mathewhe/aqua_rat huggingface dataset:
Question: If cyclist is covering a circular distance of diameter 15 inches at the speed of x inches/min, and another cyclist is covering a circular distance of diameter 25 inches at the speed of y inches/min then what is the value of y in terms of x if both the cyclists cover the distance at the same time?
(A) 2x/4
(B) 6x/2
(C) 7x/3
(D) 5x/3
(E) 4x/3
Rationale: t=S1/V1=S2/V2
or 15/x=25/y
or y=25x/15=5x/3
Answer is D
Answer: (D) 5x/3
Question: The marks obtained by Vijay and Amith are in the ratio 4:5 and those obtained by Amith and Abhishek in the ratio of 3:2. The marks obtained by Vijay and Abhishek are in the ratio of?
(A) 6:6
(B) 6:9
(C) 6:5
(D) 6:2
(E) 6:1
Rationale: 4:5
3:2
-------
12:15:10
12:10
6:5
Answer:C
Answer: (C) 6:5
Question: Zeeshan having a certain number of one rupee,fifty paise and twenty
five paise coins are in the ratio of 3:2:4, add up to
Rs 75. Then how many 1 rupee coins he have?
(A) 10
(B) 20
(C) 45
(D) 128
(E) 49
Rationale: Explanation :
Given ratio = 3:2:4.
Let us assume that there are 3 one rupee coins,2
fifty paise coins and 4 twenty-five paise coins in all.
Their value=(3*1)+(2*.50)+(4*.25)=3+1+1=Rs 5
If the total is Rs 5, number of 1 rupee coins are 3.
If the total is Rs 75, number of 1 rupee coins would be 75*3/5=45.
Answer : C
Answer: (C) 45
Question: Yesterday i noticed that in my clock , there is time when the hour needle and the minute needle are exactly between 1 and 2.
Also both the needles lie on top of each other.
What time i and talking about ?
(A) 10:00
(B) 11:00
(C) 09:00
(D) 12:00
(E) 07:00
Rationale: D
12:00
both minute and hour clock lie exactly between the number one and two in the number.
Answer: (D) 12:00
Question: Simple interest on a certain sum at a certain annual rate of interest is 1/4 of the sum. If the numbers representing rate percent is 5time of years , then the Time is:
(A) 6 1/2 years.
(B) 5 1/2 years.
(C) 4 1/2 years.
(D) 2 1/2 years.
(E) 3 1/2 years.
Rationale: Explanation :
Let sum = x. Then, S.I. = x/4
Let Time =N and R = 4 N.
[x * N * 4N / 100] = x / 4? N^2 = 25/4
N = 5/2 = 2 1/2 years.
Hence,n = 2 1/2 years.
Answer : D
Answer: (D) 2 1/2 years.
Question: If m is a positive integer, and m/15 = 8.2, what is the remainder Y when m is divided by 15?
(A) A.1
(B) B.2
(C) C.3
(D) D.4
(E) E.8
Rationale: If m were a multiple of 15, the quotient m/15 would be an integer. The fact that it's a decimal tells us that 15 goes into m eight whole times and some decimal part of a time. This decimal part, 0.2 is the remainder divided by the divisor. Let Y be the remainder.
Y/15 = 0.2 = 1/5
Y = (15)*(1/5) = 3
Answer =(C)
Answer: (C) C.3
Question: The sum of two number is 25 and their difference is 13. Find their product.
(A) 114
(B) 104
(C) 315
(D) 350
(E) 400
Rationale: Let the numbers be x and y.
Then, x + y = 25 and x - y = 13.
4xy = (x + y)2 - (x- y)2=(25)2 - (13)2
= (625 - 169) = = 456 =>114
ANSWER A
Answer: (A) 114
Question: Kim is taking a math class, and the teacher gives a multiple choice test consisting of 6 questions. If each question has 5 answer choices, and Kim answers every question, in how many different ways can she complete the test?
(A) a 40
(B) b 400
(C) c 5^8
(D) d 5^6
(E) e 40^40
Rationale: different ways to solve each question is 5.
So, 5*5*5*5.. 6 times ----> 5^6
Answer will be D.
