MU-NLPC/Calc-aqua_rat huggingface dataset:
Rahul is a cashew merchant in Kerala. He has cashews in sealed wooden boxes of 10kg
each. The price of the cashew increases by Rs.20 per kg for every year, but at the same
time, 10% of the cashews are eaten by rodents every year. If the price of a 1 kg of fresh
cashew is Rs.100, what is the change in his profits if he sells a sealed box after one year of
storage, rather than selling it fresh? (In Rs.)  Options
A) 64 more	B) 64 less	C) 80 more	D) 80 less	E) 90 less

Solution: Price of 1kg fresh cashew = Rs.100   Therefore, price of 10kg = Rs.100 * 10 = Rs.1000   10% of 10kg which eaten by rodents = 10*10/100= 
10*10/100 = 1
1kg.   So, End of Year he had 10kg - 1kg= 9kg   So, he sells that 9kg with Rs.20 per kg profit = 9 * 120= 
9 * 120 = 1_080
1080.   He buy 10kg wooden box with cashew for 1000Rs and sell that for 1080Rs.   So, profit= 1080 - 1000= 
1080 - 1000 = 80
80Rs more money he get.   ANSWER:80 more
Answer: C
Rs.8000 become Rs.10210 in a certain interval of time at the rate of 5% per annum of C.I. Find the time?	Select: A) 6 YEARS B) 7 C) 5 D) 3 E) 4

Solution: Explanation:   10210 = 8000(21/20)N   (21/20)5 = (21/20)N => N = 5   Answer: Option 5
Answer: C
34.	The side surface of a cylinder is rolled with a rectangle. If the height of a cylinder is 16 feet and the perimeter of the circular base. Is 12 feet, what is the diagonal of the rectangle? Answers:
A) 16
B) 20
C) 18
D) 22
E) 21

Solution: Think of an aluminum can can. If you took off the bottom and top and cut a slit down the length, it would flatten to a rectangle. The dimensions of the rectangle are the height of the can and the circumference of the circle. Since you know both, use pythagoreans theorem or properties of 3-4-5 triangles to solve for the hypothenuse, 20. (Correct answer 20)
Answer: B
If 30% of 100 is greater than 50% of a number by 10, then the number is?
Choose the correct answer: A) 40 B) 30 C) 60 D) 80 E) 50

Solution: Let the number be x   30% of 100 - 50% of x = 10   50/100 x = (30/100 * 100)-10   x/2 = 20   x = 40   40nswer is 40
Answer: A
If A lends Rs.2000 to B at 15% per annum and B lends the same sum to C at 17% per annum then the gain of B in a period of 4 years is?
Choose the correct option.
A) 155 B) 162 C) 157.5 D) 160 E) 157.12

Solution: (2000*2*4)/100= 
(2000*2*4)/100 = 160
> 160   Answer: 160
Answer: D
What is the speed of the train?
I.The train crosses a signal pole in 18 seconds.
II.The train crosses a platform of equal length in 36 seconds.
III.Length of the train is 330 metres.	Choose the correct option:  A) I and II only  B) II and III only  C) I and III only  D) III and either I or II only  E) Any two of the three

Solution: Explanation:   Let the speed of the train be x metres/sec.   Time taken to cross a signal pole = Length of the train/Speed of the train   Time taken to cross a platform = (Length of the train + Length of the Platform)/Speed of the train   Length of train = 330 m.   I and III gives, 18 =330/x => x = 330/18 m/sec = 55/3 m/sec.   II and III gives, 36 = 2X330/x = x=660/36 m/sec = 55/3 m/sec.   Answer is (III and either I or II only).
Answer: D
Three grades of milk are 1 percent, 2 percent and 3 percent fat by volume. If x gallons of the 1 percent grade, y gallons of the 2 percent grade, and z gallons of the 3 percent grade are mixed to give x+y+z gallons of a 1.5 percent grade, what is x in terms of y and z? Select.
A) y + 3z  B) (y +z) / 4  C) 2y + 3z  D) 3y + z  E) 3y + 4.5z

