mathewhe/aqua_rat huggingface dataset:
Question: Four-ninths of a drink mix is dye and the rest is sugar. When the mix is added to water a gallon of drink is made that is 5% sugar. What percentage of the gallon is dye?
(A)  6
(B)  4
(C)  7.5
(D)  8
(E)  24
Rationale: The proportion of Dye and sugar will remain constant.
Dye/Sugar = (4/9)/(5/9) = x/5
=> 4/5 = x/5 => x = 4*5/5 = 4.
Answer is B
Answer: (B)  4
Question: If W is the set of all the integers between 19 and 99, inclusive, that are either multiples of 3 or multiples of 2 or multiples of both, then W contains how many numbers?
(A) 26
(B) 32
(C) 33
(D) 34
(E) 54
Rationale: Multiples of 2 from 19 to 99=Multiples of 2 from 1 to 99-Multiples of 2 from 1 to 18=[99/2]-[18/2]=49-9=40
Multiples of 3 from 19 to 99=Multiples of 3 from 1 to 99-Multiples of 3 from 1 to 18=[99/3]-[18/3]=33-6=27
Multiples of2 and 3 bothi.e.6 from 19 to 99=Multiples of 6 from 1 to 99-Multiples of 6 from 1 to 18=[99/6]-[18/6]=16-3=13
These 8 Numbers have been counted twice in both the above calculation while calculating multiples of 2 and 3
i.e. Total Numbers in W = 40 + 27 -13 = 54
Answer Option E
Answer: (E) 54
Question: 3.5 can be expressed in terms of percentage as?
(A) 0.35%
(B) 3.5%
(C) 35%
(D) 350%
(E) 450%
Rationale: Explanation:
3.5 = 35/10 = (35/10 * 100) = 350%
Answer IS D
Answer: (D) 350%
Question: The average of 11 results is 45, if the average of first six results is 49 and that of the last six is 52. Find the sixth result?
(A) A)46
(B) B)111
(C) C)66
(D) D)76
(E) E)74
Rationale: 1 to 11 = 11 * 45 = 495
1 to 6 = 6 * 49 = 294
6 to 11 = 6 * 52 = 312
6th = 294 + 312 – 495= 111
Answer:B
Answer: (B) B)111
Question: The water from one outlet, flowing at a constant rate, can fill a swimming pool in 7 hours. The water from a second outlet, flowing at a constant rate, can fill the same pool in 4 hours. If both outlets are used at the same time, approximately what is the number of hours required to fill the pool?
(A)  0.22
(B)  0.31
(C)  2.54
(D)  3.21
(E)  4.56
Rationale: Always remember RT=W i.e Rate*Time = Work
Also remember that rate can be added or subtracted. For e.g if A do a work in 2 day and B do a work in 2 day.
They both of them together will do a work in 1 day.
So now your question first determine both outlets rate.
1st outlet rate = 1/7 (R=W/T here W=1 work, T = 7hrs)
2nd outlet rate = 1/4 (R=W/T here W=1 work, T = 4hrs)
Both of them working together rate = 1st outlet rate + 2nd outlet rate = 1/7+1/4 = 11/28
again apply the formula RT=W
T = W/R = 1/11/28 = 28/11 =2.54
Answer is C.
Answer: (C)  2.54
Question: The total number of digits used in numbering the pages of a book having 369 pages is
(A) 732
(B) 990
(C) 999
(D) 1305
(E) 1405
Rationale: Total number of digits
= (No. of digits in 1- digit page nos. + No. of digits in 2-digit page nos. + No. of digits in 3- digit page nos.)
= (1 x 9 + 2 x 90 + 3 x 270) = (9 + 180 + 810) = 999.
ANSWER:C
Answer: (C) 999
Question: A committee of two people is to be chosen from three married couples. What is the number of different committees that can be chosen if two people who are married to each other cannot both serve on the committee?
(A) 4
(B) 8
(C) 12
(D) 16
(E) 32
Rationale: Each couple can send only one representative to the committee. Let's see in how many ways we can choose 2 couples (as there should be 2 members) out of 3 to send only one representatives to the committee: 3C2=3.
But each of these 2 couples can send two persons (husband or wife): 2*2=2^2=4.
Total # of ways: 3C2*2^2=12.
