MU-NLPC/Calc-aqua_rat huggingface dataset:
A three-digit code for certain locks uses the digits 0, 1, 2, 3, 4, 5, 6, 7, 8, 9 according to the following constraints. The first digit cannot be 0 , 1 or 3, the second digit must be 0 or 1, and the second and third digits cannot both be 0 in the same code. How many different codes are possible?	Choose the correct choice from the following answers.
A) 144 B) 142 C) 160 D) 168 E) 176

Solution: The first digit can be filled in 8 ways   For second digit , it can either be 0 or 1 or 3   Case 1 -   If second digit is 1 ,Third digit can take 10 values   number of codes = 7 * 1 * 10= 
7 * 1 * 10 = 70
70   Case 2 -   If second digit is 0,Third digit can take 9 values ( Third digit can't be zero)   number of codes= 8 * 1 * 9= 
8 * 1 * 9 = 72
72   Total number of codes= 142   Answer 142
Answer: B
Donald has five different kinds of fruit to choose from at the grocery store. How many ways can he buy one or more types of fruit?	Choose the correct choice from the following choices
A) 125  B) 54  C) 43  D) 31  E) 29

Solution: 31onald needs to buy one or more types of fruit out of five types   => 2^5 - 1 = 31
Answer: D
What is the unit digit in (4137)^754?  Select.
A) 9  B) 11  C) 12  D) 13  E) 15

Solution: Unit digit in (4137)754 = Unit digit in {[(4137)4]188 x (4137)2}   =Unit digit in { 292915317923361 x 17114769 }   = (1 x 9) = 9   9)
Answer: A
The average of five numbers is 27. If one number is excluded, the average becomes 25. The excluded number is? Select the correct option.
A) 12 B) 72 C) 23 D) 35 E) 28

Solution: Excluded number = (27 * 5) - (25 * 4)   = 135 - 100= 
135 - 100 = 35
35.   Answer: 35
Answer: D
A rectangular football field is fenced on all four sides. The length of the football field is 3 times the length of its breadth. The cost of fencing the field was $360. The football management has decided to change the dimensions of field by increasing the breadth by 50% of its original value and reducing the length by 25% of its original value and fence the field again.. What will be the cost of the new fencing?
Choose the correct choice from the following choices:
A) $360  B) $180  C) $425  D) $337.5  E) $415

Solution: Let's take x to be the breadth. Then the length of the football field is 3x.   The perimeter of the old football field is x + 3x + x + 3x = 8x.   Now, for the new football field:   The new breadth = 1.5 times old breadth = 1.5x   The new length is 0.75 times old length = (.75)3x = 2.25x   So the new perimeter is 1.5x + 2.25x + 1.5x + 2.25x = 7.5 x.   for old perimeter rate is $360   For new perimeter  1.5  + 2.25  + 1.5  + 2.25= 
 1.5  + 2.25  + 1.5  + 2.25 = 7.5
7.5 x.   for old perimeter rate is $360   For new perimeter= (360 * 7.5)/8= 
(360 * 7.5)/8 = 337.5
337.5   Ans - $337.5
Answer: D
Two trains running in opposite directions cross a man standing on the platform in 27 seconds and 17 seconds respectively and they cross each other in 23 seconds. The ratio of their speeds is:	Choose the correct choice from the following answers
A) 3 : 1	B) 3 : 2	C) 3 : 4	D) 3 : 5	E) 3 : 28

Solution: Let the speeds of the two trains be x m/sec and y m/sec respectively. Then, length of the first train = 27 x meters, and length of the second train = 17 y meters. (27 x + 17 y) / (x + y) = 23 ==> 27 x + 17 y = 23 x + 23 y ==> 4 x = 6 y ==> x/y = 3/2.   Answer: 3 : 2
Answer: B
REDO’s manufacturing costs for sets of horseshoes include a $10,000 initial outlay, and $20 per set. They can sell the sets $50. If profit is revenue from sales minus manufacturing costs, and the company producessells 500 sets of horseshoes, what was their profit?	Choose one:
A) $4500  B) $3500  C) $5500  D) $5000  E) $6300