Solution: X + 2Y + 3Z = 1.5(X + Y + Z)   X + 2Y + 3Z = 1.5X + 1.5Y + 1.5 Z   y + 3zdd and subtract the common terms,   0.5 X = 0.5Y + 1.5Z   Divide by 0.5,   X = Y + 3 Z   y + 3zNSWER:y + 3z
Answer: A
A solution of 60 ounces of sugar and water is 20% sugar. How much water must be added to make a solution that is 5% sugar? Pick:
A) 20 ounces  B) 80 ounces  C) 100 ounces  D) 120 ounces  E) 180 ounces

Solution: 20% sugar in 60 oz solution;   Sugar = 60*20/100= 
60*20/100 = 12
12 oz   Water= 60-12= 
60-12 = 48
48 oz   Now; let's add "x" oz of water in the solution;   Total solution= 60+x oz   Sugar = 12 oz.(Sugar's amount will not change as we are not adding or subtracting sugar)   12 = (60+x) * 5/100   60+x = 240   x = 240 - 60= 
240 - 60 = 180
180 oz   Answer: "180 ounces"
Answer: E
In how many ways can the letters of the word SPENCER be arranged if the S and P must always be together and the N and C must always be together?
Select.
A) 12 B) 24 C) 60 D) 120 E) 240

Solution: There are 7 letters in the word SP240NC240R are 2240 , SP , NC , R   We will consider SP and NC as a group and there are 2 240's   No of arrangements in which S and P must always be together and the N and C must always be together   = (5! *2 *2)/2!   = 5!*2   = 120 *2= 
120 *2 = 240
240   Answer 240
Answer: E
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 26 seconds. The ratio of their speeds is?	Select the correct option
A) 3/1  B) 9/1  C) 3/3  D) 3/5  E) 5/2

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) = 26 ==> 27 x + 17 y = 26 x + 26 y   ==> 1 x = 9 y ==> x/y   = 9/1.   Answer:9/1
Answer: B
A person has to make 146 pieces of long bar. he take $ seconds to cut piece.what is total time taken by him to make 146 pieces?
Options: A) 580 seconds B) 680 seconds C) 500 seconds D) 540 seconds E) 560 seconds

Solution: if it is 4 seconds, as u have mistaken with SHIFT key, then....   we'll have to make 145 cuts for 146 pieces.   so 145 * 5 = 580 seconds   580 secondsNSWER:580 seconds
Answer: A
The manager at a health foods store mixes a unique superfruit juice cocktail that costs $1399.45 per litre to make. The cocktail includes mixed fruit juice and açai berry juice, which cost $262.85 per litre and $3104.35 per litre, respectively. The manager has already opened 32 litres of the mixed fruit juice. How many litres of the açai berry juice does he need to add?
Choose the correct answer
A) 17 litres	B) 21.3 litres	C) 11 litres	D) 07 litres	E) 38 litres

Solution: 262.85(32)+3,104.35x = 1,399.45(32 + x)   Solve the equation.   262.85(32)+3,104.35x = 1,399.45(32 + x)   8,411.2 + 3,104.35x = 44,782.4 + 1,399.45x   8,411.2 + 1,704.9x = 44,782.4   1,704.9x = 36,371.2   x ≈ 21.3   Answer is 21.3 litres.
Answer: B
The cost price of 14 articles is equal to the selling price of 11 articles. Find the profit percent?  Choose the most appropriate option
A) 18 2/91%	B) 18 2/11%	C) 27 3/11%	D) 18 2/91%	E) 12 2/11%

