mathewhe/aqua_rat huggingface dataset:
Question: A man's speed with the current is 15 km / hr and the speed of the current is 2.5 km / hr. The man's speed against the current is
(A) 8.5 km / hr
(B) 9 km / hr
(C) 10 km / hr
(D) 12.5 km / hr
(E) None
Rationale: Sol.
Man's rate in still in water = (15 - 2.5) km / hr = 12.5 km / hr.
Man's rate against the current = (12.5 - 2.5) km / hr = 10 km / hr.
Answer C
Answer: (C) 10 km / hr
Question: There are three positive intigers such that 70% of the first number , 58 1/3% of second number and 38 8/9% of the third number are all equal. Which of the following can those three numbers be?
(A) 5,6,9
(B) 10,12,18
(C) 15,18,27
(D) All the three
(E) none of these
Rationale: All the three are in the same ratio
ANSWER:D
Answer: (D) All the three
Question: A drink vendor has 60 liters of Maaza, 144 liters of Pepsi and 368 liters of Sprite. He wants to pack them in cans, so that each can contains the same number of liters of a drink, and doesn't want to mix any two drinks in a can. What is the least number of cans required?
(A) 135
(B) 137
(C) 143
(D) 310
(E) 380
Rationale: The number of liters in each can = HCF of 60, 144 and 368 = 4 liters.
Number of cans of Maaza = 60/4 = 15
Number of cans of Pepsi = 144/4 = 36
Number of cans of Sprite = 368/4 = 92
The total number of cans required = 15 + 36 + 92 = 143 cans.
ANSWER:C
Answer: (C) 143
Question: The number of singles that a baseball player hit increased 5 percent from her first season to her second season, and the number of doubles that she hit in the same time period decreased by 2 percent. If the total number of singles and doubles that she hit increased 2 percent from her first season to her second season, what is the ratio of the number of singles she hit in her first season to the number of doubles she hit in her first season?
(A) 4:3
(B) 9:11
(C) 3:1
(D) 2:1
(E) 11:3
Rationale: Soln:-
1.05S + 0.98D = 1.02[S + d]
0.03S = 0.04D
S/D = 4/3
ANSWER:A
Answer: (A) 4:3
Question: Sakshi invests a part of Rs. 12,000 in 12% stock at Rs. 120 and the remainder in 15% stock at Rs. 125. If his total dividend per annum is Rs. 1350, how much does he invest in 12% stock at Rs. 120?
(A) s. 4000
(B) s. 4500
(C) s. 5500
(D) s. 6000
(E) s. 6500
Rationale: Let investment in 12% stock be Rs. x.
Then, investment in 15% stock = Rs. (12000 - x).
12/120 * x + 15/125 * (12000- x) = 1350
x/10 + 3/25(12000-x) = 1350
5x + 72000 - 6x = 1350 x 50
x = 4500.
Answer = B
Answer: (B) s. 4500
Question: A small company is planning to rent either computer A or computer B to print customer mailing lists. Both computer A and computer B must be rented on an hourly basis. The rental fee is based only on the amount of time the computer is turned on. It will cost 40 percent more per hour to rent computer A than to rent computer B. Computer B would, however, require 20 hours more than computer A to do the job. If either computer A, or computer B were rented the total cost to rent the computer would be $700.00. What would be the approximate hourly charge to rent computer B?
(A) $9.40
(B) $10.00
(C) $13.20
(D) $17.80
(E) $22.10
Rationale: Pa = price of A
Pb = price of B
Ta = time for A to complete the job
Tb = time for B to complete the job
Given
Pa = 1.4 Pb
Ta+20 = Tb
Pa*Ta = Pb*Tb=700
1.4Pb * (Tb-20) = Pb*Tb
1.4 Pb Tb - Pb Tb = 1.4 Pb * 20
0.4PbTb = 28Pb
Tb = 28/0.4 = 70
Pb=700/70 =10
B
Answer: (B) $10.00
Question: A husband and wife can complete a certain task in 1 and 2 hours respectively. Their children, Rae and Herman, can complete the same task in 4 and 7 hours, respectively. What is the ratio of the couple's time working together to complete the task to the children's time working together to complete the task?
