MU-NLPC/Calc-aqua_rat huggingface dataset:
Three men start together to travel the same way around a circular track of 11 kilometers in circumference. Their speeds are 4, 5 and 8 kilometers per hour respectively. When will they meet at a starting point?  Choose the correct choice from the following choices.
A) 11 hours
B) 12 hours
C) 220 hours
D) 22 hours
E) 24 hours

Solution: Time for one round = 11/4, 11/5, 11/8   LCM of 11/4, 11/5, 11/8 = 11/1= 
11/1 = 11
11   11 hoursNSWER:11 hours
Answer: A
The batting average of a particular batsman is 58 runs in 46 innings. If the difference in his highest and lowest score is 150 runs and his average excluding these two innings is 58 runs, find his highest score.
Choose the correct choice from the following answers.
A) 179  B) 208  C) 210  D) 133  E) 229

Solution: Explanation:   Total runs scored by the batsman = 58*46= 
58*46 = 2_668
2668 runs   Now excluding the two innings the runs scored= 58*44= 
58*44 = 2_552
2552 runs   Hence the runs scored in the two innings= 2668 – 2552 = 116 runs.   Let the highest score be x, hence the lowest score = x – 150   x + (x - 150) = 116   2x = 266   x = 133runs   ANSWER 133
Answer: D
In a certain animal population, for each of the first 3 months of life, the probability that an animal will die during that month is 1/10. For a group of 600 newborn members of the population, approximately how many would be expected to survive the first 3 months of life?
Choose the correct choice from the following:
A) 438
B) 446
C) 452
D) 462
E) 470

Solution: Number of newborns that can die in first month = 1/10 *600= 
1/10 *600 = 60
60   Survived= 540   Number of newborns that can die in second month = 1/10 * 540= 
1/10 * 540 = 54
54   Survived= 486   Number of newborns that can die in third month = 1/10 * 486 = 48   Survived = 438   438nswer:438
Answer: A
Matt is touring a nation in which coins are issued in two amounts, 2¢ and 5¢, which are made of iron and copper, respectively. If Matt has five iron coins and five copper coins, how many different sums from 1¢ to 35¢ can he make with a combination of his coins?
Choose the correct choice from the following answers:
A) 20  B) 21  C) 35  D) 33  E) 31

Solution: The total sum is 5*2 + 5*5= 
5*2 + 5*5 = 35
35¢. If you can make each sum from 1 to 35 (1¢, 2¢, 3¢, ..., 35¢), then the answer would be 35 (maximum possible).   Now, with 2¢ and 5¢ we cannot make 1¢ and 3¢. We also cannot make 32¢ and 34¢ (since total sum is 35¢ we cannot remove 1¢ or 3¢ to get 34¢ or 32¢).   So, out of 35 sums 4 are for sure not possible, so the answer must be   35 - 4= 
  35 - 4 = 31
31 sums or less. Only A fits.   Answer: 31.
Answer: E
The rate of a certain chemical reaction is directly proportional to the square of the concentration of chemical Q present and inversely proportional to the concentration of chemical B present. If the concentration of chemical B is increased by 100 percent, which of the following is closest to the percent change in the concentration of chemical Q required to keep the reaction rate unchanged?	Pick one:	A) 100% decrease	B) 50% decrease	C) 40% decrease	D) 40% increase	E) 50% increase

Solution: Let Q and B be the concentratrations of the individual chemicals.   Rate of chemical reaction = Q^2/B   Since new B is increased by 100%   Rate = Q^2/(2B)   For the rate to be constant, new value of Q should be square root(2)   So new value of Q = 1.414Q   That means Q is increased by 41.4%   Nearest solution is 40% increase
Answer: D
The true discount on a bill of Rs. 2460 is Rs. 360. What is the banker's discount?
Choose the correct choice from the following:  A) Rs. 432  B) Rs. 422  C) Rs. 412  D) Rs. 442  E) None of these