Answer: C
Answer: (C) 12
Question: There ia truck which should reach some place at 11'o clock , if it travels with 30 mph it reaches i hour before, if it travles with 20 mph it reaches 1 hour late. what is the distance it must be travlled and what is the speed it must maintain to rech at exact time?
(A) 22 kmph
(B) 24 kmph
(C) 26 kmph
(D) 28 kmph
(E) 20 kmph
Rationale: let S T D are the speed time and distance
S=D/T
according to question,
30=D/(T-1)..........1
and
20=D/(T+1)..........2
dividing equation 1 by 2 we get T=5 hours
now,
for distance put value of T in equ 1
then D=120 m
now,
for exact time s=d/t
=120/5
=24 kmph
ANSWER:B
Answer: (B) 24 kmph
Question: If a, b, and c are consecutive integers such that a < b < c and a is an even prime number, which of the following is true?
I. a × b × c < a^3
II. 5b > 5c
III.a + b + c > a^3
(A) I only
(B) II only
(C) III only
(D) II and III
(E) I, II, and III
Rationale: Only 'A' is possible solution. If a is even prime number i.e 2, b is 3 and c is 4
Putting the values in the answers only 'A' seems valid.
Answer: (A) I only
Question: Mohit sold an article for $27000. Had he offered a discount of 10% on the selling price, he would have earned a profit of 8%. What is the cost price of the article?
(A) 16000
(B) 22500
(C) 15000
(D) 18000
(E) 17000
Rationale: Let the CP be $x.
Had he offered 10% discount, profit = 8%
Profit = 8/100 x and hence his SP = x + 8/100 x = $1.08x = 27000 - 10/100(27000) = 27000 - 2700 = $22500
=> 1.08x = 22500
=> x = 22500
B
Answer: (B) 22500
Question: In a division sum, the divisor is ten times the quotient and five times the remainder. If the remainder is 42, the dividend is?
(A) 4452
(B) 4445
(C) 4330
(D) 4334
(E) 4336
Rationale: Divisor = (5 * 42) = 210
= 10 * Quotient = Divisor
=> Quotient = 210/10 = 21
Dividend = (Divisor * Quotient) + Remainder
Dividend = (210 * 21) + 42 = 4452
A
Answer: (A) 4452
Question: If a positive integer n is divisible by both 2 and 3, then n must also be divisible by which of the following?
I. 6
II. 5
III. 18
(A) None
(B) I only
(C) II only
(D) I and II
(E) II and III
Rationale: A multiple of 2 and 3 is also a multiple of 6, but not necessarily a multiple of 5 or 18.
The answer is B.
Answer: (B) I only
Question: Three partners A,B,C starts a business. Twice A's capital is equal to thrice B's capital and B's capital is four times C's capital. Out of a total profit of Rs.16,500 at the end of the year, B's share is
(A) Rs.4000
(B) Rs.6000
(C) Rs.7500
(D) Rs.6600
(E) None
Rationale: Solution
Let C = x.
Then, B = 4x and 2A = 3x4x = 12x or A = 6x.
∴ A : B : C = 6x : 4x : x	= 6 : 4 : 1.
So B's capital	= Rs(16500 x 4 / 11)
= Rs.6000.
Answer B
Answer: (B) Rs.6000
Question: A man can swim in still water at 4.5 km/h, but takes twice as long to swim upstream than downstream. The speed of the stream is?
(A) 1.8
(B) 1.9
(C) 1.2
(D) 1.5
(E) 1.6
Rationale: M = 4.5
S = x
DS = 4.5 + x
US = 4.5 + x
4.5 + x = (4.5 - x)2
4.5 + x = 9 -2x
3x = 4.5
x = 1.5
Answer:D
Answer: (D) 1.5
Question: If m : n = 3 : 4 and n : o = 8 : 9, then m : o is :
(A) 1 :3
(B) 3 :2
(C) 2 : 3
(D) 1 : 2
(E) None of these
Rationale: Expl : m/n = m/n * n/o =3/4 * 8/9 = 2/3. So m : o = 2 : 3
Answer :C
Answer: (C) 2 : 3
Question: If in a kindergarten class, there are five children 3 feet 4 inches tall (indicated by notation 3'4"), two children 4'3" tall and thirteen children 2'6" tall, which of the following is the median height of the children?