Answer: (D) d 5^6
Question: In three coloured boxes - Red, Green and Blue, 108 balls are placed. There are twice as many balls in the green and red boxes combined as there are in the blue box and twice as many in the blue box as there are in the red box. How many balls are there in the green box ?
(A) 33
(B) 28
(C) 76
(D) 54
(E) 912
Rationale: Explanation:
Let R, G and B represent the number of balls in red, green and blue boxes respectively.
Then,
R + G + B = 108 ...(i),
G + R = 2B ...(ii)
B = 2R ...(iii)
From (ii) and (iii), we have G + R = 2x 2R = 4R or G = 3R.
Putting G = 3R and B = 2R in (i), we get:
R + 3R + 2R = 108 {\color{Blue} \Rightarrow } 6R = 108 {\color{Blue} \Rightarrow } R = 18.
Therefore Number of balls in green box = G = 3R = (3 x 18) = 54.
Answer: D
Answer: (D) 54
Question: Ten cards numbered 1 to 10 are placed in a box, mixed up thoroughly and then one card is drawn
randomly. If it is known that the number on the drawn card is more than 3, what is the probability
that it is an even number?
(A) 3/7
(B) 4/7
(C) 5/7
(D) 5/9
(E) 5/11
Rationale: Let A be the event ‘the number on the card drawn is even’ and B be the
event ‘the number on the card drawn is greater than 3’. We have to find P(A|B).
Now, the sample space of the experiment is S = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}
Then A = {2, 4, 6, 8, 10}, B = {4, 5, 6, 7, 8, 9, 10}
and A n B = {4, 6, 8, 10}
Also P(A) = 5/2, P(B) = 7/10 and P(A n B) = 4/10
Then P(A|B) = P(A n B)/P(B) = (4/10)/(7/10) = 4/7
B)
Answer: (B) 4/7
Question: a man can row 18 kmph in still water.it takes him thrice as long to row up as to row down the river.find the rate of stream.
(A) 2 km/hr
(B) 3 km/hr
(C) 7 km/hr
(D) 9 km/hr
(E) 5 km/hr
Rationale: Let manâ€™s rate upstream be x kmph.then ,his rate downstream=3xkmph.
So,2x=18 or x=9.
Rate upstream=9 km/hr,rate downstream=27 km/hr.
Hence,rate of stream=1/2(27-9)km/hr=9 km/hr.
ANSWER D
Answer: (D) 9 km/hr
Question: A 60 cm long wire is to be cut into two pieces so that one piece will be 2/5th of the other, how many centimeters will the shorter piece be?
(A) 35
(B) 20
(C) 17
(D) 36
(E) 30
Rationale: 1: 2/5 = 5: 2
2/7 * 60 =17
Answer:C
Answer: (C) 17
Question: Twelve contestants at the county fair have entered their cakes to be judged in the cake decorating competition. A purple ribbon, blue ribbon, red ribbon, and white ribbon will be given to the first, second, third, and fourth place competitors, respectively. How many different ways are there to award the four ribbons to the contestants?
(A) 8!/(4!*4!)
(B) 12!/(8!*4!)
(C) 8!/4!
(D) 12!/8!
(E) 12!/4!
Rationale: Number of ways you can select 4 people out of 12 = 12C4
Once you select the 4 people, you have the following arrangement, PBRW (PBRW being the 4 prizes) but the same group of people can also be chosen against BRWP etc. Thus you get 4! ways of arranging 4 prizes.
Thus total possible ways = 12C4*4! = 12!/8!. D is the correct answer.
Answer: (D) 12!/8!
Question: Of the five numbers in a sequence, the first term is 10,000, and each of the following terms is 30% of the previous term. What is the value range of the five numbers?
(A) 9,375
(B) 9,750
(C) 9,919
(D) 9,984
(E) 10,736
Rationale: 1st number= 10,000
2nd number =30% of 10,000= 3000
3rd number= 30% of 3000= 900
4th number = 30% of 900= 270
5th number= 30% of 270= 81
Range = 10,000-81= 9919
C is the answer
Answer: (C) 9,919
Question: If x and y are positive integers, each of the following could be the greatest common divisor of 30x and 15y EXCEPT
(A) 30x.