Solution: Explanation :   F = Rs. 2460   TD = Rs. 360   PW = F - TD = 2460 - 360 = Rs. 2100   True Discount is the Simple Interest on the present value for unexpired time   =>Simple Interest on Rs. 2100 for unexpired time = Rs. 360   Banker's Discount is the Simple Interest on the face value of the bill for unexpired time   = Simple Interest on Rs. 2460 for unexpired time   =360/2100 × 2460 = 0.17 × 2460 = Rs. 422 Answer : Option Rs. 422
Answer: B
According to the direction on a can of frozen orange juice concentrate is to be mixed with 3 cans of water to make orange juice . How many 6 - ounce cans of the concentrate are required to prepare 200 6-ounce servings of orange juice?  Options.
A) 25  B) 34  C) 50  D) 67  E) 100

Solution: Orange juice concentrate: water::1:3   total quantity of orange juice = 200*6= 
200*6 = 1_200
1200 oz   so Orange juice concentrate: water :: 300 oz:900 oz   no. of 6 oz can= 300 oz/6 oz = 50   Answer 50, 50 cans
Answer: C
A father said to his son, "I was as old as you are at the present at the time of your birth". If the father's age is 40 years now, the son's age five years back was	Choose one:  A) 14years  B) 15years  C) 17years  D) 18years  E) 19years

Solution: Let the son's present age be x years. Then, (40 - x) = x   2x = 40.   x = 20.   Son's age 5 years back (20 - 5)= 
(20 - 5) = 15
15 years.   15years)
Answer: B
A train running at the speed of 60 km/hr crosses a pole in 9 seconds. What is the length of the train? Select the correct option.
A) 75	B) 161	C) 224	D) 180	E) 150

Solution: Speed=(60 x	5/18) m/sec	=(50/3) m/sec.   Length of the train = (Speed x Time).   Length of the train =(50/3x 9) m = 150 m.   Answer is 150
Answer: E
A train is 360 meter long is running at a speed of 72 km/hour. In what time will it pass a bridge of 140 meter length?  Choose the correct option
A) 65 seconds
B) 46 seconds
C) 25 seconds
D) 97 seconds
E) 26 seconds

Solution: Speed = 72 Km/hr = 72*(5/18) m/sec = 20 m/sec   Total distance = 360+140= 
360+140 = 500
500 meter   Time= Distance/speed   = 500 * (1/20)= 
500 * (1/20) = 25
25 seconds   Answer:25 seconds
Answer: C
It costs $3 for the first 1/3 hour to use the laundry machine at the Laundromat. After the first ¼ hour it costs $12 per hour. If a certain customer uses the laundry machine for 2 hours and 35 minutes, how much will it cost him? Choose the correct choice from the following answers:
A) $30.	B) $31	C) $32.	D) $33.	E) $34.

Solution: 2 hrs 35 min = 155 min   First 20 min ------> $3   Time left is 135 min...   Now, 60 min costs $ 12   1 min costs $ 12/60   155 min costs $  12/60*155= 
 12/60*155 = 31
> $ 31   So, Total cost will be $31 + $3 => $ 34   Hence answer will be $32.31 +  3= 
31 +  3 = 34
> $ 34   Hence answer will be $32.
Answer: C
If the true discount on a certain sum due 6 months hence at 15% is Rs.120. What is the banker's discount on the same sum for the same time and at the same rate?  Options:
A) Rs. 119 B) Rs. 129 C) Rs. 131 D) Rs. 139 E) None

Solution: Solution   Sum Given, T.D =60, B.D = 72   = (B.D x T.D / B. D - T.D)   = Rs.(72x60/72-60)   = Rs.(72 x 60 / 12)   = Rs.(4320/ 12)   = Rs. 360.   Rs. 119nswer Rs. 119
Answer: A
The sum of two consecutive even integers is 26. What are the two numbers?  Select: A) 12-14 B) 13-13 C) 10-16 D) 9-17 E) 8-18

