MU-NLPC/Calc-aqua_rat huggingface dataset:
A reduction of 15% in the price of salt enables a lady to obtain 10kgs more for Rs.100, find the original price per kg?	Choose the correct answer:	A) 2.8	B) 2.3	C) 1.8	D) 2.1	E) 2.9

Solution: 100*(15/100)= 
100*(15/100) = 15
15 --- 10   ? --- 1=> Rs.1.5   100 --- 85   ? --- 1.5 => Rs.1.8   Answer: 1.8
Answer: C
In a certain game, you perform three tasks. You flip a quarter, and success would be tails. You roll a single die, and success would be a odd number. You pick a card from a full playing-card deck, and success would be picking a heart card. If exactly one of these three tasks is successful, then you win the game. What is the probability of winning?  Choose the correct answer:
A) 7/16	B) 1/16	C) 25/8	D) 11/13	E) 8/13

Solution: Event(1): Probability of getting tail in a flip of coin = 1/2   Event(2): Probability of getting odd number in a roll of dice = 3/6 = 1/2   Event(3): Probability of getting heart in a pack of card = 13/52 = 1/4   Probability of winning is having exactly one successful event is:   P(success 1)* P(Fail 2)* P(Fail 3) + P(Fail 1)* P(Success 2)* P(Fail 3) + P(Fail 1)* P(Fail 2)* P(Success 3)   = 1/2*1/2*3/4 +1/2*1/2*3/4 +1/2*1/2*1/4   =3/16 + 3/16 +1/16   =7/16   7/16nswer :7/16
Answer: A
The tax on a commodity is diminished by 20% but its consumption is increased by 20%. Find the decrease percent in the revenue derived from it?
Choose one
A) 12%
B) 4%
C) 16%
D) 20%
E) 22%

Solution: Explanation:   100 * 100= 
100 * 100 = 10_000
10000   80 * 120= 
80 * 120 = 9_600
9600   10000------- 400   100 ------- ?= 4%   4%
Answer: B
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 option.
A) 6/17 B) 6/11 C) 6/18 D) 6/19 E) 6/10

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
Two isosceles Triangles have equal vertical angles and their areas are in the ratio 9:25. Find the ratio of their corresponding heights . Choose the correct choice.
A) 4/5	B) 5/4	C) 3/2	D) 5/7	E) 3/5

Solution: We are basically given that the triangles are similar.   In two similar triangles, the ratio of their areas is the square of the ratio of their sides and also, the square of the ratio of their corresponding heights.   Therefore, area/AREA=height^2/HEIGHT^2=9/25 --> height/HEIGHT=3/5.   Answer: 3/5.
Answer: E
What is theleast number should be added to 519, so the sum of the number is completely divisible by 25?	Choose the correct choice
A) 1	B) 2	C) 5	D) 6	E) 8

Solution: (519/ 25) gives remainder 19   19 + 6= 
19 + 6 = 25
25, So we need to add 6   Answer : 6
Answer: D
A train 410 m long is running at a speed of 45 km/hr. In what time will it pass a bridge 140 m long?  Answers:	A) 40	B) 56	C) 44	D) 42	E) 34

Solution: Speed = 45 * 5/18 = 25/2 m/sec   Total distance covered = 410 + 140= 
410 + 140 = 550
550 m   Required time= 550 * 2/25= 
550 * 2/25 = 44
44 sec   Answer: Option 44
Answer: C
Two trains are moving in opposite directions at 60 km/hr and 90 km/hr. Their lengths are 1.10 km and 0.15 km respectively. The time taken by the slower train to cross the faster train in seconds is?
Choose the correct answer:  A) 65 sec  B) 30 sec  C) 48 sec  D) 33 sec  E) 12 sec

Solution: Relative speed = 60 + 90= 
60 + 90 = 150
150 km/hr.= 150 * 5/18 = 125/3 m/sec.   Distance covered = 1.10 + 0.15= 
1.10 + 0.15 = 1.25
1.25 km= 1250 m.   Required time = 1250 * 3/125= 
1250 * 3/125 = 30
30 sec.   Answer:30 sec
Answer: B
which number need to add to 859622 to get a number exactly divisible by 456?  Pick one: A) 123234 B) 345467 C) 467879 D) 356687 E) 859622

Solution: Dividend = Quotient * Divisor + Reminder   859622 / 456 gives quotient = 1885 and reminder = 62.   So, the next number divisible by 456 is 456 places infront of 456 * 1885   Which means 456 – 62 = 394 should be added to 859622.   859622
Answer: E
Tom can lay bus route between twogiven bus stop in 16 days and Andy can do the same job in 12 days. With help of John, they did the job in 4 days only. Then, John alone can do the job in how many days?  Choose the correct choice: A) 9 1/5 B) 9 3/5 C) 9 5/7 D) 10 1/5 E) 10 3/5

