mathewhe/aqua_rat huggingface dataset:
Question: An engine moves at the speed of 90 kmph without any coaches attached to it.Speed of the train reduces at the rate that varies directly as the square root of the number of coaches attached.When 4 coaches are attached speed decreases to 78 kmph.What will be the speed of train when 16 coaches are attached.
(A) 66
(B) 72
(C) 80
(D) 68
(E) 73
Rationale: 1.
No. of coaches =4
sqr root=2
speed decreases by 12
12=k*2
k=6
No. of coaches=16
swr root=4
decrease=4*6=24
New speed=90-24=66
A
Answer: (A) 66
Question: For any integer p, *p is equal to the product of all the integers between 1 and p, inclusive. How many prime numbers are there between *8 + 3 and *8 + 8, inclusive?
(A)  None
(B)  One
(C)  Two
(D)  Three
(E)  Four
Rationale: Generally *p or p! will be divisible by ALL numbers from 1 to p. Therefore, *8 would be divisible by all numbers from 1 to 8.
=> *8+3 would give me a number which is a multiple of 3 and therefore divisible (since *8 is divisible by 3)
In fact adding anyprimenumber between 1 to 8 to *8 will definitely be divisible.
So the answer is none (A)!
Supposing if the question had asked for prime numbers between *8 + 3 and *8 + 11 then the answer would be 1. For *8+3 and *8 + 13, it is 2 and so on...
A
Answer: (A)  None
Question: A fruit vendor purchased 20 dozens of bananas at Rs. 15 per dozen. But one-fourth of the bananas were rotten and had to be thrown away. He sold two-third of the remaining bananas at Rs. 22.50 per dozen. At what price per dozen should he sell the remaining bananas to make neither a profit nor a loss?
(A) Rs. 19
(B) Rs. 15
(C) Rs. 11
(D) Rs. 13
(E) Rs. 01
Rationale: Explanation:
CP of 20 dozen of bananas = 15 * 20 = Rs. 300
Number of bananas which are rotten = 1/4 * 20 = 5 dozen.
SP of two-third of remaining bananas = (2/3 * 15) * 22.5 = Rs. 225
SP of remaining 5 dozens of bananas to make no profit and no loss =(300 - 225) = Rs. 75.
SP of 1 dozen bananas = 75/5 = Rs. 15.
Answer:B
Answer: (B) Rs. 15
Question: 3 boys and 7 girls can complete a work in 10 days . But 4 boys and 6 girls need 8 days to complete the same work . In how many days will 10 girls complete the same work?
(A) 20 days
(B) 30 days
(C) 40 days
(D) 50 days
(E) 60 days
Rationale: Work done by 4 boys and 6 girls in 1 day = 1/8
Work done by 3 boys and 7 girls in 1 day = 1/10
Let 1 man does m work in 1 day and 1 woman does w work in 1 day. The above equations can be written as
4m + 6w = 1/8 ---(1)
3m + 7w = 1/10 ---(2)
Solving equation (1) and (2) , we get m=11/400 and w=1/400
Amount of work 10 girls can do in a day = 10 × (1/400) = 1/40
Ie, 10 girls can complete the work in 40 days
C
Answer: (C) 40 days
Question: if C is a whole number , C+1 is whole number after that. if A is whole number, what is whole number before that
(A) 1 whole number
(B) -1, not a whole number
(C) 0 whole number
(D) -A whole number
(E) none
Rationale: natural numbers are 0,1,2,3,4,5,...... are called whole numbers. if A is a whole number and it is greater than 0 the the whole number before that is A-1 which will always be a whole number. which means 0-1= -1, which is not whole number. correct answer (B)
Answer: (B) -1, not a whole number
Question: How many three digit numbers Z greater than 330 can be formed from the digits 1, 2, 3, 4, 5 and 6, if each digit can only be used once?
(A) 72
(B) 48
(C) 120
(D) 96
(E) 76
Rationale: Find the number of 3 digit numbers greater than 300, and then subtract from them the number of three digit numbers between 300 and 330 formed with the given 6 digits.
