MU-NLPC/Calc-aqua_rat huggingface dataset:
A man can row upstream at 8 kmph and downstream at 13 kmph. The speed of the stream is :
Choose the correct choice from the following options:
A) 2.5 km/hr	B) 4.2 km/hr	C) 5 km/hr	D) 10.5 km/hr	E) None of these

Solution: Solution   Speed of stream =1/2(13-8) kmph = 2.5 kmph. 2.5 km/hrnswer 2.5 km/hr
Answer: A
From a group of 7 men and 6 women, five persons are to be selected to form a committee so that at least 3 men are there on the committee. In how many ways can it be done?  Choose the correct choice from the following answers
A) 756
B) 700
C) 600
D) 500
E) 450

Solution: We may have (3 men and 2 women) or (4 men and 1 woman) or (5 men only).   Required number of ways	= (7C3 x 6C2) + (7C4 x 6C1) + (7C5)   = (525 + 210 + 21)= 
(525 + 210 + 21) = 756
756.   756NSWER 756
Answer: A
If f(x)=1/x and x is a natural number, what CANNOT be the answer for f(f(x))? Choose one.
A) 1/7
B) 3
C) 12/3
D) 6/6
E) 1

Solution: Answer A is impossible because the invers of 1/x is x, and the only way to have something other than a natural number is to input something other than a natural number. With the specification that only natural numbers may be used 1/7 is not a possibility for f(f(x))
Answer: A
There are 9 magazines lying on a table; 4 are fashion magazines and the other 5 are sports magazines. If 3 magazines are to be selected at random from the 8 magazines, what is the probability that at least one of the fashion magazines will be selected?
Select: A) 1/2 B) 2/3 C) 32/35 D) 20/21 E) 13/14

Solution: answer is 20/21   Total probability=9C3=84   5C3 +5C2*4C1+5C1*4C2=10+40+30= 
10+40+30 = 80
80   therefore the probability that at least one of the fashion magazines will be selected= 80/84=20/21   20/21
Answer: D
The sum of money will be double itself in 30years and simple interest find rate of interest?  Choose the correct option.
A) A)2.33%	B) B)3.33%	C) C)4.33%	D) D)5.33%	E) E)6.33%

Solution: T = 30 years   P= principle amount = x   A = total amount = 2x   SI = simple interest = A-P = 2x-x = x   R = 100SI/PT = 100x/30x =3.33%   Answer is 3.33%
Answer: B
The difference between a two-digit number and number obtained by interchanging the two digits is 63. What is the difference between the two digits of that number?	Choose the correct answer.
A) 29	B) 70	C) 92	D) 8	E) 7

Solution: Let the ten’s digit be x and unit’s digit be y   (10x+y)-(10y+x)=63   9(x-y)=63   x-y=7   Option 7
Answer: E
The total of company C's assets in 1994 was 700% greater than the total in 1993, which in turn was 400% greater than the total in 1992. If the total of company C's assets in in 1992 was N dollars, which one of the following represents company C's assets in 1994:
Select the correct option.
A) 7N  B) 18N  C) 29N  D) 32N  E) 40N

Solution: Let's use actual numbers. Starting in 1992, let's say company C had $100 in assets.   In 1993, the total assets were 400% GR40NAT40NR, which means 1992 PLUS 400% of 1992:   $100 + 4x$100 = $100 + $400 = $500   In 1994, the total assets were 700% GR40NAT40NR than they were in 1993, which means 1993 PLUS 700% of 1993:   $500 + 7x$500 100 +  400= 
100 +  400 = 500
$500   In 1994, the total assets were 700% GR40NAT40NR than they were in 1993, which means 1993 PLUS 700% of 1993:   $500 + 7x$500= $500 + $3500 = $4000   This is 40 times the 1992 number, so the correct answer is 40N.500 +  3500= 
500 +  3500 = 4_000
$4000   This is 40 times the 1992 number, so the correct answer is 40N.
Answer: E
Ten years ago, the ratio of ages of P and Q was 3:2. Ten years from now, the ratio of their ages will be 7:6. What is P's age at present? Choose one.
A) 18	B) 20	C) 21	D) 24	E) 25

