MU-NLPC/Calc-aqua_rat huggingface dataset:
A car travels uphill at 30 km/hr and downhill at 40 km/hr. It goes 100 km uphill and 50 km downhill. Find the average speed of the car?	Options
A) 32kmph B) 33kmph C) 34kmph D) 35kmph E) 36kmph

Solution: avg speed=total distance/total time.   total distance traveled=100+50= 
100+50 = 150
150km;   time taken for uphill journey=100/30=10/3;   time taken for down hill journey=50/40=5/4;   avg speed=150/(10/3+5/4)=33kmph   ANSWER:33kmph
Answer: B
In a certain pond, 80 fish were caught, tagged, and returned to the pond. A few days later, 80 fish were caught again, of which 2 were found to have been tagged. If the percent of tagged fish in the second catch approximates the percent of tagged fish in the pond, what`s the approximate number of fish in the pond?	Options: A) 400 B) 625 C) 1250 D) 3200 E) 10 000

Solution: The percent of tagged fish in the second catch is 2/80*100= 
2/80*100 = 5/2 = around 2.5
2.5%.   We are told that 2.5% approximates the percent of tagged fish in the pond. Since there are 80 tagged fish, then we have 0.025x= 80 --> x = 3,200.   Answer: 3200.
Answer: D
An empty fuel tank to a car was filled with A type of petrol. When the tank was half empty, it was filled with B type of petrol. Again when the tank was half empty, it was filled with A type of petrol. When the tank was half empty again,it was filled  Pick one:
A) 50%	B) 40%	C) 33.5%	D) 37.5%	E) None of these

Solution: Now, amount of petrol A = A⁄4 + A⁄8 = 3A⁄8   ∴ required% = 3A⁄ (8 × A) × 100 = 37.50%   Answer 37.5%
Answer: D
The H.C.F. of two numbers is 23 and the other two factors of their L.C.M. are 10 and 12. The larger of the two numbers is:	Choose the correct answer
A) 276	B) 295	C) 322	D) 345	E) 354

Solution: Clearly, the numbers are (23 x 10) and (23 x 12).   Larger number = (23 x 12) = 276.   276nswer: Option 276
Answer: A
A student has to read one history book of 200 pages and one science book of 300 pages . At the end of first day, if 57 percent of the pages in history book and 42 percent of the pages in science book were read, what percent of the total number of pages were read ?  Choose the correct choice from the following:
A) 45.5%  B) 46.5%  C) 48.0%  D) 49.5%  E) 51.0%

Solution: 57% of 200 pages in history book, hence  0.57*200= 
 0.57*200 = 114
114 pages read.   42% of 300 pages in science book, hence  0.42*300= 
 0.42*300 = 126
126 pages read   Thus (total read)/(total)= (114 + 126)/(200 + 300) = 240/500 =   48% pages read   Answer: 48.0%.
Answer: C
The population of a town is 8000. It decreases annually at the rate of 20% p.a. What will be its population after 2 years?	Choose the most appropriate option: A) 4300 B) 4500 C) 5120 D) 5230 E) 5366

Solution: Formula :   ( After =100 denominator   Ago = 100 numerator)   8000 × 80/100 × 80/100 = 5120   5120
Answer: C
A 1200 m long train crosses a tree in 120 sec, how much time will I take to pass a platform 900 m long?
Choose the correct choice from the following: A) 200 Sec B) 210 Sec C) 167 Sec D) 197 Sec E) 179 Sec

Solution: L = S*T   S= 1200/120= 
1200/120 = 10
10 m/Sec.   Total length (D)= 2100 m   T = D/S   T = 2100/10= 
2100/10 = 210
210 Sec   Answer: 210 Sec
Answer: B
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.
A) 3/7 B) 3/2 C) 3/5 D) 3/6 E) 3/1

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
The base of a parallelogram is twice its height. If the area of the parallelogram is 72 sq. cm, find its height
Choose the correct choice from the following.
A) 6
B) 8
C) 9
D) 9
E) 2

