MU-NLPC/Calc-aqua_rat huggingface dataset:
A bowl has only 2 apples and 2 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?	Answers:
A) 1/10  B) 1/6  C) 2/9  D) 2/5  E) 1/2

Solution: 2/4 * 1/3   =1/6   B. 1/6
Answer: B
If A and B get profits of Rs.15,000 and Rs.5,000 respectively at the end of year then ratio of their investments are Choose the most appropriate option:
A) 4:1  B) 1:4  C) 3:1  D) 2:3  E) 2:5

Solution: Ratio = 15000/5000= 
15000/5000 = 3
3 : 1   Answer : 3:1
Answer: C
Find the area of trapezium whose parallel sides are 22 cm and 18 cm long, and the distance between them is 15 cm.
Answers: A) 227 B) 299 C) 300 D) 161 E) 212

Solution: Area of a trapezium = 1/2 (sum of parallel sides) * (perpendicular distance between them)   = 1/2 (22 + 18) * (15)   = 300 cm2   Answer: 300
Answer: C
What is the square root of 169? Select the correct option.
A) 8	B) 16	C) 13	D) 42	E) 25

Solution: 13X13 = 169   ANSWER 13
Answer: C
Find the principle on a certain sum of money at 5% per annum for 2 2/5 years if the amount being Rs.896?
Choose the correct choice from the following.
A) 1000
B) 800
C) 2889
D) 2777
E) 2991

Solution: 896 = P [1 + (5*12/5)/100]   P= 800   Answer: 800
Answer: B
There are a red, yellow, blue and green tennis balls respectively in a set. How many subsets of these balls can I get without using the green ball?	Choose one:
A) 9	B) 7	C) 8	D) 6	E) 10

Solution: This is a combination solution   Since we have 3 different kinds of Balls other than the green ball we can take any ball from the set of 3 to make a subset as follows.   381 +382 + 383 = 7   Plus the one set that is null that is the Set having no element in it which is 380 =1   = 7 + 1= 
7 + 1 = 8
8   8= 8
Answer: C
If x = a/3 + b/3^2 + c/3^3, where a, b, and c are each equal to 0 or 1, then x could be each of the following EXCEPT:  Choose the correct choice from the following answers:
A) 1/27
B) 1/9
C) 4/27
D) 2/9
E) 4/9

Solution: x = a/3 + b/3^2 + c/3^3   = a/3 + b/9 + c/27   = (9a + 3b + c ) /27   2/9epending on whether a, b and c take 0 or 1 , the numerator can take 1 , 3 , 4 and 12   3/27 = 1/9   12/27 = 4/9   Answer 2/9
Answer: D
A part-time employee’s hourly wage was increased by 50%. She decided to decrease the number of hours worked per week so that her total income did not change. By approximately what percent should the number of hours worked be decreased?	Pick
A) 9%	B) 15%	C) 25%	D) 33%	E) 50%

Solution: Let's plug in somenicenumbers and see what's needed.   Let's say the employee used to make $1/hour and worked 100 hours/week   So, the TOTAL weekly income was $100/week   After the 50% wage increase, the employee makes $1.50/hour   We want the employee's income to remain at $100/week.   So, we want ($1.50/hour)(new # of hours) = $100   Divide both sides by 1.50 to get:   new # of hours = 100/1.50   ≈ 67 hours   So, the number of hours decreases from 100 hours to (approximately) 67 hours.   This represents a 33% decrease (approximately) .   Answer : 33%
Answer: D
If Ajay drives at 4/5th of his usual speed to his office, he is 6 minutes late. What is his usual time to reach his office?	Choose the correct option:
A) 38	B) 27	C) 24	D) 19	E) 17

Solution: Explanation:   Let t be his usual time to reach his office and v be his usual speed.   v = d/t ……….(d is the distance Ajay travels while going to his office)   vt = d   At v1 = 4v/5 ; t1 = t + 6   4v/5 = d/(t + 6)   4v/5* (t + 6) = d   4v/5* (t + 6) = vt   On solving we get,   t = 24 minutes   ANSWER:24
Answer: C
what is the value of (3)^-4 ? Choose the correct answer:  A) 1/4  B) 1/81  C) 1/65  D) 1/9  E) 1/3

Solution: 3^-4= 1/(3)^4= 1/81   ANSWER:1/81
Answer: B
Rabert’s age after 15 years will be 5 times his age 5 years back. What is the present age of Rajeev? Choose the correct choice:
A) 10 years.	B) 11 years.	C) 12 years.	D) 13 years.	E) 14 years.

