 187 m
(D) 167 m
(E) 197 m
Rationale: Speed = 90 * 5/18 = 25 m/sec
Length of the train = speed * time = 25 * 9
=225 m
Answer: A
Answer: (A) 225 m
Question: The difference between the simple interest received from two different sources on Rs. 1500 for 3 years is Rs. 13.50. The difference between their rates of interest is?
(A) 0.8%
(B) 8.3%
(C) 0.3%
(D) 2.3%
(E) 0.4%
Rationale: (1500 * R1 * 3)/100 - (1500 * R2 * 3)/100 = 13.50 4500(R1 - R2) = 1350
R1 - R2 = 0.3%
Answer:C
Answer: (C) 0.3%
Question: GOOD is coded as 164 then BAD coded as 21.if ugly coded as 260 then HUMP?
(A) 200
(B) 210
(C) 220
(D) 232
(E) 240
Rationale: GOOD=(7+15+15+4)*4=164
BAD= (2+1+4)*3=21
UGLY= (21+7+12+25)*4=260
coding follows
(sum of position of alphabets)*(no. of letters in the given word)
so,
HUMP=(8+21+13+16)*4= 232
ANSWER:D
Answer: (D) 232
Question: A certain telescope increases the visual range at a particular location from 100 kilometers to 150 kilometers. By what percent is the visual range increased by using the telescope ?
(A)  30%
(B)  33 1/2%
(C)  40%
(D)  60%
(E)  50%
Rationale: Original visual range = 100 km
New visual range = 150 km
Percent increase in the visual range by using the telescope
= (150-100)/100 * 100%
= 1/2 * 100%
= 50 %
Answer E
Answer: (E)  50%
Question: If k is a positive integer, which of the following must be divisible by 21?
(A)  (k – 4)(k)(k + 3)(k + 7)
(B)  (k – 4)(k – 2)(k + 3)(k + 5)
(C)  (k – 2)(k + 3)(k + 5)(k + 6)
(D)  (k + 1)(k + 3)(k + 5)(k + 7)
(E)  (k – 3)(k + 1)(k + 4)(k + 6)
Rationale: 24=8*3.
Note that the product of two consecutive even integers is always divisible by 8 (since one of them is divisible by 4 and another by 2). Only option B offers two consecutive even numbers for any integer value of k: k-4 and k-2, if k=even or k+3 and k+5 if k=odd.
Also from the following 3 consecutive integers:(k-4), (k-3),(k-2)one must be divisible by 3, if it's not k-4 or k-2 then it must be k-3 (if it's k-4 or k-2 option B is divisible by 3 right away). But if it's k-3 then (k-3)+6=k+3must also be divisible by 3.
So, option B: (k – 4)(k – 2)(k + 3)(k + 5) is divisible by 8 and 3 in any case.
Answer: A.
Answer: (A)  (k – 4)(k)(k + 3)(k + 7)
Question: Which expression is the greatest
(A) 3252/3257
(B) 3456/3461
(C) 3591/3596
(D) 3346/3351
(E) 3753/3758
Rationale: Options can be re-written as (x-5)x => 1-(5/x)
A) 1- (5/3257)
B) 1- (5/3461)
C) 1- (5/3596)
D) 1- (5/3351)
E) 1- (5/3758)
To get the largest among these second half should be the least and so denominator to be largest. Hence 'E'.
Answer: (E) 3753/3758
Question: The sum of first three terms of the Geometric sequence is 13/12 and their product is -1. Find the common ratio
(A) 3/4
(B) -3/4
(C) 4/3
(D) 1/2
(E) 1/8
Rationale: We make the first three terms is of a/r, a, ar
Whose sum=a(1/r+1+r)=13/12
Their product = a3=-1
Hence, (3r+4)(4r+3)=0
r=-3/4 or -4/3
ANSWER B -3/4
Answer: (B) -3/4
Question: x percent of y percent of z is decreased by y percent. What is the result?
(A) (100xyz - xy^2z) / 1,000,000
(B) (xz - y) / 100
(C) (xz - y) / 10,000
(D) (xyz - 2y) / 100
(E) (xyz - 2y) / 10,000
Rationale: X = 10
Y = 50
Z = 100
First, 50% of 100 = 50
Next, 10% of 50 = 5
Finally, 5 decreased by 50% of itself is 2.5
So we're looking for an answer that equals 2.5 when X=10, Y=50 and Z=100.
