MU-NLPC/Calc-aqua_rat huggingface dataset:
A certain collage has total of 500 seniors each majoring in exactly one of six subjects. A minimum of 20 seniors major in each six subjects. If three quarter of the seniors major in one of four subjects, what is the greatest possible number of seniors majoring in one of the other two subjects?  Options
A) 105
B) 80
C) 75
D) 60
E) 50

Solution: 105nswer 105   500 = 375 + 20 + x => x = 105   = 3/4 * 500 in 4 subjects + 20 min for 5th subject + x = 500
Answer: A
A polling company reports that there is a 70% chance that a certain candidate will win the next election. If the candidate wins, there is a 60% chance that she will sign Bill X and no other bills. If she decides not to sign Bill X, she will sign either Bill Y or Bill Z, chosen randomly. What is the chance that the candidate will sign Bill Z? Select the correct option:	A) 10	B) 14	C) 6	D) 4	E) 5

Solution: 70% - Candidate Elected   100%-60% = 40% - Candidate doesnotsigh Bill X   50% - Candidate randomly chooses between two bills.   These are multiplicative:   70% x 40% x 50%   0.7 x 0.4 x 0.5 100 -60= 
100 -60 = 40
40% - Candidate doesnotsigh Bill X   50% - Candidate randomly chooses between two bills.   These are multiplicative:   70% x 40% x 50%   0.7 x 0.4 x 0.5= 0.14 = 14%   Answer (14)
Answer: B
Find the value of (20C18)*(20C20)
Choose the correct choice from the following choices:  A) 400  B) 380  C) 360  D) 350  E) 330

Solution: 20C20 = 1   (20C2)*(20C20) = 20! * 1/18!   = 20*19*18!/18!   = 20*19*1= 
20*19*1 = 380
380   ANSWER:380
Answer: B
A contractor undertook to do a piece of work in 18 days. He employed certain number of laboures but 9 of them were absent from the very first day and the rest could finish the work in only 6 days. Find the number of men originally employed ? Choose one
A) 3.5	B) 4	C) 4.5	D) 4.2	E) 4.3

Solution: Let the number of men originally employed be x.   18x = 6(x â€“ 9)   or x = 4.5   Answer 4.5
Answer: C
A man gains 50% by selling an article for a certain price. If he sells it at double the price, the percentage of profit will be.  Choose the correct choice from the following:	A) 130%	B) 300%	C) 150%	D) 160%	E) 170%

Solution: Explanation:   Let the C.P. = x,   Then S.P. = (150/100)x = 3x/2   New S.P. = 2(3x/2) = 3x/1   Profit = 3x/1 - x 3 /1= 
3 /1 = 3
3x/1 - x= 3x/1   Profit% = (Profit/C.P.) * 100   => (3x/1) * (1/x) * 100 = 300 %   Option 300%
Answer: B
Average of 13 results is 65. If the average of first six results is 61 and average of last six results is 59 Then find the seventh result?  Choose the correct choice from the following answers:
A) 110	B) 115	C) 125	D) 140	E) 145

Solution: 125   Option '125'
Answer: C
Little Johny went to the toy shop and spent one half of the money that was in his wallet.
When he came out, he found that he had as many paise as he had rupees and half as many rupees as he had paise when he went in. Find the money in his wallet when he entered the store.  Choices:	A) 95.98	B) 97.98	C) 90.98	D) 99.9	E) 99.98

Solution: 99.98   Little Johny have Rupees 99.98 in his wallet when he entered the store.
Answer: E
A train passes a station platform in 20 sec and a man standing on the platform in 12 sec. If the speed of the train is 72 km/hr. What is the length of the platform?  Choose the correct answer.
A) 227 B) 140 C) 160 D) 120 E) 171

