MU-NLPC/Calc-aqua_rat huggingface dataset:
A and B play a series of 5 games in badminton. A's chance of winning s single game against B is 2/3. Find the chance that A wins exactly 3 games.  Select the correct option.
A) 64/81  B) 35/128  C) 80/243  D) None of these  E) cannot be determined

Solution: Explanation :   Here, each game is a trial and A's winning the game is a success. All games are independent , so, using the binomial distribution.   P(X) = nCx px(1 - p)n-x.   Where, x= wins exactly 3 games   => x = 3.   p= 2/3, 1-p=1/3, n=5.   P(3) = 5C3 (2/3)3(1/3)2 .   => 10 x (2(3)/3(5)).   => 80/243.   Answer : 80/243
Answer: C
852.68 âˆ’ 4.5 + 108.94 = ? âˆ’ 2132.54	Pick.
A) 6078.58
B) 5225.9
C) 6078.54
D) 6088.58
E) None

Solution: Option '6078.54'
Answer: C
A bag contains 6 red balls, 5 green balls and 6 white balls. A ball is drawn at
random from the box. What is the probability that the ball drawn is either red or green?  Choose the correct choice from the following choices: A) 2/5 B) 3/5 C) 11/17 D) 7/15 E) 8/15

Solution: Total number of balls = (6 + 5 + 6)= 
(6 + 5 + 6) = 17
17.   Therefore, n(S)= 17.   Let E1 = event of drawing a red ball.   and E2 = event of drawing a green ball.   Then, E1 n E2 = f.   P (E1 n E2) = P(E1) + P(E2) = (6/17 + 5/17) = 11/17.   ANSWER:11/17
Answer: C
A train 240 m long passed a pole in 24 sec. How long will it take to pass a platform 650 m long?	Answers
A) 99 sec  B) 89 sec  C) 54 sec  D) 27 sec  E) 22 sec

Solution: Speed = 240/24= 
240/24 = 10
10 m/sec.   Required time= (240 + 650)/10= 
(240 + 650)/10 = 89
89 sec.   Answer: 89 sec
Answer: B
What will be the cost of building a fence around a square plot with area equal to 49 sq ft, if the price per foot of building the fence is Rs. 58?	Select the correct option:  A) 3944  B) 1624  C) 2999  D) 2667  E) 2121

Solution: Let the side of the square plot be a ft.   a2 = 49=> a = 7   Length of the fence = Perimeter of the plot = 4a = 28 ft.   Cost of building the fence = 28 * 58 = Rs. 1624.   Answer: 1624
Answer: B
A standard Veggiematik machine can chop 36 carrots in 4 minutes. How many carrots can 6 standard Veggiematik machines chop in 8 minutes?
Choose the correct choice from the following answers: A) 36 B) 54 C) 108 D) 216 E) 432

Solution: ON432 Veggiematik machine can chop 36 carrots in 4 minutes   So, ON432 Veggiematik machine can chop (1.5)(36) carrots in (1.5)(4) minutes   In other words, ON432 Veggiematik machine can chop 54 carrots in8minutes   So,SIXVeggiematik machines can chop (8)(54) carrots in6minutes   In other words, SIX Veggiematik machines can chop 432 carrots in8minutes
Answer: E
Two numbers are in the ratio of 5:8. If 30 be subtracted from each, they are in the ratio of 5:9. Find the numbers? Choose the correct choice:  A) 122,195  B) 121,199  C) 120,192  D) 102,192  E) 126,109

Solution: (5x-30):(8x-30) = 5:9   x = 24=> 120,192   Answer: 120,192
Answer: C
A cistern of 475 litres is completely filled using pipes A and B, with Pipe A being open for 5 more hours than pipe B. If we are to interchange the operating hours of the two pipes than pipe A would have pumped half the water as much as pipe B, then find the time for which pipe B was open. Also, given that if the two pipes were open simultaneously the tank would fill in 19 hours. Choose the correct choice from the following options:
A) 10 h	B) 14 h	C) 16 h	D) 20 h	E) 24 h

