MU-NLPC/Calc-aqua_rat huggingface dataset:
At what time between 8 and 9 o’clock will the hands of a watch be in straight line but not together? Choose the correct choice from the following answers
A) 10 11⁄10 min. past 8	B) 10 10⁄11 min. past 8	C) 11 10⁄11 min. past 8	D) 12 10⁄11 min. past 8	E) None of these

Solution: At 8 o’clock, the hands of the watch are 20 min. spaces apart.   To be in straight line but not together they will be 30 min. space apart.   ∴ Minute hand will have to gain 10 min. spaces 55 min.spaces are gained in 60 min.   10 min. spaces will be gained in (60⁄55 × 50) min or 10 10⁄11 min   ∴ Required time = 10 10⁄11 min. past 8   Answer 10 10⁄11 min. past 8
Answer: B
The cost price of an article is 55% of the marked price. Calculate the gain percent after allowing a discount of 15%.  Choose the correct choice from the following
A) 40.5 %  B) 48.7 %  C) 54.5%  D) 55.6% %  E) none

Solution: Sol.   Let marked price = Rs. 100. Then, C.P. = Rs. 55. S.P = Rs. 85.   âˆ´ Gain % = [30/55 * 100]% = 54.5%.   Answer 54.5%
Answer: C
A sum of Rs. 25000 becomes Rs. 27250 at the end of 3 years when calculated at simple interest. Find the rate of interest.  Choose the correct choice from the following options.
A) 1% B) 2% C) 3% D) 4% E) 5%

Solution: Simple interest = 27250 – 25000 = 2250   Time = 3 years.   SI = PTR / 100 → R = SI * 100 / PT   R = 2250 * 100 / 25000 * 3 → R = 3%. ANSWER : 3%
Answer: C
The age of father 7 years ago was five times the age of his son. Five years hence, father's age will be thrice that of his son. The ratio of their present ages is:  Choose the correct choice:
A) 67 : 19	B) 65 : 17	C) 61 : 19	D) 63 : 15	E) 67 : 17

Solution: Let the ages of father and son 7 years ago be 5x and x years respectively.   Then, (5x + 7) + 5 = 3[(x + 7) + 5]   5x + 12 = 3x + 36   x = 12.   Required ratio = (5x + 7) : (x + 7) = 67 : 19.   67 : 19nswer: Option 67 : 19
Answer: A
Place a number in each of the following empty
boxes so that the sum of the numbers in any 3
consecutive boxes is 2015. What is the number
that should go in the box with the question
mark?	Pick one:	A) 684	B) 567	C) 892	D) 431	E) 999

Solution: To help illustrate the problem, we will label a few boxes as shown below.   Since the sum of the numbers in any 3 consecutive boxes is the same,   607 + A + B = A + B + C.   After taking away both A and B from the above equation we get 607 = C   Therefore, the number in box C should be 607.   Since the sum of the numbers in any 3 consecutive boxes is 2015,   C + 724 +? = 607 + 724 +? = 2015   Therefore, ? = 684   correct answer 684
Answer: A
Nirmala gains 10% by selling her bicycle for a certain price. If she sells it at 2 times the price, the percentage of profit will be :	Choose the correct choice from the following.
A) 130%	B) 140%	C) 160%	D) 120%	E) None of these

Solution: Explanation :   Solution: Let C.P =Rs. x. then, S.P. = Rs. (110% of x) = Rs. 11x/10.   New S.P. = Rs. (2*11x/10) =Rs. 22x/10. profit = Rs. (22x/10 - x) = Rs. 6x/5.   .'. Profit% = (6x/5 *1/x * 100) = 120%.   Answer : 120%
Answer: D
A question paper has 2 parts, A & B, each containing 8 questions. If a student has to choose 8 from part A &4 from part B, in how many ways can he choose the questions?
Choose the correct choice from the following:  A) 110  B) 70  C) 120  D) 130  E) 140