Solution: Let 2n be the first even integer and let 2n + 2 be the second integer   2n + 2n + 2 = 26   4n + 2 = 26   4n + 2 - 2 = 26 - 2   4n = 24   n = 6   So the first even integer is 2n = 2 × 6 = 12 and the second is  12 + 2= 
 12 + 2 = 14
14   correct answer is 12-14)12-14
Answer: A
If 12 men can do a piece of work in 25 hours, in how many hours will 15 men
do it ?
Choose the correct choice from the following choices
A) 20 hours
B) 30 hours
C) 40 hours
D) 50 hours
E) 60 hours

Solution: Let the required number of hours be x. Then,   Less men, More hours	(Indirect Proportion)   15 : 12 : : 25 : x<=>(15 x x) =(12 x 25)<=>(12 x 25)/15 = 20   Hence, 15 men can do it in 60 hours   20 hoursnswer is 20 hours.
Answer: A
A person buys an article at Rs.500. At what price should he sell the article so as to make a profit of 20%?	Choose the correct choice from the following answers
A) 600	B) 2877	C) 208	D) 1882	E) 191

Solution: Explanation:   Cost price = Rs.500   profit = 20% of 500 = Rs.100   Selling price = Cost price + Profit   = 500 + 100= 
500 + 100 = 600
600   600nswer:600
Answer: A
A man gains 20% by selling an article for a certain price. If the sells it at double the price, the percentage of profit will be Choose one:
A) 740%
B) 540%
C) 640%
D) 140%
E) 240%

Solution: Explanation:   Let C.P. = Rs. x.   Then, S.P. = Rs. (12% of x) = Rs. 6x/5   New S.P. = 2 * 6x/5 = Rs. 12x/5   Profit = 12x/5 - x = Rs. 7x/5   Profit = 7x/5 * 1/x * 100 = 140%.   Answer:140%
Answer: D
A man is 28 years older than his son. In two years, his age will be twice the age of his son. What is the present age of his son?	Select the correct option:	A) 23 years	B) 22 years	C) 21 years	D) 20 years	E) 26 years

Solution: Let present age of the son =x years   Then, present age the man =(x+28) years   Given that, in 2 years, man's age will be twice the age of his son   â‡’(x+28)+2=2(x+2)   â‡’x=26   ANSW26 yearsR:26 years
Answer: E
Reena took a loan of Rs. 1200 with simple interest for as many years as the rate of interest. If she paid Rs. 588 as interest at the end of the loan period, what was the rate of interest?
Choose the most appropriate option:
A) 3.6
B) 7
C) 18
D) Cannot be determined
E) None of these

Solution: let rate = R% and time = R years   Then ( 1200 x R x R /100) = 588   => 12R2= 588   => R2= 49   => R= 7   Answer 7
Answer: B
A rectangular grass field is 75 m * 55 m, it has a path of 3.5 m wide all round it on the outside. Find the area of the path and the cost of constructing it at Rs.2 per sq m?
Choose the correct option
A) s.1350
B) s.1327
C) s.1328
D) s.1397
E) s.1918

Solution: Area = (l + b +2d) 2d   = (75 + 55 +3.5 * 2) 2*3.5 => 959   959 * 2 = Rs.1918   Answer: s.1918
Answer: E
If Jack walked 4 miles in 1 hour and 15 minutes, what was his rate of walking in miles per hour? Select the correct option:
A) 3.2	B) 4.5	C) 6	D) 6.25	E) 15

Solution: Distance walked in 1 hour and 15 mins = 4 miles   Speed per hour = Distance/Time = 4/(5/4)= 
4/(5/4) = 16/5 = around 3.2
3.2 miles per hour   3.2nswer 3.2
Answer: A
The ratio between the length and the breadth of a rectangular park is 3 : 2. If a man cycling along the boundary of the park at the speed of 12 km/hr completes one round in 8 minutes, then the area of the park (in sq. m) is
Choose the most appropriate option:
A) 153200 B) 153400 C) 153600 D) 154000 E) 154200

