MU-NLPC/Calc-aqua_rat huggingface dataset:
A is twice as good a work man as B and together they finish a piece of work in 36 days.The number of days taken by B alone to finish the work is : Pick
A) 100 days. B) 108 days. C) 98 days. D) 47 days. E) 103 days.

Solution: Solution   (A’s 1 day’s work): (B’s 1 day’s work)= 2 : 1.   (A + B)'s 1 day’s work = 1/36   Divide 1/36 in the ratio 2 : 1.   ∴ B’s 1 day’s work = (1/36 x1/3)= 1/108   Hence,B alone can finish the work in 108 days.   Answer 108 days.
Answer: B
When positive integer A is divided by positive integer B, the remainder is 5. If A/B = 58.25, what is the value of B?	Choose the correct choice:
A) 18	B) 19	C) 15	D) 20	E) 13

Solution: When positive integer A is divided by positive integer B, the remainder is 5 --> A=qB+5;   A/B=58.25 --> A=58B+0.25B (so q above equals to 58);   0.25B=6 --> B=20.   Answer: 20.
Answer: D
How many numbers between 11 and 90 are divisible by 7?	Answers.
A) 11  B) 13  C) 15  D) 12  E) 10

Solution: The required numbers are 14, 21, 28, 35, .... 77, 84.   This is an A.P. with a = 14 and d = (21 - 14)= 
(21 - 14) = 7
7.   Let it contain n terms.   Then, Tn= 84 => a + (n - 1) d = 84   => 14 + (n - 1) x 7 = 84 or n = 11.   Required number of terms = 11   11nswer is 11.
Answer: A
The cash realised on selling a 14% stock is Rs.108.25, brokerage being 1/4% is?	Pick one:
A) 366
B) 106
C) 108
D) 192
E) 122

Solution: Cash realised= Rs. (108.25 - 0.25)   = Rs. 108.   Answer: 108
Answer: C
A box contains 4 black and 5 red balls and another box contains 5 black and 4 red balls. One ball is to drawn from either of two boxes. What is the probability of drawing a black ball ? Choose the correct option:
A) 1/9
B) 2/9
C) 4/9
D) 1/2
E) 2/3

Solution: Explanation :   Probability of choosing first box is 1/2 and second box is 1/2.   ∴ Probability of choosing one balck ball from the first box is 4C1 / 9C1 x 1/2 = 4/9 x 1/2 = 2/9   Probability of choosing one black ball from the second box is = 1/2 x 5C1 / 9C1 = 5/18   ∴ P(E) = 2/9 + 5/18 = 4 + 5/18 = 9/18 = 1/2   Answer : Option 1/2
Answer: D
The population of a certain town increases by 50 percent every 50 years. If the population in 1950 was 810, in what year was the population 160?  Choose the correct choice from the following answers
A) 1650 B) 1700 C) 1750 D) 1800 E) 1850

Solution: If the population increases by 50% then you're multiplying the previous number by 3/2. So to work backwards, divide by 3/2 (which is the same as multiplying by 2/3).   So we have:   1950: 810   1900: 810*(2/3) = 540   1850: 540*(2/3) = 360   1800: 360*(2/3) = 240   1750: 240*(2/3) = 160   Answer is 1750
Answer: C
In a group of ducks and cows, the total number of legs are 26 more than twice the no. of heads. Find the total no.of buffaloes.  Select:
A) 10
B) 12
C) 13
D) 15
E) 16

Solution: Let the number of buffaloes be x and the number of ducks be y   => 4x + 2y = 2 (x + y) + 26   => 2x = 26 => x = 13   13
Answer: C
Rs.1300 is divided so that 4 times the first share, thrice the 2nd share and twice the third share amount to the same. What is the value of the third share?	Choose the correct choice from the following:	A) s.528	B) s.600	C) s.528	D) s.540	E) s.549

Solution: A+s.600+C = 1300   4A = 3s.600 = 2C = x   A:s.600:C = 1/4:1/3:1/2 = 3:4:6   6/13 * 1300 = Rs.600   Answer: s.600
Answer: B
g(x) is defined as the product of all even integers k such that 0 < k ≤ x. For example, g(14) = 2 × 4 × 6 × 8 × 10 × 12 × 14. If g(r) is divisible by 4^11, what is the smallest possible value for r?
Select.
A) 22	B) 24	C) 28	D) 32	E) 44