Solution: 14 27 3/11%P = 11 SP   11 --- 2 27 3/11%P   100 --- ? =>27 3/11%   Answer:27 3/11%
Answer: C
There are 7 Physics and 1 Chemistry book in shelf A and 5 Physics books in Shelf B, one book is moved from shelf A to shelf B. A student picks up a book from shelf B. Find the probability that the Chemistry book is taken by the student.
Choose the correct choice from the following options:
A) 7/8
B) 1/8
C) 1/48
D) 5/48
E) 5/6

Solution: I)Probability that the book moved from A to B is Chemistry=1/8.   II)Probability that the boom taken from B is 1/48hemistry=1/6   P=1/8∗1/6=14/8   ANSWER: 1/48
Answer: C
A train is 360 meter long is running at a speed of 45 km/hour. In what time will it pass a bridge of 140 meter length?
Pick.
A) 38 B) 27 C) 40 D) 77 E) 21

Solution: Speed = 45 Km/hr = 45*(5/18) m/sec = 25/2 m/sec   Total distance = 360+140= 
360+140 = 500
500 meter   Time= Distance/speed   = 500 * (2/25)= 
500 * (2/25) = 40
40 seconds   Answer: 40
Answer: C
Two pipes A and B can fill a tank in 50hour and 75 hours respectively. If both the pipes are opened simultaneously, how much time will be taken to fill the tank? Select.
A) 15hrs
B) 20hrs
C) 25hrs
D) 30hrs
E) 32hrs

Solution: Part filled by A in 1 hour = 1/50   part filled by B in 1 hour = 1/75   Part filled by A+B in 1 hour = 1/50 + 1/75 = 1/30   Both the pipes will together will fill the tank in 30 hours.   Answer is 30hrs
Answer: D
A sum of Rs. 1360 has been divided among A, B and C such that A gets of what B gets and B gets of what C gets. B's share is:  Answers.
A) 240 B) 120 C) 280 D) 160 E) 200

Solution: Let C's share = Rs. x   Then, B's share = Rs. x/4, A's share = Rs. (2/3 x (x/4))= Rs. x/6   Therefore, x/6 + x/4 + x = 1360   =17x/12 = 1360   x = 1360 x 12/17= Rs. 960   Hence, B's share = Rs. (960/4)= Rs. 240.   240nswer is 240.
Answer: A
The C.P of 10 pens is equal to the S.P of 12 pens. Find his gain % or loss%? Answers:
A) 16 2/6%	B) 16 3/3%	C) 16 2/3%	D) 16 2/9%	E) 12 2/3%

Solution: 10 16 2/3%P = 12 SP   12 --- 2 16 2/3%P loss   100 --- ? => 16 2/3%   Answer:16 2/3%
Answer: C
The average (arithmetic mean) of six numbers is 10. If 3 is subtracted from each of four of the numbers, what is the new average?
Pick
A) 1.5 B) 2 C) 3 D) 8 E) 4.5

Solution: Sum of 6 numbers = 6*10= 
6*10 = 60
60   If 3 is subtracted from each of four of the numbers , we subtract  3*4= 
 3*4 = 12
12 from the total sum   Sum of 6 number after subtracting 3 from each of four of the numbers= 60 - 12= 
60 - 12 = 48
48   New average= 48/6= 
48/6 = 8
8   Answer 8
Answer: D
The speeds of 3 trains in the ratio 2:4:6. The ratio between time taken by them to travel the same distance is? Choose the correct choice from the following.
A) 6:4:3 B) 1:2:3 C) 4:8:9 D) 6:3:2 E) 4:8:7

Solution: Ratio of time taken is = 1/2 : 1/4 : 1/6 = 6:3:2   Answer is 6:3:2
Answer: D
How many diagonals does a 62-sided convex polygon have?  Choose one:  A) 1829  B) 2356  C) 3458  D) 3843  E) 4820

