MU-NLPC/Calc-aqua_rat huggingface dataset:
A and B undertake to do a piece of work for $120. A alone can do it in 4days while B alone can do it in 6days. With the help of C, they finish it in 2days. Find the share of B?  Options:
A) $150	B) $100	C) $200	D) $50	E) $40

Solution: C's 1day work = (1/2)-(1/4 + 1/6) = 1/12   A:B:C= 1/4 : 1/6: 1/12 = 3:2:1   B's share = 120*2/6= 
120*2/6 = 40
$40   Answer is $40
Answer: E
A and B can finish a work in 10 days while A alone can do the same work in 20 days. In how many days B alone will complete the work?  Choose the correct option:
A) 20 days	B) 48 days	C) 98 days	D) 31 days	E) 22 days

Solution: B = 1/10 – 1/20 = 1/20 => 20 days   20 daysnswer: 20 days
Answer: A
It takes ten minutes to fry a steak (five minutes for each side). You are frying the steaks in a pan that can accommodate only two steaks at one time. What is the least amount of time by which you can fry all the three steaks you have?	Choose one
A) 14 Minutes B) 15 Minutes C) 16 Minutes D) 17 Minutes E) 19 Minutes

Solution: Solution:   Fifteen Minutes.   After frying for five minutes, you can take out one steak and put the third one inside while turning the other one inside. After five more minutes, one steak is fried from both sides and you can take it out. Now put in the steak that we removed and turn the other one inside. After five more minutes, they both will also be fried from both sides.   Answer 15 Minutes
Answer: B
A rectangular plot measuring 40 meters by 50 meters is to be enclosed by wire fencing. If the poles of the fence are kept 5 meters apart. How many poles will be needed?  Choose the correct choice from the following choices:
A) 46m
B) 36m
C) 26m
D) 56m
E) 25m

Solution: Perimeter of the plot = 2(40+50) = 180m   no of poles =180/5= 
180/5 = 36
36m   Answer: 36m
Answer: B
There are two circles of different radii. The are of a square is 784 sq cm and its side is twice the radius of the larger circle. The radius of the larger circle is seven - third that of the smaller circle. Find the circumference of the smaller circle.  Choose the correct choice from the following answers.
A) 19∏ cm
B) 10∏ cm
C) 12∏ cm
D) 11∏ cm
E) 13∏ cm

Solution: Explanation:   Let the radii of the larger and the smaller circles be l cm and s cm respectively. Let the side of the square be a cm.   a2 = 784 = (4)(196) = (22).(142)   a = (2)(14) = 28   a = 2l, l = a/2 = 14   l = (7/3)s   Therefore s = (3/7)(l) = 6 Circumference of the smaller circle = 2∏s = 12∏ cm.   Answer: Option 12∏ cm
Answer: C
In a camp, there is a meal for 120 men or 200 children. If 150 children have taken the meal, how many men will be catered to with remaining meal?
Pick one: A) 50 B) 30 C) 40 D) 10 E) 20

Solution: Explanation :   Meal for 200 children = Meal for 120 men   Meal for 1 child = Meal for 120/200 men   Meal for 150 children = Meal for (120×150)/200 men=Meal for 90 men   Total mean available = Meal for 120 men   Renaming meal = Meal for 120 men - Meal for 90 men = Meal for 30 men . Answer : Option 30
Answer: B
Four extra-large sandwiches of exactly the same size were ordered for m students, where m > 7. Three of the sandwiches were evenly divided among the students. Since 4 students did not want any of the fourth sandwich, it was evenly divided among the remaining students. If Carol ate one piece from each of the four sandwiches, the amount of sandwich that she ate would be what fraction of a whole extra-large sandwich? Choose the most appropriate option: A) (6m-21)/[m(m-7)] B) (4m-21)/[m(m-7)] C) (8m-21)/[m(m-5)] D) (10m-21)/[m(m-5)] E) (4m-15)/[m(m-5)]