(B) 15y.
(C) 15(x + y).
(D) 15(x - y).
(E) 15,000.
Rationale: If x=1 and y=1, then 30 x=30 and 15y=15. The GCD of 30 and 15 is 15, while (C) gives 15(x+y)=30.
ANSWER:C
Answer: (C) 15(x + y).
Question: How long does a train 110 m long traveling at 60 kmph takes to cross a bridge of 170 m in length?
(A) 13.8 sec
(B) 13.2 sec
(C) 18.9 sec
(D) 16.8 sec
(E) 12.9 sec
Rationale: D = 110 + 170 = 280 m
S = 60 * 5/18 = 50/3
T = 280 * 3/50 = 16.8 sec
Answer: D
Answer: (D) 16.8 sec
Question: There are k-2 members in a certain band, including Jim and Ellen. Two members are to be selected to attend the Grammy awards ceremony. If there are 28 possible combinations in which Jim and Ellen are not selected, what is the value of k?
(A) 8
(B) 9
(C) 10
(D) 11
(E) 12
Rationale: There are k-2 members in the band, and k-4 members without Jim and Ellen.
(k-4)C2 = 28
(k-4)(k-5)/2 = 28
(k-4)(k-5) = 56 = 8*7
k = 12
The answer is E.
Answer: (E) 12
Question: If 2x + y = 4 and x + 2y = 5, then (x + y)/3 =
(A)  1
(B)  4/3
(C)  17/5
(D)  18/5
(E)  4
Rationale: We have two equations:
2x + y = 4
x + 2y = 5
Notice that something nice happens when we ADD them. We get:
3x + 3y = 9
Divide both sides by 3 to get:x + y = 3
So, (x + y)/3 =3/3=1
Answer: A
Answer: (A)  1
Question: Rasik walked 20 m towards north. Then he turned right and walks 30 m. Then he turns right and walks 35 m. Then he turns left and walks 15 m. Finally he turns left and walks 15 m. In which direction and how many metres is he from the starting position?
(A) 15 m West
(B) 30 m East
(C) 35 m East
(D) 45 m East
(E) 40 m East
Rationale: 45 m East
ANSWER:D
Answer: (D) 45 m East
Question: There are 4 more women than there are men on a local co-ed softball team. If there are a total of 14 players on the team, what is the ratio of men to women?
(A) 10/16
(B) 6/16
(C) 4/16
(D) 6/10
(E) 5/9
Rationale: w = m+4
w+m = 14
m+4+m = 14
2m = 10
m = 5
w = 9
ratio:5:9
Ans: E
Answer: (E) 5/9
Question: The ratio of ducks and frogs in a pond is 37 : 39 respectively. The average number of ducks and frogs in the pond is 152. What is the number of frogs in the pond ?
(A) 148
(B) 152
(C) 156
(D) 144
(E) None
Rationale: Solution:
Ratio of Ducks and Frogs in Pond,
= 37 : 39.
Average of Ducks and Frogs in Pond,
= 152.
So, total number of Ducks and Frogs in the Pond,
= 2* 152 = 304.
Therefore,
Number of Frogs, = (304 *39)/76 = 156.
Answer: Option C
Answer: (C) 156
Question: What comes next?
6 1 3 1 4 __
(A) 3
(B) 4
(C) 7
(D) 8
(E) 5
Rationale: e
5
The numbers are the alphabetical positions of the letters, spelling FACADE :
6-F; 1-A; 3-C; 1-A; 4-D; 5-E.
Answer: (E) 5
Question: What is the speed of the stream if a canoe rows upstream at 3km/hr and downstream at 12km/hr
(A) 1 kmph
(B) 4 kmph
(C) 3 kmph
(D) 2 kmph
(E) 4.5 kmph
Rationale: Sol.
Speed of stream = 1/2(12 -3) kmph = 4.5 kmph.
Answer E
Answer: (E) 4.5 kmph
Question: What least number must be added to 1078, so that the sum is completely divisible by 23 ?
