mathewhe/aqua_rat huggingface dataset:
Question: If 9 is a factor of 2p, then which of the following may not be an integer?
(A) 6p/54 + 2p/3
(B) (4p-18)/9
(C) (2p+27)/9
(D) (81-4p^2)/81
(E) (2p-3)/3
Rationale: I got the right answer A after plugging in 18 for p.
While going through Kaplan's explanation, I couldn't understand the part about choice A.
"6p/54 + 2p/3 = 3/6 * 2p/9 + 2p/3.
Since 9 is a factor of 2p, 3 is also factor of 2p. So 2p/3 is an integer, as is 2p/9. But 3/6 = 1/2, so if 2p/9 is not even, the expression 3/6 * 2p/9 will not be even."
But, isn't 2p/9 always even? 9 is a factor of 2p, which means that we could have 2(9), 2(2)(9), 2(3)(9), and so forth. The 9 in the denominator cancels out the 9 in the numerator. So we are left with 2 * something. So 2p/9 is even.A
Answer: (A) 6p/54 + 2p/3
Question: How many times do the hands of a clock coincide in a day?
(A) 21
(B) 22
(C) 24
(D) 25
(E) 26
Rationale: Explanation:
The hands of a clock coincide 11 times in every 12 hours (Since between 11 and 1, they coincide only once, i.e., at 12 o'clock). For 24 hours total 22 times
Answer is B
Answer: (B) 22
Question: You can throw a baseball at 9 feet per second. If that ball travels through the air for one minute, how far will the ball travel?
(A) 300 feet
(B) 361 feet
(C) 448 feet
(D) 510 feet
(E) 540 feet
Rationale: 9 feet per sec x 60= 540 feet
Answer E
Answer: (E) 540 feet
Question: The average age of an adult class is 40years. 8 new students with an avg age of 32years join the class. Therefore decreasing the average by 4year. Find what was theoriginal strength of class?
(A) 8
(B) 12
(C) 15
(D) 17
(E) 18
Rationale: Let original strength = y
Then , 40y + 8 x 32 = ( y + 8) x 36
â‡’ 40y + 256 = 36y + 288
â‡’ 4y = 32
âˆ´ y = 8
A
Answer: (A) 8
Question: 2610.0 miles - 2554.8 miles =?
(A) 75. 2 miles
(B) 45. 2 miles
(C) 95. 2 miles
(D) 85. 2 miles
(E) 55. 2 miles
Rationale: Subtract: 2610.0
- 2554.8
Answer: 55. 2 miles
correct answer E
Answer: (E) 55. 2 miles
Question: In a survey of parents, exactly 7/8 of the mothers and 3/4 of the fathers held full-time jobs. If 40 percent of the parents surveyed were women, what percent of the parents did not hold full-time jobs?
(A) 20%
(B) 23%
(C) 15%
(D) 18%
(E) 16%
Rationale: Fathers without full-time jobs are 1/4*3/5 = 3/20 of all the parents surveyed.
Mothers without full-time jobs are 1/8*2/5 = 1/20 of all the parents surveyed.
The percent of parents without full-time jobs is 3/20 + 1/20 = 1/5 = 20%
The answer is A.
Answer: (A) 20%
Question: All the students of class are told to sit in circle shape. Here the boy at the 8 th position is exactly opposite to 33 th boy. Total number of boys in the class?
(A) 40
(B) 50
(C) 28
(D) 38
(E) 48
Rationale: As half the circle shape consist of 33-8=25 boys,
So total number of boys in full circle=2*25=50
ANSWER: B
Answer: (B) 50
Question: What is the result of (5!*3! -5!*2!)/(5!*4)
(A) 1
(B) 4
(C) 2
(D) 8
(E) 6
Rationale: (5!*3! -5!*2!)/(5!*4)
=5!*(3!-2!)/5!*4
=(3!-2!)/4
=1
Answer A
Answer: (A) 1
Question: A bag contains 2 white marbles and 2 black marbles. If each of 2 girls and 2 boys randomly selects and keeps a marble, what is the probability that all of the girls select the same colored marble?