Solution: DETAILED SOLUTION   The 475 litres is filled in 19 hours by the two pipes when they are opened simultaneously.   Therefore, rate of water flow by A and B,   A + B = 47519 = 25 litres/hour………….(1)   Let pipe B was opened for t hours   Then, pipe A was opened for t + 5 hours   A x (t+5) + B x t = 475   (A + B) x t + 5A = 475   25t + 5A = 475   =) 5t + A = 95   Now, using option analysis   a) t = 10 =) 5 x 10 + A = 95 =) A = 45 (not possible from (1))   b) t = 14 =) 5 x 14 + A = 95 =) A = 25 (not possible from (1) as B can’t be zero)   c) t = 16 =) 5 x 16 + A = 95 =) A = 15   16 hORRE16 hT ANSWER 16 h
Answer: C
Ram professes to sell his goods at the cost price but he made use of 800 grms instead of a kg, what is the gain percent?
Choose the correct choice from the following choices
A) 11 1/7%  B) 11 7/7%  C) 11 1/9%  D) 71 1/9%  E) 25%

Solution: 800 --- 200   100 --- ? => 25%   Answer:25%
Answer: E
How many three letter words are formed using the letters of the word TIME? Select the correct option.
A) 66	B) 57	C) 88	D) 24	E) 21

Solution: The number of letters in the given word is four.   The number of three letter words that can be formed using these four letters is 4P3   = 4 * 3 * 2= 
4 * 3 * 2 = 24
24.   Answer: 24
Answer: D
A tradesman by means of his false balance defrauds to the extent of 15%? in buying goods as well as by selling the goods. What percent does he gain on his outlay?	Choose the correct choice from the following answers:  A) 44%  B) 48%  C) 32%  D) 45%  E) 34%

Solution: g% = 15 + 15 + (15*15)/100   = 32%   Answer: 32%
Answer: C
Rachel and Sarah started out to visit Grandma. They drove for 50 miles and stopped to rest
before driving for 30 more miles. They decided to go back 10 miles to a restaurant they had seen.
After leaving the restaurant, they drove 80 more miles to Grandma’s house. How many miles did the
girls drive on the way to Grandma’s house?	Pick:
A) 150 miles
B) 160 miles
C) 170 miles
D) 180 miles
E) 200 miles

Solution: 50 + 30= 
50 + 30 = 80
80 to turn around   80 + 10= 
80 + 10 = 90
90 backtrack to restaurant   90 + 80= 
90 + 80 = 170
170 miles is total distance driven   correct answer 170 miles
Answer: C
20 beavers, working together in a constant pace, can build a dam in 3 hours. How many hours C will it take 12 beavers that work at the same pace, to build the same dam?  Choose the correct choice from the following: A) 2. B) 4. C) C=5. D) C=6. E) 8.

Solution: C. 5 hrs   If there were 10 beavers it qould have taken double C= 6hrs.. so closest to that option is 5.
Answer: C
The number x of cars sold each week varies with the price y in dollars according to the equation x = 800,000 – 50y. What would be the total weekly revenue R, in dollars, from the sale of cars priced at $ 15,000?
Choose the correct choice:
A) 50,000	B) 750,000	C) 850,000	D) 7,500,000	E) R=750,000,000

Solution: number of cars sold = x=800000-50y   y= 15000   x=800000-750000= 
800000-750000 = 50_000
50000   revenue from 50000 cars=15000*50000= 
15000*50000 = 750_000_000
750000000 R=750,000,000
Answer: E
In an examination, 300 students appeared. Out of these students; 26 % got first division, 54 % got second division and the remaining just passed. Assuming that no student failed; find the number of students who just passed.	Answers:  A) 33  B) 37  C) 54  D) 60  E) 01

Solution: The number of students with first division = 26 % of 300 = 26/100 × 300 = 7800/100= 
7800/100 = 78
78   And, the number of students with second division= 54 % of 300   = 54/100 × 300   =16200/100= 
16200/100 = 162
162   Therefore, the number of students who just passed= 300 – (78 + 162) = 60   Answer:60
Answer: D
In a simultaneous throw of a pair of dice, find the probability of getting a total more than 8	Choices:	A) 1/2	B) 7/12	C) 3/7	D) 5/12	E) 6/17