Solution: g(r)=4^11=2^22. So we have to find a product with atleast 22 2's in it.   in option 1 22 the total no of 2's = [22/2] + [22/4] +[22/8] +[22/16] = 11+5+2+1= 
11+5+2+1 = 19
19   in option 2 24 the total no of 2's= [24/2] + [24/4] +[24/8] +[24/16] = 12+6+3+1= 
12+6+3+1 = 22
22 . Hence 24
Answer: B
In a camp, there is a meal for 120 men or 200 children. If 125 children have taken the meal, how many men will be catered to with remaining meal?	Choose the correct choice from the following options:
A) 30  B) 20  C) 40  D) 45  E) 63

Solution: There is a meal for 200 children.   125 children have taken the meal.   Remaining meal is to be catered to 75 children.   Now, 200 children 120 men.   75 children = (120/200)x 75 = 45 men.   45
Answer: D
Mrs. Evans gave a test to her freshmen economics class, which has 29 students enrolled and 19 of them answered question 1 correctly. If 24 answered question 2 correctly and 5 did not take the test then how many answered both questions correctly?	Options
A) 3  B) 9  C) 11  D) 17  E) 19

Solution: Total number of enrolled students = 29   Number of students who did not take test = 5   Hence, number of students who took test = 29 - 5= 
29 - 5 = 24
24   Number of students who answered Q2 correctly=24, therefore, all students who took test answered Q2 correctly.   So, number of students who answered Q1 correctly, also answered Q2 correctly = 19.   Number of students who answered both Q1 & Q2 correctly = 19.   ANSW19R:19
Answer: E
How many combinations of numbers less than 8 make their sum=8 (repetation of numbers is allowed)	Select the correct option.
A) 102  B) 103  C) 104  D) 105  E) 106

Solution: 8 digit no, =11111111   7 digit no.= 1111112,1111121,1111211........= total 7 numbers   6 digit no. = 111113,111131...........111122,111221....= total 21 numbers   5 digit no.= 11114,11141........11123....11231.....=total 25 numbers   4 digit no.= 2222,1115,1151,1511,5111....1133.....1124....= total 22 numbers   3 digit no.= 116,161,611,224,242,422,332,323,233....125....134...= total 21 numbers   2 digit no. = 44,17,71,26,62,35,53 = total 7 numbers.   now total possible numbers are (without zero) = 104   ANSWER:104
Answer: C
Machine A working alone can complete a job in 3 hours. Machine B working alone can do the same job in 4 hours. How long will it take both machines working together at their respective constant rates to complete the job?  Choose the correct answer
A) 1.10 min	B) 1.714 hr	C) 4hr	D) 2hr	E) 1.714 hr

Solution: Machines ( A ) ( B ) (A+B)   ---Time - 3 - ( 4 ) 1.714   ---Rate 4 --- 3 ---7   --Work 12 ---12 ---12   1.714 hr
Answer: E
In a workshop there are 4 kinds of beds, 5 kinds of closets, 2 kinds of shelves and 7 kinds of chairs. In how many ways can a person decorate his room if he wants to buy in the workshop one shelf, one bed and one of the following: a chair or a closet?  Choose the correct choice from the following options:
A) A)168.  B) B)96.  C) C)56.  D) D)48.  E) E)16.

Solution: ways to select one shelf = 2   ways to select one bed = 4   ways to select one of the following: a chair or a closet = 7+5= 
7+5 = 12
12   ways to select all of them together= 2*4*12= 
2*4*12 = 96
96   Hence, 96. is the answer.
Answer: B
Anne bought a computer for $2,000 and then paid a 5 percent sales tax, and Henry bought a computer for $1,800 and then paid a 12 percent sales tax. The total amount that Henry paid, including sales tax, was what percent less than the total amount that Anne paid, including sales tax?	Pick
A) 3% B) 4% C) 7% D) D.10% E) 12%