Solution: (A + B + C)'s 1 day's work =	1	,   4   A's 1 day's work =	1	,   16   B's 1 day's work =	1	.   12   Therefore C's 1 day's work =	1	-	(	1	+	1	)	=	(	1	-	7	)	=	5	.   4	16	12	4	48	48   So, C alone can do the work in	48	= 9 3	/5days.   5	5   9 3/5
Answer: B
At Company K, 20 percent of the employees are secretaries and 60 percent are salespeople. If there are 45 other employees of Company K, how many employees does Company K have?
Options.
A) 160	B) 180	C) 190	D) 225	E) 400

Solution: Let the total number of employees in the company be x   % of secretaries = 20%   % of salespeople = 60%   % of of employees other than secretaries and salespeople = 100 - 80= 
100 - 80 = 20
20%   But this number is given as 45   so 20% of x= 45   x = 225   Therefore there a total of 225 employees in the company K   Correct answer - 225
Answer: D
The diagonal of a rectangle is cm and its area is 20 sq. cm. The perimeter of the rectangle must be:
Choose the correct choice from the following options:  A) 18  B) 77  C) 625  D) 276  E) 191

Solution: Explanation:   (or) {\color{Black} l^{2}+b^{2}=41}   Also,   {\color{Black} (l+b)^{2}=l^{2}+b^{2}+2lb}   = 41 + 40= 
41 + 40 = 81
81   (l + b)= 9.   Perimeter = 2(l + b) = 18 cm.   18nswer: 18) 18
Answer: A
Series Problem like 4 12 x 44 46 132 134 begin of the Skype highlighting 44 46 132 134 end of the Skype highlighting. Find x?  Choose the correct option.
A) 13
B) 14
C) 15
D) 16
E) 17

Solution: 134-132= 
134-132 = 2
2   46-44= 
46-44 = 2
2   x-12=2   x=14   ANSWER:14
Answer: B
in a division sum the divisor is 12 times the quotient and 5 times the remainder.if the remainder is 48 what is the dividend
Choose the correct choice from the following
A) 4748
B) 4848
C) 4846
D) 4847
E) 4840

Solution: Dividend = divisor*quotient + remainder   divisor = 5*remainder = 5*48= 
5*48 = 240
240   now,   divisor= 12* quotient   240 = 12*quotient   quotient = 240/12= 
240/12 = 20
20   Dividend= divisor*quotient + remainder   Dividend = (240*20) + 48= 
(240*20) + 48 = 4_848
4848   ANSWER:4848
Answer: B
We bought 85 hats at the store. Blue hats cost $6 and green hats cost $7. The total price was $560. How many green hats did we buy? Choose the correct choice from the following choices
A) A)36
B) B)50
C) C)40
D) D)42
E) E)44

Solution: Let B be the number of blue hats and let G be the number of green hats.   B+G=85.   B=85-G.   6B+7G=560.   6(85-G)+7G=560.   510-6G+7G=560.   G=560-510= 
560-510 = 50
50.   The answer is 50.
Answer: B
Gary’s Gas Station serves an average of 15 cars per hour on Saturdays, 10 cars per hour on Sundays, and 9 cars per hour on all other days of the week. If the station is open from 6 a.m. to 10 p.m. every day, how many cars does Gary’s station serve over the course of a typical week?
Choose the correct choice from the following choices
A) 1,120  B) 1,200  C) 1,240  D) 1,280  E) 1,320

Solution: 6 a.m. to 10 p.m. = 16 hours   Number of cars serviced on weekdays = (16 * 9 * 5)   Number of cars serviced on Saturday = (16 * 15)   Number of cars serviced on Sunday = (16 * 10)   Number of cars served in a week = 16(45 + 15 + 10) = 16 * 70= 
16 * 70 = 1_120
1120   1,120nswer: 1,120
Answer: A
Before 7 years, dog A’s age was 4 times of dog B’s age and after 4 years, dog A’s age will be 3 times of dog B’s age. What is the difference of dog A’s age and dog B’s now?  Choose the most appropriate option.
A) 36
B) 42
C) 54
D) 60
E) 70

Solution: A - 7 = 4(B - 7) --> A - 4B = -21.............1   A + 4 = 3(B + 4) --> A - 3B = 8.............2   (2) - (1) --> B = 29 --> A =3(22)=99   A - B = 99 - 29= 
99 - 29 = 70
70   Answer: 70
Answer: E
Suresh borrows Rs. 10,000 for 2 years at 4 % p.a. simple interest. He lends it to Ramesh at 6 % p.a. for 2 years. Find his gain in this transaction per year.
Pick
A) Rs. 150 B) Rs. 200 C) Rs. 400 D) Rs. 450 E) None of these