Solution: Three of the sandwiches were evenly divided among the students   i.e. Amount of Sandwiches with each students = 3/m   Amount of 4th Sandwich with remaining (m-7) students = 1/(m-7)   The amount of Sandwich that carol ate = 3/m + 1/(m-7) = (3m-21+m)/[m(m-7)] = (4m-21)/[m(m-7)]   Answer: (4m-21)/[m(m-7)]
Answer: B
If 2|2 –f| = 5, what is the sum of all the possible values for f ?	Choose the correct choice.
A) 1/2  B) 2  C) 5/2  D) 4  E) 5

Solution: if f<2, then 2-f=5/2; f=-1/2   if f>2 , then f-2=5/2; f=9/2   9/2-1/2=8/2= 
8/2 = 4
4=4
Answer: D
Enrollment in City College in 1980 was 42 percent of enrollment in 1990. What was the percent increase in the college’s enrollment from 1980 to 1990?	Choices:  A) 10%  B) 138.09 %  C) 20%  D) 25%  E) 183 1/3%

Solution: Assume 100 enrollments present in 1990   42 % of 1990 = enrollments on 1980   enrollments on 1980 = 42   % change = (enrollment in 1990 - enrollment in 1980)*100/(enrollment in 1980)   =(100 - 42) *100 / 42   = 5800 / 42   = 138.09 %   Ans - 138.09 %
Answer: B
Company S produces two kinds of stereos: basic and deluxe. Of the stereos produced by Company S last month, 2/3 were basic and the rest were deluxe. If it takes 1.1 as many hours to produce a deluxe stereo as it does to produce a basic stereo, then the number of hours it took to produce the deluxe stereos last month was what fraction of the total number of hours it took to produce all the stereos?  Choose the correct choice from the following.
A) 7/17
B) 14/31
C) 7/15
D) 11/31
E) 1/2

Solution: The easiest way for me is to plug in numbers.   Let the number of basic stereos produced be 40, and number of delux stereos produced be 20. Total of 60 stereos.   If it takes an hour to produce a basic stereo then it will take 1.4 hours to produce a deluxe stereo.   40 basic stereos = 40 hours.   20 delux stereos = 22 hours.   Total hours = 62.   Then the fraction would be 22/62 = 11/31. Therefore answer   11/31.
Answer: D
Two pumps are connected to an empty tank. Pump X fills the tank with water at a constant rate, while pump Y drains water out of the tank at a constant rate. The two pumps finish filling the tank in six times the duration it would take pump X alone to fill the tank. If pump Y alone can empty a whole tank in 48 minutes, then how many minutes does it take pump X alone to fill the tank?
Pick one:
A) 32  B) 34  C) 36  D) 38  E) 40

Solution: Let V be the volume of the tank.   Let R be the rate per minute that pump X fills the tank.   Let T be the time it takes pump X to fill the tank.   The rate at which pump Y empties the tank is V/48 per minute.   (R - V/48)*6T=V=RT.   (R-V/48)*6=R   5R=V/8.   R=V/40.   It takes pump X 40 minutes to fill the tank.   The answer is 40.
Answer: E
A garrison of 400 men had a provision for 31 days. After 28 days 280 persons re-enforcement leave the garrison. Find the number of days for which the remaining ration will be sufficient?  Choose the correct choice from the following answers:
A) 22
B) 28
C) 10
D) 66
E) 23

Solution: 400 --- 31   400 --- 3   120 --- ?   400*3 = 120*x => x =10 days   Answer: 10
Answer: C
Of 32 applicants for a job, 14 had at least 4 years' experience, 18 had degrees, and 7 had less than 4 years' experience and did not have a degree. How many of the applicants had at least 4 years' experience and a degree?
Choose the correct choice from the following answers:
A) 14
B) 13
C) 9
D) 7
E) 5