ABC three digit numbers greater than 300 - total of 4*5*4=80, because a must be greater than 2, so 4 possibilities left; B 5 remaining, and C 4 remaining possibilities to choose from.
Between 300 and 330 there are 1*2*4=8 numbers with the given property: A = 3, 1 possibility; B can be only 1 or 2 (ABC < 330), so two possibilities; C the remaining 4 possibilities after choosing A and B.
Total possible choice 80 - 8 =72=Z
Answer: A.
Answer: (A) 72
Question: A can do a piece of work in 4 days. B can do it in 5 days. With the assistance of C they completed the work in 2 days. Find in how many days can C alone do it?
(A) 10 days
(B) 20 days
(C) 5 days
(D) 4 days
(E) 3 days
Rationale: Explanation:
C = 1/2 - 1/4 - 1/5 = 1/20 => 20 days
Answer: Option B
Answer: (B) 20 days
Question: A father was as old as his son's present at the time of your birth. If the father's age is 38 years now, the son's age seven years back was?
(A) 10 years
(B) 12 years
(C) 14 years
(D) 16 years
(E) 18 years
Rationale: Let the son's present age be x years. Then, (38 - x) = x
2x = 38.
x = 19.
Son's age 5 years back (19 - 7) = 12 years.
B
Answer: (B) 12 years
Question: A batsman makes a score of 200 runs in the 17th inning and thus increases his averages by 10 What is his average after 17th inning?
(A) 39
(B) 35
(C) 42
(D) 40
(E) 41.5
Rationale: let the average after 16th inning =x
then total run after 16th inning=16x
then total run after 17th inning=16x+200
then average run after 17th inning=(16x+200)/17
(16x+200)/17=x+10 = > 16x+200 = 17x+170
x=30;
average after 17th inning =30+10=40
ANSWER:D
Answer: (D) 40
Question: Of 30 applicants for a job, 9 had at least 4 years' experience, 18 had degrees, and 3 had less than 4 years' experience and did not have a degree.How many of the applicants had at least 4 years' experience and a degree?
(A) 14
(B) 10
(C) 9
(D) 7
(E) 5
Rationale: B. 10
30 - 3 = 27
27 - 9 - 18 = -10
Then 5 are in the intersection between 4 years experience and degree.
Answer B
Answer: (B) 10
Question: The average of 45 results is 13. The average of first 22 of them is 15 and that of last 22 is 20. Find the 23 result?
(A) 600
(B) 480
(C) 750
(D) 650
(E) 695
Rationale: 23th result = sum of 45results - sum of 44 results
13*45-15*22+20*22 = 585-330+440 = 695
Answer is E
Answer: (E) 695
Question: A man spends 10% of his income in house rent, 20% of the rest on his children’s education, 25% of the rest miscellaneous causes. If he now posses Rs. 1944 then his income is?
(A) 3600
(B) 2992
(C) 2209
(D) 2889
(E) 7881
Rationale: X * (90/100) * (80/100) * (75/100) = 1944
X * 0.9 * 0.8 * 0.75
X = 1944/0.54
X = 3600
Answer:A
Answer: (A) 3600
Question: The simple form of the ratio 2/3:2/5 is?
(A) 5:0
(B) 5:3
(C) 5:1
(D) 5:2
(E) 5:7
Rationale: 2/3 : 2/5 = 10:6
= 5:3
Answer: D
Answer: (D) 5:2
Question: In a lottery draw there are 4 jars containing 5 choices with only one choice as the lucky draw. A candidate wins the lottery draw if he/she picks up all the lucky draws from all the jars. What is the total number of ways in which a candidate will not win the lucky draw?
(A) 19
(B) 85
(C) 120
(D) 624
(E) 1024
Rationale: A candidate can pick up draws in 5*5*5*5=5^4 number of ways (each jar has 5 draws and we have total of 4 jars). Now, out of these cases there will be only one case when the candidate picked all the four lucky draws. Therefore the total number of ways in which a candidate will NOT win the lottery is 5^4-1=624.
Answer: D.