(A) a)11:42
(B) b)3:10
(C) c)12:23
(D) d)5:18
(E) e)10:3
Rationale: couples one hour work=1/1+1/2=3/2
so total time=2/3..
now, kids one hour work=1/4+1/7=11/28
so total time=28/11..
ratio=2/3:28/11=11:42
ans A
Answer: (A) a)11:42
Question: What is the units digit of (147^25)^50 ?
(A) 1
(B) 3
(C) 5
(D) 7
(E) 9
Rationale: The units digit of the exponents of 7 repeat in a cycle of four, which is {7,9,3,1}. The number 25 has the form 4n+1 so the units digit is 7 inside the bracket. The exponent 50 has the form 4n+2, so the units digit is 9. The answer is E.
Answer: (E) 9
Question: In how many different ways can the letters of the word â€˜DIVIDEDâ€™ be arranged?
(A) 250
(B) 280
(C) 300
(D) 420
(E) 360
Rationale: Number of ways = 7!/3!2! = 7X6X5X4X3X2X1/3X2X1X2X1 = 420
D
Answer: (D) 420
Question: If p and q are two different odd prime numbers, such that p < q, then which of the following must be true?
(A) (2p + q) is a prime number
(B) p + q is divisible by 4
(C) q - p is divisible by 4
(D) (p + q + 1) is the difference between two perfect squares of integers
(E) p2+q2 is the difference between two perfect squares of integers
Rationale: 1. (2p + q) for sure is an odd number , but may or may not be a prime number .
Eg - if we take 3 and 5 as p and q resp, we get 11, which is a prime number.
But if we take 7 and 11, we get 25, which is not a prime number.
2. p + q for sure gives us an even number. It may or may not be divisible by 4.
Eg - (7 + 5) = 12 , which is divisible by 4. But (11 + 7) = 18 , not divisible by 4
3. Same way as 2nd.
4. (p + q + 1) gives us an odd number.
Lets see the trend of difference between squares of consecutive integers.
2^2 - 1^2 = 3
3^2 - 2^2 = 5
4^2 - 3^2 = 7
5^2 - 4^2 = 9
6^2 - 5^2 = 11 and so on.
The trend is : The difference between squares of consc. integers is always odd number. And it covers all the odd numbers.
However , when we don't take consecutive integers, this trend is not followed.
Eg : 5^2 - 3^2 = 16 , which is an even number
3^2 - 1^2 = 8 , again not an odd number
Hence : Any odd number can be expressed as the difference of the squares of integers.
5. (p^2 + q^2) gives an even number.
ANSWER:D
Answer: (D) (p + q + 1) is the difference between two perfect squares of integers
Question: The average of 5 consecutive integers starting with m as the first integer is n. What is the average of 5 consecutive integers that start with (m + 2)?
(A) m + 3
(B) n + 6
(C) n + 3
(D) m + 5
(E) n + 2
Rationale: The average of consecutive numbers is the middle number.
Then n = m+2.
The average of 5 consecutive numbers starting from n is n+2.
The answer is E.
Answer: (E) n + 2
Question: If 0 < p < 1 < q< 5, which of the following must be less than 1? I. p/q II. pq III. q - p
(A) III only
(B) II only
(C) I only
(D) II,III only
(E) I,III only
Rationale: q > 1. So, option II, III is not possible.
So, Option I is correct.
Answer : C
Answer: (C) I only
Question: John bought a shirt on sale for 25% off the original price and another 25 % off the discounted price. If the final price was $14, what was the price before the first discount?
(A) $45.10
(B) $34.31
(C) $24.88
(D) $67.54
(E) $65.23
Rationale: let x be the price before the first discount. The price after the first discount is
x - 25%x (price after first discount)
A second discount of 25% of the discounted price after which the final price is 14
(x - 25%x) - 25%(x - 25%x) = 14
Solve for x
x = $24.88
correct answer C
Answer: (C) $24.88
Question: In a games hour 4 different types of players came to the ground? cricket 12, hokey 17, football 11, softball 10. How many players are present in the ground?