Solution: set A : people with more than 4 years exp   set B : people with degree   AUB = total - (less than 4 exp and no degree)   AUB = 32-7= 
32-7 = 25
25   AUB= A + B - AiB   AiB = 18+14-25= 
18+14-25 = 7
7   Answer 7
Answer: D
A car covers a certain distance at aspeed of 60 kmph in 5 hours. To cover the same distance in 4 hrs, it must travel at a speed of?	Pick one.
A) 567 km/hr	B) 75 km/hr	C) 782 km/hr	D) 789 km/hr	E) 720 km/hr

Solution: Distance = (60 x 5) = 300 km.   Speed = Distance/Time   Speed = 300/4= 
300/4 = 75
75 kmph   Answer : 75 km/hr
Answer: B
A sports equipment store sold ping pong rackets for a total of $490. If the average (arithmetic mean) price of a pair of rackets is $9.8, how many pairs were sold? Choose the correct choice from the following choices:	A) 50	B) 100	C) 490	D) 500	E) 980

Solution: Average price for a pair of rackets = $9.8   Total cost = $9.8*x = $490   x = 50 pairs were sold.   50NSWER:50
Answer: A
How many seconds will a 300 m long train take to cross a man walking with a speed of 3 km/hr in the direction of the moving train if the speed of the train is 63 km/hr?	Pick one.
A) 12 sec  B) 30 sec  C) 86 sec  D) 15 sec  E) 18 sec

Solution: Speed of train relative to man = 63 - 3= 
63 - 3 = 60
60 km/hr.= 60 * 5/18 = 50/3 m/sec.   Time taken to pass the man = 300 * 3/50= 
300 * 3/50 = 18
18 sec.   Answer: 18 sec
Answer: E
By walking at 4/5 of his usual speed, Mohan is 6 minute late to his office. find his usual time to cover the distance.	Choices
A) 25 minutes B) 23 minutes C) 24 minute D) 26 minute E) None of these

Solution: Here, Change in time = 6 and a/b = 4/5   We have, change in time = (b/a - 1) x original time   => Original time = Change in time/(b/a - 1)   =>6(5/4 - 1) = 24 minute.   ANSWER:24 minute
Answer: C
A farm has only chickens and pigs. When the manager of the farm counted the heads of the animals on the farm, the number totaled up to 50. When the number of legs was counted, the number totaled up to 120. How many more chickens than pigs are there on the farm? Note: Each pig has 4 legs and each chicken had 2 legs.	Answers:
A) 30 B) 32 C) 34 D) 36 E) 38

Solution: Let x be the number of chickens.   Then 50-x is the number of pigs.   2x+4(50-x)=120   2x=80   x=40 (chickens)   50-x=10 (pigs)   There are  40-10= 
 40-10 = 30
30 more chickens on the farm.   The answer is 30.
Answer: A
If the operation ∆ is defined by a ∆ b = (b - a)^2/a^2 for all numbers a and b, and a ≠ 0, then what is the result when we evaluate this expression: (-5) ∆ (5 ∆ −5) ?  Choose the correct choice from the following answers.
A) 49/9
B) 49/16
C) 81/16
D) 81/25
E) 100/81

Solution: (-5) ∆ (5 ∆ −5) =   (-5) ∆ (10^2/5^2) =   (-5) ∆ (4) =   (-9^2) / (-5)^2 = 81/25   The answer is 81/25.
Answer: D
A bag marked at $150 is sold for $120. The rate of discount is?  Choose the correct choice
A) 10%
B) 25%
C) 20%
D) 50%
E) 45%

Solution: Rate of discount = 30/150 * 100= 
30/150 * 100 = 20
20%   Answer is 20%
Answer: C
Arabica coffee costs $0.5 per ounce while Robusta coffee costs $0.4 per ounce. If the blend of Arabica and Robusta costs $0.44 per ounce, what is the share of Arabica in this blend?  Choose the correct choice from the following choices.
A) 20%	B) 24%	C) 30%	D) 33%	E) 40%