Answer: (D) 624
Question: The ratio of the number of ladies to gents at a party was 1:2 but when 2 ladies and 2 gents left, the ratio became 1:3. How many people were at the party originally?
(A) 11
(B) 16
(C) 12
(D) 18
(E) 19
Rationale: x, 2x
(x-2):(2x-2) = 1:3
3x-6 = 2x-2
x = 4
x+2x = 3x
=> 3*4 = 12
Answer: C
Answer: (C) 12
Question: A distributor sells a product through an on-line store, which take a commission of 20% of the price set by the distributor. The distributor obtains the product from a producer at the price of $15 per item. What is the price that the buyer observers on-line if the distributor wants to maintain a 20% profit on the cost of the item?
(A) 18
(B) 21.6
(C) 22
(D) 22.5
(E) 27
Rationale: Producer price = $15;
The distributor wants to maintain a 20% profit on the cost of the item, thus he must get $15*1.2 = $18 after the store takes a commission of 20% of the final price --> (final price)*0.8 = $18 --> (final price) = $22.5.
Answer: D.
Answer: (D) 22.5
Question: P sells an article to Q at 10 % profit. Q sells it to R at 25 % profit. If R pays Rs. 250 for it, What did P pay for it ?
(A) Rs. 225
(B) Rs. 198.50
(C) Rs. 181.81
(D) Rs. 162.30
(E) None of these
Rationale: Explanation:
Selling price of P = Cost price of Q
Selling Price of Q = Cost price of R = Rs. 250 ….. Given
Q sold it to R with 25 % profit.
Cost price of Q = 100/125 * 250/1 = Rs. 200 = Selling price of P.
P sold it to Q with 10 % profit.
Cost price of P = 100 / 110 * 200 / 1 = Rs. 181.81
ANSWER C
Answer: (C) Rs. 181.81
Question: If a, b, and c are consecutive positive integers and a < b < c, which of the following must be true?
I. b-a = 2
II. abc is an even integer.
III. (a + b + c)/3 is an integer.
(A)  I only
(B)  II only
(C)  I and II only
(D)  II and III only
(E)  I, II, and III
Rationale: Since a, b, and c are consecutive positive integers and a < b < c, thenb= a + 1, from which it follows that b - a = 1. So, I is false.
Next, out of 3 consecutive integers at least 1 must be even, thus abc=even. II is true.
Finally, since b = a + 1, and c = a + 2, then (a + b + c)/3 = (a + a + 1 + a + 2)/3 = a + 1 = integer. III is true as well.
Answer: D.
Answer: (D)  II and III only
Question: There is 60 lit of milk and water in which milk forms 84%.Howmuch water must be added to this solution to make it solution in which milk forms 58%
(A) 18.75
(B) 19.75
(C) 26.89
(D) 21.75
(E) 22.75
Rationale: 60*84/100=50.40 lit milk that is 9.60 lit water
let x lit water will be added then
(60+x)*58/100=50.40
so x=26.89
ANSWER:C
Answer: (C) 26.89
Question: On the number line, if x is halfway between -6 and 4, and if y is halfway between -2 and 6, what number is halfway between x and y?
(A) -2.5
(B) -1.5
(C) -0.5
(D) 0.5
(E) 1.5
Rationale: x= -1 and y = 2.
The answer is D.
Answer: (D) 0.5
Question: Today is wednesday. A person wants to meet a lawyer and as that lawyer is busy he asks him to come three days after the before day of the day after tomorrow? On which day the lawyer asks the person to come?
(A) SUNDAY
(B) MONDAY
(C) TUESDAY
(D) WEDNESDAY
(E) FRIDAY
Rationale: Today is wednesday
after three days--->saturday
now, (saturday)after before day--->friday
then, (friday)day after tomorrow--->sunday
ANSWER:A
Answer: (A) SUNDAY
Question: 3 candidates in an election and received 1136, 7636 and 11628 votes respectively. What % of the total votes did the winningcandidate got in that election?