(A) 1/35
(B) 1/10
(C) 1/3
(D) 1/4
(E) 1/5
Rationale: first, total ways to select for all boys and girls, i.e 4!/(2!*2!) = 4*3*2*1/2*1*2*1=6
then there are one two way girls can have all same colors, either white or black.
The number of ways in which 2 girls can select 2 white balls = 2C2 = 1
The number of ways in which 2 girls can select 2 black balls = 2C2 = 1
Therefore, total favorable outcomes/total outcomes = 2/6= 1/3
C
Answer: (C) 1/3
Question: If 2+3= 35, 4+5 = 189, what is 10+1=?
(A) 121
(B) 122
(C) 123
(D) 124
(E) 125
Rationale: (2*3+1)*(2+3)=35
(4*5+1)*(4+5)=189
(10*1+1)*(10+1)=11*11=121
ANSWER:A
Answer: (A) 121
Question: A man gains 20% by selling an article for a certain price. If he sells it at double the price, the percentage of profit will be.
(A) 130%
(B) 140%
(C) 150%
(D) 160%
(E) 170%
Rationale: Explanation:
Let the C.P. = x,
Then S.P. = (120/100)x = 6x/5
New S.P. = 2(6x/5) = 12x/5
Profit = 12x/5 - x = 7x/5
Profit% = (Profit/C.P.) * 100
=> (7x/5) * (1/x) * 100 = 140 %
Option B
Answer: (B) 140%
Question: Twenty-eight percent of the programmers in a startup company weigh 200 pounds or more. Twenty-five percent of the programmers that are under 200 pounds in that same company weigh 100 pounds or less. What percent of the programmers in the startup company weigh between 100 and 200 pounds?
(A) 15%
(B) 20%
(C) 25%
(D) 54%
(E) 75%
Rationale: Initially 72% and 28% split
80% is further divided as 25% and 75%
Q is asking about that 75%
let total be '100' then that 75% is (3/4)∗72
so, the required % is [(3/4)∗72/100]∗100 = 54%
ANSWER:D
Answer: (D) 54%
Question: It takes John exactly 30 minutes to rake a lawn and it takes his son Todd exactly 60 minutes to rake the same lawn. If John and Todd decide to rake the lawn together, and both work at the same rate that they did previously, how many minutes will it take them to rake the lawn
(A) 20
(B) 16
(C) 36
(D) 45
(E) 90
Rationale: 1)POE- John takes 30 min so if he takes help of someone else, it has to be less than 30 min..
only A and B are left..
if both do the work in 30 mis each, the combined time will be 15 mins, so 16 is slightly less when the other person does in 60 mins..
ans 20 A
Answer: (A) 20
Question: I have 243 pieces of candy to hand out to my class of 27 students. I would like to give each student the same amount of candy, how much should I give to each student?
(A) 12
(B) 7
(C) 9
(D) 15
(E) 6
Rationale: 243/27 = 9
The answer is C.
Answer: (C) 9
Question: A candidate got 35% of the votes and lost to the rival by 2100 votes. How many votes were cast?
(A) 7000
(B) 7200
(C) 7400
(D) 7600
(E) 7800
Rationale: 35%-----------L
65%-----------W
------------------
30% = 2100
10% = 700
100% of the votes = 7000
Answer: A
Answer: (A) 7000
Question: During 2001, a stock lost 80 percent of its value. During the following year, the stock's value increased by 200 percent. Which of the following is the percent change in the stock's value during those two years?
(A) 60 percent decrease
(B) 40 percent decrease
(C) 20 percent increase
(D) 60 percent increase
(E) 140 percent increase
Rationale: Assume initial Stock value =100
Decreased by 80%
= 100- (80% of 100)
= 20
Increased by 200%
=20+(200% of 20)
=20+40
=60
% Change = (Change/Original)*100
Change=(100-60)=40
Original = 100
40 Percent decrease
ANSWER:B
Answer: (B) 40 percent decrease
Question: What will come in place of the x in the following Number series? 177147 ,59049 ,19683 ,6561, x
(A) 2180
(B) 2189
(C) 2183
(D) 2187
(E) 2186
Rationale: Go on dividing by 3 to the next number
Answer : D
Answer: (D) 2187
Question: In how many different ways can the letters of the word LEADER be arranged so that the vowels always come together?