Solution: Perimeter = Distance covered in 8 min. = 12000 x 8 m = 1600 m.   60   Let length = 3x metres and breadth = 2x metres.   Then, 2(3x + 2x) = 1600 or x = 160.   Length = 480 m and Breadth = 320 m.   Area = (480 x 320) m2 = 153600 m2.   153600
Answer: C
If |5x-5| = 150, what is the sum of all the possible values of x?  Choose the correct choice
A) 2
B) -2
C) 6
D) -3
E) 5

Solution: There will be two cases   5x-5= 150 or 5x-5= -150   => x =31 or x= -29   sum of both the values will be  -29 +31= 
 -29 +31 = 2
2   2nswer is 2
Answer: A
Salesperson A's compensation for any week is $360 plus 6 percent of the portion of A's total sales above $1,000 for that week. Salesperson B's compensation for any week is 10 percent of A's total sales for that week. For what amount of total weekly sales would both salepeople earn the same compensation? Choose the correct choice.
A) $21,000  B) $18,000  C) $15,00  D) $ 4,500  E) $15,000

Solution: sometime, setting up an equation is an easy way to go with:   360 + 0.06 (x - 1000) = 0.1 x   x = 15,000   Ans : $15,000
Answer: E
John and Beth each drove from Smallville to Crown City by different routes. John drove an an average speed of 40 miles per hour and completed the trip in 30 minutes. Beth's route was 5 miles longer, and it took her 20 minutes more than John to complete the trip. How many miles per hour was Beth's average speed on this trip?
Select
A) 24  B) 30  C) 48  D) 54  E) 75

Solution: Speed = Distance/Time   Distance for John = Speed * Time = 40 * 1/2= 
40 * 1/2 = 20
20 miles   Distance for 30eth= Distance for John +5 = 20+5= 
20+5 = 25
25 miles   Time taken by 30eth= Time taken by John + (1/3 hour) = 1/2+1/3 = 5/6   Speed of 30eth = D/T = 25/(5/6) = 25*6/5= 
25*6/5 = 30
30 miles per hour   Hence, 30 is the answer.
Answer: B
How many odd prime numbers are there less than 125?
Choose the correct option:
A) 29  B) 34  C) 44  D) 54  E) 64

Solution: Odd prime number less than 125:3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97, 101, 103, 107, 109, 113   There is 29 the odd prime number   29nswer is 29
Answer: A
In a stack of boards at a lumber yard, the 8th board counting from the top of the stack is immediately below the 7th board counting from the bottom of the stack. how many boards are in the stack?	Choose the correct choice from the following answers
A) 18	B) 16	C) 13	D) 34	E) 12

Solution: 1 2 3 ...   ..............8 7 ................. 1   So the number of boards = 8+5= 
8+5 = 13
13   Option: 13
Answer: C
A fruit seller had some oranges. He sells 40% oranges and still has 600 oranges. How many oranges he had originally? Pick.
A) 700 B) 710 C) 1000 D) 730 E) 740

Solution: 60% of oranges = 600   100% of oranges =(600×100)/6=1000   total oranges = 1000   ANSWER : 1000
Answer: C
Calculate how much time could be saved if the train would run at its usual speed, given that it ran at 3/4 of its own speed and got to its destination in 10 hours? Pick:
A) 1.5 hrs	B) 2.5 hrs	C) 3.5 hrs	D) 1.2 hrs	E) 2.9 hrs

Solution: New speed = 3/4 of usual speed   New time = 3/4 of usual time   3/4 of usual time = 10 hrs   Usual time = 10*3/4= 
10*3/4 = 15/2 = around 7.5
7.5 hrs   Time saved= 10-7.5= 
10-7.5 = 2.5
2.5 hrs   Answer is 2.5 hrs
Answer: B
The jogging track in a sports complex is 1000 meters in circumference. Deepak and his wife start from the same point and walk in opposite directions at 20 km/hr and 17 km/hr respectively. They will meet for the first time in?	Select:
A) 50min
B) 40min
C) 35min
D) 37min
E) 20min