Solution: Sol. Let Rabert’s present age be x years. Then,   Rabert’s age after 15 years = (x + 15) years.   Rabert’s age 5 years back = (x - 5) years.   ∴ x + 15 = 5 (x - 5) ⇔ x + 15 = 5x - 25   ⇔ 4x = 40 ⇔ x = 10.   Hence, Rabert’ present age = 10 years.   10 years.nswer 10 years.
Answer: A
A machine fills 150 bottles of water every 8 minutes. How many minutes it takes this machine to fill 675 bottles? Choose the correct choice from the following choices.
A) 54
B) 27
C) 36
D) 57
E) 87

Solution: 8 minutes are needed to fill 150 bottles. How many groups of 150 bottles are there in 675 bottles?   675 ÷ 150 = 4.5 = 4 and 1/2   For each of these groups 8 minutes are needed. For 4 groups and 1/2   8 × 4 + 4 = 32 + 4= 
32 + 4 = 36
36 minutes. (4 is for 1/2 a group that needs half time)   correct answer 36
Answer: C
For every order, a certain mail-order company charges a shipping fee of $3 plus an additional $2 if the value of the order is over $50 but not over $100 or an additional $3 if the value of the order is over $100. How much greater are the total shipping fees for 2 orders of $75 each than the total shipping fee for 3 order of $150 ?	Select the correct option
A) $1
B) $2
C) $3
D) $4
E) $8

Solution: Total cost involved for each 75 $ shipment:  3+2= 
 3+2 = 5
5 $. Thus, for two such orders= 10$   Total cost involved for a 150$ shipment: 3+3= 
3+3 = 6
6$. Thus, for two such orders= 18$   The difference = 8$.   $8.
Answer: E
0.2 decades ago a person was 6 times as old as his daughter, After 18 years, he will be two times as old as his daughter. Then their current ages are,
[0.2 decades = 2 years]	Choices.
A) 7  B) 9  C) 11  D) 13  E) None of these

Solution: None of these   None of these
Answer: E
A sum of money triples itself in ten years at simple interest. Find the rate of interest?	Choices:
A) 12 1/2 % p.a.
B) 14 1/2 % p.a.
C) 20 % p.a.
D) 22 % p.a.
E) 25 % p.a.

Solution: Let the pricipal be Rs. x, then amount = 3x(where R = rate of interest) => Interest = 3x - x = Rs. 2x   R = (100 * 2x)/(x * 10) = 20 %   ANSWER:20 % p.a.
Answer: C
The banker's discount on Rs.1800 at 16% per annum is equal to the true discount on Rs.1872 for the same time at the same rate. Find the time?  Choose the correct choice from the following options
A) 3 months  B) 4 months  C) 5 months  D) 6 months  E) 7 months

Solution: Solution   S.I on Rs.1800 = T.D on Rs.1872.   P.W on Rs.1872 is Rs.1800.   Rs.72 is S.I on Rs. 1800 at 16%.   Time	=(100x72 / 16x1800)   = 1/4 year   = 3 months.   3 monthsnswer 3 months
Answer: A
As part of a game, three people each must secretly choose an integer between 1 and 3, inclusive. What is the approximate likelihood that all three people will choose different numbers?  Select the correct option.
A) 9%
B) 12%
C) 16%
D) 20%
E) 22%