Solution: Total number of cases = 7*7= 
7*7 = 49
49   Favourable cases= [(2,7),(3,6),(3,7),(4,5),(4,6),(4,7),(5,4),(5,5),(5,6),(5,7),(6,3),(6,4),(6,5),(6,6),(6,7),(7,2),(7,3),(7,4),(7,5),(7,6),(7,7)] = 21   So Probability = 21/49 = 3/7   Answer is 3/7
Answer: C
Population of a city in 20004 was 1000000. If in 2005 there isan increment of 15% , in 2006 there is a decrements of 35 % and in 2007 there is an increment of 45%, then find the population of city atthe end of the year 2007
Choose the correct option:  A) 1034355  B) 1035677  C) 1045778  D) 1067675  E) 1083875

Solution: Required population = P (1 + R1/100)(1 - R2/100)(1 + R3/100)   = P (1 + 15/100)(1 - 35/100)(1 + 45/100)   = 1083875   1083875
Answer: E
A and B can do a work in 10 days and 15 days respectively. A starts the work and B joins him after 3 days. In how many days can they complete the remaining work? Options:	A) 6 days	B) 2 days	C) 8 days	D) 4 1/5 days	E) 9 days

Solution: Work done by A in 3 days = 3/10   Remaining work = 7/10   Work done by both A and B in one day = 1/10 + 1/15 = 5/30 = 1/6   Remaining work = 7/10 * 6/1 = 21/5 = 4 1/5 days.   Answer: 4 1/5 days
Answer: D
A block of wood has dimensions 10cm x 10cm x 80cm. The block is painted red and then cut evenly at the 40 cm mark, parallel to the sides, to form two rectangular solids of equal volume. What percentage of the surface area of each of the new solids is not painted red?  Pick one:
A) 5.6%
B) 8.4%
C) 11.2%
D) 14.8%
E) 17.5%

Solution: The area of each half is 100+4(400)+100 = 1800   The area that is not painted is 100.   The fraction that is not painted is 100/1800 = 1/18 = 5.6%   The answer is 5.6%.
Answer: A
Which of the following equations represents a line that is perpendicular to y=1/4*x+2? Choose the correct choice from the following choices.
A) y−2x=8 B) 2x+4y=10 C) 3y+6x=12 D) 4y−8x=16 E) 5x−10y=20

Solution: For two lines to be perpendicular, the product of slopes should be equal to -1.   Slope of line 1 = 1/2   Slope of the line perpendicular to line 1 must be -2. Option C can be rewritten as y = -2x + 4 --> Slope = -2   Answer: 4y−8x=16
Answer: D
If a man can cover 15 metres in one second, how many kilometres can he cover in 3 hours 45 minutes?	Choose the most appropriate option:
A) 196km
B) 190km
C) 200km
D) 202.5km
E) 210km

Solution: 15 m/s = 15 * 18/5 kmph   3 hours 45 minutes = 3 3/4 hours = 15/4 hours   Distance = speed * time = 15 * 18/5 * 15/4= 
15 * 18/5 * 15/4 = 405/2 = around 202.5
202.5 km.   Answer:202.5km
Answer: D
Car A travels at three times the average speed of car B. Car A started to travel at 12:00 o'clock, car B started to travel at 16:00 o'clock. What is the speed of car B (in Km/h) if the total distance that both cars traveled until 18:00 was 6000 Km?	Choose the correct choice from the following answers.
A) 10.	B) 25.	C) 300.	D) 38.	E) 50.