Solution: Speed = 72 * 5/18= 
72 * 5/18 = 20
20 m/sec.   Length of the train= 20* 12= 
20* 12 = 240
240 m.   Let the length of the platform be x m . Then,   (x + 240)/20= 20=> x = 160 m.   Answer:160
Answer: C
A boat can travel with a speed of 13 km/hr in still water. If the speed of the stream is 4 km/hr, find the time taken by the boat to go 68 km downstream.
Choose the correct choice from the following answers.
A) 2 hours	B) 1 hours	C) 7 hours	D) 4 hours	E) 3 hours

Solution: Speed downstream = (13 + 4) km/hr = 17 km/hr.   Time taken to travel 68 km downstream = 68/17= 
68/17 = 4
4 hrs.   ANSWER:4 hours
Answer: D
22 buses are running between two places P and Q. In how many ways can a person go from P to Q and return by a different bus? Select the correct option.
A) None of these
B) 462
C) 412
D) 424
E) 442

Solution: Explanation :   He can go in any bus out of the 22 buses.   Hence He can go in 22 ways.   Since he can not come back in the same bus that he used for travelling,   He can return in 21 ways.   Total number of ways = 22 x 21 = 462. Answer : Option 462
Answer: B
The ratio between the perimeter and the width of a rectangle is 5 : 1. If the area of the rectangle is 216 sq. cm, what is the width of the rectangle? Answers:
A) 12 cm	B) 16 cm	C) 18 cm	D) 20 cm	E) 22 cm

Solution: 2L+2W = 5W   L = 3W/2   W*L = 216   3W^2/2 = 216   W^2 = 144   W = 12   The answer is 12 cm.
Answer: A
Ages of two persons differ by 16 years. If 6 year ago, the elder one be 3 times as old the younger one, find their present age	Choose one.
A) 12,28 B) 14,30 C) 16,32 D) 18,34 E) 19,32

Solution: Explanation:   Let the age of younger person is x,   Then elder person age is (x+16)   => 3(x-6) = (x+16-6) [6 years before]   => 3x-18 = x+10   => x = 14.   So other person age is x + 16 = 30   Answer: Option 14,30
Answer: B
For any integer k > 1, the term “length of an integer” refers to the number of positive prime factors, not necessarily distinct, whose product is equal to k. For example, if k = 24, the length of k is equal to 4, since 24 = 2 × 2 × 2 × 3. If x and y are positive integers such that x > 1, y > 1, and x + 3y < 940, what is the maximum possible sum of the length of x and the length of y?	Select:
A) 24
B) 22
C) 16
D) 18
E) 20

Solution: we know that : x > 1, y > 1, and x + 3y < 940,   and it is given that length means no of factors.   for any value of x and y, the max no of factors can be obtained only if factor is smallest noall factors are equal.   hence, lets start with smallest no 2.   2^1 =2   2^2 =4   2^3=8   2^4=16   2^5=32   2^6=64   2^7=128   2^8=256   2^9=512   2^10 =1024 (opps//it exceeds 1000, so, x can't be 2^10)   so, max value that X can take is 2^9 , for which haslength of integeris 9.   now, since x =512 ,x+3y<940   so, 3y<428   ==> y<428/3   so, y can take any value which is less than 428/3. and to get the maximum no of factors of smallest integer, we can say y=2^7   for 2^7 has length of integer is 7.   SO, combined together : 9+7= 
9+7 = 16
16.   16
Answer: C
A is half good a work man as B and together they finish a job in 14 days. In how many days working alone B finish the job? Answers.
A) 77 days
B) 21 days
C) 88 days
D) 55 days
E) 44 days

Solution: WC = 1:2   2x + x = 1/14 => x = 1/42   2x = 1/21 => 21 days   Answer: 21 days
Answer: B
Today John is twice as old as Sam and Sam is 2 years younger than Mike. If John, Sam, and Mike are all alive 6 years from today, which of the following must be true on that day. I. John is twice as old as Sam II. Sam is 4 years younger than Mike III. John is older than Mike Choose the correct choice from the following
A) I	B) I,II & III	C) II	D) II, III	E) III