(A) 3
(B) 2
(C) 4
(D) 5
(E) 6
Rationale: 47*23 = 1081
1081 - 1078 = 3
Answer : A
Answer: (A) 3
Question: Three pipes of same capacity can fill a tank in 8 hours. If there are only two pipes of same capacity, the tank can be filled in?
(A) 15 hours
(B) 12 hours
(C) 76 hours
(D) 16 hours
(E) 81 hours
Rationale: The part of the tank filled by three pipes in one hour = 1/8
=> The part of the tank filled by two pipes in 1 hour = 2/3 * 1/8 = 1/12.
The tank can be filled in 12 hours.
Answer: B
Answer: (B) 12 hours
Question: If the average (arithmetic mean) of five consecutive negative integers is 8k – 1, what is the difference between the greatest and least of the five integers?
(A) 4K
(B) 4k^2 -4k
(C) 4-4k
(D) 4
(E) 4k+4
Rationale: (n-2 + n - 1 + n + n + 1 + n + 2)/5 = 8k - 1
=> n = 40k - 5
Greatest = n + 2 = 40k - 5 + 2 = 40k - 3
Least = n - 2 = 40k - 5 - 2
=> Difference = 40k - 3 - (40k - 7)
= 4
Answer - D
Answer: (D) 4
Question: Cereal A is 11% sugar by weight, whereas healthier but less delicious Cereal B is 2% sugar by weight. To make a delicious and healthy mixture that is 5% sugar, what should be the ratio of Cereal A to Cereal B, by weight?
(A) 1:2
(B) 2:3
(C) 1:3
(D) 1:4
(E) 3:4
Rationale: 2% is 3%-points below 5% and 11% is 6%-points above 5%.
The ratio of A:B should be 3:6 = 1:2.
The answer is A.
Answer: (A) 1:2
Question: In a college, the ratio of the number of boys to girls is 8 : 5. If there are 350 girls, the total number of
students in the college is
(A) 420
(B) 520
(C) 620
(D) 910
(E) None of these
Rationale: Explanation:
Let the boy are 8x and Girls are 5x
=> 5x = 350
=> x = 70
Total students = 8x+5x = 13x = 13(70) = 910
Answer: D
Answer: (D) 910
Question: A train speeds past a pole in 15 seconds and a platform 100 m long in 25 seconds. Its length is:
(A) 50 m
(B) 150 m
(C) 200 m
(D) Data inadequate
(E) none of these
Rationale: Let the length of the train=xm
x/15=x+100/25
by solving this we get x=150m
ANSWER:B
Answer: (B) 150 m
Question: The number 91 is equal to the sum of the cubes of two integers. What is the product of those integers?
(A) 8
(B) 12
(C) 21
(D) 27
(E) 39
Rationale: 3^3+4^3= 91 therefore number is 3*4=12
B
Answer: (B) 12
Question: What percent of the year 2017 is 219 days?
(A) 56%
(B) 72%
(C) 64,5%
(D) 51%
(E) 60%
Rationale: Explanation :
Total days in the year 2017 = 365
Required percentage = (219/365) Ã— 100 = 60%
Answer : Option D
Answer: (D) 51%
Question: What is the population standard deviation for the numbers: 75, 83, 96, 100, 121 and 125?
(A) 18.2
(B) 20
(C) 25
(D) 26
(E) 28
Rationale: 1. Firstly find the mean:
Mean = (75 + 83 + 96 + 100 + 121 + 125) ÷ 6 = 600 ÷ 6 = 100
2. Next find the variance. To calculate the Variance, take each difference, square it, and then average the result:
(75 - 100)2 + (83 - 100)2 + (96 - 100)2 + (100 - 100)2 + (121 - 100)2 + (125 - 100)2
= (-25)2 + (-17)2 + (-4)2 + (0)2 + (21)2 + (25)2
= 625 + 289 + 16 + 0 + 441 + 625
= 1,996
So the Variance = 1,996 ÷ 6 = 332.66...
3. The Standard Deviation is just the square root of the Variance
= √(332.66...)