Solution: There 8 questions in part A out of which 8 question can be chosen as = 8C8.   Similarly,4 questions can be chosen from 8 questions of Part B as = 8C4.   Hence, total number of ways,   =8C8*8C4   =[8!/(0!8!)]*[8!/(4!*4!)]   = {1}*{8*7*6*5/(4!)}   = 70.   70
Answer: B
In what ratio P:Q should the Mixture P of milk and water in the ratio of 5:4 be mixed with another Mixture Q of milk and water in the ratio 2:7 so that the resultant mixture contains equal quantities of milk and water?  Pick one.
A) 3:2  B) 2:1  C) 4:3  D) 4:1  E) 5:1

Solution: (5/9)*P +(2/9)*Q = (4/9)*P+(7/9)*Q   P=5Q   P/Q = 5/1   The answer is 5:1.
Answer: E
If 36x = 216^y, which of the following expresses x in terms of y?	Choose the correct choice from the following options
A) 6^(3y-2)	B) 6^3y	C) 6^(3y-1)	D) 6^(y-36)	E) 6^(2y/216)

Solution: By exponential simplification. 36 = 6^2 and 216=6^3 therefore (6^2)x=(6^3)^y gives x=(6^3y)/(6^2) further simplified to x=(6^3y)(6^-2) which gives x=6^(3y-2) (because exponential is additive in multiplication. i.e. a^b*a^c=a^(b+c). 6^(3y-2)nswer: 6^(3y-2)
Answer: A
Two pipes A and B can fill a cistern in 37 1/2 minutes and 45 minutes respectively. Both pipes are opened. The cistern will be filled in just half an hour, if the pipe B is turned off after? Choose the correct answer:
A) 7
B) 6
C) 9
D) 7
E) 2

Solution: Let B be turned off after x minutes. Then, part filled by (A + B) in x min + part filled by A in (30 - x) min = 1.   x(2/75 + 1/45) + (30- x) 2/75 = 1   11x + 180 - 6x = 225 => x = 9   Answer: 6
Answer: B
What will the ratio of simple interest earned by certain amount at the same rate of interest for 5 years and that for 11 years.  Choose the correct choice:
A) 1:2	B) 2:3	C) 2:7	D) 5:3	E) None of these

Solution: None of thesexplanation:   Let the principal be P and rate be R   then   ratio = [(P∗R∗6/100) /(P∗R∗9/100)]   =5PR /11PR=5:11   OptionNone of these
Answer: E
Tanks A and B are each in the shape of a right circular cylinder. The interior of tank A has a height of 10 meters and a circumference of 6 meters, and the interior of tank B has a height of 6 meters and a circumference of 10 meters. The capacity of tank A is what percent of the capacity of tank B? Select: A) 60% B) 80% C) 100% D) 120% E) 125%

Solution: The radius of tank A is 6/(2*pi).   The capacity of tank A is 10*pi*36 / (4*pi^2) = 180 / (2*pi)   The radius of tank B is 10 / (2*pi).   The capacity of tank B is 6*pi*100 / (4*pi^2) = 300 / (2*pi)   Tank 60% / Tank B = 180/300 = 6/10 = 60%   The answer is 60%.
Answer: A
At what rate percent on simple interest will Rs.750 amount to Rs.900 in 5 years?	Answers.
A) 8%	B) 3%	C) 4%	D) 2%	E) 1%

Solution: 150 = (750*5*R)/100   R = 4%   Answer:4%
Answer: C
On decreasing the price of a Air Conditioner by 20%, its sale is increased by 40%. The effect on the revenue is?
Pick
A) 8 % decrease	B) 4 % increase	C) 16% decrease	D) 12 % increase	E) none of these

Solution: Net% change in revenue   = ( x + y + xy/100) %   = [-20 + 40 + ( -20 x 40)/100]% or 12%   ANSWER:12 % increase
Answer: D
Three workers have a productivity ratio of 1 to 2 to 3. All three workers are working on a job for 5 hours. At the beginning of the 6th hour, the slowest worker takes a break. The slowest worker comes back to work at the beginning of the 9th hour and begins working again. The job is done in ten hours. What was the ratio of the work performed by the fastest worker as compared to the slowest? Choose the correct option.
A) 42 to 1	B) 30 to 7	C) 5 to 1	D) 1 to 6	E) 1 to 5

