mathewhe/aqua_rat huggingface dataset:
Question: The average age of 3 men is increased by years when two of them whose ages are 21 years and 23 years are replaced by two new men. The average age of the two new men is
(A) 22
(B) 30
(C) 25
(D) 38
(E) 27
Rationale: total age increased = (3 * 2) years = 6 years.
Sum of ages of two new men = (21 + 23 + 6) years = 50 years
Average age of two new men = (50/2) years = 25 years.
Answer: C
Answer: (C) 25
Question: A retail store sells higher end dresses for $40 each and lower end dresses for $20 each. On every higher end dress the retail store makes a profit of $4 while on every lower end dress it makes a profit of $1. If on a given day the store's sales amounted to $400, which of the following cannot be the profit made on that day?
(A) $26
(B) $27
(C) $30
(D) $34
(E) $40
Rationale: $27 is the only option that does not fit into a combination of higher end and lower end sales profits, given the total sales of the day. Answer: B
Answer: (B) $27
Question: I walk a certain distance and ride the car back taking a total time of 33 minutes. I could walk both sides in 45 min. How long would it take me to ride both ways?
(A) 19min
(B) 20min
(C) 21min
(D) 22min
(E) 23min
Rationale: Explanation :
Time taken in walking a certain distance
from X and Y = 22 1/2 min
Time taken in riding the same distance
= 33 - 22 1/2 = 10 1/2 min
It will take 21 min to ride both ways.
Answer : C
Answer: (C) 21min
Question: By selling an article at Rs.800, a shopkeeper makes a profit of 25%. At what price should he sell the article so as to make a loss of 20%?
(A) 228
(B) 480
(C) 512
(D) 288
(E) 276
Rationale: SP = 800
Profit = 25%
CP = (SP)*[100/(100+P)]
= 800 * [100/125]
= 640
Loss = 25% = 25% of 640 = Rs.128
SP = CP - Loss = 640 - 128 = Rs.512
Answer: C
Answer: (C) 512
Question: The Winston Pool League played a total of 90 balls of which the ladies sank 30%. After getting a good night's sleep, the ladies came back the next day and sank each of the next balls played bringing their average to 50%. How many ball did the league play for the ladies to achieve this average?
(A) 25
(B) 30
(C) 46
(D) 26
(E) 36
Rationale: Explanation: Identify the parts, set up equation, and solve.
Number of balls initially sank by the ladies:
30% * 90 = 27
Total balls sank by the ladies leaving their average at 50%. (Let x represent the unknown number of additional balls sank by the ladies.) Therefore, the total number of balls played is 90+x, and the total number of balls sank by the ladies is 27+x. This gives the equation as:
50%*(90+x)=27+x
Solve: Let's get rid of the percent sign
50/100*(90+x)=27+x
1/2 *(90+x)=27+x
Get rid of the fraction:
2[1/2 * (90+x)]=2(27+x)
1 * (90+x) =54+2x
90+x =54+2x
(90-54)+x = (54-54)+2x
36+x= 2x
36=x
Answer: E
Answer: (E) 36
Question: Shawn invested one half of his savings in a bond that paid simple interest for 2 years and received $650 as interest. He invested the remaining in a bond that paid compound interest, interest being compounded annually, for the same 2 years at the same rate of interest and received $725 as interest. What was the value of his total savings before investing in these two bonds?
(A) 1000
(B) 1,250
(C) 2,250
(D) 3,250
(E) 4,250
Rationale: So, we know that Shawn received 20% of the amount he invested in a year. We also know that in one year Shawn received $325, thus 0.2x = $325 --> x = $1625
Since, he invested equal sums in his 2 bonds, then his total savings before investing was 2*$1,625 = $3,250
Answer D
Answer: (D) 3,250
Question: A palindrome is a number that reads the same forward and backward, such as 787. How many even, 8-digit numbers are palindromes?
(A) 4055
(B) 4500
(C) 5000
(D) 9000
(E) 4000
Rationale: First recognize you only need to consider the first four digits (because the second four are just the first four flipped)
There are 9000 possibilities for the first four digits of a 8 digit number, 1000-9999 inclusive. Everything starting with a 2,4,6,8 will be odd, which is 4/9ths of the combinations.