Solution: Ans:22%   1st person has option no's- (1,2,3) - there fore probability of getting a no = 3c1/3c1 = 1   2nd person has option no's any three ,   he has to choose a no from three no's - there fore probability of getting a no =2c1/3c1 = 2/3   3rd person has option no's any two ,   he has to choose a no from two no's -there fore probability of getting a no = 1c1/3c1 = 1/3   =1*2/3*1/3=2/9=22%
Answer: E
Suppose you roll a 20 sided die twice. What is the probability you will land on the same number for both rolls?	Choose the correct answer
A) 1/10  B) 1/20  C) 1/5  D) 1/25  E) 1/40

Solution: The acceptable rolls work when we roll any double: 11, 22, 33, ... 2020. Those are 20 possibilities. Then the die can fall in   20*20= 
  20*20 = 400
400 ways.   Hence the probability is 20/400= 1/20   Answer: 1/20
Answer: B
P cando a work in 15 days and Q cando the same work in 20 days. If they can work together for 4 days, what is the fraction of work left?  Choose the most appropriate option:	A) 2/7	B) 3/11	C) 8/15	D) 7/15	E) None

Solution: Amount of work P can do in 1 day = 1/15   Amount of work Q can do in 1 day = 1/20   Amount of work P and Q can do in 1 day = 1/15 + 1/20 = 7/60   Amount of work P and Q can together do in 4 days = 4 × (7/60) = 7/15   Fraction of work left = 1 – 7/15= 8/15   8/15
Answer: C
A certain board game has a row of squares numbered 1 to 100. If a game piece is placed on a random square and then moved 7 consecutive spaces in a random direction, what is the probability Y the piece ends no more than 7 spaces from the square numbered 49? Answers
A) 7% B) 8% C) 14% D) 15% E) 28%

Solution: OA is E   required prob is 7 spaces any side of 49.   so total 14 spaces are required in 7 moves which can be achieved by max 7 move on any side   so total spaces = 28   probability Y= 28%.28%
Answer: E
What will come in place of the x in the following Number series? 49920, 4160, 416, x	Answers
A) 52 B) 3 C) 4 D) 5 E) 6

Solution: 49920 /12= 
49920 /12 = 4_160
4160   3840 /10= 416   416 /8= 
416 /8 = 52
52   52
Answer: A
For an upcoming charity event, a male vocalist has agreed to sing 5 out of 7 “old songs” and 3 out of 6 “new songs.” How many ways can the singer make his selection? Choose the correct choice from the following
A) 25 B) 50 C) 140 D) 480 E) 600

Solution: =71405*61403   =7*6/3*6*5/3   =7*2*2*5= 
7*2*2*5 = 140
140   Ans= 140
Answer: C
A man walks half of the journey at 4 km/h by cycle does one third of journey at 12 km/h and rides the remainder journey in a horse cart at 9 km/h, thus completing the whole journey in 6 hours and 12 minutes. The length of the journey is	Choose one.
A) 36 km	B) 1332⁄67 km	C) 40 km	D) 28 km	E) None of these

Solution: Let the length of the journey = x km.   ∴ Journey rides by horse cart = x(1 - 1⁄2 - 1⁄3)   = 1⁄6x km   Then, total time taken to complete journey = 31⁄5hr   ⇒ t1 + t2 + t3 = 31⁄5   ⇒ x⁄2 × 1⁄4 + x⁄3 × 1⁄12 + x⁄(6 × 9) = 31⁄5   ⇒ x = 31⁄5 × 216⁄37 = 36.2 km ≈ 36 km   36 kmnswer 36 km
Answer: A
Replace the ? mark with an appropriate approximate value in the following equation’?
2 4/3 of 165.83+25% of 1847= ? - 554.7
Choices:
A) 1563.22	B) 1568.22	C) 179.22	D) 15659.22	E) 1569.22

Solution: 2 4/3 of 165.83+25% of 1847= ? - 554.7   10/3 of 165.83+25/100 of 1847= ? - 554.7   552.77+461.75= ? - 554.7   552.77+461.75 + 554.7= 
552.77+461.75 + 554.7 = 1_569.22
?   ≈ 1569.22   Answer 1569.22
Answer: E
If you write down all the numbers from 1 to 25, then how many times do you write 3 ?  Choose the correct choice from the following answers:
A) A)11  B) B)3  C) C)2  D) D)1  E) E)6