Solution: 2(P-10)/3 = (Q-10). Then Q = 2(P-10)/3 + 10   6(P+10)/7 = Q+10   6(P+10)/7 = 2(P-10)/3 + 20   18P+180 = 14P + 280   4P = 100   P = 25   The answer is 25.
Answer: E
A security company can use number 1 -7 to create a 5 digit lock combo. No numbers can be repeated and the first and last digit must be odd. How many unique lock combos can be created?  Choose the correct option:
A) 60
B) 120
C) 180
D) 240
E) 300

Solution: Lets take it this way, first and last digit needs to be odd so that means it take 1,3,5,7   So, for first digit we have 4 options and for last digit we have 3 digits   for the rest of the 3 digits we have 5 digits to choose from so 5C3=105C3=10 options   Total combinations = 4 * 3 * 10= 
4 * 3 * 10 = 120
120   ANS:120
Answer: B
A student committee on academic integrity has 56 ways to select a president and vice president from a group of candidates. The same person cannot be both president and vice president. How many candidates are there?
Choose the most appropriate option:  A) 7  B) 8  C) 9  D) 10  E) 11

Solution: xC1 * (x-1)C1=56   x^2 -x -56 =0   (X-8) (X+7) = 0   X= 8 , -7   -7 can't possible.   Hence 8 should be the answer   8
Answer: B
Four milkmen rented a pasture, A grazed 18 cows for 4 months; B 25 cows for 2 months, C 28 cows for 5 months and D 21 cows for 3 months. If A's share of rent is Rs.360, the total rent of the field is : Answers.
A) Rs.1500 B) Rs.1600 C) Rs.1625 D) Rs.1650 E) None

Solution: Explanation:   Ratio of rents   =(18×4:25×2:28×5:21×3)(18×4:25×2:28×5:21×3)   =72:50:140:63   Let total rent = Rs.x   Then, A's share = Rs.(x×72/325)= Rs.(72x/325)   72x/325=360 or x = 325×360/72=1625   Rs.1625orrect Option: Rs.1625
Answer: C
At the opening of a trading day at a certain stock exchange, the price per share of stock K was $15. If the price per share of stock K was $16 at the closing of the day, what was the percent increase in the price per share of stock K for that day?	Choose the correct answer
A) 1.4%
B) 5.9%
C) 11.1%
D) 6.67%
E) 23.6%

Solution: Opening = 15   Closing = 16   Rise in price = 1   So, percent increase = 1/15* 100 = 6.67   Answer : 6.67%
Answer: D
When x is divided by 6, the quotient is y and the remainder is 1. When x is divided by 6, the quotient is z and the remainder is 6. Which of the following is the value of y in terms of z?
Choose one
A) 4z/7 + 5
B) (7z + 5) / 6
C) (6z + 5) / 6
D) (7z + 5) / 4
E) (4z + 6) / 7

Solution: When x is divided by 6, the quotient is y and the remainder is 1: x = 6y + 1.   When x is divided by 6, the quotient is z and the remainder is 6: x = 6z + 6.   Equate those two:   6y + 1 = 6z + 6;   y = (6z + 5)/6.   Answer: (6z + 5) / 6.
Answer: C
What is the greatest positive integer x such that 3^x is a factor of 9^10? Choose the correct option
A) 5 B) 9 C) 10 D) 20 E) 30

Solution: 9^10 = (3^2)^10 = 3^20   The Answer is D. 20
Answer: D
How much time will take for an amount of Rs. 450 to yield Rs. 81 as interest at 4.5% per annum of simple interest? Choose the correct answer:
A) 8 years	B) 4 years	C) 3 years	D) 9 years	E) 5 years

Solution: Time = (100 * 81) / (450 * 4.5)= 
(100 * 81) / (450 * 4.5) = 4
4 years   Answer: 4 years
Answer: B
Two numbers are in the ratio of 2:3. If 20 be subtracted from each, they are in the ratio of 10:17. Find the numbers?
Pick one:
A) 70,105	B) 60,88	C) 80,120	D) 60,84	E) 60,81

