mathewhe/aqua_rat huggingface dataset:
Question: If xy=9, x/y=36, for positive numbers x and y, y=?
(A) 1/2
(B) 2
(C) 1/3
(D) 3
(E) 1/6
Rationale: Very easy question. 2 variables and 2 easy equations.
xy=9 ---> x=9/y - (i)
x/y=36 ---> replacing (i) here ---> 9/(y^2)=36 ---> y^2=9/36=1/4 ---> y=1/2 or -1/2
The question states that x and y are positive integers. Therefore, y=1/2 is the answer.
Answer A.
Answer: (A) 1/2
Question: The profit earned by selling an article for Rs. 832 is equal to the loss incurred when the same article is sold for Rs. 448. What should be the sale price for making 50% profit?
(A) 337
(B) 960
(C) 278
(D) 211
(E) 191
Rationale: Explanation:
Let C.P. = Rs. x.
Then, 832 - x = x - 448
2x = 1280 => x = 640
Required S.P. = 150% of Rs. 640 = 150/100 * 640 = Rs. 960.
Answer: B
Answer: (B) 960
Question: In a certain deck of cards, each card has a positive integer written on it. In a multiplication game, a child draws a card and multiples the integer on the card by the next larger integer. If each possible product is between 25 and 200, then the least and greatest integers on the card could be
(A) 3 and 15
(B) 3 and 20
(C) 5 and 13
(D) 4 and 14
(E) 5 and 14
Rationale: There child draws one number then multiplies that number by the number above it. The number must be more than 25 and less than 200.
x * (x+1)
Answer gives us choices of 3,4 and 5 (JUST ABOVE 25)
3*(3+1) =12 <- WRONG
4*(4+1) =20 <- WRONG
5*(5+1)=30 <-CORRECT AS IT IS ABOVE 25
Answer gives us choices 13,14,15 and 20 (BELOW 200)
Immediately by knowing squares you should be able to rule out 15 (225) and 20 (400). And common sense dictates that as 14^2 is 196 that 14*(14+1) is above 200.
13*(13+1)=182 <- CORRECT
Answer is C) 5 and 13
Answer: (C) 5 and 13
Question: capacity of A doing work is double than B.if both together finish a work in 21 days,then A alone in how much days can finish the work?
(A) 16
(B) 18
(C) 15
(D) 20
(E) 21
Rationale: let A alone can finish the work in x days.then B alone can finish the work in 2x days.
work of A in 1 days=1/x,and work of B in 1 days=1/2x
(A+B) work in 1 days=[1/x+1/2x]=3/2x
but,(A+B) work in 1 days=1/12
3/2x=1/12,2x=36,x=18
answer B
Answer: (B) 18
Question: Sumitra has an average of 56% on her first 7 examinations. How much should she make on her eighth examination to obtain an average of 60% on 8 examinations?
(A) 88%
(B) 78%
(C) 98%
(D) Cannot be determined
(E) None of these
Rationale: Since the weight age of eighth examination is not known, hence can not be determined.
Answer D
Answer: (D) Cannot be determined
Question: Find the number of ways in which 6 different beads can be arranged to form a necklace.
(A) 30
(B) 20
(C) 50
(D) 60
(E) 80
Rationale: Since in forming a necklace clockwise and anticlockwise arrangements are not different, therefore,6 beads can be arranged to form a necklace in(6-1)! /2ways
= 5*4*3*2/2 = 60 ways
Answer is C
Answer: (C) 50
Question: In what time will Rs. 1000 become Rs. 1331 at 10% per annum compounded annually?
(A) 7years
(B) 6years
(C) 3years
(D) 9years
(E) 2years
Rationale: Explanation:
Principal = Rs. 1000; Amount = Rs. 1331; Rate = 10% p.a. Let the time be n years. Then,
[ 1000 (1+ (10/100))^n ] = 1331 or (11/10)^n = (1331/1000) = (11/10)^3
n = 3 years
Answer: C
Answer: (C) 3years
Question: Nr Books bought Nr of People
6 3
7 1
8 5
9 2
What is the median of books bought per person?