Solution: Say Mike age is 10   Sam age is 8   John age is 16   After 6 years   Mike age is 16   Sam age is 14   John age is 28   i.e ) after 6 years   Sam is 2 years younger than Mike   John is twice as old as Sam   John is older than Mike   Answer : I,II & III
Answer: B
A batsman scored 120 runs whichincluded 3 boundaries and 8sixes. What % of his total score did he make by running between the wickets	Choose the correct choice from the following choices.
A) 40%
B) 50%
C) 60%
D) 65%
E) 72%

Solution: Number of runs made by running = 110 - (3 x 4 + 8 x 6)   = 120 - (60)= 
120 - (60) = 60
60   Now, we need to calculate 60 is what percent of 120.=> 60/120 * 100= 
60/120 * 100 = 50
50%   50%
Answer: B
A train 200m long passes a standing man in 20 seconds. What is the speed of the train?
Options
A) 30km/hr B) 36km/hr C) 42km/hr D) 50km/hr E) 32km/hr

Solution: Speed of the train = 200/20* 18/5= 
200/20* 18/5 = 36
36km/hr   Answer is 36km/hr
Answer: B
If the length of the longest chord of a certain circle is 24, what is the radius of that certain circle?
Choices
A) 12	B) 5	C) 10	D) 15	E) 20

Solution: Longest chord of a circle is the diameter of the circle   diameter = 2 * radius   If diameter of the circle is given as 24 = 2 * 12   so radius of the circle = 12   correct answer - 12
Answer: A
If a number R between 0 and 1 is selected at random, which of the following will the number most likely be between? Options:  A) 0 and 3/20  B) 3/20 and 1/5  C) 1/5 and 1/4  D) 1/4 and 3/10  E) 3/10 and 1/2

Solution: The number R will most likely be between the largest range.   A. 0 and 3/20 --> range 3/20;   B. 3/20 and 4/20 --> range 1/20;   C. 4/20 and 5/20 --> range 1/20;   D. 5/20 and 6/20 --> range 1/20;   E. 6/20 and 10/20 --> range 4/20.   Answer: 3/10 and 1/2.
Answer: E
A man walking at a constant rate of 5 miles per hour is passed by a woman traveling in the same direction along the same path at a constant rate of 25 miles per hour. The woman stops to wait for the man 5 minutes after passing him, while the man continues to walk at his constant rate. How many minutes must the woman wait until the man catches up?	Select the correct option
A) 16  B) 20  C) 24  D) 25  E) 28

Solution: When the woman passes the man, they are aligned (m and w). They are moving in the same direction. After 5 minutes, the woman (W) will be ahead the man (M):   m------M---------------W   w   In the 5 minutes, after passing the man, the woman walks the distance mW = wW, which is 5*25/60 =25/12 miles and the man walks the distance mM, which is 5*5/60 = 5/12 mile.   The difference of 25/12 - 5/12 =1/3 miles (MW) will be covered by the man in (4/3)/4 = 1/3 of an hour, which is 20 minutes.   Answer 20.
Answer: B
One fourth of one third of two fifth of a number is 25. What will be40% of that number  Choices:
A) A)140 B) B)150 C) C)180 D) D)200 E) E)300

Solution: 300xplanation:   (1/4) * (1/3) * (2/5) * x = 25   then x = 25 * 30= 
25 * 30 = 750
750   40% of 750= 300   Answer: Option 300
Answer: E
In a box there is a number of balls, out of which 1/5 are green, 1/2 are red, 1/10 are pink and the remaining 10 are orange. How many balls are green?	Choose the correct choice from the following choices:
A) 10 balls.
B) 40 balls.
C) 12 balls.
D) 50 balls.
E) 15 balls.