Solution: (2x-20):(3x-20) =10:17   x = 35 => 70,105   70,105nswer: 70,105
Answer: A
Find large number from below question The difference of two numbers is 1355. On dividing the larger number by the smaller, we get 6 as quotient and the 15 as remainder
Choose the correct choice from the following answers:	A) 1235	B) 1345	C) 1678	D) 1767	E) 1623

Solution: Let the smaller number be x. Then larger number = (x + 1355).   x + 1355 = 6x + 15   5x = 1340   x = 268   Large number = 268+1355= 
268+1355 = 1_623
1623   1623
Answer: E
A man can row 6 kmph in still water. When the river is running at 1.2 kmph, it takes him 1 hour to row to a place and back. What is the total distance traveled by the man ?  Choose the correct choice from the following
A) 7.76 kms	B) 8.76 kms	C) 5.76 kms	D) 3.76 kms	E) 4.76 kms

Solution: Explanation:   Speed in still water = 6 kmph   Stream speed = 1.2 kmph   Down stream = 7.2 kmph   Up Stream = 4.8 kmph   x/7.2 + x/4.8 = 1   x = 2.88   Total Distance = 2.88 x 2 = 5.76 kms   Answer: 5.76 kms
Answer: C
What least number must be subtracted from 652543 so that remaining no.is divisible by 12	Choose the correct choice from the following answers: A) 3 B) 5 C) 7 D) 8 E) 9

Solution: Explanation:   On dividing 652543 by 12 we get the remainder 7, so 7 should be subtracted   Option 7
Answer: C
A, B and C have Rs.250 between them, A and C together have Rs.200 and B and C Rs.350. How much does C have?  Pick one
A) A)300  B) B)290  C) C)280  D) D)270  E) E)66

Solution: 300+B+C = 250   300+C = 200   B+C = 350   --------------   300+B+2C = 550   300+B+C = 250   ----------------   C = 300   300nswer:300
Answer: A
Which one of the following numbers is the greatest positive integer x such that 3^x is a factor of 9^5?	Choose the correct choice from the following.
A) 5
B) 8
C) 10
D) 15
E) 19

Solution: 9 = 3*3= 3^2   9^5 =(3^2)^5   =3^10   we have to find the greatest positive integer value for x   when x=10, it divides exactly once and that is the least positive integer value of the quotient   therefore, the correct option is 10
Answer: C
Divide Rs. 1300 among A, B and C so that A receives 1/3 as much as B and C together and B receives 2/3 as A and C together. A's share is?  Choose the most appropriate option
A) 346
B) 368
C) 375
D) 337
E) 325

Solution: A+B+C = 1300   A = 1/3(B+C); B = 2/3(A+C)   A/(B+C) = 1/3   A = 1/4 * 1300= 
1/4 * 1300 = 325
> 325   Answer:325
Answer: E
In how many ways can a four-letter password be chosen, using the letters A, B, C, D, E, F, and/or G such that at least one letter is repeated within the password? Choose the correct choice.
A) 720 B) 864 C) 900 D) 936 E) 1561

Solution: Total number of four letter passwords = 7*7*7*7= 
7*7*7*7 = 2_401
2401 ------(1)   Total number of passwords in which no letter repeats= 7C4*4!= 35*24= 
35*24 = 840
840------(2)   therefore required value= (1)-(2)= 2401-840= 
2401-840 = 1_561
1561   1561
Answer: E
In a class, the average age of 25 boys is 12 years and the average of 18 girls is 8 years. what is the average age of the whole class?
Choices.
A) 12 Years
B) 10.3 Years
C) 12.6 Years
D) 13 Years
E) 15 Years

Solution: Total age of 43 students   (25X 12+18 X 8) = 444   Average = 444/53 = 10.3 Years   10.3 Years
Answer: B
A bag contains nine black balls, three red balls and four red balls. In how many ways can two balls be drawn from the bag?  Choose the most appropriate option.
A) ¹⁶C₂	B) ⁹C₂	C) ³C₂	D) ¹²C₂	E) ¹⁴C₂

Solution: Total number of balls = 9 + 3 + 4   Two balls can be drawn from 16 balls in ¹⁶C₂ ways.   ¹⁶C₂
Answer: A
A train 360 m long is running at a speed of 45 km/hr. In what time will it pass a bridge 140 m long? Answers:
A) 40  B) 99  C) 77  D) 66  E) 12