(A) a) 2
(B) b) 4
(C) c) 6
(D) d) 8
(E) e) 18
Rationale: 6,6,6,7,8,8,8,8,8,9,9
so you will observer that the median of the list is 8. Ans D
Answer: (D) d) 8
Question: If p is a natural number and p! ends with r trailing zeros, then the number of zeros that (5p)! ends with will be
(A) a) (p+r) trailing zeros
(B) b) (5p+y) trailing zeros
(C) c) (5p+5y) trailing zeros
(D) d) (p+5y) trailing zeros
(E) e) none of them above
Rationale: Let p = 1. p! = 1! = 1, which means r= 0
(5p)! = 5! = 120, trailing zeros = 1
1 = 1 + 0 = p + r
Answer (A).
Answer: (A) a) (p+r) trailing zeros
Question: How much interest can a person get on Rs. 7200 at 17.5% p.a. simple interest for a period of two years and six months?
(A) Rs. 4150
(B) Rs. 3850
(C) Rs. 3770
(D) Rs. 3150
(E) None of these
Rationale: I = (7200 * 2.5 * 17.5)/100 = (7200 * 5 * 35)/(100 * 2 * 2)
= Rs. 3150
ANSWER:D
Answer: (D) Rs. 3150
Question: If the operation € is defined for all x and y by the equation x € y = 2*x*y, then 7 € (4 € 5) =
(A) 80
(B) 120
(C) 160
(D) 240
(E) 560
Rationale: working inside out,
(4 € 5) = 2*4*5 = 40
7 € 40 = 2*3*40 = 560
Hence, answer is E
Answer: (E) 560
Question: A and B began business with Rs.3000 and Rs.4000 after 8 months, A withdraws Rs.1000 and B advances Rs.1000 more. At the end of the year, their profits amounted to Rs.630 find the share of A.
(A) Rs.240
(B) Rs.350
(C) Rs.340
(D) Rs.390
(E) Rs.260
Rationale: Explanation:
(3*8 + 2*4):(4*8 + 5*4)
8:13
8/21 * 630 = 240
ANSWER IS A
Answer: (A) Rs.240
Question: 10 camels cost as much as 24 horses, 16 horses cost as much as 4 oxen and 6 oxen as much as 4 elephants. If the cost of 10 elephants is Rs.140000, find the cost of a camel?
(A) s.9800
(B) s.3800
(C) s.9800
(D) s.6800
(E) s.5600
Rationale: Cost of the camel = P
10 camels = 24 horses
16 horses = 4 oxen
6 oxen = 4 elephants
10 elephants = Rs.140000
P = Rs.[(24 * 4 * 4 * 140000)/(10 * 16 * 6 * 10)]
P = Rs.(53760000/9600) => P = Rs.5600
Answer:E
Answer: (E) s.5600
Question: By selling 99 pens, a trader gains the cost of 33 pens. Find his gain percentage?
(A) 33 1/3
(B) 33 1/5
(C) 33 1/9
(D) 33 1/4
(E) 33 1/1
Rationale: Let the CP of each pen be Rs. 1.
CP of 99 pens = Rs. 99
Profit = Cost of 33 pens = Rs. 33
Profit% = 33/99 * 100 = 33 1/3%.Answer: A
Answer: (A) 33 1/3
Question: The captain of a cricket team of 11 members is 26 years old and the wicket keeper is 5 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) 26 years
(E) 27 years
Rationale: EXPLANATION
Let the average age of the whole team by x years.
11x â€“ (26 + 21) = 9(x -1)
11x â€“ 9x = 48
2x = 48
x = 24.
So, average age of the team is 24 years.
Answer B
Answer: (B) 24 years
Question: If x > y^6 > z^7, which of the following statements could be true? I.x>z II.z=x III.x>y>z
(A) I,III only
(B) I only
(C) II only
(D) III only
(E) I,II only
Rationale: Answer : A
Answer: (A) I,III only
Question: A function g(n), where n is an integer, is defined as the product of all integers from 1 to n. How many of the followings must be a prime number?
g(11) + 7; g(11) + 8; g(11) + 9; and g(11) + 10?
(A) 1
(B) 2
(C) 3
(D) 4
(E) none
Rationale: g(11) is the product of all integers from 1 to 11, so g(11) = 11!