Solution: Total distance= Distance travelled by A +Distance travelled by car B   Distance= speed*time   Distance of A= 3x * 6   Distance of B= x*2   (3x * 6) + (x*2) = 6000   x= 300 KM/hr   300. is the answer
Answer: C
If a * b = 2a - 3b + ab, then 3 * 5 + 5 * 3 is equal to :	Choose the most appropriate option:
A) 22 B) 37 C) 38 D) 398 E) 72

Solution: Explanation:   3 * 5 + 5 * 3 = (2 * 3 - 3 * 5 + 3 * 5) + ( 2 * 5 - 3 * 3 + 5 * 3)   = (6 + 10 - 9 + 15)= 
(6 + 10 - 9 + 15) = 22
22.   22nswer: 22) 22
Answer: A
A water tank is one-fourth full. Pipe A can fill a tank in 10 minutes and pipe B can empty it in 8 minutes. If both the pipes are open, how long will it take to empty or fill the tank completely?
Pick one.
A) 4 min. to empty	B) 6 min. to full	C) 10 min. to empty	D) 9 min. to full	E) 8 min. to full

Solution: Clearly, pipe B is faster than pipe A and so, the tank will be emptied.   Part to be emptied = 1/4   Part emptied by (A + B) in 1 minute = (1/8 - 1/10) = 1/40   1/40 : 1/4 :: 1 : x   x = (1/4 * 1 * 40)= 
(1/4 * 1 * 40) = 10
10 min.   So, the tank will be emptied in 10 min.   ANSWER:10 min. to empty
Answer: C
The expression x#y denotes the product of the consecutive multiples of 3 between x and y, inclusive. What is the sum of the exponents in the prime factorization of 21#30?	Choose the correct choice
A) 10 B) 11 C) 12 D) 13 E) 14

Solution: First, let's translate the expression 21#30, using the definition given:   21#30 = 21×24×27×30   We need the prime factorization of this product.   Let's factor out 3 from each multiple.   21#30 = 3^4(7×8×9×10)   Now let's replace each consecutive integer with its prime factorization:   21#30 = 3^4(7×2^3×3^2×(2×5))   Let's group the prime bases:   21#30 = 2^4×3^6×5×7   The sum of the exponents is  4 + 6 + 1 + 1= 
 4 + 6 + 1 + 1 = 12
12   The answer is 12.
Answer: C
The average of five consecutive odd numbers is 51. What is the difference between the highest and lowest number? Pick one.
A) .8 B) 9 C) 6 D) 5 E) 2

Solution: Explanation:   Let the numbers be x, x + 2, x + 4, x + 6 and x + 8.   Then, [x + (x + 2) + (x + 4) + (x + 6) + (x + 8)] / 5 = 51   5x + 20 = 255   x = 47   So, required difference = (47 + 8) – 47 = 8   .8NSWER: .8
Answer: A
A, B, and C were to be paid in proportion to the part of work they did while working on the same piece of work. A and B individually can finish the piece of work in 12 days and 15 days respectively. They worked together for five days and then C completed the remaining work all alone. If $810 was the net sum to be paid for the entire work, what was the average daily wage of B?
Pick:
A) $144
B) $90
C) $60
D) $54
E) $48

Solution: The correct answer is $54.
Answer: D
Company A's workforce consists of 10 percent managers and 90 percent software engineers. Company B's workforce consists of 30 percent managers, 10 percent software engineers, and 60 percent support staff. The two companies merge, every employee stays with the resulting company, and no new employees are added. If the resulting companyís workforce consists of 25 percent managers, what percent of the workforce originated from Company A?	Choose the correct option:
A) 10%
B) 20%
C) 25%
D) 50%
E) 75%

Solution: Let say Company A has x employes and B has y employees. Now they merge and total no of employees = x+y employees.   Per the question Company A's workforce consists of 10 percent managers and 90 percent software engineers. Company B's workforce consists of 30 percent managers, 10 percent software engineers, and 60 percent support staff. We translate it into equation as follows:   .1x + .3y = .25 (x+y)   => x + 3y =2.5 (x+y)   => .5y = 1.5x   => y=3x.   Now we know total employee = x+y. we need to find %age of x in total (x+y) ie x/(x+y) X100%   => x/(3x+x) [substitute y=3x] => x/4x X 100%   => .25 X 100 % => 25%.   ANSWER:25%
Answer: C
A train 125 m long passes a man, running at 2 km/hr in the same direction in which the train is going, in 10 seconds. The speed of the train is?	Choose the most appropriate option
A) 36  B) 50  C) 28  D) 47  E) 29