4/9*9000 = 4000
ANSWER:E
Answer: (E) 4000
Question: Calculate the ratio between x and y if 30% of x equal to 50% of y?
(A) 4 : 5
(B) 3 : 5
(C) 3 : 7
(D) 3 : 2
(E) 4 : 5
Rationale: Explanation:
30 x = 50 y
x: y = 30: 50 = 3 : 5
Answer:B
Answer: (B) 3 : 5
Question: If the wages of 6 men for 15 days be Rs.2100, then find the wages of
for 12 days.
(A) Rs.2420
(B) Rs.2500
(C) Rs.2520
(D) Rs.2020
(E) Rs.2650
Rationale: . Let the required wages be Rs. x.
More men, More wages	(Direct Proportion)
Less days, Less wages	(Direct Proportion)
Men 6: 9 : :2100:x
Days 15:12
Therefore (6 x 15 x x)=(9 x 12 x 2100)  x=(9 x 12 x 2100)/(6 x 15)=2520
Hence the required wages are Rs. 2520.
Answer is C
Answer: (C) Rs.2520
Question: To deliver an order on time, a company has to make 25 parts a day. After making 25 parts per day for 3 days, the company started to produce 5 more parts per day, and by the last day of work 100 more parts than planned were produced. Find how many parts the company made and how many days this took.
(A) 475 pieces.
(B) 575 pieces.
(C) 675 pieces.
(D) 775 pieces.
(E) None of these
Rationale: Solution:
Let xx be the number of days the company worked. Then 25x is the number of parts they planned to make. At the new production rate they made:
3⋅25+(x−3)⋅30=75+30(x−3)
Therefore: 25x=75+30(x−3)−100
25x=75+30x−90−100
190−75=30x−25
115=5x
x=23
So the company worked 23 days and they made 23⋅25+100=675 pieces.
Answer C
Answer: (C) 675 pieces.
Question: Let p be a prime number. If N = 8p, how many distinct even divisors does N have?
(A) 1
(B) 4
(C) 5
(D) 2
(E) 3
Rationale: The correct answer is D. There are two: 2 and 2p.
8p = 2*2*2p = (2*2)*2p. Since we care only about distinct divisors, we ignore the fact that 2 appears three times.
Answer: (D) 2
Question: A boy is travelling from his home to school at 12 km/hr and reached 7 min late. Next day he traveled at 16 km/hr and reached 8 min early. Distance between home and school?
(A) 12km
(B) 13km
(C) 14km
(D) 15km
(E) 16km
Rationale: Let the distance be x
T1 = x/12 hr
T2 = x/16hr
Difference in time = 7+8 = 15 =1/4hr
x/12-x/16 = 1/4
x/48 = 1/4
x = 12 km
Answer is A
Answer: (A) 12km
Question: What is the lowest positive integer that is divisible by each of the integers 1 through 8 inclusive?
(A) 420
(B) 840
(C) 1260
(D) 2520
(E) 5020
Rationale: We have to find the LCM of 1, 2, 3, 2^2, 5, 2*3, 7, and 2^3.
The LCM is 1*2^3*3*5*7= 840
The answer is B.
Answer: (B) 840
Question: Find the odd man out
6, 26, 106, 426, 1706, 4325, 27304
(A) 6
(B) 26
(C) 426
(D) 4325
(E) 6826
Rationale: 1*4+2 = 6
6*4+2 = 26
26*4+2 = 106
106*4+2 = 426
426*4+2 = 1706
1706*4+2 = 6826
6826*4+2= 6826
ANSWER:D
Answer: (D) 4325
Question: The pilot of a small aircraft with a 40-gallon fuel tank wants to fly to Cleveland, which is 520 miles away. The pilot recognizes that the current engine, which can fly only 8 miles per gallon, will not get him there. By how many miles per gallon must the aircraft’s fuel efficiency be improved to make the flight to Cleveland possible?
(A) 5
(B) 4
(C) 12
(D) 40
(E) 160
Rationale: Actual miles/gallon is = 520/40 = 13 miles/gallon.
Current engine miles/gallon is 8 miles/gallon.
Additional 5 miles/gallon is required to match the actual mileage.