Solution: Explanation:   Let the height of the parallelogram be x. cm. Then, base = (2x) cm.   6nswer: 6) 6
Answer: A
A and B can do a work in 20days, B and C can do it in 30days; A,B and C together can finish it in 40days. A and C together will do it in?
Answers
A) 25days B) 30days C) 20days D) 15days E) 10days

Solution: A+B+C 1day work = 1/40   A+B 1day work + +  1= 
+ +  1 = 1
1/40   A+B 1day work = 1/20   B+C 1day work  +  1= 
 +  1 = 1
1/20   B+C 1day work = 1/30   A+C 1day work  +  1= 
 +  1 = 1
1/30   A+C 1day work= 2*1/40 - 1/20+1/30 = 1/30   A and C together will do the work in 30 days.   Answer is 30days
Answer: B
Which of the following describes all values of x for which 25–x^2 >= 0? Choose the correct choice from the following: A) x >= 1 B) x <= –1 C) 0 <= x <= 1 D) x <= –1 or x >= 1 E) –5 <= x <= 5

Solution: 25 - x^2 >=0   means x^2 - 25 <=0   => (x-5)(x+5) <= 0   => -5 <= x <= 5   Answer - –5 <= x <= 5
Answer: E
A certain company assigns employees to offices in such a way that some of the offices can be empty and more than one employee can be assigned to an office. In how many ways can the company assign 4 employees to 2 different offices? Options: A) 5 B) 16 C) 7 D) 8 E) 9

Solution: Ans. Each employee can go into any of the two offices. Thus we have   => 2 * 2 * 2 * 2= 
2 * 2 * 2 * 2 = 16
16   Answer : 16
Answer: B
At what rate percent on simple interest will Rs.750 amount to Rs.900 in 5 years?  Answers: A) 5 B) 4 C) 5 1/2 D) 7 E) 8

Solution: 150 = (750*5*R)/100   R = 4%   ANSWER 4
Answer: B
The length of a rectangle is increased by 15% and its breadth is decreased by 20%. What is the effect on its area?
Choose the correct choice from the following options:  A) 1288  B) 1299  C) 1000  D) 10000  E) 9200

Solution: 100 * 100= 
100 * 100 = 10_000
10000   115 * 80= 
115 * 80 = 9_200
9200   Answer: 9200
Answer: E
find two integers, neither of which ends in a zero, and whose product is exactly 10,000,000  Choose the correct option
A) 64 and 15,625  B) 60 and 15,625  C) 64 and 15,620  D) 64 and 15,635  E) 128 and 78,125

Solution: 10,000,000=10^7   =10x10x10x10x10x10x10   =(2x5)x(2x5)x(2x5)x(2x5)x(2x5)x(2x5)x(2x5)   =(2^7)x(5^7)   = 128x78125   so the numbers are 128 and 78,125   ANSW128 and 78,125R:128 and 78,125
Answer: E
The prices for five dresses Susan was considering were $60, $125, $80, $70 and $x. If the median price was $5 lower than the average (arithmetic mean) price, which of the following could be $x?	Choose one:	A) $80	B) $85	C) $90	D) $95	E) $100

Solution: Look at the options available   Value of x seems to $80 < = $x < = $100   A. $80   B. $85   C. $90   D. $95   E. $100   So position of $x is fourth   $60 , $70 , $80 , $x , $125   Median = $80   Median price was $5 lower than the average, so average = $85   $60 + $70 + $80 + x + $125 = $425   $x = $90 = Answer = $90
Answer: C
How many minimum number's of whole square slabs are required for paving the floor 12.96 meters long and 3.84 meters side? Choose the most appropriate option:
A) 216  B) 192  C) 108  D) 256  E) 356

Solution: HCF of 384, 1296 = 48   48 * 48 * x = 384 * 1296   x = 216   216NSWER:216
Answer: A
A football player scores 2 goals in his fifth match thus increasing his average goals score by 0.3. The total number of goals in his 5 matches would be	Choose the correct choice
A) 4	B) 6	C) 8	D) 10	E) 12