Thus g(11) is a multiple of all the integers from 1 to 11.
Then g(11) is a multiple of 7, 8, 9, and 10.
7 divides g(11)+7
8 divides g(11)+8
9 divides g(11)+9
10 divides g(11)+10
The answer is E.
Answer: (E) none
Question: Balloons are bought at 12 for Rs.10/- and sold at 10 for Rs.12/-. Find the gain or loss percentage?
(A) 21% Loss
(B) 21% Gain
(C) 44 % Profit
(D) 44 % Loss
(E) 46 % Loss
Rationale: Explanation:
12 Balloons -----> Rs.10/-
10 Balloons -----> Rs.12/-
Note: Number of articles bought is must equal to number of articles sold.
10(12 10) ==> 120 100 = Cost price
12(10 12) ==> 120 144 = Selling price
Then, 44/100 × 100 = 44 % Profit
Answer: Option C
Answer: (C) 44 % Profit
Question: A shopkeeper gives a discount of 12, whereas a customer makes cash payment. Let 'p' denotes the percentage, above the cost price, that the shopkeeper must mark up the price of the articles ['p' is an integer] in order to make a profit of x. Which of the following can't be possible value of x?
(A) 54
(B) 76
(C) 96
(D) 32
(E) 34
Rationale: Explanation :
Let, the cost price of one article is Rs r then,
Marked price of the article,
=>r(1+p/100).
The selling price is:-
=>r(1+p/100)(1−12/100).
Profit percentage =x%
=>r(1+p/100)(1−12/100)=r(1+x100).
=>x=25(12+x)/22.
As, p is an integer, x must be multiple of 22.
All the possible values x, less than 100 are k=10,32,54,76,98.
Except option 'C' all the options are possible.
Answer : C
Answer: (C) 96
Question: Which is largest prime number?
(A) 937
(B) 983
(C) 991
(D) 997
(E) 999
Rationale: Answer:D
Answer: (D) 997
Question: Today Mary’s father is four times as old as Mary. Three years ago, he was 5 times as old. How old is Mary today?
(A) 6
(B) 8
(C) 10
(D) 12
(E) 14
Rationale: Dad's age = 4M
5*(M-3) = 4M-3
M = 12
The answer is D.
Answer: (D) 12
Question: mr. depak has $449,774 in his bank account. What is the least amount of money (in whole number of dollars) that he must add to his account if he wants to split this money evenly among her six best friends?
Options:
(A) $1
(B) $2
(C) $3
(D) $4
(E) $6
Rationale: To find the least amount deepak should add to his saving account to split the money evenly among his 6 best friends,
he needs to make the total divisible by 6
Simply add the individual digits of the total = 4+4+9+7+7+4 = 35
If you add 1 , the number is divisible by 6 (35+ 1)
Correct Option : A
Answer: (A) $1
Question: In a zoo, the ratio of the number of cheetahs to the number of pandas is 1 : 3 and was the same five years ago. If the increase in the number of cheetahs in the zoo since then is 2, then what is the increase in the number of pandas?
(A)  2
(B)  3
(C)  5
(D)  6
(E)  15
Rationale: One short cut to solve the problem is
c:p = 1:3
c increased to 3
=> 1:3 = 3:x
=> x = 9
=>p increased by 6
D is the answer
Answer: (D)  6
Question: In a library, there are certain number of books on a shelf, ranging between 75 and 100. 1/6th of them are fiction and 12.5% of them are non-fiction. Find the number of books.
(A) 68
(B) 72
(C) 96
(D) Can't be determined
(E) None of these
Rationale: Explanation:
12.5% can be written as 1/8th
Since 1/6th of the books are fiction and 1/8th are non-fiction, the total number of books must be exactly divisible by 6 and 8 and should be between 75 and 100.
Therefore, 96 is the only number, which fulfills the above criteria.
Note that the question doesn't imply that there are ONLY two varieties of books.
ANSWER: C
Answer: (C) 96
Question: 20. A certain church bell rings the bell twice at half past the hour and four
times at the hour plus an additional number of rings equal to what ever
time it is. How many rings will the clock make from 6:20 in the morning
to 11:10 in the morning?