(A) 70
(B) 50
(C) 62
(D) 49
(E) 50
Rationale: total number of players= 12+17+11+10= 50
Answer is B
Answer: (B) 50
Question: A team of 8 students goes on an excursion, in two cars, of which one can seat 5 and the other only 4. In how many ways can they travel?
(A) 126
(B) 277
(C) 188
(D) 171
(E) 181
Rationale: There are 8 students and the maximum capacity of the cars together is 9.
We may divide the 8 students as follows
Case I: 5 students in the first car and 3 in the second
Or Case II: 4 students in the first car and 4 in the second
Hence, in Case I: 8 students are divided into groups of 5 and 3 in8C3 ways.
Similarly, in Case II: 8 students are divided into two groups of 4 and 4 in 8C4ways.
Therefore, the total number of ways in which 8 students can travel is:
8C_{3}+8C_{4}}=56 + 70= 126
Answer: A
Answer: (A) 126
Question: The ages of two person differ by 20 years. If 7 years ago, the elder one be 5 times as old as the younger one, their present ages(in years) are respectively
(A) 30, 10
(B) 32, 12
(C) 29, 9
(D) 50, 30
(E) 20,10
Rationale: Let their ages be x and (x + 20) years.
Then, 5(x - 7) = (x + 20 - 7)
=> 4x = 48
=>x =12
Their present ages are 32 years and 12 year.
ANSWER:B
Answer: (B) 32, 12
Question: Peter has 9 candies, rina has 5 candies. Totally how many candies they have in all?
(A) 14
(B) 4
(C) 23
(D) 12
(E) 9
Rationale: 9+5=14. Answer is A
Answer: (A) 14
Question: The guidelines at a certain college specify that for the introductory English class, the professor may choose one of five specified novels, and choose two plays from a list of 6 specified plays. Thus, the reading list for this introductory class has one novel and two plays. How many different reading lists could a professor create within these parameters?
(A) 55
(B) 60
(C) 65
(D) 70
(E) 75
Rationale: 5C1*6C2 = 5*15 = 75
The answer is E.
Answer: (E) 75
Question: The length of a rectangle is reduced by 20%. By what % would the width have to be increased to maintainthe original area?
(A) 14%
(B) 15%
(C) 25%
(D) 30%
(E) 35%
Rationale: Sol. Required change = (20*100)/(100-20)=25%
C
Answer: (C) 25%
Question: 11, 10, ?, 100, 1001, 1000, 10001
(A) 1000
(B) 121
(C) 111
(D) 101
(E) 91
Rationale: The pattern is - 1, × 10 + 1, - 1, × 10 + 1, - 1, × 10 + 1, ....
Answer : D.
Answer: (D) 101
Question: For any non-zero a and b that satisfy |ab| = ab and |a| = -a
|b - 6| + |ab - b| = ?
(A) a) ab - 2b + 6
(B) b) 2b - ab - 4
(C) c) ab + 4
(D) d) ab - 2b + 4
(E) e) 4 - ab
Rationale: |a| = -a Suggests that 'a' is Negative
|ab| = ab Suggests that 'ab' is Positive
'ab' is Positive Suggests that 'a' and 'b' have same Sign i.e. either both positive or both negative
But since 'a' is Negative therefore 'b' is Negative too.
Since b is negative so |b - 6| = -b+6
Since ab is Positive and b is Negative so |ab - b| = ab - b
i.e. |b - 6| + |ab - b| = -b+6 + ab - b =ab - 2b + 6
Answer: Option A
Answer: (A) a) ab - 2b + 6
Question: A, B and C invested Rs.6500, Rs.1300 and Rs.7800 respectively, in a partnership business. Find the share of B in profit of Rs.11700 after a year?