Solution: Clearly, the two will meet when they are 1000 m apart   To be   20+17= 
  20+17 = 37
37 km apart, they take 1 hour   To be 1000 m apart, they take   37 * 1000/1000= 
  37 * 1000/1000 = 37
37 min.   Answer is 37min
Answer: D
In a factory, an average of 50 TV's are produced per day for the fist 25days of the months. A few workers fell ill for the next 5days reducing the daily avg for the month to 43 sets/day . The average production per day for day last 5days is ?	Choose the correct choice from the following answers:
A) 20	B) 36	C) 8	D) 50	E) 59

Solution: Production during these 5 days = Total production in a month - production in first 25 days.   = 30 x 43 - 25 x 50   = 40   ∴ Average for last 5 days = 40 / 5= 
40 / 5 = 8
8   8
Answer: C
In how many different ways can five people be seated on a five-seat bench if two of them must sit next to each other?
Choose the correct choice:
A) 24
B) 48
C) 120
D) 240
E) 480

Solution: 5 people can sit in 5! ways.   If 2 of them must sit next to each other, they can sit in 4! ways.   Now, these 2 persons who sit next to each other , can sit in 2! ways.   Therefore, total different ways in which 5 people can sit are 2! x 4! = 48.   Correct answer is 48.
Answer: B
A survey was conducted to find out how many people in a housing colony of 144 residents could swim, dance and drive a car. It was found that the number of people who could not swim was 89, the number of people who could not dance was 100 and that the number of people who could not drive a car was 90. If the number of people who could do at least two of these things, was found to be 37 and the number of people who could do all these things was found to be 6, how many people could not do any of these things? Pick.
A) 35	B) 36	C) 37	D) 39	E) 40

Solution: T=n(A)+n(B)+n(C)-n(Exactly two of the events)-2*n(All 3 Events)+n(None of the events)   T=144   n(A)=T-n(A')=144-89= 
144-89 = 55
55   n(B)=T-n(B')=144-100= 
144-100 = 44
44   n(C)=T-n(C')=144-90= 
144-90 = 54
54   n(Exactly two of the events)=n(At least 2 Events)-n(All 3 Events)=37-6= 
37-6 = 31
31   n(All 3 Events)=6   144=55+44+54-31-2*6+n(None of the events)   n(None of the events)=144-55-44-54+31+12=39   Ans:39
Answer: D
Working alone, Printers X, Y, and Z can do a certain printing job, consisting of a large number of pages, in 12, 20, and 20 hours, respectively. What is the ratio of the time it takes Printer X to do the job, working alone at its rate, to the time it takes Printers Y and Z to do the job, working together at their individual rates? Answers.
A) 4/11	B) 1/2	C) 15/22	D) 10/1	E) 11/4

Solution: P1 takes 12 hrs   Rate for P2P3 together = 1/20 + 1/20 = 1/10   Therefore they take 10   Ratio = 10/1= 
10/1 = 10
10/1
Answer: D
The average weight of 6 person's increases by 3.5 kg when a new person comes in place of one of them weighing 47 kg. What might be the weight of the new person?  Options.
A) 60 kg  B) 75 kg  C) 68 kg  D) 85 kg  E) 90 kg

Solution: Total weight increased = (6 x 3.5) kg = 21 kg.   Weight of new person = (47 + 21)= 
(47 + 21) = 68
68 kg   Option 68 kg
Answer: C
if k is a positive integer greater than 8, which of the following must be divisible by 4? Choose the most appropriate option:
A) k(-1)(k+2)(k+3)
B) k(k-1)(k+3)(k+4)
C) k(k-3)(k+2)(k+4)
D) k(k-3)(k+2)(k+3)
E) k(k+1)(k+3)(k+4)