(A) 32.
(B) 75.
(C) 42.
(D) 46.
(E) 50.
Rationale: @ 6:30 - 2
@ 7 - 4+7 =11
@ 7:30 - 2
@ 8 - 12
@ 8:30 - 2
@ 9 - 13
@ 9:30 - 2
@ 10 - 14
@10:30 - 2
@11:00 -11+4=15
totals to B=75
Answer: (B) 75.
Question: Two dice are thrown simultaneously. What is the probability of getting two numbers whose product is even?
(A) 3/4
(B) 4/3
(C) 6/5
(D) 5/9
(E) 4/5
Rationale: n(S)=36
n(E)=27
P(E)=n(S)/n(E)
=27/36
=3/4
Ans: A
Answer: (A) 3/4
Question: Joshua and Jose work at an auto repair center with 4 other workers. For a survey on health care insurance, 2 of the 6 workers will be randomly chosen to be interviewed. What is the probability that Joshua and Jose will both be chosen?
(A) 1/15
(B) 1/12
(C) 1/9
(D) 1/6
(E) 1/3
Rationale: 1) Probability of chosing Josh first = 1/6
Probability of chosing Jose second = 1/5
total = 1/30
Probability of chosing Jose first = 1/6
Probability of choosing Josh second = 1/5
Total = 1/30
Final = 1/30 + 1/30 = 1/15
2) Number of ways two persons can be chosen 6C2 = 15
Number of ways Josh and Jose are the two persons = 1
Total = 1/15
Answer will be A.
Answer: (A) 1/15
Question: A train 125 m long passes a man, running at 10 km/hr in the same direction in which the train is going, in 10 sec. The speed of the train is?
(A) 37 km/hr
(B) 50 km/hr
(C) 36 km/hr
(D) 26 km/hr
(E) 55 km/hr
Rationale: Speed of the train relative to man = 125/10 = 25/2 m/sec.
= 25/2 * 18/5 = 45 km/hr
Let the speed of the train be x km/hr. Then, relative speed = (x - 5) km/hr.
x - 10 = 45 => x = 55 km/hr.
Answer:E
Answer: (E) 55 km/hr
Question: How many factors of 440 are odd numbers greater than 1?
(A) 2
(B) 4
(C) 5
(D) 6
(E) 7
Rationale: When factorized, 440 has 4 prime factors. Of these prime factors 2 are odd and 2 are even. Hence total number of odd factors is 2*2(4), which includes 2. The total number of odd factors greater than 1 are 2.(option A)
Answer: (A) 2
Question: January 1, 2007 was Monday. What day of the week lies on Jan. 1, 2008?
(A) Monday
(B) Tuesday
(C) Wednesday
(D) Sunday
(E) Friday
Rationale: Explanation:
The year 2007 is an ordinary year. So, it has 1 odd day.
1st day of the year 2007 was Monday.
1st day of the year 2008 will be 1 day beyond Monday.
Hence, it will be Tuesday.
Answer: B
Answer: (B) Tuesday
Question: If 40 per cent of a number is added to an other number then it becomes 125 per cent of itself. What will be the ratio of first and second numbers?
(A) 8 : 5
(B) 5 : 7
(C) 5 : 8
(D) Data inadequate
(E) None of these
Rationale: 40x⁄100 + y = 125x⁄100 ⇒ x⁄y = 20⁄17
Answer E
Answer: (E) None of these
Question: Two vehicles A and B leave from Y to X. A overtakes B at 10:30 am and reaches X at 12:00. It waits for two hours and returns to Y. On its way, it meets B at 3 PM and reaches Y at 5 PM. B reaches city X waits for 1 hour and returns to y After how many hours will B reach to Y from the time A overtook him.
(A) 40.5
(B) 41.5
(C) 42.5
(D) 43.5
(E) 44.5
Rationale: Let the distance between City X and Y be D
As given - B leaves City X at 2:00 (12:00 + 2 hrs halt) and reaches City Y at 5:00
So it takes him 3 hours to cover distance D.
Now, A overtakes B at 10:30 and reaches city Y at 12:00 pm , which means that A traveled for 1:30 hr.