= 18.2 correct to 1 decimal places
Answer is A
Answer: (A) 18.2
Question: Find the odd man out. 1, 3, 9, 12, 19, 29
(A) 12
(B) 9
(C) 1
(D) 3
(E) 29
Rationale: 12 is an even number. All other given numbers are odd
Answer is A
Answer: (A) 12
Question: Zane and Thomas are among the 8 people from which a committee of 4 people is to be selected. How many different possible committees of 4 people can be selected from these 8 people if at least one of either Zane or Thomas is to be selected?
(A) 28
(B) 46
(C) 55
(D) 63
(E) 70
Rationale: Ans:C
Solution:
Z+T+6 = total 8 ,
we need to select at least one of the Z and T or both= total 4 out of 8 - 4 out of 6
8C4 - 6C4
=55
Answer: (C) 55
Question: Thabo owns exactly 200 books, and each book is either paperback fiction, paperback nonfiction, or hardcover nonfiction. If he owns 20 more paperback nonfiction books than hardcover nonfiction books, and twice as many paperback fiction books as paperback nonfiction books, how many hardcover books nonfiction books does Thabo own?
(A) 10
(B) 20
(C) 35
(D) 45
(E) 50
Rationale: I think we can use double-matrix method and solve using only one variable.
Our goal is to find the number of hardcover nonfiction books. Let that number be x. We are given that all 140 books are either paperback fiction, paperback nonfiction, or hardcover nonfiction. This implies that number of hardcover fiction books is 0.
Double-matrix: P = paperback; H = hardcover; F = fiction; NF = nonfiction
P H Total
F 2x+40 0
NF x+20 x
Total 3x+60 x 200
3x + 60 + x = 200
x = 35
Answer (C.)
Answer: (C) 35
Question: Exactly 30% of the reporters for a certain wire service cover local politics in Country X. If 25% of the reporters who cover politics for the wire service do not cover local politics in Country X, what percent of the reporters for the wire service do not cover politics?
(A) 20%
(B) 42%
(C) 60%
(D) 80%
(E) 84%
Rationale: Let's assume there are 100 reporters --> 30 reporters cover local politics.
Now, as 25% of the reporters who cover all politics do not cover local politics then the rest 75% of the reporters who cover politics do cover local politics, so if there are x reporters who cover politics then 75% of them equal to 30 (# of reporters who cover local politics): 0.75x=30 --> x=40, hence 40 reporters cover politics and the rest 100-40=60 reporters do not cover politics at all.
Answer: C.
Answer: (C) 60%
Question: For which of the following values of n is (900+n)/n NOT an integer?
(A)  1
(B)  2
(C)  3
(D)  4
(E)  5
Rationale: Solution:
This problem is easiest solved by plugging in each answer choice.
A) (900 + 1)/1 = 901/1 = 901
Answer choice A yields an integer.
B) (900 + 2)/2 = 902/2 = 451
Answer choice B yields an integer.
C) (900 + 3)/3 = 903/3 = 301
Answer choice C yields an integer.
D) (900 + 4)/4 = 904/4 = 223, remainder 2
Answer choice D DOES NOT yield an integer.
E) (900 + 5)/5 = 905/5 = 181
Answer choice E yields an integer.
Thus, the correct answer is answer choice D.
Answer: (D)  4
Question: Angelo and Isabella are both salespersons. In any given week, Angelo makes $550 in base salary plus 8 percent of the portion of his sales above $6,000 for that week. Isabella makes 10 percent of her total sales for any given week. For what amount of weekly sales would Angelo and Isabella earn the same amount of money?
(A)  3,500
(B)  24,500
(C)  25,500
(D)  26,500
(E)  27,500
Rationale: OFFICIAL SOLUTION:
The problem asks for the amount of weekly sales it takes for Angelo and Isabella to earn the same amount of money. You can write an equation that sets Angelo’s and Isabella’s weekly earnings equal to each other, with x representing weekly sales. Weekly earnings for each salesperson equal base salary plus commission. So Angelo’s earnings are 550 + (0.08)(x – 6,000), and Isabella’s are 0.10x. Set up the equation and solve:
550 + (0.08)(x – 6,000) = 0.10x
Distribute the 0.08:
550 + 0.08x – 480 = 0.10x
Combine terms and subtract 0.08x from both sides:
70 = 0.02x
Divide both sides by 0.02:
3,500 = x
Your answer is A.