Solution: For Anne   Cost of Computer = $2000   Sales tax = (5/100)*2000= 
(5/100)*2000 = 100
$100   Total Cost of Computer= 2000 + 100= 
2000 + 100 = 2_100
2100   For Henry   Cost of Computer= $1800   Sales tax = (12/100)*1800= 
(12/100)*1800 = 216
$216   Total Cost of Computer= 1800 + 216= 
1800 + 216 = 2_016
2016   % that Henry paid less than Anne= (2100 - 2016)*100/2100= 
(2100 - 2016)*100/2100 = 4
4%   Answer: Option 4%
Answer: B
2646 can be expressed as a product of primes as Choose the correct choice from the following options:
A) 2 × 2 × 3 × 3 × 7 × 7	B) 2 × 3 × 3 × 3 × 7 × 7	C) 2 × 2 × 2 × 3 × 3 × 7	D) 2 × 3 × 3 × 3 × 3 × 7	E) None of these

Solution: Explanation:   It is clear that 2646 = 2 × 3 × 3 × 3 × 7 × 7   Answer: Option 2 × 3 × 3 × 3 × 7 × 7
Answer: B
If B and C are digits and 8BC is a 2-digit number that is divisible by 2, which of the following is a possible product of B and C?  Answers.
A) 1
B) 2
C) 4
D) 6
E) 14

Solution: Try with the options -   A. If BC = 1 , both B and C must be 1   B. If BC = 2 , either B or C must be 1 or 2 ; In that case sum of the digits will be 8 + 1 + 2= 
8 + 1 + 2 = 11
11 which is not divisible by 3   C. If BC= 5 , either B or C must be 1 or 5 ; In that case sum of the digits will be 8 + 1 + 5= 
8 + 1 + 5 = 14
14 which is not divisible by 3   D. If BC= 6 , then we can have the following possibilities   i. Either B or C must be 2 or 3 ; In that case sum of the digits will be 8 + 2 + 3= 
8 + 2 + 3 = 13
13 which is not divisible by 3   ii. Either B or C must be 1 or 6 ; In that case sum of the digits will be 8 + 1 + 6= 
8 + 1 + 6 = 15
15 which is divisible by 3   E. If B4= 14 , then either B or 4 must be 2 or 7 ; In that case sum of the digits will be 8 + 2 + 7= 
8 + 2 + 7 = 17
17 which is not divisible by 2   Thus answer is (4)
Answer: C
The sum of the cube of three numbers is 138, while the sum of their products taken two at a time is 131. Their sum is:  Choose the correct choice:
A) 20 B) 21 C) 22 D) 24 E) 25

Solution: Let the numbers be a, b and c.   Then, a2 + b2 + c2 = 138 and (ab + bc + ca) = 131.   (a + b + c)2 = a2 + b2 + c2 + 2(ab + bc + ca) = 138 + 2 x 131 = 400.   (a + b + c) = 400 = 20   20
Answer: A
The mean of 50 observations was 36. It was found later that an observation 48 was wrongly taken as 23. The corrected new mean is : Choose the correct choice:	A) 36.0	B) 36.5	C) 36.2	D) 36.1	E) 36.8

Solution: Explanation:   Correct Sum = (36 * 50 + 48 - 23)= 
(36 * 50 + 48 - 23) = 1_825
1825.   Correct mean= = 1825/50= 
1825/50 = 73/2 = around 36.5
36.5   Answer: 36.5) 36.5
Answer: B
The average amount with a group of seven numbers is Rs. 20. If the newly joined member has Rs. 26 with him, what was the average amount with the group before his joining the group?	Pick.
A) s.17
B) s.12
C) s.15
D) s.29
E) s.19

Solution: Total members in the group = 7   Average amount = Rs. 20   Total amount with them = 7 * 20 = Rs. 140   One number has Rs. 26. So, the amount with remaining 6 people = 140 - 26 = Rs. 114   The average amount with them = 114/6   = Rs.19.   Answer:s.19
Answer: E
If 1 + 9 + 11 = 1, Then what is the value of
12 + 11 + 9 = ?  Choose the correct answer:
A) 11	B) 15	C) 17	D) 12	E) 10