Solution: Explanation:   Explanation:   Clearly, from 1 to 25, there are ten numbers with 3 as the unit's digit- 3, 13, 23   So, required number =3   Answer: 3
Answer: B
A batsman in his 12th innings makes a score of 60 and thereby increases his average by 2 runs. What is his average after the 12th innings if he had never been ‘not out’?
Choose the correct choice from the following answers: A) 38 B) 43 C) 44 D) 45 E) 46

Solution: Let ‘x’ be the average score after 12 th innings   ⇒ 12x = 11 × (x – 2) + 60   ∴ x = 38   38nswer 38
Answer: A
Two trains are moving in opposite directions at 60 km/hr and 90 km/hr. Their lengths are 1.10 km and 0.9 km respectively. The time taken by the slower train to cross the faster train in seconds is ?
Choose the correct choice from the following answers:	A) 42 sec	B) 44 sec	C) 46 sec	D) 48 sec	E) 50 sec

Solution: Explanation:   Relative speed = 60 + 90= 
60 + 90 = 150
150 km/hr.= 150 x 5/18 = 125/3 m/sec.   Distance covered = 1.10 + 0.9= 
1.10 + 0.9 = 2
2 km= 2000 m.   Required time = 2000 x 3/125 = 48 sec.   ANSWER IS 48 sec
Answer: D
A train travels 225 km in 3.5 hours and 370 km in 5 hours.find the average speed of train.	Pick one.
A) 80 kmph  B) 60 kmph  C) 70 kmph  D) 90 kmph  E) None of these

Solution: As we know that Speed = Distance / Time   for average speed = Total Distance / Total Time Taken   Thus, Total Distance = 225 + 370= 
225 + 370 = 595
595 km   Thus, Total Speed= 8.5 hrs   or,Average Speed = 595/8.5   or, 70kmph.   ANSWER:70 kmph
Answer: C
If -4 < x < 5 and -6 < y < 3, which of the following specifies all the possible values of xy?
Choose the correct choice from the following answers
A) -42 < xy < 21
B) -42 < xy < 24
C) -30 < xy < 24
D) -24 < xy < 21
E) -24 < xy < 24

Solution: The least value of xy is a bit more than 5*(-6)=-30 and the largest value of xy is a bit less than (-4)*(-6)= 
(-4)*(-6) = 24
24.   Therefore -30 < xy < 24.   Answer: -30 < xy < 24.
Answer: C
Salaries of Ravi and Sumit are in the ration 2:3. It the salary of each in increased by $4000, the new ration becomes 40:57, what is Sumit’s present salary?	Choose the correct choice from the following options.
A) $17000
B) $20000
C) $25500
D) $38000
E) $28500

Solution: Let the original salaries of Ravi and Sumit be $2x and $3x respectively.   Then (2x+4000)/(3x+4000)=40/57   57(2x+4000)= 40)(3x+4000)   6x = 68000   3x=34000   Sumit’s present salary = 3x+4000= 34000+4000= 
34000+4000 = 38_000
$38000   ANSWER : $38000 $38000
Answer: D
An empty bucket being filled with paint at a constant rate takes 6 minutes to be filled to 7/10 of its capacity. How much more time S will it take to fill the bucket to full capacity?	Answers:
A) 7/18  B) 9/18  C) 2  D) 18/7  E) 18/5

Solution: Solution -   Work and Time are directly proportional. W1/W2=T1/T2   7/10 work in 6 mins   1 work in T mins   (7/10)/1 = 6/T -> T = 60/7 mins.   Remaining minutes to fill the tank S= 60/7 - 6 = 18/7 mins. ANS 18/7.
Answer: D
A and B are two partially filled buckets of water. If 7 liters are transferred from A to B, then A would contain one-third of the amount of water in B. Alternatively, if 7 liters are transferred from B to A, B would contain one-half of the amount of water in A. Bucket A contains how many liters of water?	Options.
A) 77/5 B) 13 C) 17 D) 21 E) 23