(A) 45%
(B) 67%
(C) 57%
(D) 69%
(E) 70%
Rationale: Total number of votes polled = (1136 + 7636 + 11628) = 20400
So, Required percentage = 11628/20400 * 100 = 57%
C
Answer: (C) 57%
Question: If n is a prime number greater than 5, what is the remainder when n^2 is divided by 12?
(A) 0
(B) 1
(C) 2
(D) 3
(E) 5
Rationale: There are several algebraic ways to solve this question including the one under the spoiler. But the easiest way is as follows:since we can not have two correct answersjust pick a prime greater than 5, square it and see what would be the remainder upon division of it by 12.
7=5 --> n^2=49 --> remainder upon division 49 by 12 is 1.
Answer: B.
Answer: (B) 1
Question: 1, 2, 9, 64, ?
(A) 388
(B) 625
(C) 278
(D) 277
(E) 191
Rationale: ANSWER:B
Answer: (B) 625
Question: The captain of a cricket team of 11 members is 26 years old and the wicket keeper is 3 years older. If the ages of these two are excluded, the average age of the remaining players is one year less than the average age of the whole team. What is the average age of the team?
(A) 23 years
(B) 24 years
(C) 25 years
(D) None of these
(E) Cannot be determined
Rationale: Explanation: Let the average age of the whole team by x years.
11x - (26 + 29) = 9(x -1)
11x - 9x = 46
2x = 46
x = 23.
So, average age of the team is 23 years.
Answer: Option A
Answer: (A) 23 years
Question: Choose a number between 1 and 10. Add 4 and double the result. Subtract 3, then, multiply by 3. Subtract 5 times one more than the original number. Tell me the answer and I will tell you your original number.
(A) 10x
(B) x+10
(C) x-10
(D) x/10
(E) 10-x
Rationale: The calculation described in this problem is 3(2 (4+ x) -3) - 5(x + 1), we can use the Rules to rewrite the expression as follows:
= 3 (2 (4 + x) - 3) - 5(x + 1)
= 3 (8 + 2 x - 3) -5 x - 5
= 3 (2 x + 5) - 5x -5
= 6x + 15 - 5x - 5
= (6 - 5)x + 15 -5
= x + 10
Answer: B
Answer: (B) x+10
Question: Ayush was born two years after his father's marriage. His mother is five years younger than his father but 20 years older than Ayush who is 5 years old. At what age did the father get married ?
(A) 23years
(B) 24years
(C) 25years
(D) 26years
(E) 27years
Rationale: Explanation:
Ayush's present age = 5 years.
His mother's present age = (5 + 20) years = 25 years.
Ayush's father's present age = (25 + 5) years = 30 years.
Ayush's father's age at the time of Ayush's birth = (30 - 5) years = 25 years.
Therefore Ayush's father's age at the time of marriage = (25 - 2) years = 23 years.
Answer: A) 23 year
Answer: (A) 23years
Question: Addison High School’s senior class has 160 boys and 200 girls. If 75% of the boys attended the college and 40% of the girls did not attend the college, what percentage of the total class attended college?
(A) 35
(B) 64
(C) 66.67
(D) 60
(E) 84
Rationale: Number of boys attending the college : 0.75*160 = 120
number of girls not attending the college: 0.40*200 = 80
number of girls attending the college : 200-80 = 120
Total attending = 120+120 = 240
Total people = 160+200 = 360
% of people attending = 240/360 = 66.67%. C is the correct answer
Answer: (C) 66.67
Question: At the end of three years what will be the compound interest at the rate of 10% p.a. on an amount of Rs.30000?
(A) 9930
(B) 1879
(C) 2779
(D) 2672
(E) 2782
Rationale: A = 30000(11/10)^3
= 39930
= 30000
----------
9930
Answer: A
Answer: (A) 9930
Question: What amount does Kiran get if he invests Rs.8000 at 10% p.a. compound interest for two years, compounding done annually?
(A) 2778
(B) 2997
(C) 2677
(D) 2197
(E) 9680
Rationale: A= P{1 + R/100}n
=> 8000{1 + 10/100}2 = Rs.9680
Answer: E
Answer: (E) 9680
Question: If 12 lions can kill 12 deers in 12 minutes how long will it take 100 lions to kill 100 deers?