Solution: Total Manufacturing cost = 10000+500*20= 
10000+500*20 = 20_000
20000   Total Selling cost= 500*50= 
500*50 = 25_000
25000   Profit= 25000-20000= 
25000-20000 = 5_000
5000   Answer : $5000
Answer: D
A trader sells 80 meters of cloth for Rs. 6900 at the profit of Rs. 20 per metre of cloth. What is the cost price of one metre of cloth? Pick one
A) 22  B) 75  C) 90  D) 78  E) 66

Solution: SP of 1m of cloth = 6900/80 = Rs. 86   CP of 1m of cloth = SP of 1m of cloth - profit on 1m of cloth   = Rs. 86 - Rs. 20 = Rs. 66.   Answer: 66
Answer: E
Which smallest prime number is:
Select the correct option.
A) 22 B) 28 C) 32 D) 42 E) 19

Solution: 19   19
Answer: E
The average age of 8 men increases by 2 years when two women are included in place of two men of ages 20 and 24 years. Find the average age of the women?	Select.
A) 30 B) 35 C) 32 D) 40 E) 46

Solution: 20 + 24 + 8 * 2= 
20 + 24 + 8 * 2 = 60
60/2= 
60/2 = 30
30   30NSWER 30
Answer: A
A dealer offers a cash discount of 10% and still makes a profit of 20% when he further allows 45 articles to be sold at the cost price of 40 articles to a particular sticky bargainer. How much percent above the cost price were his articles listed?  Choose the correct choice from the following options:
A) 40%
B) 50%
C) 55%
D) 80%
E) 90%

Solution: Given   Cash Discount - 10%   Profit - 20%   Items Sold - 45   Price Sold at = List Price of 40   Assume List price = $10   Total Invoice = $400   -10% Cash Discount = $360   Let cost price of 45 items be x   So total cost = 45*x   Given the shopkeeper had a profit of 20%   45 * x * 120/100 = 360   or x = $20/3=$6+(2/3)   Which means his products were listed at $10 which is a 50% markup over $6+(2/3)   Answer 50%
Answer: B
s(n) is a n-digit number formed by attaching the first n perfect squares, in order, into one integer. For example, s(1) = 1, s(2) = 14, s(3) = 149, s(4) = 14916, s(5) = 1491625, etc. How many digits R are in s(99)? Choose one.
A) R=350  B) R=353  C) R=354  D) R=356  E) 357

Solution: Focus on the points where the number of digits in squares change:   1, 2, 3 - Single digit squares. First 2 digit number is 10.   4 , 5,...9 - Two digit squares. To get 9, the last number with two digit square, think that first 3 digit number is 100 which is 10^2. so 9^2 must be the last 2 digit square.   10, 11, 12, ... 31 - Three digit squares. To get 31, think of 1000 - the first 4 digit number. It is not a perfect square but 900 is 30^2. 32^2 = 2^10 = 1024, the first 4 digit square.   32 - 99 - Four digit squares. To get 99, think of 10,000 - the first 5 digit number which is 100^2.   So number of digits in s(99) = 3*1 + 6*2 + 22*3 + 68*4 = 3 + 12 + 66 + 272 =R= 353.R=353
Answer: B
Two equal containers are filled with a mixture of water and petrol. One of them contains three times as much petrol as in the other. The mixtures in the two containers are then mixed and it is found that the ratio of water to petrol is 3: 2: Find the ratio of water to petrol in each of the original containers. Choose one:
A) 2:1, 3:4
B) 1:3, 1:2
C) 2: 3, 4: 1
D) 2: 5, 4: 1
E) None of the above