IMO option A.
Answer: (A) 5
Question: A boat can travel with a speed of 22 km/hr in still water. If the speed of the stream is 5 km/hr, find the time taken by the boat to go 189 km downstream
(A) 5 hours
(B) 4 hours
(C) 3 hours
(D) 2 hours
(E) 7 hours
Rationale: Explanation :
Speed of the boat in still water = 22 km/hr
speed of the stream = 5 km/hr
Speed downstream = (22+5) = 27 km/hr
Distance travelled downstream = 189 km
Time taken = distance/speed = 189/27 = 7 hours. Answer : Option E
Answer: (E) 7 hours
Question: A bag of n peanuts can be divided into 9 smaller bags with 6 peanuts left over. Another bag of m peanuts can be divided into 12 smaller bags with 4 peanuts left over. What will be the remainder when nm is divided by 6?
(A) 2
(B) 1
(C) 0
(D) 3
(E) 4
Rationale: n = 9x + 6
m = 12y + 4
nm = (9x + 6)*(12y + 4) = 108xy + 36x + 72y + 24
Remainder of nm/6 = (108xy + 36x + 72y + 24)/6
Observe that the first three terms are a multiple of 6
hence there will be no remainder
Correct Option: C
Answer: (C) 0
Question: The value of a laptop depreciates at the rate of 30% every year. It was purchased 2 years ago. If its present value is Rs. 3430, its purchase price was
(A) 6000
(B) 6500
(C) 7000
(D) 7500
(E) 8000
Rationale: Explanation:
= Rs.7000
Answer: C
Answer: (C) 7000
Question: If x = -3/8 and y = -1/2, what is the value of the expression -2x – y^2?
(A) -3/2
(B) -1
(C) 1
(D) 1/2
(E) 7/4
Rationale: -2X- y^2
-2x-3/8 - (-1/2)^2
3/4-1/4
1/2
D correct
Answer: (D) 1/2
Question: There are 8 books in a shelf that consist of 1 paperback books and 7 hardback books. If 3 books are selected at random without replacement, how many different combinations are there that at least one paperback book is selected?
(A) 21
(B) 45
(C) 50
(D) 55
(E) 60
Rationale: 8C3 [Select any four] - 7C3 [Select all hard backs] = 21
A
Answer: (A) 21
Question: What should be the minimun mark up percentage such that after giving the discount of 200/3% ., there will neither a loss nor a profit ?
(A) 133.3%
(B) 100%
(C) neither gain nor loss
(D) 200%
(E) 120%
Rationale: Let CP = 100.
Discount = 200/3%.
Let 200% was the mark up.
MP = 100 + 200% of 100 = 300.
Now, after discount
300 - (200/3)% of 300
= 300 - 200 = 100.
So, in transaction neither gain nor loss occurs.
ANSWER - OPTION C
Answer: (C) neither gain nor loss
Question: What profit percent is made by selling an article at a certain price, if by selling at 2/3rd of that price, there would be a loss of 20% ?
(A) 30 %
(B) 25 %
(C) 15 %
(D) 20 %
(E) 23 %
Rationale: Explanation:
SP2 = 2/3 SP1
CP = 100
SP2 = 80
2/3 SP1 = 80
SP1 = 120
100 --- 20 => 20%
ANSWER IS D
Answer: (D) 20 %
Question: If a population of women in a town is 60% of men . What is the population of men as a % of population of women ?
(A) A)200%
(B) B)100%
(C) C)50%
(D) D)65%
(E) E)166%
Rationale: We're told that the number of Women in a town is equal to 60% of the number of Men in that town.
IF....
Men = 10
Women = 6
We're asked for the number of Men, as a percentage of the number of Women.
M/W = 10/6 = 5/3 = 166%
Answer is E
Answer: (E) E)166%
Question: In the set of positive integers from 1 to 100, what is the sum of all the odd multiples of 5?