(A) 3652
(B) 2450
(C) 4320
(D) 3245
(E) 5640
Rationale: Required number = 6!3! = 4320
Answer is C
Answer: (C) 4320
Question: The average of 11 results is 50, if the average of first six results is 49 and that of the last six is 52. Find the sixth result?
(A) 22
(B) 56
(C) 88
(D) 266
(E) 212
Rationale: 1 to 11 = 11 * 50 = 550
1 to 6 = 6 * 49 = 294
6 to 11 = 6 * 52 = 312
6th = 294 + 312 – 550 = 56.Answer: B
Answer: (B) 56
Question: Q is the brother of R;
P is the sister of Q;
T is the brother of S;
S is the daughter of R.
Who are the cousins of Q ?
(A) S and U
(B) S and H
(C) S and K
(D) S and T
(E) S and E
Rationale: Explanation:
T is the brother of S, who is the daughter of R. So, T and S are the children of R.
Now. Q is the brother of R. So, T and S are the cousins of Q.
Answer: D
Answer: (D) S and T
Question: Someone invested x dollars at simple annual interest, and the investment, including interest will be doubled in 8 and 1/3 years. What will be the total amount of the investment after 25 years?
(A) x
(B) 2x
(C) 5x
(D) 6x
(E) 7x
Rationale: Soln:-
x becomes 2x in 8.33 years.
x will become 3*2x in 25 years because the investment is SI and time is 25 years, 3 times 8.33
Answer: 6x
ANSWER:D
Answer: (D) 6x
Question: Sandy walked 20 meters towards south. Then Sandy turned to her left and walked 20 meters. She then turned to her left and walked 20 meters. She then turned to her right and walked 20 meters. What distance is she from the starting point and in which direction?
(A) 20 m East
(B) 40 m North
(C) 30 m West
(D) 40 m East
(E) 20 m West
Rationale: The net distance is 20 + 20 = 40 meters to the east.
The answer is D.
Answer: (D) 40 m East
Question: Anand and Deepak started a business investing Rs. 22,500 and Rs. 35,000 respectively. Out of a total profit of Rs. 13,800, Deepak's share is:
(A) 3776
(B) 2687
(C) 8400
(D) 2688
(E) 2671
Rationale: Ratio of their shares = 22500 : 35000 = 9:14
Deepak's share = 13800 * 14/23 = Rs. 8400.
Answer: C
Answer: (C) 8400
Question: The C.P of 10 pens is equal to the S.P of 16 pens. Find his gain % or loss%?
(A) loss 16 2/8%
(B) loss 16 6/3%
(C) loss 16 2/3%
(D) loss 18 2/3%
(E) loss 37.5%
Rationale: 10 CP = 16 SP
16 --- 6 CP loss
100 --- ? => 37.5% loss
Answer:E
Answer: (E) loss 37.5%
Question: Arvind's gym class can be divided into 8 teams with an equal number of players on each team or into 12 teams with an equal number of players on each team. What is the lowest possible number of students in the class?
(A)  20
(B)  24
(C)  36
(D)  48
(E)  96
Rationale: We are given that arvind's gym class can be divided into 8 teams or 12 teams, with an equal number of players on each team. Translating this into two mathematical expressions we can say, where G is the total number of students in the gym class, that:
G/8 = integer and G/12 = integer
This means that G is a multiple of both 8 and 12.
We are asked to determine the lowest number of students in the class, or the lowest value for variable “G”. Because we know that G is a multiple of 8 and of 12, we need to find the least common multiple of 8 and 12. Although there are technical ways for determining the least common multiple, the easiest method is to analyze the multiples of 8 and 12 until we find one in common.
Starting with 8, we have: 8, 16, 24, 32
For 12, we have: 12, 24
For the multiples of 12, we stopped at 24, because we see that 24 is also a multiple of 8. Thus, 24 is the least common multiple of 8 and 12, and therefore we know that the lowest possible number of students in the gym class is 24.
Answer B.
Answer: (B)  24
Question: 36 men working 8 hours per day dig 30 m deep. How many extra men should be put to dig to a depth of 50 m working 6 hours per day?