Solution: While this question can be solved with a rather straight-forward algebra approach (as the other posters have noted), it can also be solved by TESTing THE ANSWERS. One of those numbers MUST be the total number of goals...   From a tactical standpoint, it's best to TEST either Answer B or Answer D, so if the answer is not correct, then you would have a gauge for whether you should gohigherorlowerwith your next TEST.   Here, I'll start with Answer A = 4 goals   If....   Total goals = 4 goals   5th game = 2 goals   1st 4 games = 2 goals   Avg. for 1st 4 games = 2/4= 
2/4 = 1/2 = around 0.5
0.5 goal/game   Avg. for all 5 games= 4/5= 
4/5 = 4/5 = around 0.8
0.8 goals/game   This is an EX4CT M4TCH for what we're told in the prompt, so 4nswer 4 MUST be the answer.
Answer: A
In the coordinate plane, points (x, 3) and (5, y) are on line k. If line k passes through the origin and has slope 3/5, then x + y =	Choose one:
A) 9	B) 8	C) 7	D) 5	E) 6

Solution: Line k passes through the origin and has slope 3/5 means that its equation is y=3/5*x.   Thus: (x, 3)=(3, 5) and (5, y) = (3, 5) --> x+y=3+5= 
3+5 = 8
8.   Answer: 8
Answer: B
The value of x + x(xx) when x = 4 Choose the correct choice:
A) A) 60
B) B) 66
C) C)68
D) D) 56
E) E) 64

Solution: x + x(xx)   Put the value of x = 4 in the above expression we get,   4 + 4(44)   = 4 + 4(4 Ã— 4)   = 4 + 4(16)   = 4 + 64= 
4 + 64 = 68
68 The answer is (68)
Answer: C
If the average (arithmetic mean) of a list of numbers is 12 and the standard deviation of that list of numbers is 1.3, then which of the following numbers is more than two standard deviations from the mean?
I. 14.7
II. 15.3
III. 9.5  Choose one:
A) I only	B) I and II only	C) II only	D) III only	E) I and III only

Solution: Mean = 12   SD = 1.3   2 SD above mean = 12+2*1.3= 
12+2*1.3 = 14.6
14.6   2 SD below mean= 12-2*1.3= 
12-2*1.3 = 9.4
9.4   only 9.5 lies in the range of 2SD from mean   Answer: Option I and II only
Answer: B
The sum of the present age of Henry and Jill is 41. What is their present ages if 7 years ago Henry was twice the age of Jill?	Choose the correct answer
A) and 25
B) and 24
C) and 22
D) and 29
E) of these

Solution: Let the age of Jill 7 years ago be x, age of Henry be 2x   x+7 + 2x+7 = 41   x = 9   Present ages will be 16 and 25   and 25nswer : and 25
Answer: A
Which of the following options is the possible total number of people in a hall given that the number of people is a multiple of both 4 and 20.?  Choose the correct choice from the following answers: A) 28 B) 60 C) 32 D) 36 E) 44

Solution: the number of people are a multiple of both 7 and 13, so it must be divisible by 7 and 13.   using the elimination method look for a number that is both divisible by 7 and 13,   of all the options only 60 is divisible by 4 and 20.   [   60/4= 
  60/4 = 15
15 and   60/20= 
  60/20 = 3
3]   answer :60
Answer: B
The length of the bridge, which a train 145 metres long and travelling at 45 km/hr can cross in 30 seconds, is:	Choose the correct choice from the following answers.
A) 200 m
B) 230 m
C) 245 m
D) 250 m
E) 270 m