(A) 1 minutes
(B) 12 minute
(C) 120 minutes
(D) 10000 minutes
(E) 1000 minutes
Rationale: we can try the logic of time and work,our work is to kill the deers so 12(lions)*12(min)/12(deers)=100(lions)*x(min)/100(deers)hence answer is x=12
ANSWER:B
Answer: (B) 12 minute
Question: Which of the following correctly lists the data sets in order of least to greatest standard deviation?
I. 12, 13, 15, 12, 14, 24
II. 42, 52, 62, 72, 82, 92
III. 37, 38, 39, 40, 41, 42
(A) I, II, III
(B) I, III, II
(C) II, I, III
(D) III, I,II
(E) III, II, I
Rationale: (D) To answer a question such as this, you DO NOT need to know how to calculate standard deviation. You simply need to understand how to compare standard deviations of different sets. The more spread out the numbers are, the greater the standard deviation will be. Even one or two numbers that are much larger or smaller than the others will cause the standard deviation to rise drastically.
sequence III,I,II
D
Answer: (D) III, I,II
Question: 18 men can complete a piece of work in 30 days. In how many days can 15 men complete that piece of work?
(A) 23 days
(B) 36 days
(C) 22 days
(D) 29 days
(E) 20 days
Rationale: B
36 days
18 * 30 = 15 * x => x = 36 days
Answer: (B) 36 days
Question: A reduction of 20% in the price of salt enables a lady to obtain 10kgs more for Rs.100, find the original price per kg?
(A) 2.8
(B) 2.3
(C) 2.5
(D) 2.1
(E) 2.9
Rationale: 100*(20/100) = 20 --- 10
? --- 1 => Rs.2
100 --- 80
? --- 2 => Rs.2.5
Answer: C
Answer: (C) 2.5
Question: Find the probability that a year chosen at random has 53 Mondays.
(A) 5/28
(B) 3/28
(C) 1/28
(D) 3/28
(E) 3/27
Rationale: Explanation :
There are 2 kinds of year
Leap year - probability = 1/4(out of 4 years one is a leap year)
Non leap year - probability = 3/4
So it's either this OR that
Now in non leap year, there are 365 days meaning 52 Weeks with one day extra
That one day can be Monday out of 7 possible days.Hence the probability = 1/7
Similarly in leap year, there are 366 days and so 366/7= 52 Weeks with 2 days Extra
Now probability of occurrence of Monday out of possible 7 days =2/7
So what we essentially want is
(A non leap year AND Monday) OR ( A leap year AND Monday)
So it'll be [3/4*1/7] + [1/4*2/7] = 5/28
Answer : A
Answer: (A) 5/28
Question: If the sides of a triangle are 26 cm, 24 cm and 10 cm, what is its area?
(A) 120
(B) 130
(C) 140
(D) 149
(E) 133
Rationale: The triangle with sides 26 cm, 24 cm and 10 cm is right angled, where the hypotenuse is 26 cm.
Area of the triangle = 1/2 * 24 * 10 = 120 cm2
Answer: Option A
Answer: (A) 120
Question: There are 11 women and 9 men in a certain club. If the club is to select a committee of 2 women and 2 men, how many different such committees are possible?
(A) 120
(B) 720
(C) 1,060
(D) 1,520
(E) 1,980 committees
Rationale: these are two independent events. meaning picking men from a group of men has no effect on picking women from group of women. so you have to multiply here.
11c2*9c2 =1980
Answer is E.
Answer: (E) 1,980 committees
Question: In b is a positive integer smaller than 200 and (14b)/60 is an integer, then b has how many different positive prime factors?
(A) 2
(B) 3
(C) 5
(D) 6
(E) 8
Rationale: 7b/30 tells us that b is a factor of 30, which has 2, 3, and 5 as its prime factors. Each of them is distinct. Moreover, all multiples of 30 less than 200 can be derived by multiplying these prime factors alone. Thus, number of different prime factors is 3.