Solution: Let Bucket 77/5 be 77/5 and Bucket B be B   Scenario 1   77/5-7 = 1/3 (B+7) ----> 377/5-21 =B+7   Scenario 2   B-7 = 1/2 (77/5+7) -----> 2B-14 = 77/5+7   From Scenario 1, B = 377/5-28   Substitute B with this information in Stmt 2   2 (377/5-28) -14 = 77/5+7 ------> 677/5 -56-14 = 77/5+7 ------> 677/5- 77/5 = 70+7 ---> 577/5= 77   77/5= 77/5, 77/5nswer choice 77/5
Answer: A
If a solid sphere of radius 10 cms is moulded into 8 spherical solid balls of equal radius, then surface area of each ball (in cm2) is?
Select the correct option.
A) 100 pi  B) 300 pi  C) 70 pi  D) 90 pi  E) 200 pi

Solution: 4/3 Ï€ * 10 * 10 * 10 = 8 * 4/3 Ï€r3   r = 5   4Ï€ * 5 * 5 = 100Ï€   100 piNSWER 100 pi
Answer: A
What was the day on 15th august 1947 ?	Pick one.
A) monday  B) tuesday  C) wednesday  D) Thursday  E) Friday

Solution: 15 Aug, 1947 = (1946 years + Period from 1.1.1947 to 15.8.1947)   Odd days in 1600 years = 0   Odd days in 300 years = 1   46 years = (35 ordinary years +11 leap years) = (35 x 1+11x2)=57 (8 weeks + 1 day) = 1 odd day   Jan. Feb. Mar. Apr. May. Jun. Jul. Aug    (31 + 28 + 31 + 30 + 31 + 30 + 31 + 1 )= 
 (31 + 28 + 31 + 30 + 31 + 30 + 31 + 1 ) = 213
213 days= (30 weeks + 3 days) = 3 odd days.   Total number of odd days = (0 + 1 + 1 + 3)= 
(0 + 1 + 1 + 3) = 5
5 odd days.   Given day is Friday.   Answer :Friday
Answer: E
The average of 20 numbers is zero. Of them, at the most, how many may be greater than zero?  Choose the correct answer:
A) 0
B) 1
C) 10
D) 19
E) None of the above

Solution: Average of 20 numbers = 0.   ∴ Sum of 20 numbers = (0 × 20) = 0.   It is quite possible that 19 of these numbers may be positive and if their sum is a, then 20th number is (–a).   Answer 19
Answer: D
The total of 35 students in a class is 560 years. The total age of 21 students is 294. What is the total age of remaining 14 students?  Select.
A) 260 B) 270 C) 266 D) 294 E) 244

Solution: The total age of 35 students =560 The total age of 21 students =294 The total age of remaining 14 students = (560-294 )= 
(560-294 ) = 266
266 Answer : 266
Answer: C
If the average of 42, 87, 36, 78, 99, 22, and x is 59, what is x?  Answers.
A) 49	B) 42	C) 59	D) 78	E) 44

Solution: The answer is 49, because:   (42+87+36+78+99+22+x)/7=59   (42+87+36+78+99+22+x)/7 *7 = 59*7   (42+87+36+78+99+22+x)= 413   (42+87+36+78+99+22+x)-364 = 413-364= 
413-364 = 49
49,   so the correct answer is 49, 49.
Answer: A
Harold works at a resort from the beginning of March to the end of September. During the month of August this past year, he made 2 times the average (arithmetic mean) of his monthly totals in tips for the other months. His total tips for August were what fraction of his total tips for all of the months he worked?  Options:  A) 1/3  B) 2/5  C) 1/4  D) 1/2  E) 4/7

Solution: The time from beginning of March to the end of September is 7 months.   If x is the average monthly tip for all months other than August then his August month tip will be 2*x   His total tip for the 7 months = 6*(average tip for the months other than August) + 2x   =8x   August tips as a fraction of total tips = 2x/8x =1/4. So 1/4
Answer: C
How many odd numbers between 10 and 1200 are the squares of integers? Choose the correct choice from the following answers
A) 12  B) 13  C) 14  D) 15  E) 16