Solution: a= amount of arabica coffee   1-a = amount of robusta coffee. because if you subtract a from the 1 ounce, the remaining amount is robusta   therefore:   .5a + .4(1-a) = .44   .5a + .4 - .4a = .44   a= .4   therefore: .4/1 ounce = 40%. Therefore, the answer should be 40%
Answer: E
A family consists of grandparents, parents and three grandchildren. The average age of the grandparents is 67 years, that of the parents is 35 years and that of the grandchildren is 6 years. What is the average age of the family ?  Choose the correct answer:  A) 31( 5/7)  B) 31( 5/9)  C) 31( 5/2)  D) 31( 4/7)  E) 41( 5/7)

Solution: Required average = (67 * 2 + 35 * 2 + 6 * 3) / (2 + 2 + 3)   = (134 + 70 + 18) / 7 = 222 / 7   = 31(5/7) years.   31( 5/7)nswer: 31( 5/7)
Answer: A
A man is walking at a speed of 10 km per hour. After every kilometre, he takes rest for 7 minutes. How much time will be take to cover a distance of 7 kilometres?	Pick:	A) 80 min.	B) 70 min.	C) 84 min.	D) 55 min.	E) None of these

Solution: Rest time = Number of rest Ã— Time for each rest   = 6 Ã— 7 = 42 minutes   Total time to cover 7 km   = (7â„10 Ã— 60)minutes + 42 minutes = 84 minutes   Answer 84 min.
Answer: C
The first year, two cows produced 8100 litres of milk. The second year their production increased by 15% and 10% respectively, and the total amount of milk increased to 9100 litres a year. How many litres were milked from one cow?	Choose the correct choice from the following
A) 2178 lt	B) 3697 lt	C) 6583 lt	D) 4370 lt	E) 5548 lt

Solution: Let x be the amount of milk the first cow produced during the first year. Then the second cow produced (8100−x) litres of milk that year. The second year, each cow produced the same amount of milk as they did the first year plus the increase of 15%15% or 10%   So 8100+15100⋅x+10100⋅(8100−x)=9100   Therefore 8100+320x+110(8100−x)=9100   120x=190   x=3800   Therefore, the cows produced 3800 and 4300 litres of milk the first year, and 4370 and 4730 litres of milk the second year, => one cow produced 4370 litres   correct answer is 4370 lt)4370 lt
Answer: D
Three consecutive odd integers are in increasing order such that the sum of the last two integers is 13 more than the first integer. Find the three integers?  Pick: A) 9, 11, 13 B) 11, 13, 15 C) 13, 15, 17 D) 7, 9, 11 E) None of these

Solution: Let the three consecutive odd integers be x, x + 2 and x + 4 respectively.   x + 4 + x + 2 = x + 13 => x = 7   Hence three consecutive odd integers are 7, 9 and 11.   ANSWER:7, 9, 11
Answer: D
Suzie’s Discount Footwear sells all pairs of shoes for one price and all pairs of boots for another price. On Monday the store sold 22 pairs of shoes and 16 pairs of boots for $508. On Tuesday the store sold 8 pairs of shoes and 32 pairs of boots for $656. How much more do pairs of boots cost than pairs of shoes at Suzie’s Discount Footwear?	Choose the correct choice:	A) 10	B) 12	C) 14	D) 16	E) 8

Solution: Let X be pair of shoes and Y be pair of boots.   22x+16y = 508 ... eq1   8x +32y = 656....eq 2.   Now multiply eq 1 by 2 and sub eq 2.   44x =1016   8x = 656.   36x = 360 => x = 10.   Sub x in eq 2.... we get 80 + 32y = 656... then we get 32y = 576 then y = 18   Differenece between X and Y is 8   Answer : 8
Answer: E
If A speaks the truth 80% of the times, B speaks the truth 60% of the times. What is the probability that at least one will tell the truth  Choose the correct choice from the following:
A) 0.8	B) 0.92	C) 1.02	D) 1.2	E) 1.3