Answer: (A)  3,500
Question: A is half good a work man as B and together they finish a job in 20 days. In how many days working alone B finish the job?
(A) 98 days
(B) 30 days
(C) 17 days
(D) 18 days
(E) 19 days
Rationale: WC = 1:2
2x + x = 1/20 => x = 1/60
2x = 1/60 => 30 days
Answer:B
Answer: (B) 30 days
Question: If a: b = 7: 5, b: c = 9: 11, find a: b: c?
(A) 63: 45: 59
(B) 63: 45: 55
(C) 63: 45: 56
(D) 63: 45: 54
(E) 63: 45: 51
Rationale: a: b = 7: 5
b: c = 9: 11
a: b: c = 63: 45: 55
Answer:B
Answer: (B) 63: 45: 55
Question: Michelle deposited a certain sum of money in a savings account on July 1st, 2007. She earns an 14% interest compounded semiannually. The sum of money in the account on December 31st, 2009 is approximately what percent of the initial deposit?
(A) 117%
(B) 120%
(C) 121%
(D) 138%
(E) 145%
Rationale: Since Michelle earns 14% interest compounded semiannually, then she earns 7% interest every 6 months.
Now, the simple interest earned in 5 periods (30 months = 5*6 months) would be 7%*5=35%. But, since the interest iscompoundedevery 6 months, then there would be interest earned on interest (very small amount) thus the actual interest earned would be a little bit more than 35%, only answer choice D fits.
Answer: D
Answer: (D) 138%
Question: How many of the positive factors of 56 , 96 and how many common factors are there in numbers?
(A) 2
(B) 4
(C) 3
(D) 1
(E) 5
Rationale: factors of 56 - 1, 2, 4, 7, 8, 14, 28 and 56.
factors of 96 - 1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48 and 96.
Comparing both, we have four common factors of 56 and 96- 1,2,4,8
Answer(B)
Answer: (B) 4
Question: Working alone, machine X can manufacture 1,000 nails in 12 hours. Working together, machines X and Y can manufacture 1,000 nails in 5 hours. How many hours does it take machine Y to manufacture 1,000 nails working alone?
(A) 3 9/17
(B) 5 1/3
(C) 7
(D) 7 1/5
(E) 8 4/7
Rationale: Rate of machine X = 1000/12 = 250/3
Rate of machine Y = 1/Y
Rate of machine X and Y together = 1000/5 = 200
250/3 + 1/y = 200
after solving this equation we get Y= 3/350
Rate of Y = 1/y = 1/ (3/350) = 350/3
Machine Y has to manufacture 1000 nails. So work is 1000. Putting the values;
time required for machine Y = 1000/(350/3) = 1000* 3/(350) = 60/7 = 8 4/7
ANSWER:E
Answer: (E) 8 4/7
Question: A large field of 700700 hectares is divided into two parts. The difference of the areas of the two parts is one-fifth of the average of the two areas. What is the area of the smaller part in hectares?
(A) 400
(B) 365
(C) 385
(D) 315
(E) 355
Rationale: Explanation:
Average of the two areas =700/2=350
one-fifth of the average of the two areas=350/5=70
⇒ Difference of the two areas =70=70
Let area of the smaller part = x hectares.
Then, area of the larger part =x+70 hectares.
x+(x+70)=700
⇒2x=630
⇒x=315
Answer: Option D
Answer: (D) 315
Question: 0.1+ 0.1^2+0.1^3=
(A)  0.1
(B)  0.111
(C)  0.1221
(D)  0.2341
(E)  0.3
Rationale: You have a mistake in your question. Choice B should be (.111) and not (.11).
The equation in the solution can be simplified to (.1 + .01 + .001).
Adding those together you get:
.100
.010
.001
------
.111 - Which is answer choice (B)
Answer: (B)  0.111
Question: P and Q are the only two applicants qualified for a short-term research project that pays 360 dollars in total. Candidate P has more experience and, if hired, would be paid 50 percent more per hour than candidate Q would be paid. Candidate Q, if hired, would require 10 hours more than candidate P to do the job. Candidate P’s hourly wage is how many dollars greater than candidate Q’s hourly wage?