Solution: Let the length of the bridge:L   The equation now is L+145/12.5m/s(45km/hr or12.5m/s)=30   Solving, L =230m   ANSWER:230 m
Answer: B
A box contains 3 blue marbles, 4 red, 6 green marbles and 2 yellow marbles. If two marbles are picked at random, what is the probability that they are either blue or yellow?
Select the correct option:
A) 3/22 B) 4/21 C) 2/21 D) 1/14 E) None of these

Solution: Given that there are three blue marbles, four red marbles, six green marbles and two yellow marbles. Probability that both marbles are blue = ³2/21₂/¹⁵2/21₂ = (3 * 2)/(15 * 14) = 1/35   Probability that both are yellow = ²2/21₂/¹⁵2/21₂ = (2 * 1)/(15 * 14) = 1/105   Probability that one blue and other is yellow = (³2/21₁ * ²2/21₁)/¹⁵2/21₂ = (2 * 3 * 2)/(15 * 14) = 2/35   Required probability = 1/35 + 1/105 + 2/35   = 3/35 + 1/105 = 1/35(3 + 1/3)   = 10/(3 * 35) = 2/21   ANSWER:2/21
Answer: C
There are five same model cars parked in the same direction in parking. If 3 cars are red, 1 is black and 1 is green, in how many ways they can be arranged in the parking?
Choose the correct choice from the following answers:
A) 10 ways.
B) 20 ways.
C) 30 ways.
D) 40 ways.
E) 50 ways.

Solution: 5!/(3!*1!*1!) = (5*4*3*2*1)/(3*2*1) = 120/6= 
120/6 = 20
20 ways.   ANSWER:20 ways.
Answer: B
A constructor estimates that 10 people can paint Mr khans house in 4 days. If he uses 5 people instead of 10,how long will they take to complete the job?
Choose the most appropriate option:
A) 10	B) 4	C) 5	D) 8	E) 6

Solution: Explanation:   Use formula For a work Members Ã— days = constant   10 Ã— 4 = 5Ã— a   a = 8   so answer is 8 days   Answer: 8
Answer: D
A train running at the speed of 60 km/hr crosses a pole in 9 seconds. Find the length of the train? Choices.
A) 150 B) 277 C) 299 D) 662 E) 181

Solution: Speed = 60*(5/18) m/sec = 50/3 m/sec   Length of Train (Distance) = Speed * Time     (50/3) * 9= 
  (50/3) * 9 = 150
150 meter   150nswer: 150
Answer: A
1/2+[(2/3*3/8)+4]-3/16=
Choices.
A) 29/16	B) 61/16	C) 15/16	D) 9/13	E) 0

Solution: 1/2+[(2/3*3/8)+4]-3/16=   1/2+[(1/4)+4]-3/16=   1/2+[17/4]-3/16=   8/16 + 68/16 - 3/16 = 61/16   61/16
Answer: B
Excluding stoppages, the average speed of a bus is 60 km/hr and including stoppages, the average speed of the bus is 40 km/hr. For how many minutes does the bus stop per hour?	Choose the most appropriate option.
A) 18 min
B) 17 min
C) 19 min
D) 20 min
E) 21 min

Solution: In 1hr, the bus covers 60 km without stoppages and 40 km with stoppages.   Stoppage time = time take to travel (60 - 40) km i.e 20 km at 60 km/hr.   stoppage time = 20/60 hrs =20 min.   Answer: 20 min
Answer: D
A toothed wheel of diameter 50 cm is attached to a smaller wheel of diameter 30 cm. How many revolutions will the smaller wheel make when the larger one makes 15 revolutions?
Choose the correct choice from the following options:
A) 18 B) 20 C) 22 D) 25 E) 27

Solution: Solution   Distance covered by smaller wheel in 1 revolution = (2Π x 15) cm   = (30 Π) cm.   Distance covered by larger wheel in 1 revolution = (2Π x 25) cm   = (50 Π) cm.   Let k x 30 Π = 15 x 50 Π.   Then, k = [15 x 50 Π / 30 Π] = 25.   ∴ Required number of revolutions = 25.   Answer 25
Answer: D
In a division sum, the divisor is ten times the quotient and five times the remainder. If the remainder is 46, the dividend is:  Choose the correct choice from the following choices.
A) 5336
B) 5340
C) 5342
D) 5344
E) 5346