(A) 2'2"
(B) 2'6"
(C) 3'3"
(D) 3'4"
(E) 4'3
Rationale: Total number of children in class = 20
so median must be between 10th and 11th child when they are arranged in ascending order.
When arranged in ascending order 5th and 6th child will have the height of 3'4"
so required median height = (2'6"+2'6")/2 = 2'6"
Ans:Option B
Answer: (B) 2'6"
Question: If you are given $2, and the amount doubles every day, how much money will you have after 10 days?
(A) $256
(B) $512
(C) $1024
(D) $2048
(E) $4096
Rationale: 2^10=1024
The answer is C.
Answer: (C) $1024
Question: The sum of number of boys and girls in a school is 900. If the number of boys is x, then the number of girls becomes x% of the total number of students. The number of boys is?
(A) 50
(B) 40
(C) 60
(D) 90
(E) 70
Rationale: We have x+x% of 900 = 900
x + x/100 * 900 = 900
10 * x = 900
x =90
Answer is D
Answer: (D) 90
Question: Two trains, one from P to Q and the other from Q to P, start simultaneously. After they meet, the trains reach their destinations after 49 hours and 16 hours respectively. The ratio of their speeds is
(A) 4:1
(B) 4:2
(C) 4:5
(D) 4:3
(E) 4:7
Rationale: Ratio of their speeds = Speed of first train : Speed of second train
= √16−−√49
= 4:7
Answer is E.
Answer: (E) 4:7
Question: If an article with marked price of $4000 is sold at successive discount of 10%,25% and 15%,what is the price the customer has to pay?
(A) 3600
(B) 3080
(C) 2280
(D) 2760
(E) 2900
Rationale: discount=0.9*.75*.85=.57
so .57*4000=2280
ANSWER:C
Answer: (C) 2280
Question: If 4 (A's capital) = 6 (B's capital) = 10 (C's capital), then out of a profit of Rs. 682, C will receive
(A) 233
(B) 381
(C) 132
(D) 287
(E) 271
Rationale: Explanation:
Let 4A = 6B = 1OC = k. Then, A = k/4, B = k/6, and C =k/10 .
A : B :C = k/4 : k/6 : k/10 = 15 : 10 : 6.
Hence, C's share (682* 6/31) = Rs, 132.
Answer: C) Rs.132
Answer: (C) 132
Question: In a company, 58% of all its employees earn lesser than $50,000; 66% earn more than $40,000; 17% earn $45,000; 3% earn $48,000.
What is the median salary
(A) 42,000
(B) 43,000
(C) 44,000
(D) 45,000
(E) 46,000
Rationale: as only amount mentioned in the question and in the options is $45000 ($48000 not mentioned)
Rest amounts are in the form of greater than or lesser than , Hence C $45000
answer is D
Answer: (D) 45,000
Question: There are 6 working days in a regular week and for each day, the working hours are 10. A man earns Rs. 2.10 per hour for regular work and Rs. 4.20 per hour for overtime. If he earns Rs.525 in 4 weeks, how many hours did he work?
(A) 245
(B) 285
(C) 275
(D) 255
(E) 265
Rationale: Explanation :
Regular working hours in 4 weeks = (4 × 6 × 10) = 240 hours
Amount earned by working in these regular working hours
= 240 × 2.10 = Rs.504
Additional amount he earned = 525 - 504 = Rs.21
Hours he worked overtime = 21/4.2 = 210/42 = 5 hours
Total hours he worked = 240 + 5 = 245 hours
Answer : A
Answer: (A) 245
Question: Two brothers took the GMAT exam, the higher score is A and the lower one is B. If the difference between the two scores is equal to their average, what is the value of B/A ?
(A) 3
(B) 2
(C) 1/2
(D) 1/3
(E) There isn't enough data to answer the question.