Solution: In the new mixture, water : petrol = 3 : 2 = 12 : 8   => The capacity of each container =(12 + 8)/2= 
(12 + 8)/2 = 10
10 units= >The ratios of water to petrol of the containers are 4 : 6 and 8 : 2   = 2 : 3 and 4 : 1   ANSWER:2: 3, 4: 1
Answer: C
Some scientists take their boat, the Vollert, out to an artificial reef they are studying. Nice weather on the way out means they can travel at 12 knots, but a storm blows in and they can only travel at 5 knots on the way home. What was their average speed for the whole trip?	Choose the correct choice from the following answers
A) 6 knots  B) 2.5 knots  C) 17 knots  D) 7 knots  E) 8.5 knots

Solution: (12 knots +5 knots)/2 = 8.5 knots   Correct option is: 8.5 knots
Answer: E
John was thrice as old as Tom 6 years ago. John will be 9/7 times as old as Tom in 6 years. How old is Tom today? Choose the correct choice:	A) 6	B) 8	C) 10	D) 12	E) 14

Solution: J-6 = 3(T-6), so J = 3T-12   J+6 = 9/7 * (T+6)   7J + 42 = 9T + 54   7(3T-12) + 42 = 9T + 54   12T = 96   T = 8   The answer is 8.
Answer: B
Calculate the time it will take for a full tank to become completely empty due to a leak given that
the tank could be filled in 7 hours, but due to the leak in its bottom it takes 8 hours to be filled ?  Choose one:
A) 59 hours
B) 54 hours
C) 59 hours
D) 56 hours
E) 26 hours

Solution: Part filled without leak in 1 hour = 1/7   Part filled with leak in 1 hour = 1/8   Work done by leak in 1 hour   =1/7âˆ’1/8=56 hours   Answer:56 hours
Answer: D
Which greatest possible length can be used to measure exactly 12 meter 34 cm, 8 meter 98 cm and 6 meter 65 cm	Select the correct option.
A) 1cm B) 2cm C) 24cm D) 55cm E) 50cm

Solution: Explanation:   Convert first all terms into cm.   i.e. 1234 cm, 898cm, 665cm.   Now whenever we need to calculate this type of question, we need to find the HCF. HCF of above terms is 1.   Option 1cm
Answer: A
In a bag contains 8 White balls and 6 black balls from the bag two balls are taken out at random. Find the Probability that they are of the same color ?  Pick one.
A) 43/91
B) 45/91
C) 52/91
D) 61/91
E) 47/91

Solution: Here S be the sample space so,   n(S) = Number of ways of taken out balls of (8+6)= 
(8+6) = 14
14C2= (14X13)/(2X1)   = 182/2= 
182/2 = 91
91   E= Event of getting both balls of the same color   Then,n (E) = Number of ways of drawing (2 balls out of 8) or (2 balls out of 6)   = (8C2 + 6C2) = 8 x 7/2 x1 + 6x5/2x1 = 56 /2 + 30/2 = 28 +15= 
28 +15 = 43
43   P(E)= n(E) / n(S) = 43/91   43/91nswer is 43/91
Answer: A
If the square of a Positive Number X is equal to five times the same Number then what is the value of X? Choose the correct option:
A) 1
B) 25
C) 8
D) 5
E) 10

Solution: X * X = 5X   X = 5   so the correct answer is option 5
Answer: D
A, B and C enter into partnership. A invests some money at the beginning, B invests double the amount after 6 months, and C invests thrice the amount after 8 months. If the annual gain be Rs.24000. A's share is?	Options
A) s.7500  B) s.8000  C) s.6000  D) s.5750  E) s.6750

Solution: x* 12 : 2x* 6: 3x* 4   1:1:1   1/3 * 24000= 
1/3 * 24000 = 8_000
8000   ANSWER:s.8000
Answer: B
If 1535/ 1038 = a+1/[b+1/{c+(d+1/e)}]. Find a*b*c*d*e? Choose the correct choice:
A) 165/2
B) 175/2
C) 178/3
D) 187 by 2
E) 197/2