Solution: The numbers are the squares of 5, 7, 9,...,33 which includes 15 numbers.   The answer is 15.
Answer: D
Given an integer x, let f(x) be the sum of the digits of x. Compute the number of positive
integers less than 1000 where f(x) = 2.  Choose the correct choice from the following options:  A) 2  B) 4  C) 6  D) 8  E) 10

Solution: We do casework on the number of digits:   (a) The number has 1 digit. The only valid number is 2.   (b) The number has 2 digits. The only valid numbers are 11 and 20.   (c) The number has 3 digits. The only valid numbers are 101, 110, and 200.   This gives us 6 numbers.   correct answer 6
Answer: C
John has 6 people in his group of friends. How many different ways can he invite one or more of them to his house?  Pick.
A) 56 B) 97 C) 63 D) 65 E) 71

Solution: John can select one or more of his group of 6   => Required number of ways = 2^6 – 1= 63.   63
Answer: C
If u and v are negative integers, which of the following statements must be true?
I. (-u)^v is positive.
II. (-u)^(-v) is positive.
III. u^(-v) is positive.  Select the correct option:
A) None
B) II only
C) I and II
D) I and III
E) I, II and III

Solution: Let's u = -2 and v = -3   I. (-u)^v = (2)^(-3) = 1/(2^3) --> Positive   II. (-u)^(-v) is positive. = 2^3 --> Positive   III. u^(-v) is positive. = -2^3 --> Negative   Answer: I and II
Answer: C
You have 59 cubic blocks. What is the minimum number that needs to be taken away in order to construct a solid cube with none left over? Select:
A) 27
B) 43
C) 11
D) 32
E) 45

Solution: D   32   The next cube number below 64(4 ×4 ×4) is 27(3 ×3 ×3).   In order to construct a solid cube, therefore, with none left over,   59 – 27 = 32 blocks need to be taken away.
Answer: D
Three 6 faced dice are thrown together. The probability that exactly two dice show the same number on them is Options
A) 5/54  B) 5/12  C) 5/17  D) 5/18  E) 5/14

Solution: Using question number 11 and 12, we get the probability as   1 - (1/36 + 5/9) = 5/12   Answer: 5/12
Answer: B
An amount of Rs. 3000 becomes Rs. 3500 in four years at simple interest. If the rate of interest was 1% more, then what was be the total amount?
Select the correct option.
A) Rs. 4500.	B) Rs. 3800	C) Rs. 3700.	D) Rs. 2500.	E) Rs. 3500.

Solution: A = P(1 + TR/100)   => 3500 = 3000[1 + (4 * R)/100]   => R = 4.16%   Now R = 5.16%   => A = 3000[1 + (4 * 5.16)/100] = Rs. 3500.   ANSWRs. 3500.R:Rs. 3500.
Answer: E
For each color copy, Print Shop X charges $1.20 and Print Shop Y charges $1.70. How much greater is the charge for 40 color copies at Print Shop Y than at Print Shop X?	Choose the correct option.
A) $14 B) $16 C) $18 D) $20 E) $22

Solution: The difference in the two prices is $1.70 - $1.20 = $0.50 for each color copy.   Each color copy will cost an extra $0.50 at Print Shop Y.   40*$0.50 1.70 -  1.20= 
1.70 -  1.20 = 0.5
$0.50 for each color copy.   Each color copy will cost an extra $0.50 at Print Shop Y.   40*$0.50 = $20   The answer is $20.40* 0.50= 
40* 0.50 = 20
$20   The answer is $20.
Answer: D
A can finish a work in 9 days and B can do the same work in 15 days. B worked for 10 days and left the job. In how many days, A alone can finish the remaining work?
Choose the correct choice from the following:
A) 6
B) 3
C) 5.5
D) 7
E) 8

Solution: B's 10 day's work = ( 1 x 10 ) = 2 .   15 3   Remaining work = ( 1 - 2 ) = 1 .   3 3   Now, 1 work is done by A in 1 day.   9   Therefore 1 work is done by A in ( 9 x 1 ) = 3 days.   3
Answer: B
The total age of A and B is 11 years more than the total age of B and C. C is how many year younger than A	Choose the correct choice from the following answers.
A) A)11  B) B)12  C) C)13  D) D)14  E) E)15