Rationale: Answer is D : 1/3
A - B = (A + B)/2
Solving for B/A = 1/3
D
Answer: (D) 1/3
Question: There are three categories of jobs A, B and C. The average salary of the student who got the job of A and B categories is 26 lakh per annum. The average salary of the students who got the job of B and C category is 44 lakh per annum and the average salary of those students who got the job of A and C categories is 34 lakh per annum. The most appropriate (or closet) range of average salary of all the three categories (if it is known that each student gets only one category of jobs i.e. , A, B and C):
(A) lies between 30 and 44
(B) lies between 28 and 34
(C) lies between 34 and 44
(D) lies between 27 and 44
(E) None of these
Rationale: Solution: Let the number of students who got the job of A, B and C categories is a, b and c respectively,
Then the total salary,
= [{26(a+b)+44(b+c)+34(c+a)}/2(a+b+c)]
= [(60a+70b+78c)/2(a+b+c)]
= [30(a+b+c)+(5b+9c)]/(a+b+c)
= 30 + some positive value
Thus, the minimum salary must be Rs. 30 lakh and the maximum salary can not exceed 44, which is the highest of the three.
Answer: Option A
Answer: (A) lies between 30 and 44
Question: The perimeter of one square is 48 cm and that of another is 20 cm. Find the perimeter and the diagonal of a square which is equal in area to these two combined?
(A) 13√8
(B) 13√2
(C) 13√0
(D) 53√2
(E) 13√1
Rationale: 4a = 48 4a = 20
a = 12 a = 5
a2 = 144 a2 = 25
Combined area = a2 = 169 => a = 13
d = 13√2
Answer:B
Answer: (B) 13√2
Question: Two numbers are respectively 19% and 40% more than a third number. The percentage that is first of the second is?
(A) 15%
(B) 20%
(C) 25%
(D) 30%
(E) 35%
Rationale: I II III
119 140 100
140----------119
100-----------? => 15%
Answer:A
Answer: (A) 15%
Question: The average (arithmetic mean) of 10, 30, and 50 is 8 more than the average of 20, 40, and x. What is x?
(A) 2
(B) 4
(C) 6
(D) 8
(E) 10
Rationale: The average of 10, 30, and 50 is 30.
The average of 20, 40 and x is 22.
Then 20 + 40 + x = 66.
x = 6.
The answer is C.
Answer: (C) 6
Question: A sum of Rs.1400 is divided into 13 students so that each boy gets Rs.120 while each girl gets Rs.100. Find the number of boys and number of girls
(A) 8B, 5G
(B) 5B, 8G
(C) 4B, 9G
(D) 9B, 4G
(E) 9B, 5G
Rationale: 120B+100G=1400-----i
B+G=13-------ii
from i
100B+20B+100G=1400
100(B+G)+20B=1400
100(13)+20B=1400
By simplifing we get
B=5;G=8
ANSWER:B
Answer: (B) 5B, 8G
Question: What approximate value will come in place of the question mark (?) in the following equation?
√625.04×16.96+136.001÷17=?
(A) 418
(B) 441
(C) 425
(D) 433
(E) 449
Rationale: ?=−−−−−√625.04×16.96+136.001÷17?=≈ 25 × 17 + 8
= 425 + 8 = 433
Answer D
Answer: (D) 433
Question: Seats for Maths, Physics and Biology are in the ratio of 8 : 7 : 8 respectively. There is a proposal to increase these seats by 40%, 50% and 75% respectively. What will be the respective ratio of increased seats?
(A) 16 : 15 : 20
(B) 16 : 7 : 8
(C) 16 : 8 : 9
(D) Cannot be determined
(E) None of these
Rationale: Reqd ratio 8 Ã— 140â„100 : 7 Ã— 150â„100 : 8 Ã— 175â„100
= 8 Ã— 140 : 7 Ã— 150 : 8 Ã— 175 = 16 : 15 : 20
Answer A
Answer: (A) 16 : 15 : 20
Question: A boat can move upstream at 25 kmph and downstream at 37 kmph, then the speed of the current is?
(A) 5 kmph
(B) 7 kmph
(C) 8 kmph
(D) 6 kmph
(E) 4 kmph
Rationale: US = 25
DS = 37
M = (37 - 25)/2 = 6
Answer:D
Answer: (D) 6 kmph
Question: A sun is divided among X, Y and Z in such a way that for each rupee X gets, Y gets 45 paisa and Z gets 30 paisa. If the share of Y is RS. 27, what is the total amount?