(A) 180
(B) 245
(C) 320
(D) 405
(E) 500
Rationale: reduce 1 - 100
5 - 15 - 25 - 35 - 45 --55--65--75--85--95 are valid multiples. Add them -->500
E
Answer: (E) 500
Question: What is the unit digit in (632)^179×(615)^316×(341)^476
(A) 0
(B) 1
(C) 2
(D) 3
(E) 4
Rationale: unit digit in (632)179
= unit digit in (4)1797
= unit digit in [(42)898 × 4]
= unit digit in [16898 × 4]
= unit digit in (6 × 4)
= 4
unit digit in (615)316
= unit digit in (5)316
= 5
unit digit in (341)476
= unit digit in (1)476
= 1
Hence, unit digit in (6324)1797 × (625)316 × (341)476
= unit digit in [4 × 5 × 1]
= 0
A
Answer: (A) 0
Question: A box contains 3 blue marbles, 4 red, 6 green marbles and 2 yellow marbles. If four marbles are picked at random, what is the probability that none is blue?
(A) 33/96
(B) 33/91
(C) 33/67
(D) 33/28
(E) 33/19
Rationale: Given that there are three blue marbles, four red marbles, six green marbles and two yellow marbles. When four marbles are picked at random, then the probability that none is blue is
= ¹²C₄/¹⁵C₄
= (12 * 11 * 10 * 9)/(15 * 14 * 13 * 12)
= 33/91
Answer: B
Answer: (B) 33/91
Question: Find the sum of all 2 digit numbers divisible by 3.
(A) 16387
(B) 26787
(C) 1267
(D) 1665
(E) 1781
Rationale: Explanation:
No explanation is available for this question!
ANSWER:D
Answer: (D) 1665
Question: If the simple interest on a certain sum of money after 3 1⁄8 years is 1⁄4 of the principal, what is the rate of interest per annum?
(A) 6%
(B) 4%
(C) 8%
(D) 5%
(E) 12%
Rationale: Explanation :
Let the the sum of money(P) be Rs.x
Time(T) = 3 1⁄8 Years = 25⁄8 Years
Simple interest (SI) = x⁄4
Rate of interest per annum(R) = 100×SI/PT=100×x/4/x × 25/8
=100× x ×8/4× x × 25
=8%
Answer : Option C
Answer: (C) 8%
Question: If 0.75 : x :: 5 : 8, then x is equal to:
(A) 1.25
(B) 1.62
(C) 2.0
(D) 1.21
(E) 1.2
Rationale: (x x 5) = (0.75 x 8)
x = 6/5 = 1.20
ANSWER E
Answer: (E) 1.2
Question: The difference between the place values of 6 and 1 in the number 527631 is
(A) 596
(B) 587
(C) 533
(D) 568
(E) 599
Rationale: Sol.= (Place value of 6) – (place Value of 1)= (600 - 1)= 599 Answer E
Answer: (E) 599
Question: Enrollment in City College in 1980 was 83 1/3 percent of enrollment in 1990. What was the percent increase in the college’s enrollment from 1980 to 1990?
(A) 10%
(B) 16 2/3 %
(C) 20%
(D) 25%
(E) 183 1/3%
Rationale: Let 100 is the enrollment in 1990.
Enrollment in 1980= 83.3
% increase= (Increase from 1980 to 1990)/Enrollment in 1983
=>16.7*100/83.3 =20%
ANSWER:C
Answer: (C) 20%
Question: Mary is traveling from one end of a forest to the other. In order to find her way back, she is leaving morsels of bread in the following pattern: 2 morsels of white, 3 morsels of wheat, and 1 morsel of rye. The pattern repeats after she leaves the morsel of rye. If Mary drops 2,000 morsels of bread, what are the last 3 morsels of bread that she drops?
(A) rye − white − white
(B) white − white − wheat
(C) wheat − rye − white
(D) wheat− wheat − wheat
(E) wheat − wheat− rye
Rationale: In a single round Mary drops 6 morsels.
Remainder (2000/6) = 2
Final action = 2 drops of Wheat --> Options B, C, D and E can be eliminated
Answer: A
Answer: (A) rye − white − white
Question: A person's present age is two-fifth of the age of his mother. After 8 years, he will be one-half of the age of his mother. How old is the mother at present?
(A) 32 years
(B) 36 years
(C) 40 years
(D) 48 years
(E) 45 years
Rationale: let the age be x
2/5x=x (2/5 the age of son = mothers age)
after 8 yrs
2/5x+8=x+8/2
4=x/10
x=40.