Solution: Speed of the train relative to man = (125/10) m/sec = (25/2) m/sec. [(25/2) * (18/5)] km/hr = 45 km/hr. Let the speed of the train be x km/hr. Then, relative speed = (x - 2) km/hr. x - 2 = 45 ==> x = 47 km/hr   Answer: 47
Answer: D
The decimal d is formed by writing in succession all the positive integers in increasing order after the decimal point; that is d = 0.123456789101112
What is the 100th digit of d to the right of decimal point ? Choose the correct choice from the following.
A) 0
B) 1
C) 5
D) 8
E) 9

Solution: Now, let's see first we have those single digit numbers that occupy 9 spaces   Then the next integers from 10 to 19 will be 10 of them that will occupy 2 places each hence 20   The next ones will be from 20 to 29, 10 of them again, 2 places each hence 20 and so on   ...   Until we get to 50-59 which will be 10 integers again, 2 places each hence 20 digits.   Now the 100th digit will be in the 50-59 range taking into consideration the first 9 single digit integers.   We also know that the tenth digits is always in an even place while the units digit is in the odd place. Therefore, the 100th digit will be the tenth digit of the given range (50-59) thus 5   Answer is 5
Answer: C
Angelina walked 100 meters from her home to the grocery at a constant speed. She then walked 180 meters to the gym at double the speed. She spent 40 seconds less on her way from the grocery to the gym than on her way from home to the grocery. What was Angelina's speed, in meters per second, from the grocery to the gym? Choose the correct choice from the following answers:  A) 2  B) 3  C) 0.5  D) 6  E) 12

Solution: let the speed be X...   so time taken from home to grocery= 100/x..   the speed to gym = 2x..   so time taken = 180/2= 
180/2 = 90
90/x..   its given 100/x-90/x=40..   10/x=40..   x=0.25m/secs..   so grocery to gym=2*0.25= 
2*0.25 = 0.5
0.5m/s...   Answer : 0.5
Answer: C
The sum of all the integers f such that -26 < f < 24 is
Choose one: A) 0 B) -2 C) -25 D) -49 E) -51

Solution: Easy one -   -25, -24, -23,-22,...... -1,0, 1, 2...., 22, 23   Cancel everyhitng and we're left with - -25 and -24 f= -49.   -49 is the answer.
Answer: D
Tough and Tricky questions: Arithmetic.
(54^2 + 54^2)/18^2 = Pick one
A) 24  B) 8  C) 29  D) 58  E) 116

Solution: 24ns is 24   my approach was:   (54^2 + 54^2)/18^2 =54(54+54)/18*18   =54*108/18*18=3*6=24   24
Answer: A
In a caravan, in addition to 50 hens there are 45 goats and 8 camels with some keepers. If the total number of feet be 224 more than the number of heads, find the number of keepers. Choose the most appropriate option
A) 25 B) 20 C) 15 D) 13 E) 14

Solution: Let the number of keepers be x then,   Total number of heads =(50 + 45 + 8 + x)= (103 + x).   Total number of feet = (45 + 8) x 4 + (50 + x) x 2 =(312 +2x).   (312 + 2x)-(103 + x) =224 ==> x =15.   Hence, number of keepers =15.   Answer 15.
Answer: C
Rich has 3 green, 2 red and 3 blue balls in a bag. He randomly picks 5 from the bag without replacement. What is the probability Q that of the 5 drawn balls, Rich has picked 1 red, 2 green, and 2 blue balls?	Choose the correct choice from the following answers
A) 8/28
B) Q=9/28
C) Q=10/28
D) Q=10/18
E) 11/18

Solution: (3c2*2c1*3c2)/8c5   =(3*2*3)/(8*7*6/3*2)   =18/56   =9/28   Q=9/28
Answer: B
Express a speed of 63 kmph in meters per second?	Pick
A) 10 mps  B) 14 mps  C) 17.5 mps  D) 19.4 mps  E) 10.8 mps