Solution: Speed = 45 * 5/18 = 25/2 m/sec   Total distance covered = 360 + 140= 
360 + 140 = 500
500 m   Required time= 500 * 2/25= 
500 * 2/25 = 40
40 sec   40nswer: 40
Answer: A
The ratio between the number of sheep and the number of horses at the Stewart farm is 3 to 7, If each horse is fed 230 ounces of horse food per day and the farm needs a total 12,880 ounces of horse food per day, what is the number of sheep in the farm?
Choose the correct choice from the following:
A) 24 B) 28 C) 32 D) 56 E) 60

Solution: Let the number of sheeps and horses be 3x and 7x.   Now total number of horses = total consumption of horse food/consumption per horse = 12880/230= 
12880/230 = 56
56, which is equal to 7x.=> x = 8   Sheeps = 3x = 3*8= 
3*8 = 24
24. Hence 24
Answer: A
Of the teams competing in the world archery championships, Sxity percent are from Europe. Half as many are from the United States and one twentieth are from Africa. What fraction of teams are from neither Europe, the US or Africa.  Choices:  A) 2/20  B) 15/20  C) 3/15  D) 1/20  E) 13/17

Solution: Half as manymeans half of EU, then   EU 60%   US 30%   AF 5%   the rest is 5%, answer 1/20
Answer: D
An express traveled at an average speed of 100 km/hr, stopping for 4 min after every 75 km. How long did it take to reach its destination 600 km from the starting point ?	Select the correct option
A) 8 hrs 29 min	B) 6 hrs 28 min	C) 2 hrs 28 min	D) 6 hrs 28 min	E) 1 hrs 28 min

Solution: Explanation:   Time taken to cover 600 km = 600/100= 
600/100 = 6
6 hrs.   Number of stoppages= 600/75 - 1= 
600/75 - 1 = 7
7   Total time of stoppages= 4 x 7 = 28 min   Hence, total time taken = 6 hrs 28 min.   Answer: 6 hrs 28 min
Answer: D
Running at the same rate, 8 identical machines can produce 560 paperclips a minute. At this rate, how many paperclips could 12 machines produce in 6 minutes?	Choose the correct choice from the following answers:  A) 1344  B) 3360  C) 8400  D) 5040  E) 67200

Solution: 8 machines produce 560 in 1 min   8 machines produce 560* 6 in 6 min   12 machine produce 560*6*(12/8) in 6 minutes     560*6*12/8= 
  560*6*12/8 = 5_040
5040 answer is 5040.
Answer: D
In a rectangular axis system, what is the area of a parallelogram with the coordinates: (1,3), (5,3), (2,6), (6,6) ?
Choose the correct answer:
A) 21. B) 12. C) 35. D) 49. E) 52.

Solution: Delta x will give us the dimension of one side of the parallelogram = 5-1= 
5-1 = 4
4 unit   Delta y will give us the dimension of the other side of parallelogram= 6-3= 
6-3 = 3
3 unit   Area of parallelogram= 4*3= 
4*3 = 12
12   ANSWER IS 12.
Answer: B
John Purchased 1365 large bottles at $1.89 per bottle and 720 small bottles at $1.42 per bottle. What was the approximate average price paid per bottle?	Choose the correct choice from the following options: A) $1.63 B) $1.64 C) $1.68 D) $1.73 E) $1.76

Solution: (1365*1.89+720*1.42)/(1365+720) =~1.73   Option ($1.73)
Answer: D
One week, a certain truck rental lot had a total of 20 trucks, all of which were on the lot Monday morning. If 50% of the trucks that were rented out during the week were returned to the lot on or before Saturday morning of that week, and if there were at least 16 trucks on the lot that Saturday morning, what is the greatest number of different trucks that could have been rented out during the week?
Choose the correct choice from the following answers:
A) 18  B) 16  C) 12  D) 14  E) 8

Solution: N - Not rented trucks; R - Rented trucks   N + R = 20   N + R/2 = 16   R = 8   8
Answer: E
Find the average of first 18 natural numbers.  Choices:
A) 9.5
B) 19.5
C) 171
D) 18
E) 5.9