Solution: The fastest worker who does 3 units of job worked for all 10 hours, so he did   3*10= 
  3*10 = 30
30 units of job;   The slowest worker who does 1 unit of job worked for only   5+2= 
  5+2 = 7
7 hours (first 5 hours and last 2 hours), so he did   1*7= 
  1*7 = 7
7 units of job;   The ratio thus is 30 to 7.   Answer: 30 to 7.
Answer: B
Jennifer had $150 to spend on herself. She spent 1/5 of the money on a sandwich, 1/6 for a ticket to a museum, and 1/2 of it on a book. How much money does Jennifer have left over?	Choose the correct choice:
A) $4  B) $14  C) $5  D) $15  E) $20

Solution: 1/5 x $150 = $30 for sandwich   1/6 x $150 = $25 for museum   1/2 x $150 = $75 for book   $30 + $25 + $75 = $130 spent   $150 - $130  30 +  25 +  75= 
 30 +  25 +  75 = 130
$130 spent   $150 - $130 = $20 left over   correct answer $20 150 -  130= 
 150 -  130 = 20
$20 left over   correct answer $20
Answer: E
The cost price of 16 articles is equal to the selling price of 11 articles. Find the profit percent? Choose the correct choice from the following answers:	A) 18 2/15	B) 45 5/11	C) 36 2/14	D) 18 2/16	E) 45 2/12

Solution: 16 CP = 11 SP   11 --- 2 CP   100 --- ? =>45 5/11%.Answer: 45 5/11
Answer: B
For a party 240 guests were invited.Contracted have gained 12.5% profit but 30 guest were absent.He charged same cost , lost 100 rs. what is the meal cost?
Select:	A) 20/3	B) 80/3	C) 10/3	D) 40/3	E) 50/3

Solution: Let Cost of one meal be x.   Hence, C.P. of 240 meals = 240 x.   Since contractor gains 12.5 % profit therefore   total selling price = 240x + 240*12.5/100 x   = 270x.   Now 30 guest were absent.   Therefore C.P will remain same 240  + 240*12.5/100= 
240  + 240*12.5/100 = 270
270x.   Now 30 guest were absent.   Therefore C.P will remain same= 240x   And new S.P for 210 guest = (270/240 ) *   210 x   In this case he incurrs a loss of Rs 100.   240x - (9/8) x * 210 = 100   x=80/3.   So, cost of one meal is Rs. 80/3.   ANSWER:80/3
Answer: B
A certain basketball team that has played 2/3 of its games has a record of 16 wins and 4 losses. What is the greatest number of the remaining games that the team can lose and still win at least 3/4 of all of its games?
Choose the correct choice from the following answers
A) 7  B) 6  C) 5  D) 4  E) 3

Solution: 16 wins, 4 losses - total 20 games played.   The team has played 2/3rd of all games so total number of games = 30   3/4th of 30 is 22.5 so the team must win 23 games and can afford to lose at most 7 total games. It has already lost 4 games so it can lose another 3 at most.   Answer (3)
Answer: E
Present ages of Sameer and Anand are in the ratio of 5:4 respectively. Three years hence, the ratio of their ages will become 11:9 respectively. What is Anand's present age in years?
Choose the correct choice from the following choices:
A) 24  B) 25  C) 26  D) 27  E) 28

Solution: Let the present ages of Sameer and Anand be 5x and 4x years respectively.   Then, (5x + 3)/(4x + 3) = 11/9   9(5x + 3) = 11(4x + 3) => x = 6   Anand's present age = 4x = 24 years.   24NSWER:24
Answer: A
The owner of a furniture shop charges his customer 20% more than the cost price. If a customer paid Rs. 8337 for a computer table, then what was the cost price of the computer table?  Choose the correct choice
A) Rs.6725
B) Rs.6727
C) Rs.6908
D) Rs.6725
E) Rs.6947.5

Solution: CP = SP * (100/(100 + profit%))   = 8337(100/120) = Rs.6947.5   Answer: Rs.6947.5
Answer: E
A trader sells 85 meters of cloth for Rs. 8925 at the profit of Rs. 10 per metre of cloth. What is the cost price of one metre of cloth?
Pick.
A) 26  B) 95  C) 90  D) 42  E) 22