Answer: B
Answer: (B) 3
Question: What is the sum of three consecutive numbers if the product of the numbers can be expressed as 3079+3080+3081?
(A) 62
(B) 63
(C) 61
(D) 65
(E) 67
Rationale: Addition of any 3 consecutive numbers is always divisible by 3
that rules out options a, c, d and e
20, 21, 22 (Matches fine)
Answer =B
Answer: (B) 63
Question: A and B are two fixed points 5 cm apart and C is a point on AB such that AC is 3cm. if the length of AC is increased by 6%, the length of CB is decreased by
(A) 6%
(B) 7%
(C) 8%
(D) 9%
(E) None
Rationale: Solution: As A and B are fixed, C is any point on AB, so if AC is increases then CB decreases.
A________3 cm_________ C _____2 cm____B
Then, solution can be visualized as,
Increase in AC 6% = (106*3)/100=3.18 cm.
Decrease in CB = 0.18 cm
% decrease = (0.18/2)*100 = 9%.
Alternatively,
AC = 3 Cm.
BC = 2 Cm.
Increase in AC by 6%, then
New, AC = 3 + 6% of 3 = 3 + 0.18 = 3.18 cm.
0.18 cm increase in AC means 0.18 cm decrease in BC as already mentioned AB as the fixed point.
So, % decrease in BC,
= (Actual Decrease in BC /Original BC)*100
= (0.18/2) *100 = 9%.
Answer: Option D
Answer: (D) 9%
Question: If y = 2 + 2K and y≠0y≠0, then 2/y + 2/y + 1/y + 1/y = ?
(A) 1/(8+8k)
(B) 3/(1+k)
(C) 1/(8+k)
(D) 4/(8+k)
(E) 4/(1+k)
Rationale: 2/Y + 2/Y + 1/Y + 1/Y
= 6/Y
= 6/(2 + 2K)
= 3/(1 + K)
ANSWER:B
Answer: (B) 3/(1+k)
Question: A bowl has only 3 apples and 3 bananas. If one piece of fruit is selected from the bowl at random, and a second piece is selected from the bowl without replacing the first, what is the probability that both pieces of fruit chosen are apples?
(A) 1/10
(B) 1/5
(C) 2/9
(D) 2/5
(E) 1/2
Rationale: 3/6 * 2/5
=1/5
B. 1/5
Answer: (B) 1/5
Question: The cross section of a canal is trapezium in shape. The canal is 12m wide at the top and 8m wide at the bottom. If the area of the cross section is 840 sq.m, the depth of the canal is:
(A) 42m
(B) 84m
(C) 63m
(D) 8.75m
(E) 9.75m
Rationale: ½ (12+8)d=840 or d=84m
ANSWER:B
Answer: (B) 84m
Question: A gardener increased the length of a rectangle-shaped garden by 30 percent and decreased its width by 20 percent. The area of the new garden
(A) has increased by 4 percent
(B) has increased by 8 percent
(C) has increased by 12 percent
(D) is exactly the same as the old area
(E) cannot be expressed in percentage terms without actual numbers
Rationale: Let L be the original length and let W be the original width.
The original area was L*W.
The new area is 0.8W*1.3L = (0.8)(1.3)L*W = 1.04L*W
The answer is A.
Answer: (A) has increased by 4 percent
Question: Arjun buys a toy at Rs 100 and sells it at Rs 120. Amin buys the same toy at Rs 120 but sells it at Rs 100. What are the respective profit/loss per cent for the two persons?