Solution: Explanation:   Sum of first n natural numbers = n(n+1)/2   Hence, sum of first 18 natural numbers = (18 x 19)/2 = 171   Therefore, required average of = 171/18= 
171/18 = 19/2 = around 9.5
9.5   9.5NSWER: 9.5
Answer: A
The sum of the present ages of two persons A and B is 60. If the age of A is twice that of B, find the sum of their ages 5 years hence?
Choose the correct choice from the following answers:  A) 87  B) 27  C) 70  D) 27  E) 20

Solution: A + B = 60, A = 2B   2B + B = 60 => B = 20 then A = 40.   5 years, their ages will be 45 and 25.   Sum of their ages = 45 + 25= 
45 + 25 = 70
70.   Answer:70
Answer: C
Ratio of the earnings of A and B is 4:7. If the earnings of A increases by 50% and those of B decreased by 25%, the new ratio of their earnings becomes 8:7. What are A's earnings?  Answers.
A) 8:6 B) 8:9 C) 8:3 D) 8:7 E) 8:1

Solution: Let the original earnings of A and B be Rs. 4x and Rs. 7x.   New earnings of A = 150% 0f Rs. 4x = (150/100 * 4x) = Rs. 6x   New earnings of B = 75% of Rs. 7x = (75/100 * 7x) = Rs. 21x/4   6x:21x/4 = 8:7   This does not give x. So, the given data is inadequate.   Answer: 8:7
Answer: D
A man buys a cycle for Rs. 1400 and sells it at a loss of 25%. What is the selling price of the cycle? Select the correct option.
A) s. 1090  B) s. 1160  C) s. 1190  D) s. 1202  E) s. 1050

Solution: S.P. = 75% of Rs. 1400 = Rs.75/100x 1400	= Rs. 1050   ANSWs. 1050R :s. 1050
Answer: E
A set of books costs the merchant $500. At what price would the merchant be sold the set of books if he got loss of 5% ?  Select:	A) $475	B) $480	C) $485	D) $495	E) None of these

Solution: Cost Price = $500   Loss % = 5   Selling Price = ?   Selling Price = (100 - loss %) * Cost Price /100   = (100 - 5) * 500 / 100= 
(100 - 5) * 500 / 100 = 475
475   $475nswer is $475
Answer: A
In how many ways can a cricket eleven be chosen out of a batch of 15 players.
Answers:
A) 1365
B) 1500
C) 1406
D) 1879
E) 2000

Solution: Required number of ways   = 15C 11 = 15C (15-11)   = 15 C 4   15C4 = 15 * 14 * 13 * 12 / 4 * 3 * 2 *1   = 1365   1365NSWER 1365
Answer: A
A train running at the speed of 180 km/hr crosses a pole in 9 seconds. Find the length of the train.
Choose the correct option:
A) 150 meter  B) 286 meter  C) 186 meter  D) 288 meter  E) 450 meter

Solution: Speed = 180*(5/18) m/sec   = 50 m/sec   Length of Train (Distance)   = Speed * Time     (50) * 9= 
  (50) * 9 = 450
450 meter   Answer:450 meter
Answer: E
In a bag containing 3balls, a white ball was placed and then 1ball was taken out at random. What isthe probability that theextracted ball would turn on to be white, if all possible hypothesis concerning the color of the balls that initially in the bag were equally possible ?  Choose one.
A) 2/3 B) 5/8 C) 3/5 D) 4/7 E) 5/8

Solution: Since, all possible hypothesis regarding the colour of the balls are equally likely, therefore these could be 3 white balls, initially in the bag.   ∴ Required probability = 1/4 [1 + 3/4 + 1/2 + 1/4]   = 1/4 [(4 + 3 + 2 + 1)/4] = 5/8   5/8
Answer: B
A and B can do a piece of work in 30 days, while B and C can do the same work in 24 days and C and A in 20 days. They all work together for 10 days when B and C leave. How many days more will A take to finish the work? Choose one
A) 18 days	B) 24 days	C) 30 days	D) 36 days	E) 35 days