Solution: SP of 1m of cloth = 8925/85 = Rs. 105   CP of 1m of cloth = SP of 1m of cloth - profit on 1m of cloth   = Rs. 105 - Rs. 10 = Rs. 95   Answer:95
Answer: B
The sum of the numbers is 550. If the first number be twice the second and third number be one-third of the first, then the second number is: Choose the correct choice from the following.
A) 48	B) 150	C) 72	D) 84	E) 27

Solution: Let the second number be x. Then, first number = 2x and third number = 2x/3.   2x + x + 2x/3 = 550   11x/3 = 550   x = 150   ANSWER:150
Answer: B
In how many ways can a committee consisting of three men and four women be formed from a group of six men and seven women?
Choose the correct answer.
A) ⁶C₄ ⁷C₃  B) ⁶C₃ ⁷C₅  C) ⁷C₄ ⁶C₃  D) ⁶C₃ ⁷C₃  E) ⁷C₅ ⁶C₄

Solution: The group contain six men and seven women   Three men can be selected from six men in ⁶C₃ ways.   Four women can be selected from seven women in ⁷C₄ ways.   Total number of ways = (⁷C₄)(⁶C₃).   Answer:⁷C₄ ⁶C₃
Answer: C
Find the number which is nearest to 3105 and is exactly divisible by 21?	Select the correct option
A) 3100
B) 2500
C) 2545
D) 5800
E) 3108

Solution: On dividing 3105 by 21, we get 18 as remainder.   Number to be added to 3105 = (21 - 18) - 3.   Hence, required number = 3105 + 3= 
3105 + 3 = 3_108
3108.   Answer 3108
Answer: E
A Sum of Rs.2600, is lent out in 2 parts SI at 10% for 5yrs is equal to SI on 2nd part at 9% rate for 6 yrs. find the ratio of parts.
Select:
A) 13:15
B) 27:25
C) 15:17
D) 17:19
E) 21:23

Solution: Solution :   Given SI1 = SI 2   P1 : P2 = 1/R1T1 : 1/R2T2   = 1/(10*5) : 1/(9:6)   27:25   27:25
Answer: B
If 102y = 25, then 10-y equals:  Choose the most appropriate option.
A) 3 B) 2 C) 6 D) 9 E) 1/5

Solution: 102y = 25   (10y)2 = 52   10y = 5   1/10y = 1/5   10-y = 1/5   Answer :1/5
Answer: E
Anand and Deepak started a business investing Rs. 4,500 and Rs. 8,000 respectively. Out of a total profit of Rs. 3,000. Deepak's share is?
Choose the correct choice from the following options.
A) s. 1600	B) s. 1500	C) s. 2450	D) s. 1920	E) s. 1400

Solution: Ratio of their shares = 4500 : 8000 = 9 : 16   Deepak's share = Rs. (3000 * 16/25) = Rs. 1920 ANSWER "s. 1920
Answer: D
What will be the difference in simple and compound interest on 7000 after three years at the rate of 10 percent per annum? Pick one
A) 160	B) 42	C) 62	D) 217	E) None of these

Solution: For 3 years:   217iff.=Sum×(rate)2(300+rate)/(100)3   = 7000×10×10×310/100×100×100 = 217   Answer 217
Answer: D
16 men went to a restaurant. Fifteen of them paid Rs.80 each and the sixteenth man paid Rs.75 more than the average of all the 16 men. What is the total bill?	Choose the correct answer
A) 1360 B) 1560 C) 1660 D) 1760 E) 1460

Solution: 15 paid Rs.80 each = 15*80= 
15*80 = 1_200
1200   total= x   then 16th man would have paid = x-1200   that is = 75+(x/16)   ((x/16)=average)   equating these two   x-1200 = 75+(x/16)   x-(x/16)= 1275   15/16x = 1275   x = 1275*16/15= 
1275*16/15 = 1_360
1360   1360NSWER:1360
Answer: A
A is thrice as efficient as B and is, therefore, able to finish a piece of work 10 days earlier than B. In how many days A and B will finish it together?	Choose the correct choice from the following answers
A) 3 1/2 days
B) 3 4/5 days
C) 3 days
D) 5 days
E) 6 days