Solution: by expanding 1535/1038 make form like a+1/[b+1/{c+(d+1/e)}   =1+(497/1038) now a=1   =1+{1/(1038/497)}   =1+{1/ (2+42/497)}   =1+{1/(2+1/(497/42)} now b= 2 similarly expand   c=11 d= 1 e=34/8   finally a*b*b*c*d*e   1*2*11*1*34/8   187/2   ANSWER:187 by 2
Answer: D
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? Choices.
A) 11 days	B) 22 days	C) 27 days	D) 12 days	E) 99 days

Solution: 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, A alone can finish the work in 27 days.   Answer : 27 days
Answer: C
If shares of two persons in profits are Rs.1600 and Rs.1200 then ratio of their capitals is Choose the correct choice from the following choices: A) 3:4 B) 2:3 C) 4:3 D) 1:3 E) 1:2

Solution: profit=time*capital   so 1600:1200=4:3   ANSWER:4:3
Answer: C
The diagonals of a rhombus are 15 cm and 20 cm. Find its area?	Choose the correct choice from the following answers.
A) 176	B) 190	C) 150	D) 278	E) 292

Solution: 1/2 * 15 * 20= 
1/2 * 15 * 20 = 150
150   Answer:150
Answer: C
The sum of the two digits of a number is 10. If the number is subtracted from the number obtained by reversing its digits, the result is 54. Find the number?	Choices
A) 13 B) 28 C) 12 D) 45 E) 21

Solution: Answer: Option B   any two digit number can be written as (10P + Q), where P is the digit in the tens place and Q is the digit in the units place.   P + Q = 10 ----- (1)   (10Q + P) - (10P + Q) = 54   9(Q - P) = 54   (Q - P) = 6 ----- (2)   Solve (1) and (2) P = 2 and Q = 8   The required number is = 28
Answer: B
The C.P of 15 books is equal to the S.P of 18 books. Find his gain% or loss%?	Choose the correct choice from the following options:
A) 16 2/3% loss	B) 16 7/3% loss	C) 16 2/8% loss	D) 17 2/3% loss	E) 13 2/3% loss

Solution: 15 CP = 18 SP   18 --- 3 CP loss   100 --- ? => 16 2/3% loss   16 2/3% lossnswer: 16 2/3% loss
Answer: A
1,3,5,7,9,....50 find term of sequnce  Choose the correct option:
A) 1000  B) 1200  C) 1300  D) 1800  E) 2500

Solution: This is an arithmetic progression, and we can write down   a=1a=1 ,d=2d=2 , n=50n=50 .   We now use the formula, so that   Sn=12n(2a+(n−1)l)Sn=12n(2a+(n−1)l)   S50=12×50×(2×1+(50−1)×2)S50=12×50×(2×1+(50−1)×2)   =25×(2+49×2)=25×(2+49×2)   =25×(2+98)=25×(2+98)   =2500=2500 .   2500
Answer: E
In how many ways can 5 letters be posted in 3 post boxes, if any number of letters can be posted in all of the three post boxes?
Choose the correct choice.
A) 3^5	B) 2^3	C) 5^3	D) 2	E) 4

Solution: The first letter can be posted in any of the 3 post boxes. Therefore, we have 3 possibilities.   Similarly, the second, the third, the fourth and the fifth letter can each be posted in any of the 3 post boxes.   Each of the 5 letters has 3 possibilities because we can post any number of letters in all of the boxes.   Therefore, the total number of ways the 5 letters can be posted in 3 boxes is   3 * 3 * 3 * 3 * 3 = 3^5.   3^5ns: 3^5
Answer: A
When positive integer n is divided by 5, the remainder is 1. When n is divided by 7, the remainder is 3. What is the smallest positive integer k such that k + n is a multiple of 40.	Select.
A) 3 B) 4 C) 7 D) 32 E) 35