(A) 228
(B) 105
(C) 288
(D) 277
(E) 299
Rationale: x:y:z = 100:45:30
20:9:6
9 --- 27
35 --- ? => 105
Answer: B
Answer: (B) 105
Question: A certain store sells only black shoes and brown shoes. In a certain week, the store sold x black shoes and y brown shoes. If 2/9 of all shoes sold that week were black, which of the following expressions represents the value of y, in terms of x?
(A) 7x/2
(B) x/2
(C) 2x/3
(D) 3x/2
(E) 2x
Rationale: x/(x+y) = 2/9
9x = 2x+2y
7x = 2y
y = 7x/2
Answer A
Answer: (A) 7x/2
Question: If in a $210 mln portfolio of stock, twice as much is invested in stock A as is invested in all the other stocks, how much is invested in all the other stocks?
(A) 70mln
(B) 60mln
(C) 50mln
(D) 40mln
(E) 30mln
Rationale: Let x denote the amount invested in all the other stocks. Then the amount invested in stock A is 2x. As we have the $210 mln portfolio, x+2x=3x=210 mln from where x=70 mln.
Answer: A
Answer: (A) 70mln
Question: If 55^4*11^6*16^3 = x, what is the units digit of x ?
(A) 2
(B) 6
(C) 0
(D) 1
(E) 5
Rationale: 55^4*11^6*16^3 = x
Units digit of x will be
5^4 * 1^6 * 6^3
=5* 1 *6
=30
Therefore , units digit of x = 0
Answer C
Answer: (C) 0
Question: For how many integers n is 1^n+1 = (n+1)^1?
(A) 0
(B) 1
(C) 2
(D) 3
(E) None of these
Rationale: If n=0
1^0+1 = (0+1)^1
1^1 =1 ok
If n=1
1^2 =1 ; (2)^1=2 not OK
So, Answer : A
Answer: (A) 0
Question: If x^2 − 2x − 15 = (x + r)( x + s) for all values of x, and if r and s are constants, then which of the following is a possible value of( r − s)/2?
(A) 8
(B) 2
(C) − 2
(D) − 4
(E) − 5
Rationale: We know that given ax^2 + bx + c = 0, Sum of the roots = -b/a and product of the roots = c/a.
The roots here are -r and -s.
-r - s = -(-2)/1 = r + s = -2
(-r)*(-s) = -15/1 = rs
So one of r and s is -5 and the other is 3. So (r - s)/2 could be 4 or -4.
Answer (D)
Answer: (D) − 4
Question: A student is ranked 12th from right and 6th from left. How many students are there in totality ?
(A) 17
(B) 19
(C) 20
(D) 21
(E) 22
Rationale: From right 12 , From left 6
Total = 12+6-1 = 17
ANSWER:B
Answer: (B) 19
Question: If all the fractions 3/10, 1/16, 4/11, 2/9, 1/7, 5/14 and 5/24 arranged in descending order of their values, then which one will be the third?
(A) 3/17
(B) 3/15
(C) 3/10
(D) 3/14
(E) 2/10
Rationale: Explanation:
3/10 = 0.3, 1/16 = 0.0625, 4/11 = 0.36, 2/9 = 0.22, 1/7 = 0.14, 5/14 = 0.36 and 5/24 = 0.21
4/11 > 5/14 > 3/10 > 2/9 > 5/24 > 1/7 > 1/16
3/10 will be the third.
Answer: C
Answer: (C) 3/10
Question: A train speeds past a pole in 10seconds and a platform 50 m long in 20 seconds. Its length is:
(A) 30 m.
(B) 40 m.
(C) 60 m.
(D) 50 m.
(E) 70 m.
Rationale: Let the length of the train be x meters and its speed be y m/sec.
They, x / y = 10 => y = x/10
x + 50 / 20 = x / 10
x = 50 m.
Answer: Option D
Answer: (D) 50 m.
Question: If A^2 + B^2 = 25 and AB = 10, what is the value of the expression (A - B)^2 + (A + B)^2?
(A) 10
(B) 20
(C) 30
(D) 50
(E) 70
Rationale: (a-b)^2 = a^2 + b^2 - 2ab = 25-20= 5
(a+b)^2 = a^2 + b^2 + 2ab = 25+20=45
so (a+b)^2 + (a-b)^2 = 45 + 5 = 50
D
Answer: (D) 50
Question: The price of a car is marked at $12,000. If the car has successive discounts of 20%, 15% and 5%, then at what price does a customer buy the car?