Solution: Explanation:   WC = 3:1   WT = 1:3   x 3x   1/x – 1/3x = 1/10   x = 20/3   3/20 + 1/20 = 1/5 => 5 days   Answer: 5 days
Answer: D
A book store bought copies of a new book by a popular author, in anticipation of robust sales. The store bought 400 copies from their supplier, each copy at wholesale price x. The store sold the first 150 copies in the first week at 80% more than x, and then over the next month, sold a 100 more at 20% more than x. Finally, to clear shelf space, the store sold the remaining copies to a bargain retailer at 40% less than x. What was the bookstore’s net percent profit or loss on the entire lot of 400 books?
Choices
A) 30% loss	B) 10% loss	C) 10% profit	D) 20% profit	E) 60% profit

Solution: [[x(150)(1.8)+x(100)(1.2)+x(150)(0.6)]/400x] - 1   [50[(3)(1.8) + (2)(1.2) + (3)(0.6)] / (50)(8)] - 1   [(5.4 + 2.4 + 1.8)/8] - [8/8]   +1.6/8   +20%   answer is 20% profit
Answer: D
A dice is rolled 3times & sum of 3 no.'sappearing on the uppermost face is 15. The chance that the first roll was four is?	Options.
A) 2/113	B) 3/114	C) 1/108	D) 2/119	E) 3/117

Solution: Sol. Total number of favorable outcomes n(S) . e . 216 1/108ombinations of outcomes for getting sum of 15 on uppermost face = (4, 5, 6) (5, 4, 6) (6, 5, 4) (5, 6, 4), (4, 6, 5), (6, 4, 5), (5, 5, 5), (6, 6, 3), (6, 3, 6) (3, 6, 6) Now outcomes on which first roll was a four, n(E) = (4, 5, 6), (4, 6, 5) P(E) n(E) 2 1 Pt') = n(S) = 216 = 1/108   1/108
Answer: C
Two persons start running simultaneously around a circular track of length 300 m from the same point at speeds of 15 km/hr and 25 km/hr. When will they meet for the first time any where on the track if they are moving in opposite directions?	Choose the correct choice:  A) 16 seconds  B) 17 seconds  C) 19 seconds  D) 27 seconds  E) 87 seconds

Solution: Time taken to meet for the first time anywhere on the track   = length of the track / relative speed   = 300 / (15 + 25)5/18 = 300* 18 / 40 * 5   = 27 seconds.   Answer: 27 seconds
Answer: D
The ratio between the present ages of P and Q is 6:7. If Q is 4 years old than P, what will be the ratio of the ages of P and Q after 4 years Answers:
A) A)3:4  B) of these  C) C)4:3  D) inadequate  E) B)3:5

Solution: Let P's age and Q's age be 6x and 7x years respectively.   Then, 7x - 6x = 4 => x = 4   Required ratio = (6x + 4) : (7x + 4)   28 : 32 = 7:8   ANSWER:of these
Answer: B
If x is equal to the sum of the integers from 50 to 70, inclusive, and y is the number of even integers from 50 to 70, inclusive, what is the value of x + y?  Choose one:
A) 1211
B) 1231
C) 1251
D) 1271
E) 1291

Solution: x = 50 + 51 +...+ 70 = 21(60) = 1260   y = 11   x+y = 1271   The answer is 1271.
Answer: D
Jordan took a bus from home to market, that travels at 20 kmph. While walking back at 2 kmph,
halfway through, he suddenly realized he was getting late and he cycled back the remaining distance in 10 kmph. Find the average speed.  Pick
A) 2.9 kmph B) 4.3 kmph C) 5.1 kmph D) 1.8 kmph E) none of these

Solution: Let the distance be 2x(one way)   Time taken by bus = 2x/20, by walking =x/2, by cycling = x/10 hours   :. 2.9 kmphverage speed = Total Distance/Total time   = 2x / x/10 + x/2 + x/10   = 2 *60 / 6+30+6   = 2.9   2.9 kmphNSWER:2.9 kmph
Answer: A
A is twice as good a workman as B and together they finish a piece of work in 18 days. In how many days will A alone finish the work?  Choose the correct choice from the following:  A) 27 days.  B) 32 days.  C) 18 days.  D) 33 days.  E) 29 days.