Solution: First, let us say I have a number n which is divisible by 5 and by 7. We all agree that it will be divisible by 35, the LCM of 5 and 7.   Now, if I have a number n which when divided by 5 gives a remainder 1 and when divided by 7 gives a remainder 1, we can say the number is of the form   n = 5a + 1 e.g. 5 + 1, 10 + 1, 15 + 1, 20 + 1, 25 + 1, 30 + 1, 35 + 1 etc   and   n = 7b + 1 e.g. 7 + 1, 14 + 1, 21 + 1, 28 + 1, 35 + 1 etc   So when it is divided by the LCM, 35, it will give 1 as remainder (as is apparent above)   Next, if I have a number n which when divided by 5 gives a remainder 1 and when divided by 7 gives a remainder 3, we can say the number is of the form   n = 5a + 1   and   n = 7b + 3   Now, the only thing you should try to understand here is that when n is divided by 5 and if I say the remainder is 1, it is the same as saying the remainder is -4. e.g. When 6 is divided by 5, remainder is 1 because it is 1 more than a multiple of 5. I can also say it is 4 less than the next multiple of 5, can't I? 6 is one more than 5, but 4 less than 10.   Therefore, we can say n = 5x - 4 and n = 7y - 4 (A remainder of 3 when divided by 7 is the same as getting a remainder of -4)   Now this question is exactly like the question above. So when you divide n by 40, remainder will be -4 i.e. n will be 4 less than a multiple of 40. So you must add 7 to n to make it a multiple of 40   7
Answer: C
A train after traveling for 50km meets with an accident and then proceeds at 3/4 of its former speed and arrives at its destination 35 minutes late . Had the accident occurred 24 km farther, it would have reached the destination only 25 minutes late. What is the speed T of the train. Choose the correct choice from the following choices
A) a) 45  B) b) 33  C) c) 48  D) d) 55  E) e) 61

Solution: Let y be the balance distance to be covered and x be the former speed.   A train after traveling for 50km meets with an accident and then proceeds at 3/4 of its former speed and arrives at its destination 35 minutes late   so, y/(3x/4) - y/x = 35/60   4y/3x - y/x = 7/12   y/x(4/3-1)=7/12   y/x*1/3=7/12   y/x=7/4   4y-7x=0 ........ 1   Had the accident occurred 24 km farther, it would have reached the destination only 25 minutes late   so, (y-24)/(3x/4) - (y-24)/x = 25/60   4(y-24)/3x - (y-24)/x = 5/12   (y-24)/x (4/3-1) = 5/12   (y-24)/x *1/3 = 5/12   (y-24)*12 = 3x*5   (y-24)*4 = 5x   4y-5x = 96 ....... 2   eq2 - eq1   2x=96   x=48=T   Ans = c) 48
Answer: C
If the average (arithmetic mean) of a and b is 45 and the average of b and c is 90, what is the value of c âˆ’ a?	Choose the most appropriate option
A) 25  B) 90  C) 100  D) 140  E) It cannot be determined from the information given

Solution: the arithmetic mean of a and b =(a+b)/2=45 -- a+b=90 --1   similarly for b+c=180 --2   subtracting 1 from 2 we have   c-a=90;   ANSWER:90
Answer: B
In a party there are 5 couples. Out of them 5 people are chosen at random. Find the probability that there are at the least two couples?
Choices
A) 5/21
B) 5/28
C) 5/27
D) 5/29
E) 5/25

Solution: Number of ways of (selecting at least two couples among five people selected) =   As remaining person can be any one among three couples left.   Required probability   = (10 * 6)/252 = 5/21   5/21nswer:5/21
Answer: A
The difference of two numbers is 1365. On dividing the larger number by the smaller, we get 6 as quotient and the 15 as remainder. What is the smaller number ? Choose the correct choice from the following options
A) 270
B) 280
C) 290
D) 300
E) 310