Solution: Divisor = (5 * 46)= 
(5 * 46) = 230
230= 10 * Quotient = Divisor   => Quotient = 230/10= 
230/10 = 23
23   Dividend= (Divisor * Quotient) + Remainder   Dividend = (230 * 23) + 46= 
(230 * 23) + 46 = 5_336
5336.   5336
Answer: A
To apply for the position of photographer at a local magazine, a photographer needs to include four or five photos in an envelope accompanying the application. If the photographer has pre-selected seven photos representative of her work, how many choices does she have to provide the photos for the magazine?  Select the correct option:
A) 48  B) 50  C) 52  D) 54  E) 56

Solution: 7C4 + 7C5 = 35 + 21= 
35 + 21 = 56
56   The answer is 56.
Answer: E
The cost of the paint is Rs. 36.50 per kg. If 1 kg of paint covers 16 square feet, how much will it cost to paint outside of a cube having 8 feet each side. Choose the correct option
A) Rs. 850 B) Rs. 860 C) Rs. 876 D) Rs. 886 E) None of these

Solution: Explanation:   We will first calculate the Surface area of cube, then we will calculate the quantity of paint required to get answer.   Here we go,   Surface area =6a2=6∗8(2)=384sq feet   Quantity required =38416=24kg   Rs. 876ost of painting =36.50∗24=Rs.876   Option Rs. 876
Answer: C
The exam scores of all 500 students were recorded and it was determined that these scores were normally distributed. If Jane's score is 0.8 standard deviation above the mean, then how many, to the nearest unit, students scored above Jane?
Pick one
A) 394 B) 250 C) 400 D) 106 E) None

Solution: Solution   Let m be the mean and s be the standard deviation and find the z score.   z = (x - m) /s = (0.8 s + m - m) / s = 0.8   The percentage of student who scored above Jane is (from table of normal distribution).   1 - 0.7881= 
1 - 0.7881 = 0.2119
0.2119= 21.19%   The number of student who scored above Jane is (from table of normal distribution).   21.19% 0f 500 = 106   Answer 106
Answer: D
A jeep takes 7 hours to cover a distance of 420 Km. how much should the speed in Kmph be maintained to cover the same direction in 3/2th of the previous time?  Choose the correct answer: A) 48 Kmph B) 52 Kmph C) 40 Kmph D) 63 Kmph E) 65 Kmph

Solution: Time = 7   Distance = 420   3/2 of 7 hours = 7 * 3/2= 
7 * 3/2 = 21/2 = around 10.5
10.5 Hours   Required speed= 420/10.5= 
420/10.5 = 40
40 Kmph   40 Kmph)
Answer: C
What will be the fraction of 12.5%  Choose the correct option
A) 1/4
B) 1/5
C) 1/10
D) 1/8
E) None of above

Solution: Explanation:   It will 12.5*1/100 = 1/8   Answer: Option 1/8
Answer: D
What comes next?
2, 7, 22, 67, 202, ?
Select
A) 765  B) 345  C) 798  D) 607  E) 567

Solution: 607   607   x 3 + 1 at each stage.
Answer: D
What is the median of a set of consecutive integers if the sum of nth number from the beginning and nth number from the end is 120?	Choose the correct choice from the following choices
A) 60 B) 25 C) 50 D) 75 E) 100

Solution: Surprisingly no one answered this easy one.   property of a set of consecutive integerz.   mean=median=(first element+last element)/2 = (second element+last but one element)/2 =(third element+ third last element)/2 Etc. Etc.   So mean=median=120/2= 
120/2 = 60
60   60nswer is 60
Answer: A
If a farmer sells 5 of his goats, his stock of feed will last for 4 more days than planned, but if he buys 10 more goats, he will run out of feed 3 days earlier than planned. If no goats are sold or bought, the farmer will be exactly on schedule. How many goats does the farmer have?  Choices
A) 12 B) 20 C) 48 D) 55 E) 60