(A) A)44
(B) B)77
(C) C)66
(D) D)55
(E) E)37
Rationale: (36 * 8)/30
= (x * 6)/50
=> x =80
80 – 36
= 44
Answer:A
Answer: (A) A)44
Question: A train moves past a telegraph post and a bridge 264 m long in 8 seconds and 20 seconds respectively. What is the speed of the train?
(A) 69.5 km/hr
(B) 70 km/hr
(C) 79 km/hr
(D) 79.2 km/hr
(E) None of these
Rationale: Explanation:
Let the length of the train be L m.
L/8 = (264+L)/20
20L = 8L + 2112
L = 176 m.
Speed of train = 176/8 = 22 m/s = 22 X 18/5 = 79.2 Km/hr
Answer D
Answer: (D) 79.2 km/hr
Question: The factorial expression 12!/2! is not divisible by which of the following integers?
(A) 3
(B) 5
(C) 6
(D) 7
(E) None of these
Rationale: 12!/2! => 12 x 11 x 10 x 9 x 8x7x6x5x4x3
(A) 3 Can divide 3,12 or 9
(B) 5 Can divide 10
(C) 6 Can divide 12
(D) 7 can divide 7, 21, 42
Hence answer will be (E)
Answer: (E) None of these
Question: A given line L has an equation 3x+4y=5. Which of the following is the equation of line which is parallel to the above line?
(A)  4x + 3y = 5
(B)  3x + 4y = 10
(C)  3x + 5y = 5
(D)  3x + 5y = 3
(E)  3x – 4y = 5
Rationale: 3x+4y=5 --- equation 1
2 lines are parallel if
a1/a2 = b1/b2 ≠ c1/c2
Comparing the original line with option B
3x+4y = 10 -- equation 2
From equations 1 and 2 , we get
5=10
which is not possible
Hence our answer is 3x + 4y = 10
Answer B
Answer: (B)  3x + 4y = 10
Question: Raj tossed 3 dices and there results are noted down then what is the probability that Raj gets 10?
(A) 27/219
(B) 27/216
(C) 27/212
(D) 27/211
(E) 27/210
Rationale: Always remember when 3 dice are rolled the number of ways of getting n ( where n is the sum of faces on dice)
= (n−1)C2(n−1)C2 where n = 3 to 8
= 25 where n = 9, 12
= 27 where n = 10, 11
= (20−n)C2(20−n)C2 where n = 13 to 18
The required probability = 27/3 = 27/216
Answer:B
Answer: (B) 27/216
Question: The maitre 'd at an expensive Manhattan restaurant has noticed that 60% of the couples order dessert and coffee. However, 20% of the couples who order dessert don't order coffee. What is the probability T that the next couple the maitre 'd seats will not order dessert?
(A)  20%
(B)  25%
(C)  40%
(D)  60%
(E)  75%
Rationale: could you use a venn diagram and just go with the number 100.
60 people order dessert and coffee... which is the union of D and C.
T=2/10 of D aren't in D U C = so 8/10 of D are in DUC which means =60 =8/10D. So D in total=75, and 15 D's aren't in D union C. which means 25 people are in C only + Neither.
B 25%
Answer: (B)  25%
Question: Find the remainder when 2^31 is divided by 5.
(A) 3
(B) 7
(C) 1
(D) 9
(E) None of them
Rationale: 2^10 = 1024. Unit digit of 2^10 x 2^10 x 2^10 is 4 [as 4 x 4 x 4 gives unit digit 4].
Unit digit of 231 is 8.
Now, 8 when divided by 5, gives 3 as remainder.
Hence, 231 when divided by 5, gives 3 as remainder.
Answer is A.
Answer: (A) 3
Question: If a train, travelling at a speed of 90 kmph, crosses a pole in 5 sec, then the length of train is?
(A) 135 m
(B) 125 m
(C) 129 m
(D) 120 m
(E) 165 m
Rationale: Explanation:
D = 90 * 5/18 * 5 = 125 m
Answer: Option B
Answer: (B) 125 m
Question: A number when divided by 899 gives a remainder 63. If the same number is divided by 29, the remainder will be
(A) 11
(B) 13
(C) 15
(D) Data inadequate
(E) NOne
Rationale: Sol.
Number = (31 x Q) + 29.
Given data is inadequate.