Answer A. (100 xyz - xy^2z) / 1,000,000 = (5,000,000 - 2,500,000)/1,000,000 = 2,500,000/1,000,000 = 2.5 This is a MATCH
Answer B. (xz - y) / 100 = (1,000 - 50)/100 = 950/100 = 9.5 NOT a match
Answer C. (xz - y) / 10,000 = 950/10,000 = .095 NOT a match
Answer D. (xyz - 2y) / 100 = (50,000 - 100)/100 = 49,900/100 = 499 NOT a match
Answer E. (xyz - 2y) / 10,000 = 49,900/10,000 = 4.99 NOT a match
Final Answer:A
Answer: (A) (100xyz - xy^2z) / 1,000,000
Question: Thefactor countof an integer n greater than 1 is the number of distinct prime factors of n. For example, the factor count of 36 is 2, since 2 and 3 are the distinct prime factors of 36 = 2 x 2 x 3 x 3. For which of the following integers is the factor count greatest R?
(A)  60
(B)  61
(C)  62
(D)  63
(E)  64
Rationale: 60 = 2*2*3*5 factor count =3
61= prime number
62 = 2*31 factor count=2
63=3*3*7 factor count=2
64=2*2*2*2*2*2 factor count=1=R
answer is A.
Answer: (A)  60
Question: 212:436::560:?
(A) 786
(B) 682
(C) 784
(D) 688
(E) 622
Rationale: 2+2=4
1+2=3
2+4=6
like that,
5+2=7
6+2=8
0+4=4
answer C
Answer: (C) 784
Question: If n is an integer, which of the following must be an even integer?
(A) n^2-n-1
(B) n^2-4n+6
(C) n^2-5n+5
(D) n^2+3n+8
(E) n^2+2n+10
Rationale: Check the options by plugging in some values ( Preferably smaller integers like 1 and 2 )
A: n^2-n-1 = -1 { If n = 1 }
B: n^2-4n+6 = 3 { If n = 1 }
C: n^2-5n+5 = 1 { If n = 1 }
D: n^2+3n+8 = 12 { If n = 1 }n^2+3n+8 = 18 { If n = 2 }
E: n^2+2n+10 = 13 { If n = 1 }
Thus the only possible answer is (D)
Answer: (D) n^2+3n+8
Question: What is the simplified result of following the steps below in order?
(1)	add 5y to 2f
(2)	multiply the sum by 3
(3)	subtract f + y from the product
(A) 5f + 14y
(B) 5x + 16y
(C) 5x + 5y
(D) 6x + 4y
(E) 3x + 12y
Rationale: 3(5Y+2F) -F-Y= 14Y+5F
'A' is the answer
Answer: (A) 5f + 14y
Question: Martin bought 10 concert tickets, some at the full price of $2.00 per ticket, and some at a discounted price of $1.60 per ticket. If he spent a total of $17.60, how many discounted tickets did he buy?
(A) 3
(B) 4
(C) 5
(D) 6
(E) 7
Rationale: Let x be the number of tickets he bought at $2 per ticket.
then 2 x + (10-x)1.6 = 17.6
0.4x = 1.6 => x = 4
discounted tickets = 10 -x = 6
Ans : D
Answer: (D) 6
Question: Last year Mrs. Long received $160 in dividends on her shares of Company X stock, all of which she had held for the entire year. If she had had 12 more shares of the stock last year, she would have received $15 more in total annual dividends. How many shares of the stock did she have last year?
(A)  128
(B)  140
(C)  172
(D)  175
(E)  200
Rationale: A
1. Realize that if there were 12 more shares and 15 more dollars, the shares are worth more than a dollar a share, so there would have to be less than 160. Cancel out c, d, e.
2. Now there are at least three ways of doing it, all of which depend on who you are and how you think. I'll put as many below as I can think of - I think they're all fine and expediant. Remember - if you're spending time looking for the most sophisticated way, you could be just wasting time, especially if you know how to do it algebraically.
Method 1: Algebra
160/x = 175/(x+12)
That's because each stock is worth the same, so if you divide the 160 by the number of shares, or 175 by the number of shares plus 12, you get the same answer. Solve for x = 128.
Method 2: 12 more shares cost $15, so that means each one cost $1.25. So 160/1.25. To do this quickly, convert 1.25 into 5/4(I LOVE FRACTIONS!)Now you've got 160/(5/4) = 160x4/5 = 32x4 = 128.
answer is A
Answer: (A)  128
Question: A & B started a partnership business. A's investment was thrice the investment of B and the period of his investment was two times the period of investments of B. If B received Rs 3000 as profit , what is their total profit?
(A) 21000
(B) 30000
(C) 32000
(D) 34000
(E) None of these
Rationale: Explanation :
Suppose B's investment = x. Then A's investment= 3x
Suppose Bs period of investment = y, then A's period of investment = 2y
A : B = 3x * 2y : xy
= 6 : 1
Total profit * 1/7 = 3000
=> Total profit = 3000*7 = 21000. Answer : Option A
Answer: (A) 21000
Question: When tossed, a certain coin has equal probability of landing on either side. If the coin is tossed 3 times, what is the probability that it will land once on heads and twice tails?