Solution: probability of A speaks truth p(A)=8/10;false=2/10   probability of 0.92 speaks truth p(0.92)=6/10;false=4/10.For given qtn   Ans=1-(neither of them tell truth).0.92ecause A & 0.92 are independent events   =1-[(2/10)*(4/10)]=1-8/10=1-0.08= 
1-0.08 = 0.92
0.92   ANSWER:0.92
Answer: B
A certain sum of money doubles itself in 10 years in how much many years will it trible itself at the same rate?  Choose the correct choice:
A) 20 years  B) 76 years  C) 88 years  D) 44 years  E) 11 years

Solution: 100 ---- 100 --- 10   100 --- 10   --------------------   300 ---- 20 years   20 yearsnswer: 20 years
Answer: A
if deepak has 5 pants and 3 shirts how many combinations can deepak make? Select the correct option:
A) 10
B) 9
C) 15
D) 20
E) 25

Solution: If deepak can only choose one of each, there are   5*3= 
  5*3 = 15
15 possible combinations.   Answer:15
Answer: C
How many possible ways can 1 girls (Rebecca, Kate, Ashley) go on a date with 3 boys (Peter, Kyle, Sam)?  Choose the correct choice from the following.
A) 3	B) 4	C) 5	D) 6	E) 8

Solution: Any one girl can go with 3 boys.   3 (3) is the answer
Answer: A
A painter intends to mixed two jars of paint to create a new color. He chooses one paint jar randomly from a display containing 3 red and 2 blue samples, and a second jar is chosen at random from a different display containing 3 red and 2 blue samples. If he plans on mixing the two chosen jars together, what is the probability that when mixed together, the result will be purple paint? (The color purple is created with 1 part red and 1 part blue.)	Choose the correct choice from the following answers.
A) 1/5  B) 1/2  C) 2/3  D) 4/5  E) 6/5

Solution: Painter has two buckets he has to randomly pick from 2 different lists ... Let these Lists be A and B ... He has to choose the first bucket from List A , and the second bucket from List B   FOR THE FIRST BUCKET ...   Red color - 2   Blue color - 2   FOR THE SECOND BUCKET   Red color - 3   Blue color -2   In order to get Purple he has to mix red with blue .. Both the LISTS contain either blue or red , therefore we have two scenarios :   Scenario I - He picks Red color from List A and Blue color from List B   Scenario II - He picks Blue color from List A and Red color from List B   Scenario I - Odds for red color from List A are 1/2 .. and for Blue color from List B are 2 /5 .. Multiplying them (because we have to find the odds that both colors are selected from their respective lists together (this is a AND not an OR problem) we get 1/5   Scenario II - Odds for blue color from List A are 1/2 , and for Red color from List B are 3/5 ... Multiplying them we get 3/10 ...   Both the scenarios are equally possible therefore we must ADD the two (not multiply ) because both of them do not have to hold true together (have to independently) for our desired result to be achieved ...   We get 1/5 + 3/10 = 2/3 (2/3)
Answer: C
The average weight of a class of 20 boys was calculated to be 58.4 kgs and it was later found that one weight was misread as 56 kg instead of 66 kg. What is the correct weight? Choose the correct choice from the following answers:	A) 58kgs	B) 58.85kgs	C) 58.9kgs	D) 59kgs	E) 59.85kgs

Solution: Actual total weight is (20X 58.4 - 56 + 66) = 1178 Kgs   Actual average weight is   1178/20= 
  1178/20 = 589/10 = around 58.9
58.9kgs   58.9kgs
Answer: C
What is the value of 3x^2 − 1.8x + 0.7 for x = 0.6?
Choose the correct answer.
A) −0.3 B) 0 C) 0.3 D) 0.7 E) 2.46