Answer D
Answer: (D) Data inadequate
Question: If paint costs $3.20 per quart, and a quart covers 120 square feet, how much will it cost to paint the outside of a cube 10 feet on each edge?
(A) $ 1.60
(B) $ 16.00
(C) $ 96.00
(D) $108.00
(E) $196.00
Rationale: total surface area = 6a^2 = 6*10*10 = 600
each quart covers 20 sqr ft
thus total number of quarts = 600/120 = 5
cost will be 5*3.2 = $16
Ans: B
Answer: (B) $ 16.00
Question: If one root of the equation 2x^2 + 3x – k = 0 is 4, what is the value of k?
(A) 35
(B) 40
(C) 44
(D) 45
(E) 56
Rationale: We just enter this root into the equation in order to recieve an equation to find the answer!
2*4^2+3*4-k=0
k=32+12=44
The answer is C
Answer: (C) 44
Question: Ramu rides his bike at an average speed of 45 km/hr and reaches his desitination in four hours. Somu covers the same distance in six hours. If Ramu covered his journey at an average speed which was 9 km/hr less and Somu covered his journey at an average speed which was 10 km/hr more, then the difference in their times taken to reach the destination would be (in minutes)?
(A) 11
(B) 30
(C) 88
(D) 66
(E) 41
Rationale: Distance travelled by Ramu = 45 * 4 = 180 km
Somu travelled the same distance in 6 hours.
His speed = 180/6 = 30 km/hr
Hence in the conditional case, Ramu's speed = 45 - 9 = 36 km/hr and Somu's speed = 30 + 10 = 40km/hr.
Therefore travel time of Ramu and Somu would be 5 hours and 4.5 hours respectively. Hence difference in the time taken = 0.5 hours = 30 minutes.
Answer:B
Answer: (B) 30
Question: A person travels equal distances with speeds of 3 km/hr, 4 km/hr and 5 km/hr and takes a total time of 47 minutes. The total distance is?
(A) 1 km
(B) 2 km
(C) 3 km
(D) 4 km
(E) 5 km
Rationale: C
3 km
Let the total distance be 3x km.
Then, x/3 + x/4 + x/5 = 47/60
47x/60 = 47/60 => x = 1.
Total distance = 3 * 1 = 3 km.
Answer: (C) 3 km
Question: What is the units digit of (493) (915) (381) (756)
(A) 0
(B) 1
(C) 4
(D) 5
(E) 6
Rationale: Just multiply the digits in the units place for each term and you will get the answer. It should be 0. you got a 5 as a unit digit and an even number term. so the multiplication of this will definitely yield a 0. Answer has to be 0.
I also tried it using the calculator and the answer is 4.
IMO C.
Answer: (C) 4
Question: 15 men can complete a work in 10 days while 20 boys can complete the same work in 15 days .How many days will 10 men and 10 boys together take to complete the same work
(A) 9 days
(B) 10 days
(C) 11 days
(D) 12 days
(E) 13 days
Rationale: Solution:Work done by one man in one day=1/(15*10)
Work done by one boy in one day=1/(20*15)
Work done by 10 men and 10 boys in one day=10[ 1/(15*10) + 1/(20*15)]
Days taken=1/Work done by 10 men and 10 boys in one day
Answer B
Answer: (B) 10 days
Question: If b does not equal zero, and ab = b/3, what is the value of a?
(A) A)1/8
(B) B)1/4
(C) C)1/3
(D) D)1/2
(E) of the above
Rationale: Explanation:
To solve for a, divide both sides of the equation by b: ab = b/3
(ab)/b = (b/3)/b
a = (b/3)*1/b
a = 1/3
Answer: (C).
Answer: (C) C)1/3
Question: If x = (y)(y + 1) and y is a prime number less than 9, which of the following could not be the product of 2 consecutive integers?
(A) a) 5x
(B) b) 11x
(C) c) 20x
(D) d) 30x
(E) e) 57x
Rationale: Given y is a prime number less than 11
possible values of y are 2 3 5 7
given, x=y*(y+1)
if y = 2 x=2*3=6
if y = 3 x=3*4=12
if y = 5 x=5*6=30
if y = 7 x=7*8=56
so possible values of x are 6,12,30,56
So from options
A. 5x can be (5*6)
B. 11x can be (11*12)
C. 20x can be (20*21)
D. 30x can be (30*31)
E. 57x can be (56*57)
So answer option C
Answer: (C) c) 20x
Question: An amount of Rs.1560 was divided among A, B and C in the ratio 1/2:1/3:1/4. Find the share of C?