ANSWER:C
Answer: (C) 40 years
Question: Express a speed of 36 kmph in meters per second?
(A) 10 mps
(B) 14 mps
(C) 18 mps
(D) 19 mps
(E) 11 mps
Rationale: 36 * 5/18 = 10 mps
Answer: A
Answer: (A) 10 mps
Question: A and B invests Rs.3000 and Rs.4000 respectively in a business. If A doubles his capital after 6 months. In what ratio should A and B divide that year's profit?
(A) 9:9
(B) 9:8
(C) 9:4
(D) 9:1
(E) 9:2
Rationale: (3*6 + 6*6): (4*12)
54:48 => 9:8
Answer: B
Answer: (B) 9:8
Question: How many different possible arrangements D can be obtained from the letters G, M, A, T, I, I, and T, such that there is at least one character between both I's?
(A) 360
(B) 720
(C) 900
(D) 1800
(E) 5040
Rationale: Total ways for arranging without restriction = 7!/ (2!2!) { 2! is becoz of two T's and other 2! for two I's)
Restriction : atleast one character between I's = Possible ways - both I's together i.e.o character between I's
_ _ _ _ _ (I I)
Both I's Together = 6! (Assuming 2 I's as one unit) /2!(for 2 T's) * 2! (No of arrangements of 2 I's)/2! (for 2 I's)
=6!/2!
Therefore ans D= 7!/ (2!2!) -6!/2! = 900
HENCE C.
Answer: (C) 900
Question: Each of the integers from 1 to 14 is written on the a seperate index card and placed in a box. If the cards are drawn from the box at random without replecement, how many cards must be drawn to ENSURE that the product of all the integers drawn is even?
(A) 19
(B) 12
(C) 11
(D) 10
(E) 8
Rationale: Out of the 14 integers: 7 are odd and 7 are even.
If we need to make sure that the product of all the integers withdrawn is even then we need to make sure that we have at least one even number. In the worst case:
1. we will end up picking odd numbers one by one, so we will pick all 7 odd numbers first
2. 8th number will be the first even number
So we need to withdraw at least 8 numbers to make sure that we get one even number and the product of all the integers picked is even.
So, answer will be 8. (E)
Answer: (E) 8
Question: A train with a length of 100 meters, is traveling at a speed of 72 km/hr. The train enters a tunnel 1.1 km long. How many minutes does it take the train to pass through the tunnel from the moment the front enters to the moment the rear emerges?
(A) 1.0
(B) 1.2
(C) 1.4
(D) 1.6
(E) 1.8
Rationale: 72 km/hr = 1.2 km/min
The total distance is 1.2 km.
1.2 / 1.2 = 1 minute
The answer is A.
Answer: (A) 1.0
Question: A tour group of 25 people paid a total of $620 for entrance to a museum. If this price included a 5% sales tax, and all the tickets cost the same amount, what was the face value of each ticket price without the sales tax?
Choices
(A) $22
(B) $23.56
(C) $24
(D) $25.20
(E) $30
Rationale: B.
Answer: (B) $23.56
Question: Will is 7 years older than Judy while George is 5 years younger than Judy. What is the age of Judy, If the sum of all of their ages is 32 years?
(A) 17 years
(B) 20 years
(C) 10 years
(D) 15 years
(E) 19 years
Rationale: Let Judy's age be x, Will's age be x+7 and George's age be x-5
x + x+7 + x-5 = 32
x = 10
Judy's age is 10 years
Answer : C
Answer: (C) 10 years
Question: Which of the numbers 1, 2, 3, 4, or 5 is nearest in value to the sum
2007/2999+8001/5998+2001/3999=?
(A) 1
(B) 2
(C) 3
(D) 4
(E) 5
Rationale: The sum is a little more than (2/3) + (8/6) + (2/4) = 2.5.
correct answer C
Answer: (C) 3
Question: A sum of money is put out at compound interest for 2 years at 20%. It would fetch Rs.482 more if the interest were payable half-yearly, then it were pay able yearly. Find the sum.