Solution: Let x be the total number of balls.   The number of green, red and pink balls is x(1/5+1/2+1/10)=8x/10   The number of orange balls is x-8x/10=2x/10.   Thus, 2x/10=10, from where x=100/2, x=50.   The number of green balls is   1/5*50= 
  1/5*50 = 10
10.   10 balls.nswer 10 balls. 10.
Answer: A
The integer W has a tens digit of 6 and a units digit of 7. The units digit of integer y is 8. The product of W and y has a tens digit of 8. Which of the following is a possible tens digit of integer y?
Answers:  A) 3  B) 4  C) 5  D) 6  E) 7

Solution: Let W be 67 and y be a8. Then the product of W and y can be written as (60+7)*(10a+8)=600a + 480+70a+56=600a+536+70a. Since 600a dose not affect on the tens digit we can ignore 600a.   So tens digit should be the unit of 3+7a. That means 3+7a =8, 18, 28, 38, 48 or 58 (since 3+7a<=3+7*9= 
3+7*9 = 66
66) --->7a=5, 15, 25, 35, 45, 55. So the only possibility is a=5.   So the answer is (5).
Answer: C
Three unbased coins are tossed. the probability of getting at most one head two tail is ?  Choose the correct choice:
A) 1/2
B) 7/8
C) 3/4
D) 3/8
E) 2/3

Solution: S={TTT,TTH,THT,HTT,THH,HTH,HHT,HHH}   E be the event of getting at least two head is {TTH,THT,HTT}   P(E)=n(E)/n(S)=3/8   Answer(3/8)
Answer: D
Rahul went to a shop and bought things worth Rs. 75, out of which 30 Paise went on sales tax on taxable purchases. If the tax rate was 6%, then what was the cost of the tax free items?  Select.
A) A)19.7	B) B)29.9	C) C)39.7	D) D)69.7	E) E)99.7

Solution: Total cost of the items he purchased = Rs.75   Given that out of this Rs.75, 30 Paise is given as tax   => Total tax incurred = 30 Paise = Rs.30/100   Let the cost of the tax free items = x   Given that tax rate = 6%   ∴ (75−30/100−x)6/100 = 30/100   ⇒ 6(75 −0.3 −x) = 30   ⇒ (75 − 0.3 − x) = 5   ⇒ x = 75 − 0.3 − 5 = 69.7   69.7)
Answer: D
You collect pens. Suppose you start out with 5. Mike gives you another 20 pens. Since her father makes pens, Cindy decides to double your pens. Since you're nice, you give Sharon 19 pens. How many pens do you have at the end?  Options.
A) 39  B) 40  C) 31  D) 42  E) 43

Solution: Solution   Start with 5 pens.   Mike gives you 20 pens:  5 + 20= 
 5 + 20 = 25
25 pens.   Cindy doubles the number of pens you have: 25 Ã— 2= 50 pens.   Sharon takes 19 pens from you:  50 - 19= 
 50 - 19 = 31
31 pens.   So you have 31 at the end.   31orrect answer: 31
Answer: C
An Ant is climbing 30 meters tall pole. It climbs 3 meter during the day and slips down 2 meters down during night in sleep, How many days it takes to reach the top of the pole? Choose one.
A) A - 30
B) B - 29
C) C - 28
D) D - 27
E) E - 26

Solution: Ants overall distance covered is 3 -2= 
3 -2 = 1
1 meter per day.   In 27 days it will climb 27 meters. On 28 th day it will reach the top of the pole.   Answer: C - 28
Answer: C
If john makes a contribution to a charity fund at school, the average contribution size will increase by 50% reaching $75 per person. If there were 6 other contributions made before john's, what is the size of his donation?
Options: A) $225 B) $150 C) $200 D) $250 E) $450

Solution: Cavg = average contribution before John   Cavg*1.5 = 75, therefore the average cont is $50 before John.   If he needs to increase the average contribution by $25, he must put in $25 for each of the 6 people.   so $150.   But, he also has to put in the average for himself (the seventh person), so add $75.   So $225 is your answer.   $225nswer $225
Answer: A
Ashok secured average of 74 marks in 6 subjects. If the average of marks in 5 subjects is 74, how many marks did he secure in the 6th subject? Choose the correct choice.
A) 66 B) 74 C) 78 D) 80 E) None of these