(A) 1300
(B) 3877
(C) 1170
(D) 975
(E) 7800
Rationale: Explanation:
6500:1300:7800
5:1:6
1/12 * 11700 = 975
Answer:D
Answer: (D) 975
Question: 6 mangoes are equal to as many apples as are equal to 4 kiwi. All of them weigh 90kg only. Mango’s weighs are?
(A) 6
(B) 5
(C) 2
(D) 7
(E) 2
Rationale: 6M = xA = 4K
6M + xA + 4K ----- 90 Rs.
6M+6M+6M----- 90 Rs.
18M ------ 90 Rs. => 1M = 5Rs.
Answer: B
Answer: (B) 5
Question: The average weight of a class is x pounds. When a new student weighing 100 pounds joins the class, the average decreases by 1 pound. In a few months the student’s weight increases to 110 pounds and the average weight of the class becomes x + 4 pounds. None of the other students’ weights changed. What is the value of x?
(A) 85
(B) 86
(C) 88
(D) 90
(E) 92
Rationale: When the student weighs 80 pounds the average weight is x - 1 pounds;
When the student weighs 110 pounds the average weight is x + 4 pounds.
So, the increase in total weight of 110 - 80 = 30 pounds corresponds to the increase in average weight of (x + 4) - (x - 1) =5 pounds, which means that there are 30/5 = 6 students (including the new one). So, initially there were 5 student.
Total weight = 5x + 80 = 6(x-1) --> x = 92 pounds.
Answer: E.
Answer: (E) 92
Question: There are 2 white plates, 6 green plates, 8 red plates, 4 pink plates, and 10 purple plates in the cabinet. What is the least number of plates that you have to pull out to make sure that you will have a matching pair? (Assume that all the plates are identical except for the color)
(A) 2
(B) 4
(C) 12
(D) 7
(E) 6
Rationale: Since there are 5 colors, if you take 5 plates, you could still have 1 plate per color and not have a match.
Therefore, upon taking the 6th plate, you will definitely have a match since the 6th plate will form at least a pair with the 1st 5
So 5+1 = 6
Answer is E
Answer: (E) 6
Question: The probability that a brand A widget is defective is x, the probability that a brand B widget is defective is 0.06, and the probability that a brand C widget is defective is 0.08. There are 40 brand A widgets, 30 brand B widgets, 30 brand C widgets, and nothing else in a container. If a widget is selected at random from the container, the probability that the widget selected is defective is 0.053. What is the value of x?
(A) 0.02
(B) 0.095
(C) 0.03
(D) 0.0275
(E) 0.4
Rationale: Given probability of defective items in each brand,
So, the number of items defective in brand A=x*40, in brand B=0.06*30 and brand C=0.08*30
Total number of widgets=40+30+30=100
the probability that the widget selected is defective is 0.053=(x*40+0.06*30+0.08*30)/100
=> 40x+1.8+2.4 =5.3
=>40x=1.1
>x=1.1/40=0.0275
Ans D
Answer: (D) 0.0275
Question: Three numbers are in the ratio 5 : 6 : 7. The sum of its longest and smallest numbers equals the sum of the third number and 48. Find the third number?
(A) 54
(B) 75
(C) 48
(D) 46
(E) 63
Rationale: Let the numbers be 5x, 6x, 7x.
Largest number = 7x.
Smallest number = 5x.
Third number = 6x.
7x + 5x = 6x + 48
6x = 48 => third number is 48.
Answer:C
Answer: (C) 48
Question: If two typists can type two pages in two minutes, how many typists will it take to type 22 pages in eleven minutes?
(A) 3
(B) 4
(C) 6
(D) 12
(E) 36
Rationale: In 2 minutes 2 typists type 2 pages which means that in 11 minutes they will type 11 pages but to type 22 pages (2 times) we need 2 times more typists i.e. 2 x 2 = 4 typists.
B
Answer: (B) 4
Question: Excluding stoppages, the average speed of a bus is 120 km/hr and including stoppages, the average speed of the bus is 40 km/hr. For how many minutes does the bus stop per hour?
(A) 15 min
(B) 18 min
(C) 16 min
(D) 20 min
(E) 40 min
Rationale: In 1hr, the bus covers 120 km without stoppages and 40 km with stoppages.