Now see,
A takes 3 hrs takes to cover distance D
so in 1.5 hrs A will cover D / 2 distance
Now see another part -
"On its way, it meets B at 3 PM and reaches Y at 5 PM."
Given that - B leaves City Y at 2 PM
So distance covered by A in 1 hr (3 - 2) = D / 3
Now Total Distance covered by B during (A overtaking B + A wait for two hour + A on its way back ) is
D / 2 [when they first overtake] - D / 3 [when they again overtake]
= D / 6
Now Time elapsed during this period (A overtaking B + A wait for two hour + A on its way back )
=1.5 + 2 + 1
=4.5
so to cover D / 6 distance B took 4.5 hr
to cover D distance B will take (4.5 * 6)
= 27 hr.
Now "After how many hours will B reach to Y from the time A overtook him."
Time to reach X after A overtook (D / 2) + wait + Time to reach Y from X (D)
= 13.5 + 1 + 27
= 41.5
ANSWER:B
Answer: (B) 41.5
Question: By selling 22 pencils for a rupee a man loses 20%. How many for a rupee should he sell in order to gain 20%?
(A) 83
(B) 63
(C) 53
(D) 33
(E) 13
Rationale: 80% --- 22
120% --- ?
80/120 * 22 = 33
Answer:D
Answer: (D) 33
Question: In a group of 100 people,60 like volleyball,50 like hockey. How many like both volleyball and hockey?
(A) 20
(B) 15
(C) 10
(D) 5
(E) 25
Rationale: Make a Venn diagram, and enter your data.
Let the number of people who like both volleyball and hockey be x
60-x+x+50-x = 100
x = 10
so number who like both volleyball and hockey = 10
Answer C
Answer: (C) 10
Question: In an examination, a student scores 4 marks for every correct answer and loses 1 mark for every wrong answer. If he attempts all 60 questions and secures 160 marks, the no of questions he attempts correctly is :
(A) 35
(B) 38
(C) 40
(D) 42
(E) 44
Rationale: Explanation:
Let the number of correct answers be X.
Number of incorrect answers = (60 – X).
4x – (60 – x) = 160
=> 5x = 220
=> x = 44
Answer: E
Answer: (E) 44
Question: A man can row downstream at 20 kmph and upstream at 10 kmph. Find the speed of the man in still water and the speed of stream respectively?
(A) 3
(B) 5
(C) 6
(D) 4
(E) 9
Rationale: Let the speed of the man in still water and speed of stream be x kmph and y kmph respectively.
Given x + y = 20 --- (1)
and x - y = 10 --- (2)
From (1) & (2) 2x = 30 => x = 15, y = 5. Answer: B
Answer: (B) 5
Question: Jim covers a distance of 8km in 50 minutes. If he covers 3km distance in 2/5th of time then, What speed should he maintain to cover the remaining distance in the remaining time?
(A) 15 Kmph
(B) 18 Kmph
(C) 19 Kmph
(D) 20 Kmph
(E) 21 Kmph
Rationale: Total distance = 8 Km
Total time = 50 Km
Time taken to cover the distance of 3 Km = 50*2/5 = 20 min = 1/3 hours
Remaining distance = 8 - 3 = 5 Km
Required speed = 5/1/3 = 15 Kmph
A)
Answer: (A) 15 Kmph
Question: The H.C.F. of two numbers is 23 and the other two factors of their L.C.M. are 13 and 17. The larger of the two numbers is:
(A) 276
(B) 299
(C) 391
(D) 345
(E) 354
Rationale: Clearly, the numbers are (23 x 13) and (23 x 17).
Larger number = (23 x 17) = 391.
Answer: Option C
Answer: (C) 391
Question: If 25% of a number is subtracted from a second number the second number reduces to its five-sixths. What is the ratio between the first number and the second number?
(A) 2 : 3
(B) 3 : 2
(C) 1 : 3
(D) Data inadequate
(E) None of these
Rationale: Let the first and second number be x and y respectively.
x - y × 25⁄100 = y × 5⁄6
or, y - x⁄4 = 5⁄6y
or, 1⁄6y = x⁄4y
\ x : y = 2 : 3
Answer A
Answer: (A) 2 : 3
Question: There are c cities. What is the number of airlines that connected 2 different cities (airline from city A to city B is different with airline from city B to city A)?