Solution: Explanation:   Number of subjects = 6   Average of marks in 6 subjects = 74   Therefore total marks in 6 subjects = 74 * 6= 
74 * 6 = 444
444   Now, No. of subjects= 5   Total marks in 5 subjects = 74 * 5= 
74 * 5 = 370
370   Therefore marks in 6th subject= 444 – 370 = 74   ANSWER 74
Answer: B
Set S is given as S = {1,3,5,7,9,11,13,15,17}. In how many ways can three numbers be chosen from Set S such that the sum of those three numbers is 18?	Choose the correct choice from the following answers:
A) zero
B) one
C) two
D) three
E) four

Solution: 1,3,5,7,9,11,13,15,17 are all odd numbers and as such we can not get an even number from three odd number...   Sum of Odd Number of Odd Numbers = Odd Number..   So, zeronswer will be (zero) Zero...
Answer: A
HE SUM OF EVEN INTEGERS:
The sum of the even numbers between 1 and k is 79*80, where k is an odd number, then k=? Choices.
A) 79
B) 80
C) 81
D) 157
E) 159

Solution: (E) 159   sum of numbers till n = n(n+1)/2 , sum of even numbers will be almost half of this i.e. n(n+1)/4 .   so if S = 79.80, then n= 159.
Answer: E
Kiran had 85 currency notes in all , some of which were of Rs.100 denaomination and the remaining of Rs.50 denomination the total amount of all these currency note was Rs.5000.how much amount did she have in the denomination of Rs.50?	Choose the correct choice from the following answers.
A) rs.2500
B) rs.3500
C) rs.1500
D) rs.4500
E) rs.5500

Solution: 100X +50 (85-X) =5000   on solving:   x=15   100-x=no. of 50 notes = 70   amount =70*50= rs.3500   ANSWER:rs.3500
Answer: B
How many liters of water must be evaporated from 50 liters of a 3 percent sugar solution to get a 4 percent sugar solution?  Choose the most appropriate option: A) 12.5 B) 15.5 C) 17.5 D) 21.5 E) 24.5

Solution: Let x be the amount that needs to be evaporated.   0.03(50) = 0.04(50-x)   0.04x = 2 - 1.5= 
2 - 1.5 = 0.5
0.5/0.04= 
0.5/0.04 = 12.5
12.5 liters   The answer is 12.5.
Answer: A
A committee of 4 people is to be selected from 6 people. How many different committees are possible? Choices:
A) 28
B) 40
C) 56
D) D.168
E) 15

Solution: Because the order does not matter in selecting 4 people for the committee, this is a combination question.   The number of ways to select 4 people from 6 = 6C4 = 6!/4!*2! = 15. Hence 15.
Answer: E
A firm has 3 senior partners and 5 junior partners. How many different groups of 3 partners can be formed in which at least one member of the group is a senior partner. (2 groups are considered different if at least one group member is different) Pick one:  A) 30  B) 34  C) 38  D) 42  E) 46

Solution: The total number of ways to form a group of 3 is 8C3 = 56   The number of groups without a senior partner is 5C3 = 10   The number of groups which include a senior partner is  56-10= 
 56-10 = 46
46   The answer is 46.
Answer: E
Which of the following fractions is greater than 3/5 and less than 6/7?	Choose the correct choice from the following:	A) 7/8	B) 1/3	C) 2/3	D) 1/3	E) 6/7

Solution: Explanation :   LCM of 5, 7, 2, 3, 3, 8 = 840   3/5 = 504/840   6/7 = 720/840   Hence, the question is to find out a number which is between the above numbers   The given choices are   1/2 = 420/840   2/3 = 560/840   1/3 = 280/840   7/8 = 735/840   Clearly, 560/840 = 2/3 . Answer : Option 2/3
Answer: C
1200 men have provisions for 15 days. If 200 more men join them, for how many days will the provisions last now? Pick
A) 12.85	B) 12.62	C) 12.5	D) 12.24	E) 12.1

Solution: 1200*15 = 1400*x   x = 12.85.12.85nswer: 12.85
Answer: A
I. a3 - 988 = 12,
II. b2 - 51 = 49 to solve both the equations to find the values of a and b?	Options:
A) a > b
B) a ≥ b
C) a < b
D) a ≤ b
E) a = b or the relationship between a and b cannot be established.