Solution: Explanation:   Given that 11+B = 11 + B + C   => 11 – C = 11 + B – B = 11   => C is younger than 11 by 11 years   11nswer: Option 11
Answer: A
A 140 meter long train crosses a man standing on the platform in 6 sec. What is the speed of the train?  Options
A) 228	B) 108	C) 84	D) 188	E) 211

Solution: S = 140/6 * 18/5= 
140/6 * 18/5 = 84
84kmph   Answer: 84
Answer: C
A car moves at 80 km/hr. What is the speed of the car in meters per second ?
Options:
A) 20 2/9m sec B) 22 2/9m sec C) 24 2/9m sec D) 26 2/9m sec E) 28 2/9m sec

Solution: Explanation:   Speed=(80∗5/18)m/sec   =200/9m/sec   =22 2/9msec   Option 22 2/9m sec
Answer: B
If n is the smallest integer such that 432 times n is the square of an integer, what is the value of n? Select:	A) 2	B) 3	C) 6	D) 12	E) 24

Solution: The prime factorization of a square has to have even powers of all its prime factors. If the original number has a factor, say of 7, then when it’s squared, the square will have a factor of 7^2. Another way to say that is: any positive integer all of whose prime factors have even powers must be a perfect square of some other integer. Look at the prime factorization of 432   432 = (2^4)*(3^3)   The factor of 2 already has an even power —- that’s all set. The factor of 3 currently has an odd power. If n = 3, then 432*n would have an even power of 2 and an even power of 3; therefore, it would be a perfect square. Thus, n = 3 is a choice that makes 432*n a perfect square.   Answer: 3.
Answer: B
If 15% of A is the same as 20% of B, then A : B is :	Select the correct option:	A) 3 : 4	B) 4 : 3	C) 17 : 16	D) 16 : 17	E) 1:2

Solution: 15% of A I= 20 % of 4 : 3   15A/100 = 204 : 3/100   =4/3 = 4:3   ANSWER:4 : 3
Answer: B
A man saves Rs 300 at the end of each year and lends the money at 5% compound interest. How much will it become at the end of 3 years.
Select:  A) Rs 962  B) Rs 962.01  C) Rs 662.02  D) Rs 993.03  E) None of these

Solution: Explanation:   =[300(21/20Ã—21/20Ã—21/20)+300(21/20Ã—21/20)+300(21/20)]=993.03   Option Rs 993.03
Answer: D
In May Mrs Lee's earnings were 70 percent of the Lee family's total income. In June Mrs Lee earned 20 percent more than in May. If the rest of the family's income was the same both months, then, in June, Mrs Lee's earnings were approximately what percent of the Lee family's total income ?
Choose the correct choice from the following answers:
A) 64%  B) 68%  C) 72%  D) 74%  E) 83%

Solution: Let in May Lee family's total income =100   in May Mrs Lee's income =70   in May rest of the family's income = 30   In june Mrs Lees income = 70*120/100= 
70*120/100 = 84
84   In june Total income= 84+ 30= 
84+ 30 = 114
114   % of Mrs Lee's income=84/114 =73.68   (74%)
Answer: D
The average of 45 results is 8. The average of first 22 of them is 15 and that of last 22 is 20. Find the 23 result?
Choose the correct choice from the following answers.
A) 600 B) 470 C) 750 D) 650 E) 560

Solution: 23th result = sum of 45results - sum of 44 results   8*45-15*22+20*22 = 360-330+440= 
360-330+440 = 470
470   Answer is 470
Answer: B
If the area of circle is 616 sq cm then its circumference?	Select:
A) 78 m B) 88 m C) 75 m D) 70 m E) 80 m

Solution: Area of Circle = ∏r2   = 22/7(r2) = 616   = r2 = (616)(7/22)   = r = 14   Circumference = 2∏r = (2)(22/7)(14)   = 88 m   Answer: 88 m
Answer: B