(A) 20%, 20%
(B) 20%, 16.7%
(C) 16.7%, 16.7%
(D) 16.7%, 10%
(E) None of these
Rationale: Percentage profit = [(120 - 100) / 100] x 100 = 20%
Percentage loss = [(120 - 100) / 120] x 100 = 16.7 %
ANSWER:B
Answer: (B) 20%, 16.7%
Question: The compound interest on a sum for 2 years is Rs. 832 and the simple interest on the same sum for the same period is Rs. 800. The difference between the compound and simple interest for 3 years will be
(A) Rs. 48
(B) Rs. 98.56
(C) Rs. 66.56
(D) Rs. 66.58
(E) None of these
Rationale: Explanation:
Given that simple interest for 2 years is Rs.800
i.e., Simple interest for 1st year is Rs.400
and simple interest for 2nd year is also Rs.400
Compound interest for 1st year will be 400
and Compound interest for 2nd year will be 832 - 400 = 432
you can see that compound interest for 2nd year is more than simple interest for 2nd year by 432 - 400 = Rs.32
i.e, Rs. 32 is the interest obtained for Rs.400 for 1 year
Rate, R = 100 × SI/PT = (100×32)/(400 × 1) = 8%
Difference between compound and simple interest for the 3rd year
= Simple Interest obtained for Rs.832
= PRT/100 = (832 × 8 × 1)/100 = Rs. 66.56
Total difference between the compound and simple interest for 3 years
= 32 + 66.56 = Rs.98.56
Answer: Option B
Answer: (B) Rs. 98.56
Question: $500 will become $1000 in 7 years find the rate of interest?
(A) A)10%
(B) B)20%
(C) C)14.29%
(D) D)30%
(E) E)50%
Rationale: SI = simple interest = A-P = 1000-500 = $500
R = 100SI/PT = 100*500/500*7 =14.29%
Answer is C
Answer: (C) C)14.29%
Question: Andrew travelling to 7 cities. Gasoline prices varied from city to city. What is the median gasoline price?
(A) $1
(B) $1.84
(C) $1.92
(D) $2.13
(E) $2.15
Rationale: Ordering the data from least to greatest, we get:
$1.61, $1.75, $1.79, $1.84, $1.96, $2.09, $2.11
The median gasoline price is $1.84. (There were 3 states with higher gasoline prices and 3 with lower prices.)
B
Answer: (B) $1.84
Question: Country C imposes a two-tiered tax on imported cars: the first tier imposes a tax of 15% of the car's price up to a certain price level. If the car's price is higher than the first tier's level, the tax on the portion of the price that exceeds this value is 10%. If Ron imported a $15,000 imported car and ended up paying $1800 in taxes, what is the first tier's price level?
(A) $7000
(B) $6500
(C) $6050
(D) $6000
(E) $6100
Rationale: Let T be the tier price, P be total price = 15000
Per the given conditions:
0.15T + 0.10(P-T) = 1800
0.15T+0.10*15000-0.10T =1800
0.05T +1500 = 1800
0.05T = 1800-1500 = 300
T = 300/0.05 =6000
Answer D
Answer: (D) $6000
Question: The ratio between the perimeter and the breadth of a rectangle is 5 : 1. If the area of the rectangle is 216 sq. cm, what is the length of the rectangle?
(A) 16cm
(B) 18cm
(C) 24cm
(D) Data inadequate
(E) None of these
Rationale: Explanation:
2(l+b)/b=5/1
2l + 2b = 5b
3b = 2l
b = 2/3 l
Then, Area = 216 cm2
l x b = 216
l x (2/3)l = 216
l2 = 324.
l = 18 cm.
Answer: B
Answer: (B) 18cm
Question: In Town X, 120 percent of the population are employed, and 80 percent of the population are employed males. What percent of the employed people in Town X are females?
(A) 16%
(B) 25%
(C) 33%
(D) 40%
(E) 52%
Rationale: Total employed people 12%, out of which 80 are employed males, hence 40% are employed females.
(employed females)/(total employed people)=40/120=1/3=33%
Answer: C.
Answer: (C) 33%
Question: Which of the following is not the square of an integer?
(A) 276676
(B) 400689
(C) 228484
(D) 261121
(E) 432458
Rationale: The square of an integer (n^2) can have only the following units digit:
0, if the units digit of n is 0;
1, if the units digit of n is 1 or 9;
4, if the units digit of n is 2 or 8.
5, if the units digit of n is 5;
6, if the units digit of n is 6 or 4;
9, if the units digit of n is 3 or 7.
The square of an integer cannot have the units digit of 2, 3, 7, or 8.
The answer is E.
Answer: (E) 432458