(A) 1/3
(B) 1/6
(C) 1/4
(D) 1/8
(E) 1/5
Rationale: Must be once on heads and twice on tails
1/2*1/2*1/2 = 1/8
Answer: D
Answer: (D) 1/8
Question: What profit percent is made by selling an article at a certain price, if by selling at 2/3rd of that price, there would be a loss of 15%?
(A) 20%
(B) 27.5%
(C) 10%
(D) 80%
(E) 90%
Rationale: SP2 = 2/3 SP1
CP = 100
SP2 = 85
2/3 SP1 = 85
SP1 = 127.5
100 --- 27.5 => 27.5%
Answer: B
Answer: (B) 27.5%
Question: Find the value of y from (12)^3 x 6^4 ÷ 432 = y?
(A) 1234
(B) 2343
(C) 4546
(D) 3435
(E) 5184
Rationale: Given Exp. = (12)3 x 64 = (12)3 x 64 = (12)2 x 62 = (72)2 = 5184
432 12 x 62
E
Answer: (E) 5184
Question: Stuart bought a sweater on sale for 30% off the original price and another 25% off the discounted price. If the original price of the sweater was $30, what was the final price of the sweater?
(A) $15.75
(B) $25.75
(C) $35.75
(D) $45.75
(E) $55.75
Rationale: The price with 30% off
30 - 30% of 30 = 30 - (30 / 100) ? 30 = 30 - 9 = 21
The price with another 25% off
21 - 25% of 21 = 21 - (25/100) ? 21
= 21 - (525 / 100) = 21 - 5.25 = $15.75
correct answer A
Answer: (A) $15.75
Question: A and B invests Rs.10000 each, A investing for 8 months and B investing for all the 12 months in the year. If the total profit at the end of the year is Rs.25000, find their shares?
(A) Rs.10000, Rs.15029
(B) Rs.10000, Rs.15209
(C) Rs.10000, Rs.15129
(D) Rs.10000, Rs.15000
(E) Rs.10000, Rs.35000
Rationale: The ratio of their profits A:B = 8:12 = 2:3
Share of A in the total profit = 2/5 * 25000 = Rs.10000 Share of A in the total profit = 3/5 * 25000 = Rs.15000.Answer:D
Answer: (D) Rs.10000, Rs.15000
Question: By selling an article at Rs.600, a profit of 25% is made. Find its cost price?
(A) Rs.350
(B) Rs.400
(C) Rs.573
(D) Rs.480
(E) Rs.580
Rationale: SP = 600
CP = (SP)*[100/(100+P)]
= 600 * [100/(100+25)]
= 600 * [100/125] = Rs.480
ANSWER:D
Answer: (D) Rs.480
Question: If population of certain city increases at the rate of 5%. If population in 1981 was 138915, then population in 1979 was?
(A) 12,6000
(B) 130000
(C) 261000
(D) 627000
(E) 12690
Rationale: Explanation:
X * (105/100) * (105/100) = 138915
X = 138915/1.1025
X = 126000
Answer: Option A
Answer: (A) 12,6000
Question: The ratio of the number of ladies to gents at a party was 1:4 but when 2 ladies and 2 gents left, the ratio became 1:3. How many people were at the party originally?
(A) 18
(B) 25
(C) 29
(D) 20
(E) 24
Rationale: x, 4x
(x-2):(4x-2) = 1:3
3x-6 = 2x-2
x = 4
x+4x = 5x
=> 5*4 = 20
ANSWER:D
Answer: (D) 20
Question: R is the set of positive odd integers less than 10, and S is the set of the squares of the integers in R. How many elements does the intersection of R and S contain ?
(A) None
(B) One
(C) Four
(D) Five
(E) Two
Rationale: squares < 10 {1,4,9 }
S = {1,9}
R = {1,3,.....10}
Hence E
Answer: (E) Two
Question: Today Joelle opened an interest-bearing savings account and deposited $7,000. If the annual interest rate is 5 percent compounded interest, and she neither deposits nor withdraws money for exactly 2 years, how much money will she have in the account?
(A) $7727.50
(B) $7717.50
(C) $7737.50
(D) $7747.50
(E) $7757.50
Rationale: Interest for 1st year = 7000*5/100 = 350
Interest for 2nd year = 7350 *5/100 = 367.50
Total =7000+350+367.50 = 7717.50
Answer : B
Answer: (B) $7717.50
Question: In a certain group of 10 members, 5 members teach only French and the rest teach only Spanish or German. If the group is to choose 3-member committee, which must have at least 1 member who teaches French, how many different committee can be chosen ?