(A) c(c-1)
(B) n(n+1)
(C) n(n-1)/2
(D) n(n+1)/2
(E) n2
Rationale: First of all, the possible number of airlines is c. Then, the possible number of airlines departing from one city to another becomes (c-1). Hence, the answer is c(c-1), A
Answer: (A) c(c-1)
Question: A dishonest grocer professes to sell pure butter at cost price, but he mixes it with adulterated fat and thereby gains 20%. Find the percentage of adulterated fat in the mixture assuming that adulterated fat is freely available?
(A) 20%
(B) 25%
(C) 33.33%
(D) 40%
(E) 35%
Rationale: Say 100g pure butter costs $100
But; $100 is his 25% profit because he just used 80gram pure butter.
80g would have costed him $80 and he sold it for $100 by adding 20g of freely available fat. $100 is 1.20(75)
so;
total weight=100g
fat=20g
25%
B
Answer: (B) 25%
Question: The work done by a man, a woman and a child is in the ratio of 3:2:1. There are 20 men, 30 women & 48 children in a factory. Their weekly wages amount to Rs.840, which is divided in the ratio of work done by the men, women and children. What will be the wages of 15 men, 21 women & 30 children for 2 weeks?
(A) Rs.1000
(B) Rs.1050
(C) Rs.1170
(D) Rs.1900
(E) Rs.1230
Rationale: sax Ratio of wages of 20 men, 30 women
and 45 chﬂdren perweek
: (3 x 2o):(2 x 30) (1 x 43) 5
Total wages or 20 men per week
= R5 300
Therefore, wages of a man per week : Rs 15,
sirmlarly, wages of woman per week
: Rs 10 and wages ofchwld perweek Rs 5
Total wages of (15 men, 21 women and 30
chﬂdrenj perweek
= 15x15 + 21x10 + 30x5 = 585
Total wages for 2 weeks = Rs.1170
C
Answer: (C) Rs.1170
Question: 5^100 is divided by 18. Then what is the remainder?
(A) 10
(B) 11
(C) 13
(D) 15
(E) 19
Rationale: Here N = 18=2×32
ϕ(18)=18(1−12)(1−13) = 6
So 56 when divided by 18, remainder is 1.
So we can write the given expression 5100=(56)16×54 = (1)16×54 = 52×52=7×7=49
Now 49 when divided by 18, remainder is 13.
C
Answer: (C) 13
Question: A certain bus driver is paid a regular rate of $16 per hour for any number of hours that does not exceed 40 hours per week. For any overtime hours worked in excess of 40 hours per week, the bus driver is paid a rate that is 75% higher than his regular rate. If last week the bus driver earned $920 in total compensation, how many total hours did he work that week?
(A) 36
(B) 50
(C) 44
(D) 48
(E) 52
Rationale: For 40 hrs = 40*16=640
Excess = 920-640=280
For extra hours =.75(16)=12+16=28
Number of extra hrs =280/28=10
Total hrs =40+10=50
Answer B 50
Answer: (B) 50
Question: The bankerâ€™s gain on a sum due 3 years hence at 10% per annum is Rs. 120. The bankerâ€™s discount is
(A) Rs.960
(B) Rs.840
(C) Rs.520
(D) Rs.760
(E) None
Rationale: Solution
T.D	=(B.G x 100 / R x T)
= Rs.(120x100/10 x 3)
= Rs.400.
B.D
=Rs(400+ 120)
= Rs.520.
Answer C
Answer: (C) Rs.520
Question: Three people took GMAT practice tests in which the minimum and maximum possible scores are 200 and 800, respectively. They each took a test 4 times, and no one scored below 610 or over 780. If the individual ranges of the three people's scores in those 4 practice tests were 50, 80 and 90, what is the difference between the maximum and minimum possible ranges of all their scores put together.
(A) 70
(B) 80
(C) 90
(D) 100
(E) 110
Rationale: According to the information in the question the maximum range would be between 610 and 780(170). The minimum range would be the greatest range for any one individual, which is listed in the problem as 90. So the difference between these would be 170-90 or 80.