Stoppage time = time take to travel (120 - 40) km i.e 80 km at 120 km/hr.
stoppage time = 80/120 hrs
= 40 min
Answer: E
Answer: (E) 40 min
Question: How many figures are required for numbering the pages of a book containing 1000 pages?
(A) 2726
(B) 2878
(C) 2893
(D) 2765
(E) 1811
Rationale: Explanation:
1 to 9 = 9 * 1 = 9
10 to 99 = 90 * 2 = 180
100 to 999 = 900 * 3 =2700
1000 = 4
-----------
2893
Answer:C
Answer: (C) 2893
Question: 18 beavers, working together in a constant pace, can build a dam in 8 hours. How many hours will it take 36 beavers that work at the same pace, to build the same dam?
(A) 2.
(B) 4.
(C) 5.
(D) 6
(E) 8.
Rationale: Total Work = 18*8= 144 Beaver hours
36 Beaver * x =144Beaver hours
x=144/36 = 4
ANSWER:B
Answer: (B) 4.
Question: A certain city with a population of 72,000 is to be divided into 11 voting districts , and no district is to have a population that is more than 10 percent greater than the population of any other district What is the minimum possible population that the least populated district could have ?
(A) a) 6,000
(B) b) 10,800
(C) c) 10,900
(D) d) 11,000
(E) e) 11,100
Rationale: Let x = number of people in smallest district
x*1.1 = number of people in largest district
x will be minimised when the number of people in largest district is maximised
10*x*1.1 = 11x = total number of people in other districts
So we have 11x + x = 72k
x = 6,000
Answer : A
Answer: (A) a) 6,000
Question: Excepting B, the rest of the sentences can be the beginners of a paragraph. Excepting in the first answer choice–a, sentence B breaks the sequence of the rest of the choices.
(A) 87
(B) 9
(C) 917
(D) 777
(E) 811
Rationale: Answer:C
Answer: (C) 917
Question: A retailer sells pashminas at a ten percent discount. If a pashmina cost him $75 and he wants to make a profit of no less than twenty percent on the cost (after the discount), what is the minimum tag price he needs to put on a pashmina?
(A) 90
(B) 100
(C) 120
(D) 140
(E) 150
Rationale: The minimum tagged price the retailer needs to sell at to make a profit of at least 20%, after offering a 10% discount on tagged price is 1.2*CP(90).
Since, he has to sell the pashmina at 10% discount.
Marked price is 100$
ANS (Option B)
Answer: (B) 100
Question: Here 10 programmers, type 10 lines with in 10 minutes then 60lines can type within 60 minutes. How many programmers are needed?
(A) 16
(B) 6
(C) 10
(D) 60
(E) 50
Rationale: formulas for it (men1*time1)/work1=(m2*t2)/w2
(10*10)/10=(m2*60)/60
(10*10*60)/(10*60)
ans is 10.
ANSWER:C
Answer: (C) 10
Question: A bank lent $250 to a customer for a one-month loan. At the end of the month, the bank received y dollars more than than the amount that was lent due to interest. The bank also charged a service fee $5. In terms of y, what fraction of the amount that the bank received was the service fee?
(A) 5/(255+y)
(B) 5y-1
(C) 5y/(250-y)
(D) 5/(250-y)
(E) 5y-250
Rationale: The amount of money the bank received was (250 + 5+ y) dollars. The $5 service fee as a fraction of the amount received was, therefore, 5/(255+y).
Answer: A.
Answer: (A) 5/(255+y)
Question: In what time will Rs.4800 lent at 3% per annum on simple interest earn as much interest as Rs.5000 will earn in 5 years at 4% per annum on simple interest?
(A) 7
(B) 7 1/6
(C) 7 1/3
(D) 7 1/2
(E) 8
Rationale: (4800*3*R)/100 = (5000*5*4)/100
R = 7
Answer: A
Answer: (A) 7
Question: Find the value(s) of k for which there is no solution for the given set of equations.