(A) Rs.278
(B) Rs.361
(C) Rs.369
(D) Rs.360
(E) Rs.363
Rationale: Let the shares of A, B and C be a, b and c respectively.
a:b:c = 1/2:1/3:1/4
a:b:c = 6/12:4/12:3:12 = 6:4:3
Share of C = 3/13 * 1560 = Rs.360.
Answer: D
Answer: (D) Rs.360
Question: Calculate the value of y: 5y^2-8y+55 = 59
(A) 7
(B) 1
(C) 2
(D) 9
(E) 8
Rationale: Using the elimination method substitute options for x and find the correct option.
Answer: C
Answer: (C) 2
Question: How many divisions are there on the face of a clock?
(A) 1
(B) 5
(C) 6
(D) 22
(E) 25
Rationale: B
5
Any clock or watch except a digital watch, has a dial. On the circular border of the dial of a watch or clock there are the hour numbers from 1 to 12 at equal intervals. Between the two numbers there are 5 divisions.
Answer: (B) 5
Question: 4, 12, 48, (...)
(A) 7620
(B) 10080
(C) 6200
(D) 10020
(E) 240
Rationale: Explanation :
Go on multiplying the given numbers by 3, 4, 5, 6, 7
Answer : Option E
Answer: (E) 240
Question: If a and b are positive even integers, and the least common multiple of a and b is expressed as a*b/n, which of the following statements could be false?
(A) n is a factor of both a and b
(B) (a*b)/n < ab
(C) ab is multiple of 2.
(D) (a*b)/n is a multiple of 2
(E) n is a multiple of 4.
Rationale: If we divide by n and get a multiple of a and of b, then n must be a common factor. Answer A must be true.
If a and b are even integers, dividing by a factor (also an integer) results in something smaller than the product ab. Answer B must be true.
If either a or b is even, then ab must be even. Answer C must be true.
If both are even, the smallest either number can be is 2. Thus, the smallest common factor must be 2. Answer D must be true.
If b is 6 and a is 2, n would be 6, which is not 4. E can be false.
ANSWER:E
Answer: (E) n is a multiple of 4.
Question: The side of a square is increased by 40% then how much % does its area increases?
(A) 96
(B) 56.25
(C) 50.75
(D) 42.75
(E) 52.75
Rationale: a = 100 a2 = 10000
a = 140 a2 = 19600
----------------
10000 --------- 9600
100 -------? => 96 %
ANSWER: A
Answer: (A) 96
Question: John is three times as old as Sam. If John will be twice as old as Sam in five years, how old was Sam two years ago?
(A) 2
(B) 4
(C) 6
(D) 3
(E) 16
Rationale: j= 3s
after 5 years
j +5 = 2(s+5)
j= 2s+5
2s +5 = 3s
s= 5
two years ago
s= 5-2= 3
D is the answer
Answer: (D) 3
Question: Population of a city in 2004 was 1000000. If in 2005 there is an increment of 40% , in 2006 there is a decrements of 35 % and in 2007 there is an increment of 45%, then find the population of city at the end of the year 2007
(A) 967532
(B) 977522
(C) 984424
(D) 997454
(E) 1319500
Rationale: Required population = P (1 + R1/100)(1 - R2/100)(1 + R3/100)
= P (1 + 40/100)(1 - 35/100)(1 + 45/100)
= 1319500
E
Answer: (E) 1319500
Question: If x=2, which of the following is(are) true? I. x^2=2x II x/-4 = 1 III |x|=-x
(A) II only
(B) III only
(C) II,III only
(D) I only
(E) I,III only
Rationale: 2^2 = 2 * 2
Answer : D
Answer: (D) I only
Question: Two trains 140 m and 160 m long run at the speed of 60 km/hr and 40 km/hr respectively in opposite directions on parallel tracks. The time which they take to cross each other is?
(A) 10.9 sec
(B) 10.3 sec
(C) 10.7 sec
(D) 10.8 sec
(E) 10.1 sec
Rationale: Relative speed = 60 + 40 = 100 km/hr.