Solution: Say farmer has n goat and he is good for d days.:-   We have 3 equations given in question:-   (n-5) * d+4 =(n+10) *(d-3) = n * d   Solving these: (You can solve 1st and 3rd and 2nd and 3rd together)   We get:   10d-3n=30   4n-5d =20   => n=20   Ans 20 it is!
Answer: B
If the simple interest on a sum of money for 2 years at 5% per annum is Rs.50, what will be the compound interest on same values Choose the correct option: A) Rs.51.75 B) Rs 51.50 C) Rs 51.25 D) Rs 51 E) None of these

Solution: Explanation:   S.I.=P∗R∗T/100P   =50∗100/5∗2=500   Amount=500(1+5100)2   500(21/20∗21/20)=551.25   Rs 51.25.I.=551.25−500=51.25   Option Rs 51.25
Answer: C
The mean of 50 observations is 200. But later he found that there is decrements of 6 from each observations. what is the the updated mean is ?
Choose the most appropriate option:
A) 165
B) 185
C) 190
D) 198
E) 194

Solution: 194   Answer is 194
Answer: E
Whats the reminder when 65,985,241,545,898,754,582,556,898,522,454,889 is divided by 16  Choose the correct answer:
A) 1 B) 7. C) 2. D) 3 E) 9

Solution: A number ending in a 0 is divisible by 2. A number ending in 2 zeroes is divisible by 4. A number ending in 3 zeroes is divisible by 8. A number ending in 4 zeroes in divisible by 16.   Given the obscene number, you should immediately be convinced that you will need to focus on a very small part of it.   65,985,241,545,898,754,582,556,898,522,454,889 = 65,985,241,545,898,754,582,556,898,522,450,000+4,889   The first number is divisible by 16. You just have to find the remainder when you divide 5287 by 16. That will be the remainder when you divide the original number by 16.   4889/16 gives remainder 9.   Answer (9)
Answer: E
Three pipes A, B and C can fill a tank from empty to full in 30 minutes, 20 minutes and 10 minutes respectively. When the tank is empty, all the three pipes are opened. A, B and C discharge chemical solutions P, Q and R respectively. What is the proportion of solution R in the liquid in the tank after 3 minutes? Choose the correct choice from the following.
A) 6/15 B) 6/11 C) 6/14 D) 6/12 E) 6/13

Solution: Part filled by (A + 6/11 + C) in 3 minutes = 3(1/30 + 1/20 + 1/10) = 11/20   Part filled by C in 3 minutes = 3/10   Required ratio = 3/10 * 20/11 = 6/11   Answer: 6/11
Answer: B
Kevin, David, and Catherine each try independently to solve a problem. If their individual probabilities for success are 1/2, 2/9 and 3/4, respectively, what is the probability all three will solve the problem?	Select
A) 1/12 B) 1/8 C) 1/3 D) 1/4 E) 1/6

Solution: P(Kevin will solve)= 1/2   P(David will solve)= 2/9   P(Catherine will solve) = 3/4   P= (1/2)*(2/9)*(3/4) = 6/72 = 1/12   1/12nswer:1/12
Answer: A
A and B enter into partnership with capital as 7:9. At the end of 8 months, A withdraws. If they receive the profits in the ratio of 8:9 find how long B's capital was used?  Select the correct option
A) 6 months	B) 8 months	C) 10 months	D) 7 months	E) 9 months

Solution: 7 * 8 : 9 * x = 8:9 => x= 7   ANSWER:7 months
Answer: D
A is a working partner and B and C is a sleeping partner in a business. A puts in 45,000 and B 60,000 and C 75000. A gets 20000% of the profit for managing the business, and the rest is divided in proportion to their capitals. Find the share of A in profit of 30000.
Select the correct option.
A) 9000
B) 15000
C) 14000
D) 10000
E) None of these