2x - ky = -3 and 3x + 2y = 1
(A) 4/9
(B) 2/9
(C) 2/1
(D) 4/3
(E) 2/5
Rationale: 3x + 2y = 1
If there are no set of solutions, then 2−k=322−k=32 or k = −43−43
For k = −43−43, the two lines in the coordinate planes are parallel to each other.
Answer:D
Answer: (D) 4/3
Question: Four people each roll a four die once. Find the probability that at least two people will roll the same number ?
(A) 3378
(B) 27778
(C) 2211
(D) 1318
(E) 2882
Rationale: The number of ways of rolling a dice where no two numbers probability that no one rolls the same number = 6 x 5 x 4 x 3
Now total possibilities of rolling a dice = 64
The probability that a no one gets the same number = 6×5×4×364=518
So the probability that at least two people gets same number = 1−518=1318
Answer:D
Answer: (D) 1318
Question: How many numbers amongst the numbers 6 to 45 are there which are exactly divisible by 15 but not by 10?
(A) Nil
(B) 1
(C) 2
(D) 3
(E) More than 3
Rationale: 15,30,45 are divisible by 15.
30 is divisible by 10 also.
So there are 2 numbers exactly divisible by 15 but not by 10
ANSWER:C
Answer: (C) 2
Question: Last year, the price of a vacation package was P. At the beginning of this year, the price went up 40%. Lucas used a travel voucher to purchase the vacation package at 30% off this year’s price. In terms of P, how much did Lucas pay?
(A) P + 10
(B) 1.1*P
(C) 1.12*P
(D) 0.9*P
(E) 0.98*P
Rationale: Last year price = P;
This year price = 1.4P;
Lucas used a travel voucher to purchase the vacation package at 30% off this year’s price, thus he paid (1 - 0.3)*1.4P = 0.98P.
Answer: E.
Answer: (E) 0.98*P
Question: Roy opened a shop investing Rs.20000. Alex joined him 8 months later, investing Rs.34000. They earned a profit of Rs.32000 after completion of two years. What will be Roy's share of profit?
(A) 18000
(B) 19000
(C) 20000
(D) 15000
(E) 17000
Rationale: SoL = ~s- So Roy's share = [15/32] x 32000 = 15000
Answer : D
Answer: (D) 15000
Question: A group of men decided to do a work in 10days, but 5 of them became absent. If the rest of the group did the work in 12days, Find the original number of men?
(A) 15
(B) 20
(C) 30
(D) 25
(E) 18
Rationale: Original number of men = 5*12 / (12-10) = 30
Answer is C
Answer: (C) 30
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 $18.00, 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 = 18
0.4x = 2 => x = 5
discounted tickets = 10 -x = 5
Ans : C
Answer: (C) 5
Question: Sum of two consecutive even terms lacks by 98 from their product. Find the sum of these numbers?
(A) 22
(B) 38
(C) 22
(D) 98
(E) 19
Rationale: Explanation:
x(x + 2) â€“ (x + x + 2) = 98
Answer: D
Answer: (D) 98
Question: Siddharth wants to borrow Rs.6000 at rate of interest 6% p.a. at S.I and lend the same amount at C.I at same rate of interest for two years. What would be his income in the above transaction?
(A) Rs.21.60
(B) Rs.21.68
(C) Rs.21.18
(D) Rs.21.98
(E) Rs.21.29
Rationale: Amount of money Siddharth borrowed at S.I at 6% p.a. for two years = Rs.6,000
He lend the same amount for C.I at 6% p.a. for two years.
=> Siddharth's income = C.I - S.I
= p[1 + r/ 100]n - p - pnr/100
= p{ [1 + r/ 100]2 - 1 - nr/100
= 6,000{ [1 + 6/100]2 - 1 - 12/100}
= 6,000 {(1.06)2- 1 - 0.12} = 6,000(1.1236 - 1 - 0.12)
= 6,000 (0.0036) = 6 * 3.6
= Rs.21.60
Answer: A
Answer: (A) Rs.21.60
Question: A dealer originally bought 200 identical batteries at a total cost of q dollars. If each battery was sold at 50 percent above the original cost per battery, then, in terms of q, for how many dollars was each battery sold?