(A) $3
(B) $6
(C) $9
(D) $12
(E) $15
Rationale: Let Q's hourly wage be x, then P's hourly wage is 1.5x
Let T be the number of hours that Q needs, then P needs T-10 hours to do the job.
Since they both are paid an equal total amount of $360:
x*T=1.5x*(T-10)
T = 30 hours and Q's hourly wage is 360/30 = $12
P's hourly wage is 360/(T-10) = $18 which is $6 per hour more.
The answer is B.
Answer: (B) $6
Question: The price of commodity X increases by 40 paise every year, while the price of commodity Y increases by 15 paise every year. If in 2001, the price of commodity X was Rs. 4.20 and that of Y was Rs. 6.30, in which year commodity X will cost 40 paise more than the commodity Y?
(A) 2013
(B) 2015
(C) 2014
(D) 2011
(E) 2010
Rationale: Suppose commodity X will cost 40 paise more than Y after z years.
Then, (4.20 + 0.40z) - (6.30 + 0.15z) = 0.40
0.25z = 0.40 + 2.10
z = 2.50/0.25
= 250/25
= 10.
Therefore, X will cost 40 paise more than Y 10 years after 2001 i.e., 2011.
Answer is D.
Answer: (D) 2011
Question: The contents of a certain box consist of 14 apples and 24 oranges. How many oranges must be removed from the box so that 70 percent of the pieces of fruit in the box will be apples?
(A) 18
(B) 6
(C) 14
(D) 17
(E) 20
Rationale: The objective here is that 70% of the fruit in the box should be apples.
Now, there are 14 apples at start and there is no talk of removing any apples, so number of apples should remain 14 and they should constitute 70% of total fruit, so total fruit = 14/0.7 = 20
So we should have 20-14 = 6 oranges.
Right now, there are 24 oranges, so to get to 6 oranges, we should remove 24 - 6 = 18 oranges.
Answer A
Answer: (A) 18
Question: A shopkeeper buys two articles for Rs.1000 each and then sells them, making 15% profit on the first article and 15% loss on second article. Find the net profit or loss percent?
(A) 200
(B) 150
(C) 282
(D) 202
(E) 270
Rationale: Profit on first article = 15% of 1000 = 150.
This is equal to the loss he makes on the second article. That, is he makes neither profit nor loss.
Answer: B
Answer: (B) 150
Question: A grocer buys apples for 72¢ per pound. If 10% of the apples goes bad and he still wants to make a 20% profit over his purchase price, what should be the sales price?
(A) 96¢
(B) 70¢
(C) 80¢
(D) 85¢
(E) 98¢
Rationale: for making calculation simple let us consider he buys 10pounds @ 72/pound=720¢ in total .
10% apples lost...means 9 pounds left.
further he wants 20% profit on 720 ¢
means he wants to earn 864¢
sales price should be 864/9=¢ 96
Ans A
Answer: (A) 96¢
Question: The difference between a number and its three-fourth is 100. what is 25% of that number?
(A) 120
(B) 100
(C) 125
(D) 150
(E) None of these
Rationale: Explanation :
Solution: Let the number be x. then, x - 3/4x = 100
=> x/4 = 100
=> x =400.
25% of x = 25% of 400 = 25/100 *400 = 100.
Answer : B
Answer: (B) 100
Question: If each digit in the set of A = (1,2,3,4,5) is exactly used once, in how many ways can the digits be arranged such that the 2 and 5 are not adjacent?
(A) 6
(B) 24
(C) 72
(D) 96
(E) 112
Rationale: The answer should be = total arrangements - arrangements when 2 and 5 are together.
= 5! - 4! * 2! = 120 -48 = 72
ANS:C
Answer: (C) 72
Question: A car covers a distance of 624 km in 6 Â½ hours. Find its speed?
(A) 104 kmph
(B) 106 kmph
(C) 108 kmph
(D) 110 kmph
(E) 120 kmph
Rationale: 624/6 = 104 kmph
ANSWER A
Answer: (A) 104 kmph