(A) Rs.4000
(B) Rs.1000
(C) Rs.1250
(D) Rs.2000
(E) Rs.3000
Rationale: Explanation:
P(11/10)4 - P(6/5)2 = 482
P = 2000
ANSWER IS D
Answer: (D) Rs.2000
Question: If in a triangle, the area is numerically equal to the perimeter, then the radius of the inscribed circle of the triangle is
(A) 1
(B) 2
(C) 3
(D) 4
(E) 5
Rationale: Solution
Radius = Area / Semi perimeter
= [Area x 2 / Area]
= 2.
Answer B
Answer: (B) 2
Question: A and B together can do a piece of work in 8 days. If A alone can do the same work in 12 days, then B alone can do the same work in?
(A) 66 days
(B) 88 days
(C) 24 days
(D) 55 days
(E) 77 days
Rationale: B = 1/8 – 1/2 = 1/24 => 24 days
Answer:C
Answer: (C) 24 days
Question: A seven-digit phone number is divisible by 9. After adding the two digits of the area code the number is not divisible by 9, which of the following cannot be the area code?
(A) 07.
(B) 06.
(C) 05.
(D) 04.
(E) 09.
Rationale: Given that 7 digit number is divisible by 9
we know any number will not be divisible by 9 if the sum of all digits of the number is not the multiple of 9.
Hence looking at the option we can say that the number that should be added to the seven digit number must be 09 as adding it will make it divisible by 9... hence answer is E
Answer: (E) 09.
Question: A chair is bought for Rs.200/- and sold at Rs.310/- find gain or loss percentage
(A) 15% loss
(B) 20% gain
(C) 25% gain
(D) 30% gain
(E) 55% gain
Rationale: Formula = (Selling price ~ Cost price)/Cost price * 100
= (310- 200)/200= 55% gain
E
Answer: (E) 55% gain
Question: If the average (arithmetic mean) of x + 1, x + 5, and x + 9 is 0, then x =
(A) –5
(B) –4
(C) –2
(D) –1
(E) 0
Rationale: (x+1 + x+5 + x+9)/3 = 0
=>3x + 15 = 0
=>x = -5
Answer A
Answer: (A) –5
Question: If each of 3 digit code is formed of integers from 1 to 30, inclusively, and each of the digits are different, how many possible codes are there?
(A) 22896
(B) 25423
(C) 26980
(D) 24698
(E) 24360
Rationale: Code consists of 3 digits and no digit is repeated.
First digit of the code can have 30 possibilities
Second digit can have 29 possibilities
Third digit can have 28 possibilities
Total number of possible codes = 30*29*28 = 24360
Answer: E
Answer: (E) 24360
Question: One side of a triangle has length 6 and a second side has length 5. Which of the following could be the area of the triangle?
I. 20
II. 15
III. 5
(A) I only
(B) II only
(C) III only
(D) II and III only
(E) I, II and III
Rationale: The triangle will have a maximum area when it is a right angled triangle
The largest triangle will be formed when 6 and 5 are the base and height of triangle .
Area = 1/2 * 6 * 5 = 15
There is no lower limit on the area of any triangle whose only 2 sides are known.
Then 0 < Area <= 15
The answer is D.
Answer: (D) II and III only
Question: a is the product of each integer from 1 to 50, inclusive and b=100^k, where k is an integer . What is the greatest value of k for which y is a factor of a?
(A) 6
(B) 7
(C) 8
(D) 9
(E) 10
Rationale: The number of trailing zeros in the decimal representation of n!, the factorial of a non-negative integer n, can be determined with this formula:
n5+n52+n53+...+n5k, where k must be chosen such that 5k≤n
x = 1*2*3....*50 = 50!
No. of trailing zeros in 50! = 50/5 + 50/5^2 = 10+2 = 12
100^k = 10^2k → k = 12/2 = 6
A
Answer: (A) 6
Question: On what sum will the compound interest for 2 1⁄2 years at 10% amount to Rs. 31762.5?