(A) $7524
(B) $7752
(C) $7880
(D) $8196
(E) $8324
Rationale: 0.95*0.85*0.8*12000 = $7752
The answer is B.
Answer: (B) $7752
Question: If a^2=b^2 and b^2=1 ,then what will be the value of a^2+b^2?
(A) 0
(B) 1
(C) 2
(D) 3
(E) 4
Rationale: The answer is 2.
a^2+b^2=b^2+b^2(a^2=b^2)
=1+1(b^2=1)
So the option is C
Answer: (C) 2
Question: a,b,c,d,e,f,g,h sitting in a row what is the probability that a,b,d are sitting together?
(A) 1/5
(B) 3/28
(C) 1/7
(D) 1/14
(E) 5/28
Rationale: total number of arrangement is= 8!= 40320
Favorable event i.e a,b and d can be arranged in 3! and the remaining can be arranged in 6! since abd can be in any of the six positions.
so 3!*6!/8! = 3/28
ANSWER:B
Answer: (B) 3/28
Question: A 300 meter long train crosses a platform in 39 seconds while it crosses a signal pole in 18 seconds. What is the length of the platform?
(A) 766m
(B) 587m
(C) 350m
(D) 686m
(E) 986m
Rationale: Speed = [300 / 18] m/sec = 50/3 m/sec.
Let the length of the platform be x meters.
Then, x + 300 / 39 = 50/3
3(x + 300) = 1950 è x = 350m.
Answer:C
Answer: (C) 350m
Question: If the wheel is 14 cm then the number of revolutions to cover a distance of 2288 cm is?
(A) 26
(B) 28
(C) 17
(D) 12
(E) 88
Rationale: 2 * 22/7 * 14 * x = 2288 => x = 26
Answer: A
Answer: (A) 26
Question: In the storage room of a certain bakery, the ratio of sugar to flour is 3 to 8, and the ratio of flour to baking soda is 10 to 1. If there were 60 more pounds of baking soda in the room, the ratio of flour to baking soda would be 8 to 1. How many pounds of sugar are stored in the room?
(A) 600
(B) 900
(C) 1500
(D) 1600
(E) 1750
Rationale: Sugar:Flour = 3:8 = 15:40;
Flour:Soda = 10:1 = 40:4;
Thus we have that Sugar:Flour:Soda = 15x:40x:4x.
Also given that 40x/(4x+60) = 8/1 --> x=60 --> Sugar = 15x = 900.
Answer: B.
Answer: (B) 900
Question: How much more would Rs.10000 fetch, after two years, if it is put at 20% p.a. compound interest payable half yearly than if is put at 20% p.a. compound interest payable yearly?
(A) 241
(B) 725
(C) 992
(D) 837
(E) 923
Rationale: 10000(11/10)4 - 10000(6/5)2 = 241
Answer:A
Answer: (A) 241
Question: A four-sided shape has angles with ratio 1:2:3:4. What is the measurement of one of its angles?
(A) 32Â°
(B) 70Â°
(C) 112Â°
(D) 144Â°
(E) 168Â°
Rationale: The angles of a four-sided shape should add up to 360Â°. Using the 1:2:3:4 ratio, we use the equation
x + 2x + 3x + 4x = 360Â°
10x = 360Â°
x = 36Â°
x = 36Â°
2x = 72Â°
3x = 108Â°
4x = 144Â°, which is D, so this is the correct answer.
Answer: (D) 144Â°
Question: Find the odd man out. 18, 16, 12, 24, 12, 34, 15
(A) 16
(B) 46
(C) 15
(D) 11
(E) 18
Rationale: Explanation :
15 is the only odd number in the given series
Answer : Option C
Answer: (C) 15
Question: The size of a television screen is given as the length of the screen's diagonal. If the screens were flat, then the area of a square 22-inch screen would be how many square inches greater than the area of a square 20-inch screen?
(A) 2
(B) 4
(C) 16
(D) 42
(E) 40
Rationale: Pythogoras will help here!
let the sides be x and diagonal be d
Then d ^2 = 2x^2
and
Area = x^2
Now plug in the given diagonal values to find x values
and then subtract the areas
Ans will be 22^2/2 - 20^2 /2 = 84 /2 = 42
Ans D.