Solution: Let the smaller number be x. Then larger number = (x + 1365).   x + 1365 = 6x + 15   5x = 1350   x = 270   Smaller number = 270.   270)
Answer: A
The residents of Town X participated in a survey to determine the number of hours per week each resident spent watching television. The distribution of the results of the survey had a mean of 21 hours and a standard deviation of 7 hours. The number of hours that Pat, a resident of Town X, watched television last week was between 1 and 2 standard deviations below the mean. Which of the following could be the number of hours that Pat watched television last week?
Pick one
A) 30  B) 20  C) 18  D) 12  E) 6

Solution: Given: mean=21 and SD=7   The number of hours that Pat watched television was between 1 and 2 standard deviations below the mean: 1 SD below the mean ismean-1*SD=14 and 2 SD below the mean ismean-2*SD=7 ,so the number of hours that Pat watched television was between 7 and 14 hours.   Answer: 12.
Answer: D
Statement: Unemployment allowance should be given to all unemployed Indian youth above 18 yrs of age.
Assumptions:
1) There are unemployed youth in India who needs monetary support.
2) The government has sufficient funds to provide allowance to all unemployed youth.  Choose the correct choice from the following:  A) Only assumption I is implicit  B) Only assumption II is implicit  C) Either I or II is implicit  D) Neither I nor II is implicit  E) Both I and II are implicit

Solution: I directly follows from the statement and so is implicit. Also, the statement is a suggestion and does not tell about a government policy or its position of funds. So, II is not implicit.   Only assumption I is implicit
Answer: A
In a nationwide poll, N people were interviewed. If 1/6 of them answered yes to question 1, and of those, 1/3 answered yes to question 2, which of the following expressions represents the number of people interviewed who did NOT answer yes to both questions?
Choose the most appropriate option:
A) N/9
B) 8N/9
C) 11N/18
D) 17N/18
E) 31N/36

Solution: The number of people who answered yes to both questions is (1/3)(1/6)N = N/18   The number of people who did not answer yes to both is 1 - N/18 = 17N/18   The answer is 17N/18.
Answer: D
Two persons starting from the same place walk at a rate of 10kmph and 12.5kmph respectively. What time will they take to be 10km apart, if they walk in the same direction?	Choose the most appropriate option
A) 17 hrs	B) 4 hrs	C) 6 hrs	D) 12 hrs	E) 16 hrs

Solution: The relative speed of the boys = 12.5kmph – 10kmph   = 2.5 kmph   Distance between them is 10 km   Time= 10km / 2.5 kmph = 4 hrs   Answer : 4 hrs
Answer: B
A truck driver drove for 2 days. On the second day, he drove 3 hours longer and at an average speed of 15 miles per hour faster than he drove on the first day. If he drove a total of 1,020 miles and spent 21 hours driving during the 2 days, what was his average speed on the first day, in miles per hour?  Choose one:
A) 25
B) 30
C) 35
D) 40
E) 45

Solution: 40ay 1   2t+3=21   t=9   40ay 2   t+3   9+3= 
9+3 = 12
12   9r+12(r+15)=1020   r=40   Answer:40
Answer: D
The number of positive integer solutions for the equation x +y +z + t = 18 is	Pick.
A) 640  B) 780  C) 380  D) 540  E) 680

Solution: The number of positive integer solutions for the equatio fx1+x2+⋯+xn=k   (k-1)C(n-1)- where k is the number and n is number of variable in the equation.   18-1 C 4-1 = 17C3 = 680   Answer : 680
Answer: E
A man rows his boat 90 km downstream and 72 km upstream, taking 3 hours each time. Find the speed of the stream? Choose the correct choice from the following options:
A) 6  B) 5  C) 7  D) 3  E) 2

Solution: Speed downstream = d/t = 90/3= 
90/3 = 30
30 kmph   Speed upstream= d/t = 72/(3)= 
72/(3) = 24
24 kmph   The speed of the stream= (30 - 24)/2= 
(30 - 24)/2 = 3
3 kmph   Answer:3
Answer: D
Pipe A can fill a tank in 20 hrs and pipe B can fill it in 60 hrs. If both the pipes are opened in the empty tank. In how many hours will it be fill quarter of that tank? Choose the correct choice from the following choices.
A) 3 hr 15 mins B) 3 hr 25 mins C) 3 hr 35 mins D) 3 hr 45 mins E) 3 hr 55 mins