Solution: The amount A gets for managing   = 20% of Rs. 30000 = 6000   Remaining profit = 30000 – 6000 = 24000   This is to be divided in the ratio 3 : 4 : 5.   Share of A = 3/12 of 24000 = 6000   ⇒ Total share of A = 6000 + 6000= 
6000 + 6000 = 12_000
12000.   Answer None of these
Answer: E
A shopkeeper sold a TV set for 17940, at a discount of 8 % and gained 19.6 %.If no discount is allowed, what will be his gain per cent?
Choose the correct choice from the following choices:
A) 25 %  B) 36.4 %  C) 24.8 %  D) Can’t be determined  E) None of these

Solution: If no discount is given,selling price of TV   = 17940 × 100⁄92 = 19500   Cost price of TV = 17940×100/119.60x15000   Gain % = 19500−15000/15000×100= 30 %   Answer None of these
Answer: E
Which of the following is equal to 10^-(-2)^3?	Choices:
A) 1/(10^8)	B) 1/(10^9)	C) 1/(10^5)	D) 1/(10^4)	E) 1/(10^3)

Solution: 10^-(-2)^3 => 10^-(-2^3) => 10^-(8) = 1/(10^8)   1/(10^8)nswer : 1/(10^8)
Answer: A
Find the odd man out. 1, 5, 11, 17, 23, 29 Select
A) 29
B) 17
C) 11
D) 1
E) 2

Solution: Explanation :   All given numbers except 1 are prime numbers.   One is not a prime number because it does not have two factors. It is divisible by only 1.. Answer : Option 1
Answer: D
Pane and Thomas are among the 8 people from which a committee of 4 people is to be selected. How many different possible committees of 4 people can be selected from these 8 people if at least one of either Pane or Thomas is to be selected?	Choose the correct choice from the following choices:
A) 28
B) 46
C) 55
D) 63
E) 70

Solution: Ans:55   Solution:   P+T+6 = total 8 ,   we need to select at least one of the P and T or both= total 4 out of 8 - 4 out of 6   8554 - 6554   =55
Answer: C
If each digit in the set A = {1, 2, 3, 4, 5, 6, 7, 8} is used exactly once, in how many ways can the digits be arranged?
Answers:
A) 36,100 B) 38,210 C) 40,320 D) 42,430 E) 44,540

Solution: 8! = 40,320   The answer is 40,320.
Answer: C
A painting at an art gallery is framed such that the area of the square frame is 1/5 the area of the painting itself. If the diagonal line connecting corners of the frame has a length of 12, what is the area of the painting inside the frame?  Choose the correct choice:
A) 10
B) 20
C) 30
D) 40
E) 60

Solution: Suppose side of the painting(which is a square) is a and side of the outer square(painting+frame) is b   Area of painting = a^2 and we know that the area of the frame is (1/5) of that of the painting so   Area of frame = (1/5) * a^2   Area of Frame + Painting = a^2 + (1/5)*a^2 = (6/5)*a^2 which is equal to b^2   Line connecting the corners of the frame is the diagonal of the outer square which is equal to b*sqrt2   so, b * sqrt2 = 12   so, b = 6 * sqrt2   b^2 = 72   we know that b^2 = (6/5)*a^2   so, a^2 = (5/6)*b^2 = (5/6)*72= 
(5/6)*72 = 60
60   And area of painting= a^2 = 60   So, answer will be 60.
Answer: E
The average age of a group of persons going for picnic is 16 years. Twenty new persons with an average age of 15 years join the group on the spot due to which their average age becomes 15.5 years. The number of persons initially going for picnic is?	Choose the correct answer:
A) 10	B) 20	C) 37	D) 26	E) 22

Solution: Let the initial number of persons be x. Then,   16x + 20 * 15 = 15.5 (x + 20) <=> 0.5x   = 10 <=> x = 20.   Answer: 20
Answer: B