= 100 * 5/18 = 250/9 m/sec.
Distance covered in crossing each other
= 140 + 160 = 300 m.
Required time
= 300 * 9/250 = 54/5 = 10.8 sec.
Answer:D
Answer: (D) 10.8 sec
Question: In a can, there is a mixture of milk and water in the ratio 2 : 5. If it is filled with an additional 8 litres of milk the can would be full and ratio of milk and water would become 4 : 5. Find the capacity of the can?
(A) 40
(B) 44
(C) 48
(D) 50
(E) 8
Rationale: Let the capacity of the can be T litres.
Quantity of milk in the mixture before adding milk = 2/7 (T - 8)
After adding milk, quantity of milk in the mixture = 4/9 T.
4T/9 - 8 = 2/7(T - 8)
2T = 72 - 56 => T = 8.
Answer:E
Answer: (E) 8
Question: What will be the cost of building a fence around a square plot with area equal to 289 sq ft, if the price per foot of building the fence is Rs. 58?
(A) Rs.3944
(B) Rs.3942
(C) Rs.3987
(D) Rs.3929
(E) Rs.3938
Rationale: Let the side of the square plot be a ft.
a2 = 289 => a = 17
Length of the fence = Perimeter of the plot = 4a = 68 ft.
Cost of building the fence = 68 * 58
= Rs.3944.
Answer:A
Answer: (A) Rs.3944
Question: The juice stall at the circus stocked just 2 brands of orange juice tetra packs. Brand A costs $1 per pack and brand B costs $1.5 per pack. Last week , brand A contributed to p% of stall’s revenue and accounted for q% of sales of juice tetra packs. Which of the following expresses p in terms of q?
(A) 100q/(150 – q)
(B) 200q/(250-q)
(C) 200q/(300-q)
(D) 250q/(400-q)
(E) 300q/(500-q)
Rationale: 1. Let the number of units sold be 100. Then q units of A are sold and (100-q ) units of B are sold.
Total revenue= Revenue due to A + Revenue due to B
= (No.of units of A sold * Cost/unit of A) + (No.of units of B sold * cost/unit of B)
= q *1 + (100-q ) *1.5
= q + (150-1.5q ) --- (1)
2. But we know, revenue due to A = p%. of the total revenue --- (2)
3. To express p in terms of q we need to relate (1) and (2)
4. p% = q / ( q + (150-1.5q ))
C
or m= 100n / 150-0.5n = 200n/(300-n)
Answer: (C) 200q/(300-q)
Question: If the average of a sequence of consecutive multiple of 18 is 153, and the greatest term is 270, how many terms E in the sequence are smaller than the average?
(A) 5
(B) 6
(C) 7
(D) 8
(E) 9
Rationale: Let the sequence have N terms starting 18*K
--> 18K, 18(K+1), 18(K+2), .... , 18(K+N-1) is the sequence.
The sum of the sequence is
---> 18K + 18(K+1) + 18(K+2) + .... + 18(K+N-1) =18*(K+(K+1)+...+(K+N-1)) = 18*(N*(2K+N-1)/2).
So the average is
153=[18*(N*(2K+N-1)/2)]/N = 18*(2K+N-1)/2 = 9 *(2K+N-1) ---> by cancelling 9 we get 2K+N-1=17 --> 2K+N=18 ---*).
On the other hand, since the greatest term is 270, 18(K+N-1)=270 --> by cancelling 18 we get K+N-1=15 --> K+N=16 ---**).
By *), **) we have K=2, N=14.
Since 153/18 = 8.5, 18*8<153<18*9. So the number of terms E which are smaller than the average is 18*2, 18*3, ..... ,18*8 ---> 7. The answer is C.
Answer: (C) 7
Question: A hall is 18 meters long and 9 meters wide. If the sum of the areas of the floor and the ceiling is equal to the sum of the areas of four walls, what is the volume of the hall (in cubic meters)?
(A) 640
(B) 758
(C) 862
(D) 972
(E) 1024
Rationale: 2HL + 2HW = 2LW
H = LW / (L+W)
Volume = LWH = (LW)^2 / (L+W) = 972
The answer is D.
Answer: (D) 972