Solution: Part filled A in 1 hr= (1/20)   Part filled B in 1 hr= (1/60)   Part filled by (A+B) together in 1 hr=(1/20)+(1/60)=1/15   So, The tank will be full in 15 hrs   Time taken to fill Exact quarter tank = (15) * (1/4) = 3.45 hr= 3 hr 45 mins   Answer : 3 hr 45 mins
Answer: D
A shopkeeper loses 15%,if an article is sold for $102. What should be the selling price of the article to gain 20%? Options
A) $165	B) $174	C) $144	D) $164	E) $183

Solution: C   $144   Given that SP = $102 and loss = 15%   CP = [100(SP)]/(100 - l%) = (100 * 102)/85 = 20 * 6= 
20 * 6 = 120
$120.   To get 20% profit, New SP= [(100 + p%)$144P]/100 = (120 * 120)/100= 
(120 * 120)/100 = 144
$144
Answer: C
If a coin is tossed 5 times what is the probability that it will land either heads 5 times or tails 5 times? Choose the correct answer
A) 1/4	B) 1/8	C) 1/16	D) 1/32	E) 1/64

Solution: The probability of 5 heads is (1/2)^5 = 1/32   The probability of 5 tails is (1/2)^5 = 1/32   The probability of 5 heads or 5 tails is 1/32 + 1/32 = 1/16   The answer is 1/16.
Answer: C
Out of 10 persons working on a project, 4 are graduates. If 3 are selected, what is the probability that there is at least one graduate among them?
Choose the correct choice
A) 5/5
B) 5/3
C) 5/2
D) 5/6
E) 5/9

Solution: P(at least one graduate) = 1 - P(no graduates)   = 1 - 6C1/10C3 = 1 - (6 * 5 * 4)/(10 * 9 * 8)   = 5/6   Answer:5/6
Answer: D
Two trains of length 100 m and 200 m are 100 m apart. They start moving towards each other on parallel tracks, at speeds 54 kmph and 72 kmph. In how much time will the trains cross each other? Answers
A) 57/7 sec B) 80/7 sec C) 20/7 sec D) 60/7 sec E) 65/7 sec

Solution: Explanation:   Relative speed = (54 + 72)* 5/18 = 7 * 5= 
7 * 5 = 35
35 mps.   The time required= d/s = (100 + 100 + 200)/35   = 400/35 = 80/7 sec.   ANSWER IS 80/7 sec
Answer: B
At 6'o clock clock ticks 6 times. The time between first and
last ticks was 30sec. How much time it takes at 9'o clock.  Choices:
A) 60sec
B) 62sec
C) 66sec
D) 48sec
E) 76sec

Solution: At 6'0 clock, clock ticks 6 times.   So, there must be 5 intervals between clock ticks.   Time Between first and last ticks = 30sec   So, 1 interval = 30/5= 
30/5 = 6
6sec   So 6'o clock 5 *6= 
5 *6 = 30
30sec   7'o clock 6 *6= 
6 *6 = 36
36sec   8'o clock 7 *6= 
7 *6 = 42
42sec   9'o clock 8 *6= 
8 *6 = 48
48sec   So, 48sec at 9'o clock.   ANSWER:48sec
Answer: D
The speed of a boat in still water is 20 km/hr and the rate of current is 5 km/hr. The distance travelled downstream in 12 minutes is: Answers: A) 9 B) 5 C) 7 D) 6 E) 51

Solution: Explanation:   Speed downstream = (20+5)= 
(20+5) = 25
25 kmph   Distance travelled= (25*(12/60))= 
(25*(12/60)) = 5
5 km.   ANSWER:5
Answer: B