Solution: a3 = 1000 => a = 10   b2 = 100 => b = ± 10   a ≥ b   ANSWER:a ≥ b
Answer: B
If w is 40 percent less than r, r is 40 percent less than y, and z is 46 percent less than y, then z is greater than w by what percent of w?  Choose the correct choice from the following answers
A) 4%
B) 18%
C) 36%
D) 40%
E) 50%

Solution: GIven w= 0.6r, r=0.6y, z=0.54y, substituting, w=2/3 Z----> z= 1.5w and thus z is 50% greater than w. 50% is the correct answer.
Answer: E
In My, Xiang sold 15 used cars. For these 15 used cars the range of selling prices was 15,000 and the lowest selling price was 4,500. In June, Xiang sold 10 cars. For these 10 cars the range of selling was 9,000 and the lowest selling price was 6,100. What was the range of selling prices for the 25 used car sold by xiang in May and June?  Choose the correct choice from the following answers.
A) 15,600 B) 15,750 C) 16,820 D) 18,100 E) 19,200

Solution: for 10 cars - 9000+ 6100 = 15,100   for 15 cars - 15000+ 4500 = 19,500   max = 19,500 min 4500   answer is approx 15,000.   Option 15,600 is closest.
Answer: A
Two numbers are in the ratio of 1 : 2. If 9 be added to both, their ratio changes to 3 : 5. The greater number is
Choose the correct answer:	A) 20	B) 24	C) 28	D) 32	E) 36

Solution: Let the ratio be X : Y,   Given X/Y = 1/2 ,   (X + 9)/(Y + 9) = 3/5   => X = 18   And Y = 36   ANSW36R:36
Answer: E
X and Y can do job in 25 days and 30 days respectively. They work together for 5 days and then X leaves. Y will finish the rest of the work in how many days?  Choose the correct choice from the following answers: A) 18 days B) 19 days C) 20 days D) 21 days E) None of these

Solution: X’s one day’s work = 1.25 th part of whole work.   Y’s one day’s work = 1⁄30 th part of whole work.   Their one day’s work = 1⁄25 + 1⁄30 = 1⁄150 th part of whole work.   Now, work is done in 5 days = 11⁄150 × 5 = 11⁄30 th of whole work   ∴ Remaining work = 1 - 11⁄30 = 19⁄30 th of whole work   Now, 1⁄30 th work is done by Y in one day.   ∴ 19⁄30 th work is done by Y in 1 /1/30×19/30 = 19 days.   Answer 19 days
Answer: B
The present ages of three persons in proportions 2 : 3 : 5. Eight years ago, the sum of their ages was 36. Find their present ages (in years). Choose the correct choice from the following
A) 15, 20, 28  B) 22, 28, 36  C) 25, 35, 45  D) 12,18,30  E) of these

Solution: Let their present ages be 2x, 3x and 5x years respectively.   Then, (2x - 8) + (3x - 8) + (5x - 8) = 36   10x = 60   x = 6.   Their present ages are 2x = 12 years, 3x = 18 years and 5x = 30 years respectively.   ANSWER:12,18,30
Answer: D
Which of the following equations represents a line that is perpendicular to the line described by the equation 3x + 4y = 10?
Choose the correct option.
A) 3x + 4y = 12 B) 3x – 4y = 20 C) 4y – 3x = 22 D) 1.5y + 2x = 18 E) 8x – 6y = 24

Solution: Perpendicular lines have slopes which are negative reciprocals of each other.   The line 3x + 4y = 10 in slope-intercept form is y = -(3/4)x + 2.5   The slope of this line is - 3/4.   The slope of a perpendicular line is 4/3.   8x - 6y = 24 in slope-intercept form is y = (4/3)x - 4   The answer is 8x – 6y = 24.
Answer: E
The number of years of service of the eight employees in a production department are 15, 10, 9, 17, 8, 7, 14 and 16. What is the range in the number of years of service of the eight employees?  Choose the correct choice from the following options.
A) 10
B) 11
C) 12
D) 13
E) 14