Solution: A 62-sided convex polygon has 62 vertices.   If we examine a single vertex, we can see that we can connect it with 59 other vertices to create a diagonal. Note that we can't connect the vertex to itself and we can't connect it to its adjacent vertices, since this would not create a diagonal.   If each of the 62 vertices can be connected with 59 vertices to create a diagonal then the total number of diagonals would be (62)(59) = 3658   However, we must recognize that we have counted every diagonal twice.   To account for counting each diagonal twice, we must divide 3658 by 2 to get 1829.   The answer is 1829.
Answer: A
The sum of the present ages of a father and his son is 60 years. Six years ago, father's age was five times the age of the son. After 7 years, son's age will be:	Choose the correct answer.
A) 12 years  B) 14 years  C) 18 years  D) 20 years  E) 21 years

Solution: Explanation:   Let the present ages of son and father be x and (60 -x) years respectively.   Then, (60 - x) - 6 = 5(x - 6)   54 - x = 5x - 30   6x = 84   x = 14.   Son's age after 7 years = (x+ 7) = 21 years..   Answer: 21 years
Answer: E
A person travels from P to Q a speed of 50 km/hr and returns by increasing his speed by 50%. What is his average speed for both the trips? Options:
A) 62.5	B) 77	C) 48	D) 99	E) 21

Solution: Speed on return trip = 150% of 50 = 75 km/hr.   62.5verage speed of trip = 50 + 75 /2 =125/2= 
125/2 = 125/2 = around 62.5
62.5 km/hr   62.5nswer : 62.5
Answer: A
Express 5 mps in kmph?	Pick:
A) 22
B) 88
C) 90
D) 18
E) 24

Solution: 5 * 18/5= 
5 * 18/5 = 18
18 kmph   Answer: 18
Answer: D
In your classes you counted 126 hands. How many students were at the class? Select the correct option
A) 63
B) 61
C) 85
D) 86
E) 88

Solution: Total number of hands = 126   We have 2 hands.   To find how many students were at the class, divide the total number of hands by the number of hands we have.   We get, divide 126 by 2   126 ÷ 2 = 63   Therefore, there were 63 students at the class.   63NSWER IS 63
Answer: A
A man engaged a servant on the condition that he would pay him Rs.900 and a uniform after 1year service. He served only for 9 months and receiveduniform and Rs.650, find the priceof the uniform?
Select the correct option.
A) Rs.90
B) Rs.100
C) Rs.120
D) Rs.150
E) Rs.160

Solution: 9/12 = 3/4 * 900= 
3/4 * 900 = 675
675   650   -------------   25   1/4 -------- 25   1 --------- ?=> Rs.100   Rs.100
Answer: B
In a certain voting district, 40 percent of registered voters live in Town A and the rest live in Town B. In the last election, 70 percent of the registered voters from Town A voted. If equal numbers of registered voters from both towns voted, approximately what percent of the registered voters from Town B voted?	Choose the correct choice from the following
A) 72%  B) 47%  C) 42%  D) 34%  E) 28%

Solution: Town A is 40%, therefore town 47% must be 60%   Town A registered voters:0.70∗0.40=0.28   Town 47% registered voters: 0.60x=0.28 --> x=28/60 which is a little bit less than 50 percent   ANSWER:47%
Answer: B
A volunteer organization is recruiting new members. In the fall they manage to increase their number by 4%. By the spring however membership falls by 19%. What is the total change in percentage from fall to spring?
Choose the correct answer
A) 16.16%	B) 15.76%	C) 14.14%	D) 13.13%	E) 12.12%

Solution: (100%+4%)*(100%-19%) = 1.04*.81 = 0.8424.   1-0.8424 = 15.76% lost = -15.76%   The Answer is 15.76%   The organization has lost 15.76% of its total volunteers from fall to spring.
Answer: B
Alicia lives in a town whose streets are on a grid system, with all streets running east-west or north-south without breaks. Her school, located on a corner, lies three blocks south and three blocks east of her home, also located on a corner. If Alicia s equally likely to choose any possible path from home to school, and if she only walks south or east, what is the probability she will walk south for the first two blocks?  Choose the most appropriate option
A) 1/3  B) 1/5  C) 1/6  D) 1/7  E) 2/5