Solution: Explanation:   2(A + B + C)'s 1 day's work =(1/30 +1/24+1/20)=15/120=1/8   Work done by A, B, C in 10 days =10/6=5/8.   A's 1 day's work =(1/16 - 1/24)=1/48   Now,	1/48 work is done by A in 1 day   So,	3/8 work will be done by A in (48 X 3/8)= 18 days.   18 daysNSWER IS 18 days
Answer: A
A man in a train travelling at 25km/hr notices that a train going in the opposite direction passes him in 7 sec.If the length of this train is 180m find its speed . Choose the correct answer:  A) 30 km/hr  B) 40 km/hr  C) 50 km/hr  D) 68 km/hr  E) 70 km/hr

Solution: relative speed of trains = 180/7 mtrs/sec = 180*18/(7*5)= 93 km/hr   speed of 2nd train = 93-25= 
93-25 = 68
68 km/hr   ANSWER:68 km/hr
Answer: D
7 persons a, b, c, d, e, f and g are to be lined up in a row. If a, b, and c adhere always together, how many possible cases are there?  Choose the correct option:
A) 24 B) 36 C) 480 D) 720 E) 2880

Solution: firstly it is not GEOMETRY but COMBINATIONS, so changing the TAG accordingly..   total 7 are there..   take a,b, and c as one,so total =5..   these 5 can be arranged in 5! ways..   a,b, and c can be arranged within themselves in 3! ways ..   TOTAL = 5!*3!=720   720
Answer: D
A student is mixing oil and water as part of an experiment. The student's mixture has a 5:3 oil to water ratio. If the student used 12 more units of oil than water, how many units of water were used?
Choose the most appropriate option:
A) 14
B) 18
C) 19
D) 22
E) 24

Solution: Let 5u and 3u be the units of oil and water, respectively   5u - 3u = 12   2u = 12 => u = 6   Water => 3u = 18   Answer: 18
Answer: B
The number of the members of a club is more than 20 and less than 50. When 4 people sit at a table, other people exactly divided to 6-people groups (6 people sit at a table) or 7-people groups (7 people sit at a table). If the members are divided to 8-people groups, how many people will be left?  Choose the correct choice from the following choices.
A) 3  B) 4  C) 5  D) 6  E) 7

Solution: The number of members is 7k+4 = 6j+4   The only number in this range which satisfies this is 46.   46/8 = 5(8) + 6   The answer is 6.
Answer: D
If the sum of two numbers is 18 and the sum of their squares is 180, then the product of the numbers is  Choose the correct choice from the following options:
A) 72
B) 44
C) 80
D) 88
E) 48

Solution: according to the given conditions x+y = 18   and x^2+y^2 = 180   now (x+y)^2 = x^2+y^2+2xy   so 18^2 = 180 + 2xy   so xy = 144/2= 
144/2 = 72
72   72NSWER:72
Answer: A
A man can swim in still water at 12 km/h, but takes twice as long to swim upstream than downstream. The speed of the stream is?	Choose one:
A) 4
B) 5
C) 3
D) 2
E) 8

Solution: M = 12   S = x   DS = 12 + x   US = 12 - x   12 + x = (12 - x)2   12 + x = 24 -2x   3x = 24   x = 4   4nswer:4
Answer: A
In a container of vegetables there are 25% potatoes, 40% onions and the rest are tomatoes. If there are 200 kgs vegetables in the container, how many tomatoes are there in the container? Choose the most appropriate option
A) 70 kg  B) 58 kg  C) 110 kg  D) 85 kg  E) 65 kg

Solution: Explanation :   100% of Vegetables = 200 kgs   Tomatos = 100% (25% + 40%) = 100% 65% = 35%   Therefore 35% = 200 X 35/100 = 70 Kgs   70 kgnswer : 70 kg
Answer: A
The cost of 8 gel pens and 12 ball pens is Rs.82. What would be the cost of 36 gel pens and 54 ball pens?  Choices:  A) Rs.366  B) Rs.365  C) Rs.369  D) Rs.364  E) None of these