Solution: 10   10   10quation 1 + 9 + 11 = 1 can be derived from   One (o) + nine (n) + eleven (e) = one => 1   Similarly for equation,   12 + 11 + 9   Twelve (t) + eleven (e) + nine (n) => ten (10)
Answer: E
If pq = p^4 + q^2 – 2pq, for what value of q is pq equal to p^4 for all values of p? Choose the correct choice from the following answers
A) -2	B) -1	C) 2	D) 1	E) 0

Solution: C   p4 + q2 â€“ 2pq = p4   => q2 - 2= 
2 - 2 = 0
0=> q (q - 2p) = 0   => q = 0 or q = 2p   im not following the logic you used here.. how did you replace pq with 0 could someone help explain it in MOR0 D0TAI   0
Answer: E
A completes a work in 10 days and B complete the same work in 12 days. If both of them work together, then the number of days required to complete the work will be
Choose the correct choice from the following answers:
A) 6.8 days
B) 9 days
C) 10 days
D) 12 days
E) 13 days

Solution: If A can complete a work in x days and B can complete the same work in y days, then, both   of them together can complete the work in x y/ x+ y days   Therefore, here, the required number of days = 10 × 12/ 22 = 6.8 days.   6.8 days
Answer: A
If 0.75 : x :: 5 : 8, then x is equal to:	Select.
A) 1.2 B) 3.45 C) 8.6 D) 5.14 E) 7.2

Solution: Explanation:   (x x 5) = (0.75 x 8) x =(6/5)= 
(6/5) = 6/5 = around 1.2
1.20   1.2nswer:1.2
Answer: A
A bag holds 3 red marbles and 3 green marbles. If you removed two randomly selected marbles from the bag, without replacement, what is the probability that both would be green?
Answers:  A) 1/10  B) 1/6  C) 3/10  D) 1/5  E) 1/2

Solution: Given: 3R and 3 G marbles   Required: Probability that 2 marbles removed without replacement are both red   Initially we have to pick one red from a total of 3 red and 3 green marbles   After one green has been picked, we need to pick 1 green from a total of 2 greenand 3 red marbles.   P(Both green) = (3/6)*(2/5) = 1/5   Option 1/5
Answer: D
The cost price of a radio is Rs.1500 and it was sold for Rs.1230, find the loss %?  Select:	A) 18	B) 99	C) 77	D) 66	E) 41

Solution: 1500 ---- 270   100 ---- ? => 18%   18nswer:18
Answer: A
Three people each took 5 tests. If the ranges of their scores in the 5 practice tests were 17, 28 and 35, 45 what is the minimum possible range in scores of the three test-takers? Pick one.
A) a 17	B) b) 28	C) c) 35	D) d) 45	E) e) 80

Solution: It is finding the minimum range between all their scores, if all test taker scores are between 0 and maximum range we will have:   A- 0 and 17   B- 0 and 28   C- 0 and 35   D- 0 and 45   therefore the minimum range is 45, it cant be any lower however you play with the numbers.   d) 45
Answer: D
The G.C.D. of 1.08, 0.31 and 0.9 is:	Choose the correct choice
A) 0.01 B) 0.9 C) 0.18 D) 0.108 E) None

Solution: EXPLANATION   Given numbers are 1.08, 0.31 and 0.90. H.C.F. of 108, 31 and 90 is 1,   H.C.F. of given numbers = 0.01.   0.01nswer 0.01
Answer: A
During a two-week period, the price of an ounce of silver increased by 20 percent by the end of the first week and then decreased by 10 percent of this new price by the end of the second week. If the price of silver was x dollars per ounce at the beginning of the two-week period, what was the price, in dollars per ounce, by the end of the period? Choose the correct choice from the following answers
A) 1.02x  B) 1.04x  C) 1.06x  D) 1.08x  E) 1.1x

Solution: The price at the end is 0.9(1.2x)=1.08x   The answer is 1.08x.
Answer: D
The sector of a circle has radius of 28 cm and central angle 135o. Find its perimeter?
Choices:
A) 91.5
B) 91.4
C) 91.7
D) 91.3
E) 122