Solution: Total number of ways to go home, considering that the order order matters =   Options: SSSEEE   Slots : ------   total permutations of 6 options in 6 slots: 6P6 = 6! = 6*5*4*3*2   Total ways to select "South" in the first 2 positions and anything else in the subsequent 4 positions =   Options: SS ????   Slots: -- ----   Permutations of 3 "S" in 2 slots AND Permutations of 4 Choices in 4 slots =   3P2 * 4P4 = 3! * 4! = 3*2*4*3*2   The probability is therefore:   3P2 * 4P4 = 6P6   3*2*4*3*2= 1/5   ANSWER:1/5
Answer: B
There are 4 more women than men on Centerville's board of education. If there are 4 members on the board, how many are women?  Select:
A) 3
B) 4
C) 6
D) 7
E) 8

Solution: Given: M=W-4 so, W+(W-4)=4 --> W=4.   Answer: 4.
Answer: B
If O is the center of the circle in the figure above and the area of the unshaded sector is 5, what is the area of the shaded region?
Choose the correct choice from the following
A) 25/√π	B) 30/√π	C) 20	D) 25	E) 30

Solution: 60/360 = 1/6   1/6 of total area = 5   5/6 of total area = 5*5= 
5*5 = 25
25   ANSWER:25
Answer: D
What quantity of water should taken out to concentrate 27 liters of 40% acidic liquid to 60% acidic liquid?	Select.
A) 5liters	B) 10liters	C) 15liters	D) 9liters	E) 6liters

Solution: Required answer is = 27(60-40)/60 = 9 liters   Answer is 9liters
Answer: D
A rectangular grass field is 75 m * 55 m, it has a path of 3.2 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? Select the correct option.
A) s.1350
B) s.1327
C) s.1328
D) s.1364
E) s.1927

Solution: Area = (l + b +2d) 2d   = (75 + 55 +3.2 * 2) 2*2.5 => 682   682 * 2 = Rs.1364   Answer: s.1364
Answer: D
Two sides of a triangle have length 6 and 8. Which of the following are possible areas of the triangle?
I. 6
II. 12
III. 24	Choices.
A) I, II, and III B) I and II only C) II and III only D) I and III only E) II only

Solution: Answer = A. I, II, and III   With dimensions of only 2 sides given (for a triangle), this becomes an open ended question   I, II, and IIIny area is possible out of the three
Answer: A
A 240 meter long train running at the speed of 120 kmph crosses another train running in the opposite direction at the speed of 80 kmph in 9 seconds.What is the lenght of other train.	Options
A) 260m  B) 220m  C) 230m  D) 240m  E) 250m

Solution: Relative speeds=(120+80)km/hr   =200km/hr=(200*5/18)m/s=(500/9)m/s   let length of train be xm   x+240/9=500/9   x=260   260mns is 260m   260mNSWER: 260m
Answer: A
A rower can row upstream at 7 km/hr and downstream at 15 km/hr. What is the rower's rate in still water?
Choices
A) 9 km/hr	B) 10 km/hr	C) 11 km/hr	D) 12 km/hr	E) 13 km/hr

Solution: The rate in still water is 1/2 * (15 + 7)= 
1/2 * (15 + 7) = 11
11 km/hr   The answer is 11 km/hr.
Answer: C
If W is the set of all the integers between 49 and 88, inclusive, that are either multiples of 3 or multiples of 2 or multiples of both, then W contains how many numbers? Choose one.
A) 11	B) 44	C) 48	D) 28	E) 26