Answer: (D) 42
Question: Which of the following is not the square of an integer?
(A) 640828
(B) 478864
(C) 227529
(D) 690561
(E) 748225
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 A.
Answer: (A) 640828
Question: Six people are on an elevator that stops at exactly 6 floors. What is the probability that exactly one person will push the button for each floor?
(A) 6!/6^6
(B) 6^6/6!
(C) 6/6!
(D) 6/6^6
(E) 1/6^6
Rationale: Each person out of 6 has 6 options, hence total # of outcomes is 6^6;
Favorable outcomes will be 6!, which is # of ways to assign 6 different buttons to 6 people:
1-2-3-4-5-6 (floors)
A-B-C-D-E-F (persons)
B-A-C-D-E-F (persons)
B-C-A-D-E-F (persons)
...
So basically # of arrangements of 6 distinct objects: 6!.
P=favorable/total=6!/6^6
Answer: A.
Answer: (A) 6!/6^6
Question: What are the last two digits of 63*35*37*82*71?
(A)  10
(B)  30
(C)  40
(D)  70
(E)  80
Rationale: We know that to find the last two digits, we need to find the remainder we get when we divide the product by 100.
Remainder of (63*35*37*82*71*41)/ 100
Note that we can simplify this expression by canceling out the 5 and 2 in the numerator and denominator. But before we do that, here is an important note:
Note: We cannot just cancel off the common terms in the numerator and denominator to get the remainder. But, if we want to cancel off to simplify the question, we can do it, provided we remember to multiply it back again.
So say, we want to find the remainder when 14 is divided by 10 i.e. 14/10 (remainder 4). But we cancel off the common 2 to get 7/5. The remainder here will be 2 which is not the same as the remainder obtained by dividing 14 by 10. But if we multiply 2 back by 2 (the number we canceled off), the remainder will become 2*2 = 4 which is correct.
Take another example to reinforce this – what is the remainder when 85 is divided by 20? It is 5.
We might rephrase it as – what is the remainder when 17 is divided by 4 (cancel off 5 from the numerator and the denominator). The remainder in this case is 1. We multiply the 5 back to 1 to get the remainder as 5 which is correct.
So keeping this very important point in mind, let’s go ahead and cancel the common 5 and 2.
We need the
Remainder of (63*7*37*41*71*41*5*2)/10*5*2
Remainder of (63*7*37*41*71*41)/10
Now using concept 2, let’s write the numbers in form of multiples of 10
Remainder of (60+3)*7*(30+7)*(40+1)*(70+1)*(40+1)/10
Remainder of 3*7*7*1*1*1/10
Remainder of 147/10 = 7
Now remember, we had canceled off 10 so to get the actual remainder so we need to multiply by 10: 7*10 = 70.
When 63*35*37*82*71*41 is divided by 100, the remainder is 70. So the last two digits of 63*35*37*82*71*41 must be 40.
Answer (C)
Answer: (C)  40
Question: A train moves fast a telegraph post and a bridge 264 m long in 2 sec and 20 sec respectively. What is the speed of the train?
(A) 89
(B) 23
(C) 52.8
(D) 79.2
(E) 67
Rationale: Let the length of the train be x m and its speed be y m/sec.
Then, x/y = 2=> x = 2y
(x + 264)/20 = y
y = 14.67
Speed = 14.67 m/sec = 14.67 * 18/5 = 52.8 km/hr.
Answer: Option C
Answer: (C) 52.8
Question: In Town X, 72 percent of the population are employed, and 36 percent of the population are employed males. What percent of the employed people in Town X are females?
(A) 16%
(B) 25%
(C) 32%
(D) 40%
(E) 50%
Rationale: Total employed people 72%, out of which 36 are employed males, hence 36% are employed females.
(employed females)/(total employed people)=36/72=1/2=50%
Answer: E.
Answer: (E) 50%
Question: If x > 0, x/40 + x/20 is what percent of x?
(A) 6%
(B) 25%
(C) 37 1/2%
(D) 60%
(E) 75 %
Rationale: Just plug and chug. Since the question asks for percents, pick 100. (but any number will do.)
100/40 + 100/20= 2.5+5=7.5
7.5 is 75% of 100=E
Answer: (E) 75 %