Solution: 3x^2-1.8x+0.7 for x=0.6   =3(0.6*0.6)-3*0.6*(0.6)+0.7   =0+0.7= 
0+0.7 = 0.7
0.7   ANSWER:0.7
Answer: D
The number of timeshare condos available at Sunset Beach is 3/5 the number of timeshare condos available at Playa del Mar. If the total number of timeshare condos available at the two beaches combined is 400, what is the difference between the number of condos available at Sunset Beach and the number of condos available at Playa del Mar?	Choose the correct choice from the following answers: A) 60 B) 90 C) 120 D) 100 E) 240

Solution: Let x be the number of timeshare condos available at Playa del Mar.   Then number of timeshare condos available at Sunset Beach = 3/5x   We know, x + 3/5 x = 400   Hence, x = 250. So, number of timeshare condos available at Playa del Mar = 250   the difference between the number of condos available at Sunset Beach and the number of condos available at Playa del Mar = x - 3/5x = 2/5x = 2/5(250) = 100   The correct answer is 100
Answer: D
Find the next no.
82, 51, 28, 20, ?	Choices:	A) 10	B) 11	C) 12	D) 13	E) 14

Solution: 82=9^2+1   51=7^2+2   28=5^2+3   20=4^2+4   then next no is   3^2+5=14   ANSW14R:14
Answer: E
If a is a positive integer, then 2^a + 2^(a + 1) + 2^(a + 2)= Choose the most appropriate option:  A) 3^(a + 1)  B) 2^(a + 1)  C) 2a  D) 2a^(a + 1)  E) 7(2^a)

Solution: If a is a positive integer, then 2^a + 2^(a + 1) =   2^a + 2^(a + 1)+2^(a + 2)   2^a(1+2+4)   2^a(7)   E. 7(2^a)
Answer: E
A reduction of 25% in the price of oil enables a house wife to obtain 5kgs more for Rs.600, what is the reduced price for kg? Choose the most appropriate option:
A) 30  B) 60  C) 70  D) 80  E) 20

Solution: 30   600*(25/100)= 
600*(25/100) = 150
150 ---- 5   ? ---- 1=> Rs.30
Answer: A
A is three times as old as B. C was twice-as old as A four years ago. In four years' time, A will be 31. What are the present ages of B and C ?  Choose the correct answer:
A) 9, 46  B) 9, 50  C) 10, 46  D) 10, 50  E) 10, 60

Solution: B = x   A = 3x-4   c = 6x-4   so. given A=3x-4 = 31   after 4 year A=3x = 31 -4= 
31 -4 = 27
27   9, 50= x = 9   c = 6*9 -4= 
6*9 -4 = 50
50   ANSWER:9, 50
Answer: B
A fifth of Arunâ€™s marks in mathematics exceed a third of his marks in English by 20.If he got 260 marks in two subjects together how many marks did he got in English? Pick one.
A) 120,80	B) 180,60	C) 200,60	D) 200,40	E) None of them

Solution: Let Arunâ€™s marks in mathematics and english be x and y   Then (1/5)x-(1/3)y=20   3x-5y=300â€¦â€¦>(1)   x+y=260â€¦â€¦.>(2)   solving (1) and (2)   x=200   and y=60   Answer is 200,60.
Answer: C
Which of the following is closest in value to (9^10)-(9^2)?  Choose the correct choice from the following answers
A) 9^10
B) 9^8
C) 9^7
D) 9^6
E) 9^5

Solution: 9^10 is much larger number than 9^2 and as we need approximate value then it's pretty much negligible in this case, so: (9^10)-(9^2) = ~9^10.   Answer: A.   Similar questions to practice:   Hope it helps.
Answer: A
The arithmetic mean and standard deviation of a certain normal distribution are 15 and 1.5, respectively. What value is exactly 2 standard deviations less than the mean?	Choose the correct choice from the following answers:
A) 10.5 B) 11 C) 11.5 D) 12 E) 12.5