Solution: Official Solution:   Number of multiples of 3   Step 1. Subtract the extreme multiples of 3 within the range (The greatest is 87, the smallest is 51): 87 - 51 = 36   Step 2. Divide by 3: 36 / 3 = 12   Step 3. Add 1: 12 + 1 = 13.   So there are 13 multiples of 3 within the range: examples are 51, 54, 57, 60, etc.   Number of multiples of 2   Step 1. Subtract the extreme multiples of 2 within the range (The greatest is 88, the smallest is 50): 88 - 50 = 38   Step 2. Divide by 2: 38 / 2 = 19   Step 3. Add 1: 19 + 1 = 20.   So there are 19 multiples of 2 within the range: examples are 50, 52, 54, 56, 58, 60 etc.   Add the 13 multiples of 3 and the 19 multiples of 2: 13+19=32.However, by adding the multiples of 2 and the multiples of 3, we are effectively counting several numbers twice: for example, 54 and 60 are parts of both the lists above. So we can't just take   13+19= 
  13+19 = 32
32. Find the Number of multiples of 6 (which are the double counted, as 6 is divisible by both 2 and 3), and subtract it from 32:   Step 1. Subtract the extreme multiples of 6 within the range (The greatest is 72, the smallest is 54): 84 - 54= 30   Step 2. Divide by 6: 30 / 6 = 5   Step 3. Add 1: 5 + 1 = 6.   So there are 6 multiples of 6 within the range: we counted 6 numbers twice.   Subtract the 6 multiples of 6 from the sum of the multiples of 2 and 3:   =13+19 - 6   = 32 - 6= 
32 - 6 = 26
26   Therefore, the final number of multiples of 2, 3 or 6 is 26.   Hence, this is the correct answer. (26)
Answer: E
Two vertical pole of 2 m and 8 m stand apart on a horizontal plane.The height in meters at the point of intersection of the line joining the top of each pole to the bottom of other pole is ....	Choose the correct choice from the following:
A) 1.8 B) 1.6 C) 1.4 D) 5.4 E) cannot be determined without knowing the distance bw the bottom of the pole

Solution: formula is...(p*q)/p+q   here p=2,q=8   height in meters=(8*2)/8+2=16/10= 
16/10 = 8/5 = around 1.6
1.6   ANSWER:1.4
Answer: C
The perimeter of a triangle is 28 cm and the inradius of the triangle is 2.5 cm. What is the area of the triangle? Choose the correct choice from the following answers:
A) 11  B) 61  C) 88  D) 66  E) 35

Solution: Area of a triangle = r * s   Where r is the inradius and s is the semi perimeter of the triangle.   Area of triangle = 2.5 * 28/2= 
2.5 * 28/2 = 35
35 cm2   Answer:35
Answer: E
To be considered for “movie of the year,” a film must appear in at least 1/4 of the top-10-movies lists submitted by the Cinematic Academy’s 760 members. What is the smallest number of top-10 lists a film can appear on and still be considered for “movie of the year”?
Choose the correct choice from the following answers.
A) 191  B) 190  C) 193  D) 212  E) 213

Solution: Total movies submitted are 760.   As per question we need to take 1/4 of 760 to be considered for top 10 movies = 190   approximate the value we 190.   IMO option 190 is the correct answer...
Answer: B
If 4 people are selected from a group of 8 married couples, what is the probability that none of them would be married to each other?  Choose the correct choice from the following answers:	A) 1/33	B) 2/33	C) 8/13	D) 16/33	E) 11/12

Solution: If we are to select 4 people from 8 couples WITHOUT any restriction, how many ways can we make the selection? 16!/4!12! = 1820   If we are to select 4 people from 8 couples WITH restriction that no married couple can both make it to the group, only a representative?   8!/4!4! = 70   But we know that to select a person from each couple, take 2 possibilities     70*2*2*2*2= 
  70*2*2*2*2 = 1_120
1120   Probability= Desired/All Possibilities = 1120/1820 = 8/13   Answer: 8/13
Answer: C
The cost of 3 chairs and 10 tables is Rs 9856. What is the cost of 6 chairs and 20
tables? Choose the correct answer:	A) Rs 17227	B) Rs 18712	C) Rs 19172	D) Rs 19712	E) None