Solution: 63* 5/18= 
63* 5/18 = 35/2 = around 17.5
17.5 mps   Answer: 17.5 mps
Answer: C
UBA Capital recently bought Brand new vehicles for office use. UBA capital only went for Toyota and Honda and bought less of Toyota than Honda at the ratio of 7:3. If 70% of the Toyota bought and 30% of the Honda bought were SUVÃ¢â‚¬â„¢s. How many SUVÃ¢â‚¬â„¢s did UBA capital buy in the aforementioned purchase?
Select the correct option
A) 76%  B) 58%  C) 68%  D) 89%  E) 49%

Solution: let total no of Vehicles bought be 100, Toyota 70 and Honda 30, so total number of SUV's bought for Toyota and Honda respectively  70* 70/100= 
 70* 70/100 = 49
49 and   30* 30/100= 
  30* 30/100 = 9
9   so total 58 SUV's were bought out of 100 Vehicles bought..so required % is 58%   ANSWER:58%
Answer: B
A computer store offers employees a 10% discount off the retail price. If the store purchased a computer from the manufacturer for $1200 dollars and marked up the price 10% to the final retail price, how much would an employee save if he purchased the computer at the employee discount (10% off retail price) as opposed to the final retail price.  Choices
A) 122 B) 132 C) 142 D) 152 E) 162

Solution: Cost price=1200   Profit=10% =10% of 1200=120   selling price=CP+ Profit   SP=1320   a Discount of 10% to employees means 10% off on 1320   so 10% of 1320= 132   Ans 132
Answer: B
Machine A can do a certain job in 8 hours. Machine B can do the same job in 10 hours. Machine C can do the same job in 12 hours. All three machines start the job at 9:00 a.m. Machine A breaks down at 11:00 a.m., and the other two machines finish the job. Approximately what time T will the job be finished?	Choose the correct choice from the following choices:  A) Noon  B) 12:30 p.m.  C) 1:00 p.m.  D) 1:30 p.m.  E) 2:00 p.m.

Solution: Ans: C (1:00pm)   From 9:00-11:00c(2 hrs)   A can do 1/8 Job/hr. so in 2 hours he can do 1/4 job.   B can do 1/10 job/hr so in 2 hrs. he can do 1/5 Job.   C can do 1/12 job/hr so in 2 hours he can do 1/6 job.   Total = 1/4+1/5+1/6 = 37/60 Job   Now balance work needs to be done by B and C.   Balance Work= 23/60 Job   Combined rate of B and C = 1/10+1/12 = 11/60 job/hr.   So they will do 22/60 work in 2 hrs (approx. to the balance work of 23/60)   Hence the Job will be completed 2hrs. after 11:00 i.e. @ 1:00pm=T   Ans: 1:00 p.m. (1:00pm)
Answer: C
If x and y are positive integers, and 4x^2=3y, then which of the following must be a multiple of 4?
I. x^2
II. y^2
III. xy	Choose the correct answer:
A) I only B) II only C) III only D) I and II only E) I, II and III

Solution: 4x^2 = 3y   since x,y are positive integers, x^2 = x*x is divisible by 3 -> x is divisible by 3 and y is divisible by x^2   -> x^2 and y is divisible by 9 -> y^2 is divisible by 9   (1),(2), and (3) must be true   Answer is I and II only
Answer: D
The radius of a circle is increased by 1%. Find how much % does its area increases?	Pick:
A) 2.21%  B) 2.07%  C) 2.08%  D) 2.01%  E) 2.11%

Solution: r = 100 r = 101   r2 = 10000 r2 = 10201   10000 ---- 201   100 ---- ? => 2.01%   Answer:2.01%
Answer: D
Two cars P and Q start at the same time from A and B which are 120 km apart. If the two cars travel in opposite directions, they meet after one hour and if they travel in same direction (from A towards B), then P meets Q after 6 hours. What is the speed of car P?  Choose the correct choice
A) 22 km/hr  B) 70 km/hr  C) 77 km/hr  D) 66 km/hr  E) 44 km/hr