Solution: A   27 days.   If A takes x days to do a work then B takes 2x days to do the same work.   --> 1/x+1/2x = 1/18   --> 3/2x = 1/18   --> x = 27 days.   Hence, 27 days. alone can finish the work in 27 days.
Answer: A
What is the lowest positive integer that is divisible by each of the integers 1 through 9 inclusive? Choose the correct choice from the following options.
A) 420
B) 840
C) 1260
D) 2520
E) 5020

Solution: We have to find the LCM of 1, 2, 3, 2^2, 5, 2*3, 7, 2^3, and 3^2.   The LCM is 1*2^3*3^2*5*7= 2520   The answer is 2520.
Answer: D
At a recent small town election for mayor a total of 963 votes were cast for the four candidates, the winner exceding his opponents by 53, 79 and 105 votes, respectively. How many votes were cast for each candidate?	Select the correct option
A) 134	B) 178	C) 195	D) 166	E) 194

Solution: C   195   The number of votes the winning candidate received was   963 + 53 + 79 + 105	/4= 300.   The second received 300 – 53 = 247,   The third received 300 – 105 = 195.
Answer: C
A palindrome is a number that reads the same forward and backward, such as 242. How many even three-digit numbers are palindromes?	Choose the correct choice.
A) 40  B) 400  C) 500  D) 5,000  E) 100,000

Solution: if the palindrome must be even, it must begin and end in 2,4 6 and 8 ( 4 ways) e.g 212,414.   The middle number in the three-digit could be 0-9 ( 10 ways), e.g 252, 282   we thus have, 4 *10 = 40.   40
Answer: A
A sum of money deposited at compound interest (compounded yearly) amounts to $1210 in 2 years and to $1452 in 3 years. What is the interest rate?	Choices.
A) 20% B) 10% C) 60% D) 70% E) 30%

Solution: 1452 - 1210= 
1452 - 1210 = 242
242   242 / 1210= 
242 / 1210 = 1/5 = around 0.2
0.2= 20%   The answer is 20%.
Answer: A
In a game of billiards, A can give B 20 points in 60 and he can give C 30 points in 60. How many points can B give C in a game of 100?  Answers
A) 33
B) 67
C) 25
D) 66
E) 81

Solution: A scores 60 while B score 40 and C scores 30.   The number of points that C scores when B scores 100 = (100 * 30)/40 = 25 * 3= 
25 * 3 = 75
75.   In a game of 100 points, B gives (100 - 75)= 
(100 - 75) = 25
25 points to C.   Answer: 25
Answer: C
There are a lot of houses such that the numbers of their doorplates are odd numbers and the first number of the doorplates is 685, the last number of the doorplates is 705. How many houses are there?  Choose the correct choice.
A) 12
B) 11
C) 13
D) 9
E) 10

Solution: So it starts from 685 and goes like 687, 689,...... 705. and both first and last number are inclusive. Since every other number is odd, it's just 1/2 of the numbers and since it starts with an odd and ends with an odd inclusive add one to the result.   i.e., ([705-685][/2]+1 = 11   Ans 11
Answer: B
A and B starts a business investing Rs.85000 and Rs.15000 respectively. Find out the ratio in which the profits should be shared.
Choose the correct choice from the following.
A) 3:17	B) 17:3	C) 10:3	D) 3:10	E) 5:12

Solution: Here A's and B's capitals are there for equal time. Hence   A : 17:3 = 85000 : 15000   = 85 : 15   = 17 : 3   Answer is 17:3.
Answer: B
What is the lowest positive integer that is divisible by each of the odd integers between 15 and 23, inclusive?	Answers
A) 3×17×19×21	B) 5×17×19×23	C) 7*15*17*19*21	D) 7×15×19×21	E) 7*15*17*19*23.