(A) 3q/400
(B) 3q/2
(C) 300q
(D) q/200
(E) 300/q
Rationale: The cost of each battery was q/200.
Each battery was sold for 1.5q/200 = 3q/400.
The answer is A.
Answer: (A) 3q/400
Question: Jack and Jill are marathon runners. Jack can finish a marathon (41 km) in 4.5 hours and Jill can run a marathon in 4.1 hours.What is the ratio of their average running speed? (Jack: Jill)
(A) 41/45
(B) 15/14
(C) 4/5
(D) 5/4
(E) Cannot be determined
Rationale: Average Speed of Jack =Distance/ Time
= 41 /(9/2) = 82/9
Average Speed of Jill = 41/(4.1) = 10
Ratio of Average speed of Jack to Jill = (82/9)/10 = 82/90 = 41/45
Answer A
Answer: (A) 41/45
Question: All the water in container A which was filled to its brim was poured into two containers B and C. The quantity of water in container B was 62.5% less than the capacity of container A. If 150 liters was now transferred from C to B, then both the containers would have equal quantities of water. What was the initial quantity of water in container A?
(A) 1289
(B) 1198
(C) 281
(D) 1200
(E) 282
Rationale: Explanation:
B has 62.5% or (5/8) of the water in A. Therefore, let the quantity of water in container A(initially) be 8k.
Quantity of water in B = 8k - 5k = 3k.
Quantity of water in container C = 8k - 3k = 5k
Container: A B C
Quantity of water: 8k 3k 5k
It is given that if 150 liters was transferred from container C to container B, then both the containers would have equal quantities of water.
5k - 150 = 3k + 150 => 2k = 300=> k = 150
The initial quantity of water in A = 8k = 8 * 150= 1200 liters.
Answer: Option D
Answer: (D) 1200
Question: If the speed of X meters per minute is equivalent to the speed of Y kilometers per hour, what is Y in terms of X? (1 kilometer=1000 meters)
(A) 0.06
(B) 0.6
(C) 6
(D) 0.03
(E) 0.3
Rationale: X meters per second -->
--> 60X meter per hour(as there are 60 minute in one hour);
--> 60X/1,000=kilometers per hour (as there are 1,000 meters in one kilometer).
Answer: A.
Answer: (A) 0.06
Question: How many bricks, each measuring 25 cm x 11.25 cm x 6 cm, will be needed to build a wall of 8 m x 6 m x 22.5 cm?
(A) 6000
(B) 6200
(C) 6400
(D) 6600
(E) 6650
Rationale: Number of bricks = Volume of the wall/Volume of 1 brick
= (800 x 600 x 22.5/25 x 11.25 x 6) = 6400.
ANSWER C
Answer: (C) 6400
Question: A milk vendor sells milk at Cost Price but still gains 20%. Find the ratio of milk and water in every gallon that he sells.
(A) 4:1
(B) 5:1
(C) 5:2
(D) 6:1
(E) None of these
Rationale: Let the vendor buy 100 L of milk. For him to make 20% profit, he has to turn this 100 L into 120 L without incurring any cost. So he has to mix 20 L of water. So ratio of milk to water is 100/20=5 ;ANSWER:B
Answer: (B) 5:1
Question: If x is the product of the positive integers from 1 to 9, inclusive, and if i, k, m, and p are positive integers such that x=2i3k5m7px=2i3k5m7p, then i + k + m + p =
(A) 4
(B) 7
(C) 8
(D) 11
(E) 13
Rationale: x= 9!
= 9* 8 * 7 * 6 * 5 * 4 * 3 * 2 * 1
= (3^2) * (2^3) * 7 * (2*3) * 5 * 2^2 * 3 * 2 * 1
= 2^7 * 3^4 * 5 * 7
= 2^i * 3^k * 5^m * 7^p
i+k+m+p = 7+4+1+1
= 13
Answer E
Answer: (E) 13