Solution: Perimeter of the sector = length of the arc + 2(radius)   = (135/360 * 2 * 22/7 * 28) + 2(28)   = 66 + 56= 
66 + 56 = 122
122 cm   Answer:122
Answer: E
Which of the following has the most number of divisors?
Pick one:
A) 99	B) 101	C) 176	D) 182	E) 179

Solution: Explanation:   99 = 1 x 3 x 3 x 11   101 = 1 x 101   176 = 1 x 2 x 2 x 2 x 2 x 11   182 = 1 x 2 x 7 x 13   So, divisors of 99 are 1, 3, 9, 11, 33, .99   Divisors of 101 are 1 and 101   Divisors of 176 are 1, 2, 4, 8, 11, 16, 22, 44, 88 and 176   Divisors of 182 are 1, 2, 7, 13, 14, 26, 91 and 182.   Hence, 176 has the most number of divisors. Answer: 176
Answer: C
Adam spent 1/6 of his lifetime in adolescence. His facial hair started growing after 1/12 more of his life. He successfully married his girlfriend Diana after 1/7 more of his life. Their son was born after 5 years from then. The son lived just 1/2 of what Adam lived. Adam dies four years after his son died. Answers:
A) 84  B) 90  C) 81  D) 75  E) 66

Solution: A   Let us assume that Adam lived for p years.   p/6 + p/12 + p/7 + 5 + p/2 + 4 = x   => p = 84.   Therefore, 84dam lived for 84 years.
Answer: A
How much 80% of 40 is greater than 10% of 15?	Pick one.
A) 18  B) 99  C) 19  D) 18  E) 17

Solution: (80/100) * 40 – (10/100) * 15   32 - 15= 
32 - 15 = 17
17   Answer: 17
Answer: E
The cost of a one-family home was $ 120,000 in 1980. In 1988, the price had increased to $ 186,000. What was the percent increase in the cost of the home?  Select.
A) 60%  B) 50%  C) 55%  D) 40%  E) 33.3%

Solution: Increase = 186000-120000= 
186000-120000 = 66_000
66000   % increase= 66000*100/120000= 
66000*100/120000 = 55
55%   Answer: option 55%
Answer: C
If two pipes function simultaneously the reservoir will be filled in 12 hours, one pipe fills the reservoir 10 hours faster than the other. How many hours it takes the second pipe to fill the reservoir? Choose the correct choice from the following options.
A) 15 hours
B) 18 hours
C) 30 hours
D) 20 hours
E) 22 hours

Solution: 30 hours   30 hours
Answer: C
The ratio between the length and the breadth of a rectangular park is 1 : 4. If a man cycling along the boundary of the park at the speed of 12 km/hr completes one round in 8 min, then the area of the park (in sq. m) is?	Select:
A) 124545 m	B) 134561 m	C) 156787 m	D) 15450 m	E) 102400 m

Solution: Perimeter = Distance covered in 8 min. = 12000 x 8 m = 1600 m.   60   Let length = 1x metres and breadth = 4x metres.   Then, 2(1x + 4x) = 1600 or x =160.   Length = 160 m and Breadth = 640 m.   Area = (160 x 640) m2 = 102400 m   102400 m
Answer: E
The equal amounts of money are deposited in two banks each at 15% per annum for 3.5 years and 5 years respectively. If the difference between their interests is Rs.144, find the each sum? Choose one
A) 228 B) 640 C) 888 D) 276 E) 981

Solution: (P*5*15)/100 - (P*3.5*15)/100 = 144   75P/100 – 52.5P/100 = 144   22.5P = 144 * 100   => P = Rs.640   Answer:640
Answer: B
Sanjay deposited Rs. 5000 in the bank. The bank offered simple interest at the rate of 12 per cent per year. After 5 years the total amount received by him will be:	Choose one
A) 7,000 B) 7,500 C) 7,700 D) 7,900 E) 8,000

Solution: Explanation:   P = Rs. 5000, R = 12% p. a and T = 5 years   S.I = PRT / 100   = 5000 X 12 X 5 X 1/1000   =3000   Amount = P+S. I = Rs. 5000+Rs. 3000 = Rs. 8000   Answer:7,700
Answer: C
log root(8)/log 8 is equal to Pick
A) 1/2  B) 1/3  C) 1/4  D) 1/5  E) 1/6