Solution: D.   For any integer k, D is the only answer choice which will always be divisible by 4.   A product of 4 consecutive integers will always be divisible by 4. Since, none of the answer choices are a product of 4 consecutive integers, we have to ensure at least one of the integers is always a multiple of 4. The best way to do that is to ensure the answer choice isk* [(k-1)OR(k+3)] * [(k-2)OR(k+2)] * [(k-3)OR(k+1)]. (answer k(k-3)(k+2)(k+3))
Answer: D
Sometimes one is mystified at the starting reductions some people make in their price and wonders on what principle the reductions are based. To quote an example three years ago a friend offered me a used typewriter for $1024. A year later he offered me the same for $640 and last year he wanted $400 and now he is willing to sell it to me for $250. But I have decided to buy it when he reduces next time.
If he does a consistent reduction, at what price will he offer the typewriter to me next?	Choose one:
A) $224.25
B) $643.25
C) $156.25
D) $160.25
E) $234.25

Solution: $156.25   $156.25   It is obvious that the seller of the typewriter follows the rule to reduce three-eights of the price at every reduction, and , therefore, after the consistent reduction, the typewriter should be next offered for $156.25.
Answer: C
A train passes a station platform in 36 sec and a man standing on the platform in 20 sec. If the speed of the train is 54 km/hr. What is the length of the platform?	Choose the correct option:
A) 287 m
B) 167 m
C) 167 m
D) 240 m
E) 187 m

Solution: Speed = 54 * 5/18= 
54 * 5/18 = 15
15 m/sec.   Length of the train= 15 * 20= 
15 * 20 = 300
300 m.   Let the length of the platform be x m . Then,   (x + 300)/36= 15 => x   = 240 m.   Answer:240 m
Answer: D
In how many different number of ways 3 boys and 1 girl can sit on a bench?	Choose the correct choice from the following.
A) 700
B) 710
C) 720
D) 730
E) 24

Solution: npn = n!   4p4 = 4 Ã— 3 Ã— 2 Ã— 1 = 24   24
Answer: E
Five years ago, the average age of A, B, C and D was 45 yr. with E joining them now, the average of all the five is 49 yr. How old is E? Choose the correct choice from the following answers:
A) 25 yr	B) 40 yr	C) 45yr	D) 64 yr	E) NOne

Solution: Solution:   Total present age of A, B, C and D,   = (45*4)+(4*5)= 
(45*4)+(4*5) = 200
200 yr;   Total age present age of A, B, C, D and E,= 49*5= 
49*5 = 245
245 yr.   So, age of E= 45 yr.   Answer: Option 45yr
Answer: C
An internet recently hired 8 new network,in addvertisement 20 network already employed.All new network cam from university A.In addition 75%of computer addvertisement came from same university A.what fraction of original 20 network addvertisement came from same univerity A? pls help to solve	Choose the correct choice:
A) 13/20
B) 15/20
C) 14/20
D) 12/20
E) 11/20

Solution: New networks= 8   Already employed networks= 20   Total networks= 28   computer advt. from uni.13/20= 28*(75/100)= 
28*(75/100) = 21
21   out 28 networks 21 came from uni.13/20   among these 21 we know 8 are newly hired   so  21-8= 
 21-8 = 13
13 networks among previously employed networks came from uni.13/20   13/20nswer is : 13/20   13/20NSWER:13/20
Answer: A
The H.C.F. of two numbers is 11 and their L.C.M. is 693. If one of the numbers is 77, find the other. Choose the correct choice:
A) 99  B) 97  C) 95  D) 91  E) 96