Solution: Explanation:   From the given statement we have,   The cost of 4 gel pens + 6 ball pens = Rs.41.   Multiplying each terms by 9, we get   The cost of 36 gel pens + 54 ball pens = Rs.369   Answer: Option Rs.369
Answer: C
The numerator of a certain fraction is 8 less than the denominator. If 3 is added to the numerator and 3 is subtracted from the denominator, the fraction becomes 3/4. Find the original fraction?  Choose the correct answer:
A) 3/16	B) 3/28	C) 3/11	D) 3/19	E) 3/29

Solution: The denominator be P, the numerator will be (P - 8).   The fraction will be (P - 8)/P.   Adding 3 to the numerator and subtracting 3 from the denominator, (P - 8 + 3)/(P - 3) = 3/4.   (P - 5)/(P - 3) = 3/4   P = 20 - 9 => P = 11.   The fraction is: 3/11.   Answer:3/11
Answer: C
A 280 metres long train running at the speed of 120 kmph crosses another train running in opposite direction at the speed of 80 kmph in 9 seconds. What is the length of the other train?
Choose the correct choice from the following choices:
A) 220 m
B) 240 m
C) 260 m
D) 320 m
E) 330 m

Solution: Relative speed = (120 + 80) km/hr   =	(200 x(5/18))m/sec   =	(500/9)m/sec.   Let the length of the other train be x metres.   Then,	(x + 280)/9 = 500/9   x + 280 = 500   x = 220.   220 m
Answer: A
A man on tour travels first 160 km at 64 km/hr and the next 160 km at 80 km/hr. The average speed for the first 320 km of the tour is:
Choose the most appropriate option
A) 35.55 km/hr B) 36 km/hr C) 71.11 km/hr D) 71 km/hr E) 81 km/hr

Solution: Total time taken =(160/64 + 160/80) hrs. =	9/2 hrs.   Average speed =(320 x 2/9) km/hr = 71.11 km/hr.   Answer:71.11 km/hr
Answer: C
A tap can fill a tank in 6 hours. After half the tank is filled, three more similar taps are opened. What is the total time taken to fill the tank completely?
Choose the correct choice: A) 3 hrs 25 min B) 3 hrs 45 min C) 3 hrs 48 min D) 3 hrs 35 min E) 2 hrs 45 min

Solution: Explanation:   Time taken by one tap to fill half of the tank = 3 hrs.   Part filled by the four taps in 1 hour ={\color{Black} \left ( 4\times \frac{1}{6} \right )=\frac{2}{3}}   Remaining part ={\color{Black} \left ( 1- \frac{1}{2} \right )=\frac{1}{2}}   {\color{Black} \therefore \frac{2}{3}:\frac{1}{2} ::1:x}   {\color{Black} \Rightarrow x=\left ( \frac{1}{2} \times 1\times \frac{3}{2}\right )=\frac{3}{4}}   So, total time taken = 3 hrs. 45 mins.   Answer: 3 hrs 45 min) 3 hrs 45 min
Answer: B
When average age of 23 members are 0, how many members greater than 0?
Pick one
A) 17	B) 22	C) 21	D) 24	E) 25

Solution: Average of 23 numbers = 0.   Sum of 23 numbers (0 x 23) = 0.   It is quite possible that 22 of these numbers may be positive and if their sum is a then 23rd number is (-a)   Answer is 22 (22)
Answer: B
If 2*f(x) - f(1/x) = x2x2 , then f(x) is?	Choose the most appropriate option
A) f(x) = 3{2*x2x2 + (1x)2(1x)9 }	B) f(x) = 3{2*x2x2 + (1x)2(1x)2 }	C) f(x) = 3{2*x2x2 + (1x)2(1x)3 }	D) f(x) = 3{2*x2x2 + (1x)2(1x)4 }	E) f(x) = 3{2*x2x2 + (1x)2(1x)1 }

Solution: 2*f(x) - f(1/x) = x2x2 ..............(1)   Take x = (1/x),   2*(1/x) - f(x) = (1x)2(1x)2 ...............(2)   Add: 2 (equation 1) + equation 2   3*f(x) = 2*x2x2+ (1x)2(1x)2   f(x) = {2*x2x2 + (1x)2(1x)2}/3   Answer:f(x) = 3{2*x2x2 + (1x)2(1x)2 }
Answer: B