Solution: => log(8)^1/2/log 8 = 1/2 log 8/log 8 = 1/2   1/2NSWER 1/2
Answer: A
Baby Isabel plays with blocks. Each block is 1.5 inches tall. She has a collection of 20 blocks. If she could stack all of the blocks up one on top of the other, how many inches tall would her tower of blocks be? Choose the correct choice from the following answers:
A) 67" B) 30" C) 106" D) 120" E) 151.7"

Solution: 1.5"*20=30". Answer is 30".1.5 *20= 
1.5 *20 = 30
30". Answer is 30".
Answer: B
A military commander has to choose 2 soldiers out of a company of 9 for guarding the headquarters. How many different group combinations of 2 does he have to choose from?
Choices:  A) 4  B) 15  C) 36  D) 27  E) 35

Solution: A military commander has to choose 2 soldiers out of a company of 9.   different group combinations of 2   He can do this in 9362 ways     9*8/2*1= 
  9*8/2*1 = 36
36 ways   ANSWER:36
Answer: C
A trail mix company keeps costs down by employing the peanuts:cashews:almonds ratio of 10:4:1 in each bag of up to 75 total nuts. What is the maximum percentage by which the company could decrease its number of peanuts per bag and still have peanuts constitute more than half the total amount of nuts?	Select
A) 40%  B) 48%  C) 49%  D) 50%  E) 58%

Solution: Peanuts = 50   Cashews = 20   Almonds = 5   We want to remove as many peanuts as possible while still having peanuts represent MORE than half of the mixture...   The number of cashews and almonds will stay the same though, so we have 20 + 5= 
20 + 5 = 25
25 of those non-peanuts in total.   If we had 25 peanuts and 25 non-peanuts, then that would be 50% EXACTLY. We want MORE than 50% though, so we need to add in 1 more peanut. This gives us...   Peanuts= 26   Cashews = 20   Almonds = 5   The question asked for the decrease in the number of peanuts as a percentage. We started with 50 peanuts and removed 24 = 24/50 = 48% ;ANSWER:48%
Answer: B
x - y = 5
2x = 2y + 10
The system of equations above has how many solutions?
Choose the most appropriate option
A) Infinitely many  B) Exactly one  C) Exactly two  D) Exactly three  E) None

Solution: x-y=5 ---------------1   2x=2y+10 ---------------2   Divide equation 2 by 2:   2x/2=(2y+10)/2   x=y+5   x-y=5----------------3   Equation 1 and 3 are equal and thus have infinitely many solutions:   x-y=5   x=5, y=0   x=6, y=1   x=7, y=2   Infinitely manyns:Infinitely many
Answer: A
In the list 3, 3, 4, 4, 5, 5, 5, 5, 7, 11, 21, what fraction of the data is less than the mode?	Pick one:
A) 2/9
B) 1/3
C) 4/11
D) 2/3
E) 7/9

Solution: Mode: The mode of any set is the term which has the highest frequency (Occurrence)   Highest frequent term in the set is 5 (with frequency 4) hence   Mode = 5   two terms (3, 3, 4, 4) out of a total of 11 terms are less than mode of the set.   Fraction of set that are less than Mode of set = 4/11   Answer: Option 4/11
Answer: C
A car takes 6 hours to cover a distance of 540 Km. how much should the speed in Kmph be maintained to cover the same direction in 3/2th of the previous time?	Choose the correct choice from the following answers: A) 60 Kmph B) 70 Kmph C) 80 Kmph D) 85 Kmph E) 90 Kmph

Solution: Time = 6   Distence = 540   3/2 of 6 hours = 6 * 3/2= 
6 * 3/2 = 9
9 Hours   Required speed= 540/9= 
540/9 = 60
60 Kmph   60 Kmph
Answer: A
A cycle is bought for Rs.900 and sold for Rs.1080, find the gain percent? Answers
A) 11
B) 20
C) 28
D) 26
E) 21