Solution: Other number = 11 X 693/77 = 99   99nswer is 99.
Answer: A
John, Karen, and Luke collected cans of vegetables for a food drive. The number of cans that John collected was 1/3 the number of cans that Karen collected and 1/4 the number of cans that Luke collected. The number of cans that Luke collected was what fraction of the total number of cans that John, Karen, and Luke collected? Select the correct option.
A) 1/5	B) 1/3	C) 2/5	D) 1/2	E) 2/3

Solution: John = (1/3)Karen --> Karen = 3(John)   John = 1/4(Luke) --> Luke = 4(John)   Total = 12(John)   Luke/Total = 4/12 = 1/3   Answer: 1/3
Answer: B
8 men and 14 women are working together in a field. After working for 3 days, 5 men and 8 women leave the work. How many more days will be required to complete the work ?
I. 19 men and 12 women together can complete the work in 18 days.
II. 16 men complete two-third of the work in 16 days
III. In a day, the work done by three men is equal to the work done by four women.  Choose the correct choice from the following choices: A) I only B) II only C) III only D) I or II or III E) None of these

Solution: Sol.(d) Clearly, I only gives the answer   Similarly, II only gives the answer   And, III only gives the answer   Answer I or II or III
Answer: D
What is the total gain or loss if a merchant sold two items for Rs.2100 each, and makes a profit of 18% from the first item and a loss of 15% from the second item.	Options:
A) 12.7	B) 3.7	C) 5.7	D) 2.7	E) 1.7

Solution: (18*15)/100= 
(18*15)/100 = 27/10 = around 2.7
2.7%   Answer: 2.7
Answer: D
If Rs. 782 be divided into three parts, proportional to 1/2:2/3:3/4, then the third part is?	Options
A) A)426  B) B)306  C) C)207  D) D)204  E) E)297

Solution: Given ratio   = 1/2:2/3:3/4 = 6:8:9   1st part = 782 * 9/23   = Rs. 306.   Answer:306
Answer: B
Three consecutive even numbers are such that thrice the first number exceeds double the third number by four. What is the third number? Options:
A) 10  B) 12  C) 14  D) 16  E) 18

Solution: Let the three numbers be x, x+2, and x+4.   3x = 2(x+4) + 4   x = 12 and then the third number is x+4 = 16.   The answer is 16.
Answer: D
What is the largest number of infinite lines that intersect at exactly two vertices?
Choose the most appropriate option
A) 3
B) 4
C) 5
D) 6
E) Any number of lines may intersect at exactly two vertices.

Solution: Point where minimum two lines intersect is called a vertex.   So Maximum of 3 lines can intersect at two vertices.   3NSWER:3
Answer: A
A river 2m deep and 45 m wide is flowing at the rate of 2 kmph the amount of water that runs into the sea per minute is?
Answers
A) 3000 M3  B) 4580 M3  C) 18500 M3  D) 4900 M3  E) 4700 M3

Solution: Explanation:   (2000 * 2 * 45)/60= 
(2000 * 2 * 45)/60 = 3_000
3000 M3   3000 M3nswer: Option 3000 M3
Answer: A
A family consists of 2 man, 2 women and 3 transgender. The average age of the man is 67 years, that of the women is 35 years and that of the transgender is 6 years. What is the average age of the family?
Choose the correct answer.
A) 20 1/5	B) 21 2/7	C) 31 5/7	D) 35 4/5	E) 35 7/11

Solution: Required average   = 67 x 2 + 35 x 2 + 6 x 3   2 + 2 + 3   = 134 + 70 + 18   7   =	222   7   = 31 5/7 years   31 5/7
Answer: C
How many seconds will it take for a car that is traveling at a constant rate of 90 miles per hour to travel a distance of 22 yards?	(1 mile = 1,160 yards)	Choose the correct choice from the following answers:
A) 0.8	B) 0.5	C) 1.0	D) 1.1	E) 1.2

Solution: speed = 90 miles/hr = 44 yard/s   distance = 22 yards   time = distance/speed   =22/44= 
22/44 = 1/2 = around 0.5
0.5 sec   ans - 0.5
Answer: B