(A) Rs.5000
(B) Rs.20000
(C) Rs.25000
(D) Rs.30000
(E) Rs.50000
Rationale: Explanation:
P(1+10/100)^2×(1+1/2×10/100))=31762.5
P(11/10)^2×(21/20)=31762.5
P=31762.5×20×10×10/21×11×11=1512.5×20×10×10/11×11
=137.5×20×10×10/11
=12.5×20×10×10=Rs. 25000
Answer : Option C
Answer: (C) Rs.25000
Question: If 10,000 microns = 1 decimeter, and 1,000,000angstroms = 1 decimeter, how many angstroms equal 1 micron?
(A) 100
(B) 10,000
(C) 100,000
(D) 0.01
(E) 0.0001
Rationale: 10,000 microns = 1 decimeter, and 1,000,000angstroms = 1 decimeter
10,000 microns = 1,000,000 angstroms
1 micron = 100
Answer : A
Answer: (A) 100
Question: What least number must be subtracted from 2000 to get a number exactly divisible by 17 ?
(A) 9
(B) 8
(C) 5
(D) 11
(E) 15
Rationale: On dividing 2000 by 17, we get 11 as remainder.
Required number to be subtracted = 11
Answer D
Answer: (D) 11
Question: In how many ways can the letters of the word RAVES be arranged in a row so that the vowels appear in alphabetic order?
(A) 60
(B) 30
(C) 120
(D) 240
(E) 90
Rationale: Two letters can be arranged in 2! ways.
only one combination EIU is required.
5 letters can be arranged in 5! ways.
thus 5!/ 2! * 1 = 60.
A
Answer: (A) 60
Question: In a fuel station the service costs $1.75 per car, every liter of fuel costs 0.65$. Assuming that a company owns 12 cars and that every fuel tank contains 50 liters and they are all empty, how much money total will it cost to fuel all cars?
(A) 320$
(B) 380$
(C) 411$
(D) 450$
(E) 480$
Rationale: Total Cost = ( 1.75*12 ) + ( 0.65 * 12 * 50 ) = 21 + 390 => 411
Hence answer will be (C) 411
Answer: (C) 411$
Question: If the function Q is defined by the formula Q = 5w/(4d(z^2)), by what factor will Q be multiplied if w is quadrupled, d is doubled, and z is tripled?
(A) 1/9
(B) 2/9
(C) 4/9
(D) 3/9
(E) 2/27
Rationale: We just need to find the factor thats all,
w -> quadrupled -> 4w
d-> doubled -> 2d
z-> tripled -> 3Z
Hence, Z^2 = 9Z^2
W is in numerator, and d*z in denominator.
Hence,
Additional factor being introduced = 4/2*9
=4/18 = 2/9 = B
Answer: (B) 2/9
Question: Annie and Sam set out together on bicycles traveling at 15 and 12 km per hour respectively. After 40 minutes, Annie stops to fix a flat tire. If it takes Annie 25 minutes to fix the flat tire and Sam continues to ride during this time, how many minutes will it take Annie to catch up with Sam assuming that Annie resumes riding at 15 km per hour?
(A) 20
(B) 40
(C) 60
(D) 80
(E) 100
Rationale: Annie gains 3 km per hour (or 1 km every 20 minutes) on Sam.
After 40 minutes Annie is 2 km ahead.
Sam rides 1 km every 5 minutes.
In the next 25 minutes, Sam rides 5 km so Sam will be 3 km ahead.
It will take Annie 60 minutes to catch Sam.
The answer is C.
Answer: (C) 60
Question: What is the sum of all 3 digit positive integers that can be formed using the digits 1, 3, and 6, if the digits are allowed to repeat within a number?
(A) 6660
(B) 7770
(C) 8880
(D) 9990
(E) 10,110
Rationale: The number of these 3-digit numbers is 3*3*3 = 27
Each digit 1, 3, and 6 will appear in the ones, tens, and hundreds place 9 times each.
The sum equals 9(111) + 9(333) + 9(666) = 9,990
The answer is D.
Answer: (D) 9990
Question: A shop owner sells 100 lemons and gains SP of 40 lemons. Find the gain %?
(A) 62 2/3%
(B) 64 2/3%
(C) 66 2/3%
(D) 66 5/3%
(E) 68 2/3%
Rationale: Gain=40 lemonsTotal 100 lemonsCP 100-40=60(40/60)*100=66 2/3%Ans C
Answer: (C) 66 2/3%