Solution: = 17-7= 
17-7 = 10
10   10nswer 10
Answer: A
A box contains 23 electric bulbs, out of which 4 are defective. Two bulbs are chosen at random from this box. The probability that at least one of these is defective is Select
A) 4/19  B) 7/19  C) 12/37  D) 21/95  E) None

Solution: Solution   P( None is defective)   = 19C2 / 23C2   = 25/37.   P( at least one is defective)   = (1- 25/37)   = 12/37.   Answer 12/37
Answer: C
If four coins are tossed, the probability of getting two heads and two tails is?	Choose the correct choice from the following options:
A) 3/8	B) 7	C) 6	D) 5	E) 3

Solution: Since four coins are tossed, sample space = 24   Getting two heads and two tails can happen in six ways.   n(E) = six ways   p(E) = 6/24 = 3/8   3/8nswer:3/8
Answer: A
Sachin is younger than Rahul by 5 years. If the ratio of their ages is 7:9, find the age of Sachin  Choose the correct choice
A) 24.58 B) 24.5 C) 24.3 D) 24.9 E) 15.5

Solution: If Rahul age is x, then Sachin age is x-5,   so (x-5)/x = 7/9   => 9x-45 = 7x   => 2x = 45   => x = 22.5   So Sachin age is   22.5 - 7= 
  22.5 - 7 = 15.5
15.5   Answer: 15.5
Answer: E
A can do a piece of work in 10 days and B can do the same work in 12 days. A and B worked together for 1/2 days. How many more days are required to complete the remaining work if they work together?  Choose the correct answer.
A) 3 (5/18)
B) 3 (5/16)
C) 3 (5/11)
D) 4 (21/22)
E) 3 (5/21)

Solution: A can do 1/10 of the work in a day.   B can do 1/12 of the work in a 1 day.   Both of them together can do (1/10 + 1/12) part of work in 1 day = (6 + 5)/60 = 11/60   They take 60/11 days to complete the work together.   Given that they already worked for 1/2 days.   The number of days required to complete remaining work => 60/11 - 1/2 = 109/22 = 4 (21/22) days.   Answer:4 (21/22)
Answer: D
A pump can fill a tank with water in 8 hours. Because of a leak, it took 16 hours to fill the tank. The leak can drain all the water in ?
Choose the correct choice from the following:
A) 16hr
B) 12hr
C) 13hr
D) 14hr
E) 16hr

Solution: Work done by the leak in 1 hour = 1/8 - 1/16 = 1/16   Leak will empty the tank in 16 hours   16hrnswer is 16hr
Answer: A
On a test consisting of 30 questions. No. of wrong answers is 50% less than number of right answers. Each answer was either right or wrong. What is the ratio of right answers to wrong answers?	Choose the correct option:	A) 3 : 2	B) 2 : 3	C) 2 : 1	D) 1 : 4	E) 2 : 5

Solution: Sol. Let the number of wrong answer - x and number of right answer = 30-x x = 50/100 of (30-x) x = 10   Required ratio = 20 : 10 = 2 : 1   2 : 1
Answer: C
If b equals 10% of a and c equals 20% of b, then which one of the following equals 30% of c?	Select.
A) 0% B) 0.6% C) 0.06% D) 6.0% E) None of these

Solution: Explanation :   Given,   b=10% of a   =>(10/100)= 
(10/100) = 1/10 = around 0.1
>0.1a.   And, c=20% of b   =>(20/100)= 
(20/100) = 1/5 = around 0.2
>0.2b=>0.2×0.1a   Now, 30% of c=(30/100)×c.   =>0.3c=(0.3)(0.2)(0.1a)   =>0.006a=0.6%   Answer : 0.6%
Answer: B