(A) 40
(B) 50
(C) 64
(D) 80
(E) 110
Rationale: Case 1
1french 2either German or Spanish: 5C1 * 5C2 = 50
Case 2
2french 1either German or Spanish: 5C2 * 5C1 = 50
Case 3
3french 5C3 = 10
Answer is E = 110
Answer: (E) 110
Question: A machine, working at a constant rate, manufactures 18 dies in 25 minutes. How many dies does it make in 1 hr 15 min?
(A) 55
(B) 53
(C) 54
(D) 52
(E) 50
Rationale: Change 1 hr 15 min to 75 min. For this, we need to set up a simple proportion of Dies per time
18/25= S/75
The absolutely worst thing you could do at this point in the problem is to cross-multiply. That would be a supremely unstrategic move. We can cancel the common factor of 25 in the two denominators.
18/1 = S/3
S = 3* 18
S = 54
The machine would be 54 dies in 1 hr 15 min.
Answer: C
Answer: (C) 54
Question: If it costs d dollars to make the first 100 copies of a poster and e dollars for each poster after that, what is the total cost of 125 posters?
(A) 25d + 100e
(B) 100d + 25e
(C) 125de
(D) d + 25e
(E) 125/(de)
Rationale: Dollars needed for first 100 copies = d
Dollars needed for each successive copy = e
Cost of 125 copies = cost of 100 copies + cost of 25 copies = d + 25e
Correct Option: D
Answer: (D) d + 25e
Question: If the sides of a cube are in the ratio 4:3. What is the ratio of their diagonals?
(A) 4:3
(B) 16:9
(C) 64:27
(D) 3:4
(E) 3:8
Rationale: a1:a2 = 4:3
d1:d2 = 4:3
ANSWER:A
Answer: (A) 4:3
Question: Rodrick mixes a martini that has a volume of 'n' ounces having 38% Vermouth and 60% Gin by volume. He wants to change it so that the martini is 25% Vermouth by volume. How many ounces of Gin must he add?
(A) n/6
(B) n/3
(C) 13n/25
(D) 5n/6
(E) 8n/5
Rationale: total V G
1 ounce 0.38 0.6
n ounce 0.38n 0.6n -------------initial expression
lets say g ounces of gin is added to this mixture
n+g 0.38n 0.6n+g --------------final expression
given that after adding g ounces of gin , V should become 25% of the total volume.
=>Volume of V/total volume = 25/100
=> 0.38n /n+g = 1/4
=> 1.52n = n+g
=> g = 3n/5
Answer is C.
Note that after we add pure Gin, the volume of Vermouth will remain the same. Based on this set the equation:
0.38n=0.25(n+g) --> g=13n/25
Answer: C.
Answer: (C) 13n/25
Question: The radius of a wheel is 22.4 cm. What is the distance covered by the wheel in making 1250 resolutions?
(A) 794 m
(B) 704 m
(C) 454 m
(D) 1860 m
(E) 1760 m
Rationale: In one resolution, the distance covered by the wheel is its own circumference. Distance covered in 1250 resolutions.
= 1250 * 2 * 22/7 * 22.4
= 176000 cm
= 1760 m
Answer: E
Answer: (E) 1760 m
Question: A man walking at a constant rate of 9 miles per hour is passed by a woman traveling in the same direction along the same path at a constant rate of 15 miles per hour. The woman stops to wait for the man 3 minutes after passing him, while the man continues to walk at his constant rate. How many minutes must the woman wait until the man catches up?
(A) 1
(B) 2
(C) 3
(D) 4
(E) 5
Rationale: When the woman passes the man, they are aligned (m and w). They are moving in the same direction. After 5 minutes, the woman (W) will be ahead the man (M):
m------M---------------W
w
In the 5 minutes, after passing the man, the woman walks the distance mW = wW, which is 3*15/60 =15/20 miles and the man walks the distance mM, which is 3*9/60 = 9/20 mile.
The difference of 15/20 - 9/20 =3/10 miles (MW) will be covered by the man in (3/10)/9 = 1/30 of an hour, which is 2 minutes.
Answer B.
Answer: (B) 2
Question: Let S be the set of all positive integers n such that n^2 is a multiple of both 24 and 108. Which of the following integers are divisors of every integer n in S ?
(A) 12
(B) 24
(C) 120
(D) 72
(E) 182
Rationale: 4 = 2^3*3;
108 = 2^2*3^3.
The smallest perfect square (n^2) which is a multiple of both 24 = 2^3*3 and 108 = 2^2*3^3 is 2^4*3^4, thus the smallest n is 2^2*3^2 = 36. So, only 12 is a divisor of all integers in S.
Answer: A.
Answer: (A) 12