Solution: Let the cost of one chair be Rs x and that of a table be = Rs y   According to the question,   3x + 10y = Rs 9856   ⇒ 2 × (3x + 10y) = 2 × 9856   ∴ 6x + 20y = Rs 19712   Answer Rs 19712
Answer: D
A certain hall contains two cuckoo clocks. If the first clock chirps 20 times per hour and the second clock chirps 7 times per hour, and both clocks chirp for the first time at 2:03 pm, at what time will the first clock have chirped three times as many times as the second clock can chirp per hour?
Choose the correct choice from the following options:
A) 2:53 pm
B) 3:03 pm
C) 3:13 pm
D) 3:23 pm
E) 3:33 pm

Solution: The question is asking when the first clock will have chirped 21 times (3*7 chirps).   The first clock chirps once every 3 minutes.   If the first chirp is at 2:03, then the 21st chirp is at 63 minutes after 2:00.   The answer is 3:03 pm.
Answer: B
How many cubes of 10cm edge can be put in a cubical box of 1m edge	Choose the correct option:
A) 10  B) 100  C) 1000  D) 10000  E) 100000

Solution: Number of cubes=(100x100x100)/(10x10x10)=1000 Answer: 1000) 1000
Answer: C
Which greatest possible length can be used to measure exactly 10 meter 40 cm, 14 meter 10 cm and 7 meter 90 cm  Choose the correct choice from the following options
A) 45cm
B) 25cm
C) 24cm
D) 15cm
E) 10cm

Solution: Explanation:   Convert first all terms into cm.   i.e. 1040 cm, 1410cm, 790cm.   Now whenever we need to calculate this type of question, we need to find the HCF. HCF of above terms is 10.   Option 10cm
Answer: E
The subsets of the set {w, x, y} are {w}, {x}, {y}, {w, x}, {w, y}, {x,y}, {w, x, y}, and { } (the empty subset).
How many subsets of the set {w, x, y, z} contain w?  Choose one:
A) Four
B) Five
C) Seven
D) Eight
E) Sixteen

Solution: The number of ways of selecting 0 or more from n elements is 2^n.   Hence here, once you select w , the number of ways of selecting 0 or more from x,y and z ( 3 elements) is 2^3 = 8.   The same applies for {w, x, y}. If you select w here, the number of ways of selecting 0 or more from x and y = 2^2 = 4   FourNSWER:Four
Answer: A
The greatest common factor of two numbers is 5!. Which of the following can be the second number, if one of the numbers is 6!?
Pick.
A) 3(5!)  B) 5(5!)  C) 4(5!)  D) 6(5!)  E) 7(5!)

Solution: GCF is the product of common factors of the numbers involved.   GCF = 5!   a = 6! = 6*5!   b will certainly have 5! and cannot have any more common factors with a (as this will increase the GCF)   Looking at the answers only 5 (5!) and 6! will have GCF as 5!   Ans 5(5!)
Answer: B
There are twelve consecutive flags at an equal interval of distance. A man passes the 8th flag in 8 seconds. How many more seconds will he take to pass the remaining 4 flags ?	Pick one:
A) 2.57 seconds
B) 3.57 seconds
C) 4.57 seconds
D) 5.57 seconds
E) 6.57 seconds

Solution: let the 1st flag i placed at the origin and the remaining on the X-axis.......then the coordinate on 8th flag is (7,0)..therefore distance travelled is 7 units in 4 second ......and coordinate of 12th flag is (11,0)..there r 4 units ....so time taken is (8*4)/7=4.57 seconds   ANSWER:4.57 seconds
Answer: C
A box contains nine bulbs out of which 4 are defective. If four bulbs are chosen at random, find the probability that atleast one bulb is good?  Pick one.
A) 125/129 B) 125/122 C) 125/126 D) 125/128 E) 125/112

Solution: Required probability   = 1 - 1/126   = 125/126   Answer: 125/126
Answer: C