Solution: The value which isexactlytwo SD less than the mean is:mean-2*SD=15-2*1.5= 
15-2*1.5 = 12
12.   Answer: 12.
Answer: D
Set A contains all the even numbers between 10 and 50 inclusive. Set B contains all the even numbers between 110 and 150 inclusive. What is the difference between the sum of elements of set B and the sum of the elements of set A? Choose the correct choice from the following options.
A) 2100
B) 2550
C) 5050
D) 6275
E) 11325

Solution: Set A contains 10, 12,14 , 16 ... 50   Set B contains 110 , 112 , 114 ... 150   Number of terms in each set = 21   Difference between corresponding terms in set 2100 and B = 100   Difference between Sum of set B and set 2100 = 100*21= 
100*21 = 2_100
2100   2100nswer 2100
Answer: A
A bag contains 6 green balls and 8 white balls. If two balls are drawn simultaneously, what is the probability that both balls are the same colour?
Choose the most appropriate option:
A) 5/14	B) 8/21	C) 12/21	D) 43/91	E) 47/91

Solution: The total number of ways to draw two balls is 14C2 = 91   The number of ways to draw two green balls is 6C2 = 15   The number of ways to draw two white balls is 8C2 = 28   P(two balls of the same colour) = 43/91   The answer is 43/91.
Answer: D
A’s speed is 20/16 times that of B. If A and B run a race, what part of the length of the race should A give B as a head start, so that the race ends in a dead heat?	Choose the correct answer:
A) 1/17	B) 3/17	C) 1/10	D) 4/20	E) 3/10

Solution: We have the ratio of A’s speed and B’s speed. This means, we know how much distance A covers compared with B in the same time.   This is what the beginning of the race will look like:   (Start) A_________B______________________________   If A covers 20 meters, B covers 16 meters in that time. So if the race is 20 meters long, when A reaches the finish line, B would be 4 meters behind him. If we want the race to end in a dead heat, we want B to be at the finish line too at the same time. This means B should get a head start of 4 meters so that he doesn’t need to cover that. In that case, the time required by A (to cover 20 meters) would be the same as the time required by B (to cover 16 meters) to reach the finish line.   So B should get a head start of 4/20th of the race.   Answer (4/20)
Answer: D
What is the probability of randomly selecting one of the shortest diagonals from all the diagonals of a regular octagon?
Choose the most appropriate option
A) 1/4
B) 1/3
C) 1/2
D) 2/5
E) 7/8

Solution: From any vertex, there are two vertices on sides, which do not make a diagonal but a side.   So the remaining n-3 vertices make diagonals.   There are 2 of these diagonals which are the shortest.   The probability of choosing one of the shortest diagonals is 2/5.   The answer is 2/5.
Answer: D
In a regular week, there are 5 working days and for each day, the working hours are 8. A man gets Rs. 2.40 per hour for regular work and Rs. 3.20 per hours for overtime. If he earns Rs. 432 in 4 weeks, then how many hours does he work for ?  Choose the correct answer:  A) 223  B) 175  C) 297  D) 267  E) 911

Solution: Explanation:   Suppose the man works overtime for x hours.   Now, working hours in 4 weeks = (5 x 8 x 4) = 160.   {\color{Blue} \therefore } 160 x 2.40 + x x 3.20 = 432   => 3.20x = 432 - 384= 
432 - 384 = 48
48=> x = 15.   Hence, total hours of work = (160 + 15)= 
(160 + 15) = 175
175.   Answer: 175) 175
Answer: B
A boy has Rs. 480 in the denominations of one-rupee notes, five-rupee notes and ten-rupee notes. The number of notes of each denomination is equal. What is the total number of notes that he has ?	Choose the most appropriate option:
A) 90	B) 110	C) 140	D) 130	E) 120

Solution: Let number of notes of each denomination be x.   Then x + 5x + 10x = 480   16x = 480   x = 30.   Hence, total number of notes = 3x = 90.   90
Answer: A