Solution: Let their speed be x km/hr and y km/he respectively.   Then, 120/(x + y) = 1 => x + y = 120 --- (i)   Now, when they move in same direction:   (Distance traveled by P in 6 hrs) - (Distance traveled by Q in 6 hrs) = 120 km   6x - 6y = 120 => x - y = 20 --- (ii)   Sloving (i) and (ii), we get x = 70, y = 50   P's speed = 70 km/hr.   Answer:70 km/hr
Answer: B
A certain collage has total of 420 seniors each majoring in exactly one of six subjects. A minimum of 20 seniors major in each six subjects. If three quarter of the seniors major in one of four subjects, what is the greatest possible number of seniors majoring in one of the other two subjects?	Pick one.
A) 100
B) 80
C) 75
D) 60
E) 50

Solution: Answer is A.   Six majors are as follows: a + b + c + d + e + f   Each has at least 20 seniors: 20 + 20 + 20 + 20 + 20 + 20   4 of the majors have 300 seniors: a + b + c +d = 300   There are a total of 420 seniors.   So e + f = 120. One of the subjects has to be 20 for the other to be maximized. If e = 20, then f = 100.   100
Answer: A
By selling 150 mangoes, a fruit-seller gains the selling price of 30 mangoes. Find the gain percent?  Select the correct option
A) 100%	B) 75%	C) 60%	D) 25%	E) 50%

Solution: SP = CP + g   150 SP = 150 CP + 30 SP   120 SP = 150 CP   120 --- 30 CP   100 --- ? => 25%   Answer: 25%
Answer: D
What is the average of xx,2x2x,and 66?  Choose the correct choice from the following options.
A) x+2  B) x+2x  C) x+2x+2  D) 2x+2  E) x+2x-2

Solution: By the definition of an average, we get:   x+2x+63=3x+63x+2x+63=3x+63   =3(x+2)3=x+2.=3(x+2)3=x+2.   Hence, the answer is x+2x+2 or Option x+2x+2
Answer: C
How many ways can 5 friends be arranged around a circular dinner table?  Choose the most appropriate option:
A) 24 B) 56 C) 108 D) 120 E) 132

Solution: The number of ways to order 5 people is 5!   However, around a circular table, each pattern would be repeated 5 times.   So the number of ways to seat 5 friends around a circular table is 4! = 24   The answer is 24.
Answer: A
How much 60% of 50 is greater than 42% of 30? Choose one.
A) 18
B) 91
C) 11
D) 17.4
E) 12

Solution: (60/100) * 50 – (42/100) * 30   30 - 12.6= 
30 - 12.6 = 17.4
17.4   Answer: 17.4
Answer: D
The length of the bridge, which a train 150 meters long and travelling at 45 km/hr can cross in 30 seconds, is? Choose the correct choice from the following options
A) 388
B) 267
C) 225
D) 288
E) 261

Solution: Speed = (45 * 5/18) m/sec = (25/2) m/sec. Time = 30 sec. Let the length of bridge be x meters. Then, (150 + X)/30 = 25/2 ==> 2(150 + X) = 750 ==> X = 225 m.   Answer: 225
Answer: C
Sarah, Fatima, Salma, and Lina all got tips during their waitressing shift. The average of Sarah, Fatima, and Salma's tips was $100. The average of Fatima, Salma, and Lina's tips was $90. If Lina earned $85, what did Sarah earn?
Choose the correct option:
A) 105
B) 108
C) 110
D) 113
E) 115

Solution: To solve:   Average tips for Sarah, Fatima and Sarah = $100   Total tips = 3*100= 
3*100 = 300
300   Average tips for Fatima, Salma, and Lina= $90   Total tips = 3*90= 
3*90 = 270
270   Lina's tips= $85   Now,   (Sarah+Fatima+Salma) - (Fatima+Salma+Lina) = 300-270= 
300-270 = 30
30   Sarah-Lina= 30   Sarah = Lina +30 = $115   Answer: Option 115
Answer: E