Solution: We should find the LCM of 15 = 3*5, 17, 19, and 21 = 3*7,23 --> LCM = 3*5*7*17*19*23 = 7*15*17*19*23.   Answer: 7*15*17*19*23.
Answer: E
A jar is filled with red, white, and blue tokens that are equivalent except for their color. The chance of randomly selecting a red token, replacing it, then randomly selecting a white token is the same as the chance of randomly selecting a blue token. If the number of tokens of every color is a multiple of 5, what is the smallest possible total number of tokens in the jar?  Choose the correct choice from the following answers.
A) 9  B) 12  C) 15  D) 18  E) 21

Solution: (Red / Total Coins)*(White / Total Coins) = (Blue / Total Coins)   i.e. Red*White = Blue*Total Coins   Let, Red = 3a   White = 3b   Blue = 3c   Total Coins = 3(a+b+c)   i.e. 3a * 3b = 3c*3(a+b+c)   i.e. a*b = c*(a+b+c)   For smallest values of a, b and c   2*3 = 1*(1+2+3)   i.e. Minimum Total Coins = 3*(1+2+3) = 12   Answer: Option 12
Answer: B
Two trains of equal lengths take 10 sec and 15 sec respectively to cross a telegraph post. If the length of each train be 200 m, in what time will they cross other travelling in opposite direction? Choose one:
A) 17 sec  B) 12 sec  C) 16 sec  D) 15 sec  E) 20 sec

Solution: Speed of the first train = 120/10= 
120/10 = 12
12 m/sec.   Speed of the second train= 120/5 = 8 m/sec.   Relative speed = 12 + 8= 
12 + 8 = 20
20 m/sec.   Required time= (200 + 200)/20= 
(200 + 200)/20 = 20
20 sec.   Answer:20 sec
Answer: E
What is the least number to be subtracted from 800 to make it a perfect square?	Choose the most appropriate option.
A) 1  B) 16  C) 20  D) 71  E) 60

Solution: The numbers less than 800 and are squares of certain number is 784.   The least number that should be subtracted from 800 to make it perfect square = 800 - 784= 
800 - 784 = 16
16.   ANSWER:16
Answer: B
Working alone at a constant rate, Alan can paint a house in a hours. Working alone at a constant rate, Bob can point 1/4 of the same house in b hours. Working together, Alan and Bob can paint 1/3 of the house in c hours. What is the value of b in terms of a and c?	Select:
A) (3ac)/(a+c)
B) (4a-12c)/(3ac)
C) (3ac)/(4a-12c)
D) (ac)/(a+2c)
E) (ac)/(a+c)

Solution: work time   A 1 a   B 1/4 b   A+B 1/3 c   A's rate = 1/a   B's rate = 1/4b   when they are working together , their combined rate is 1/a + 1/(4b) = (1/3)/c   1/(4b) = 1/(3c) - 1/a   => b = 3ac /(4a-12c)   Answer is (3ac)/(4a-12c).
Answer: C
Two trains, one from Howrah to Patna and the other from Patna to Howrah, start simultaneously. After they meet, the trains reach their destinations after 9 hours and 25 hours respectively. The ratio of their speeds is?	Select.
A) 4:5	B) 5:3	C) 4:4	D) 4:9	E) 4:2

Solution: Let us name the trains A and B.   Then, (A's speed) : (5:3's speed)   = √b : √a = √25 : √9 = 5:3   Answer:5:3
Answer: B
What is the smallest positive integer that can be multiplied by 605 to make it a perfect square?
Select.
A) 2	B) 3	C) 5	D) 7	E) 11

Solution: 605 is multiplied by 5 gives 3025   Its a square root of 55   Answer is 5 -Option 5
Answer: C
WINK, Inc. follows a certain procedure that requires two tasks to be finished independently in order for a job to be done. On any given day, there is a 5/8 probability that task 1 will be completed on time, and a 3/5 probability that task 2 will be completed on time. On a certain day, what is the probability that task 1 will be completed on time, but task 2 will not?  Pick one:  A) 1/4  B) 3/40  C) 13/40  D) 7/20  E) 13/22

Solution: P(1 and not 2)=5/8*(1-3/5)=1/4   1/4nswer: 1/4.
Answer: A