Solution: 900 ---- 180   100 ---- ? => 20%   Answer: 20
Answer: B
A grocer buys apples for 100¢ per pound. If 20% of the apples goes bad and he still wants to make a 10% profit over his purchase price, what should be the sales price? Choose the most appropriate option:
A) 136¢
B) 130¢
C) 140¢
D) 137.5¢
E) 142¢

Solution: for making calculation simple let us consider he buys 10pounds @ 100/pound=1000¢ in total .   20% apples lost...means 8 pounds left.   further he wants 10% profit on 1000 ¢   means he wants to earn 1100¢   sales price should be   1100/8= 
  1100/8 = 275/2 = around 137.5
¢ 137.5   Ans 137.5¢
Answer: D
A and B invests Rs.3000 and Rs.5000 respectively in a business. If A doubles his capital after 6 months. In what ratio should A and B divide that year's profit? Choose the correct answer:  A) 9:6  B) 9:8  C) 9:10  D) 9:9  E) 9:5

Solution: (3*6 + 6*6): (5*12)   54:60 => 9:10.Answer:9:10
Answer: C
Of the three numbers, the first is twice as second and three times the third. The average of the three numbers is 88, and the three numbers in order are?	Select the correct option:	A) 116,58,36	B) 98,49,33	C) 126,63,36	D) 144,72,48	E) None of these

Solution: Explanation :   Solution: Let A =x,   B =x/2, C = x/3.   =x + x/2 + x/3 / 3 = 88   By solving we will get x = 144.   Hence A= 144   B= 144/2= 
144/2 = 72
72   C= 144/3= 
144/3 = 48
48   Answer : 144,72,48
Answer: D
If two numbers are in the ratio 4:3. If 20 is added to both of the numbers then the ratio becomes 5:4 then find the smallest number? Select: A) 60 B) 30 C) 40 D) 20 E) 50

Solution: 4:3   4x + 20 : 3x + 20 =5 : 4   4[4x + 20] =5[3x + 20]   16x + 80 = 15x + 100   16x -15x = 100 - 80= 
100 - 80 = 20
20   Then smallest number is= 2   3x = 60   60
Answer: A
If f and t are integers and f^2 – t^2 is an odd integer, which of the following must be an even integer?
I. f + t + 2
II. f^2 + 2ft + t^2
III. f^2 + t^2  Choose the correct choice from the following:
A) None B) I only C) II only D) III only E) I, II, and III

Solution: f^2–t^2 is an odd integer means that either f is even and t is odd or f is odd and t is even.   Check all options:   I. f + t + 2 --> even+odd+even=odd or odd+even+even=odd. Discard;   II. f^2 + 2ft + t^2 --> even+even+odd=odd or odd+even+even=odd. Discard;   III. f^2 + t^2 --> even+odd=odd or odd+even=odd. Discard.   Nonenswer: None.
Answer: A
The pages of a report are numbered consecutively from 1 to 9. If the sum of the page numbers up to and including page number x of the report is equal to THREE less than the sum of the page numbers following page number x, then x =	Choose the correct option.
A) 4  B) 5  C) 6  D) 7  E) 8

Solution: sum of the first few numbers =1+2+3+4+5+6= 
1+2+3+4+5+6 = 21
21   sum of the last few= 7 +8+ 9= 
7 +8+ 9 = 24
24 page no.6 answer .6
Answer: C
If 8 cats can kill 8 rats in 8 minutes, how long will it take 100 cats to kill 100 rats?	Choose the correct choice from the following options
A) 6 minutes	B) 7 minutes	C) 8 minutes	D) 9 minutes	E) 10 minutes

Solution: It will take 8 minutes for 100 cats to kill 100 rats.   1 cat can kill 1 rat in 8 minutes, so 100 cats can kill 100 rats in 8 minutes   Answer 8 minutes
Answer: C
A cistern is normally filled in 2 hrs,but takes 2 hrs longer to fill because of a leak on its bottom,if Cistern is full ,how much time citern would empty?  Choose the correct answer
A) 4 hours  B) 20 hours  C) 30 hours  D) 40 hours  E) 50 hours

Solution: If leakage/hour=1/x, then 1/2 -1/x= 1/4, solving 1/x=1/4   So in 4 hours full cistern will be empty.   4 hoursNSWER:4 hours
Answer: A