Answer: B
Answer: (B) 80
Question: Nine men went to a hotel. 8 of them spent 3 each over their meals and the ninth spent 8 more than the average expenditure of all the nine. The total money spent by all of them was
(A) 36
(B) 40
(C) 29.25
(D) 27
(E) None of the above
Rationale: Let the average expenditure of all the ninte be x
Then, 3 × 8 + x + 8 = 9x
⇒ x = 4
∴ Total money spent = 9x = 9 × 4 = 36
Answer A
Answer: (A) 36
Question: At 12:00 a.m., Tom begins traveling on a certain bike path from Riverdale at a constant rate of 10 mph. If, at 3:00 p.m., Jim begins traveling from Riverdale on the same path at a constant rate of 20 mph, at what time will he catch up to Peter?
(A) 5:00 p.m.
(B) 6:00 p.m.
(C) 7:00 p.m.
(D) 8:00 p.m.
(E) 9:00 p.m.
Rationale: By the time Jim starts, Tom has already covered = 3 hr * 10 mph = 30 miles
Relative speed = 20- 10 = 10mph
To catch up, Jim needs to cover 30 miles which can be covered in = 30/10= 3hours
If Jim leaves at 3 pm, he will catch Tom at 6 pm
Answer: B
Answer: (B) 6:00 p.m.
Question: In a certain province in France there are 19 cities. If a single road segment connects only two cities, how many road segments are required in order to connect the cities so that each city is connected to all other cities with a single road segment?
(A) 30
(B) 105
(C) 330
(D) 143
(E) 171
Rationale: 1 city needs 18 roads to connect directly to the rest => 19 city needs 19*18 roads.
One road is counted twice => the number of road needed is 19*18/2 = 171
Answer E
Answer: (E) 171
Question: The difference between C.I. and S.I. on an amount of $10,000 for 2 years is $49. What is the rate of interest per annum?
(A) 5%
(B) 6%
(C) 7%
(D) 8%
(E) 9%
Rationale: $49 is the interest on the first year of interest.
Let x be the interest rate.
The interest after the first year is 10000*x.
The interest on the first year's interest is 10000*x*x
10000*x^2 = 49
x = 0.07
The answer is C.
Answer: (C) 7%
Question: 75% of the guestrooms at the Stagecoach Inn have a queen-sized bed, and each of the remaining rooms has a king-sized bed. Of the non-smoking rooms, 60% have a queen-sized bed. If 32% of the rooms at the Stagecoach Inn are non-smoking rooms with king-sized beds, what percentage of the rooms permit smoking?
(A) 20%
(B) 30%
(C) 50%
(D) 55%
(E) 75%
Rationale: Let x be the number of non-smoking rooms.
Let N be the total number of rooms at the inn.
40% of non-smoking rooms have a king-sized bed.
0.4x = 0.32N
x = 0.8N
The percentage of rooms which permit smoking is 1 - 0.8 = 20%
The answer is A.
Answer: (A) 20%
Question: A single discount equivalent to the discount series of 30%, 10% and 5% is?
(A) 31.5
(B) 31.8
(C) 40.1
(D) 31.3
(E) 31.1
Rationale: 100*(70/100)*(90/100)*(95/100)
= 59.9
100 - 59.9 = 40.1
Answer:C
Answer: (C) 40.1
Question: A table is bought for Rs.800/- and sold at a loss of 10% find its selling price
(A) s.500/-
(B) s.530/-
(C) s.540/-
(D) s.600/-
(E) s.720/-
Rationale: 100 % ------> 800 (100 * 8 = 800)
90 % ------> 720 (90 * 8 = 720)
Selling price = Rs.720/-
E
Answer: (E) s.720/-
Question: A merchant marks his goods up by 40% and then offers a discount of 15% on the marked price. What % profit does the merchant make after the discount?
(A) 21%
(B) 25%
(C) 69%
(D) 31%
(E) 19%
Rationale: Let the original price be 100.
After 40% markup, price = 140
After 15% discount on this marked-up price, price = 140 - (15% of 140) = 140 - 21 = 119
Final profit = ((119-100) / 100) * 100 = 19%
Option E
Answer: (E) 19%