Solution: Explanation:   Given:   We have to calculate the gain in 2 years.   1) In case of Suresh   S.I.(10000 × 4 × 2)/100= Rs. 800   2) In case of Ramesh   S.I.(10000 × 6 × 2)/100= Rs. 1200   Suresh has a pay a simple interest of Rs. 80 to the person from whom he borrowed Rs. 1000 and Ramesh has to pay Rs. 120 to Suresh.   Hence, gain in 2 years = 1200 – 800 = Rs. 400   But we are asked to find gain of Suresh per year. Therefore,   Gain in 1 year = 400 / 2 = Rs. 200   ANSWER IS Rs. 200
Answer: B
The area of a rectangular field is equal to 300 square meters. Its perimeter is equal to 70 meters. Find the width of this rectangle.
Answers.
A) W = 27 B) W = 15 C) W = 38 D) W =43 E) W = 13

Solution: L * W = 300 : area , L is the length and W is the width.   2 L + 2 W = 70 : perimeter   L = 35 - w : solve for L   (35 - W) * W = 300 : substitute in the area equation   W = 15 and L = 20 : solve for W and find L using L = 35 - w.   correct answer W = 15
Answer: B
If the product of 2 integers is negative, at most how many of the integers can be negative?	Choose the most appropriate option:
A) 1
B) 3
C) 4
D) 5
E) 6

Solution: The product of 2 integers is negative   Thus an odd number of integers need to be negative to have a negative product   We are asked at most how many are required.   So, the highest odd integer before 6,i.e. 1   Correct Option : 1
Answer: A
The sum of the two numbers is 12 and their product is 35. What is the sum of the reciprocals of these numbers ?
Choose the correct answer.
A) 12/35  B) 24/32  C) 31/24  D) 12/26  E) 12/25

Solution: Let the numbers be a and b. Then, a + b = 12 and ab = 35.   a + b/ab = 12/35   1/b+ 1/a= 12/35   Sum of reciprocals of given numbers =12/35   12/35NSWER: 12/35
Answer: A
A and B complete a work in 20 days. A alone can do it in 40 days. If both together can do the work in how many days? Choose the correct choice from the following choices:
A) 1.0875 days  B) 0.1875 days  C) 0.0675 days  D) 0.075 days  E) 0.0175 days

Solution: 1/20 + 1/40= 
1/20 + 1/40 = 3/40 = around 0.075
0.075 days   ANSWER:0.075 days
Answer: D
In a mayoral election, Candidate X received 1/5 more votes than candidate Y, and Candidate Y received 1/2 fewer votes than Z. If Z received 20,000 votes how many votes did candidate X received?
Options:
A) 12000  B) 22000  C) 24000  D) 26000  E) 32000

Solution: Z=20 --> Y received 1/2 fewer votes than Z --> Y=Z-1/2*Z=10;   X received 1/5 more votes than Y --> X=Y+1/5*Y=12.   12000nswer: 12000.
Answer: A
If a and b are odd integers, a Δ b represents the product of all odd integers between a and b, inclusive. If y is the smallest prime factor of (3 Δ 47) + 2, which of the following must be true? Choose the most appropriate option.
A) y is greater than 50
B) 30 ≤ y ≤ 50
C) 10 ≤ y < 30
D) 3 ≤ y < 10
E) y = 2

Solution: (3 Δ 47) + 2 = 3*5*7*...*47+2 = odd + 2 = odd.   Now, 3*5*7*...*47 and 3*5*7*...*47 +2 are consecutive odd numbers. Consecutive odd numbers are co-prime, which means that they do not share any common factor but 1. For example, 25 and 27 are consecutive odd numbers and they do not share any common factor but 1.   Naturally every odd prime between 3 and 47, inclusive is a factor of 3*5*7*...*47, thus none of them is a factor of 3*5*7*...*47 +2. Since 3*5*7*...*47+2 = odd, then 2 is also not a factor of it, which means that the smallest prime factor of 3*5*7*...*47 +2 is greater than 50.   y is greater than 50nswer: y is greater than 50.
Answer: A
If -3x > 9, which of the following must be true?	Choose the correct choice from the following options:
A) x < -3 B) x < -2 C) x > 3 D) x > -2 E) x > 0

Solution: -3x > 9   => -x > 3   => x < - 3   x < -3nswer x < -3
Answer: A
Boy sells a book for Rs. 810 he gets a loss of 10 %, To gain 10%, what should be the SP? Choose the most appropriate option.
A) 430
B) 990
C) 550
D) 590
E) 600

Solution: Cost price = 810/90 x 100 = 900   To gain 10% = 900 x 10/100 = 90   SP = CP + gain = 900 + 90= 
900 + 90 = 990
990   Answer : 990
Answer: B
Each of the 59 members in a Arts class is required to sign up for a minimum of one and a maximum of three academic clubs. The three clubs to choose from are the poetry club, the history club, and the writing club. A total of 22 students sign up for the poetry club, 27 students for the history club, and 28 students for the writing club. If 6 students sign up for exactly two clubs, how many students sign up for all three clubs?	Choose the correct answer:
A) 2  B) 5  C) 6  D) 8  E) 9

Solution: Each of the 59 members in a Arts class is required to sign up for a minimum of one and a maximum of three academic clubs. Total = G1 + G2 + G3 - (# In exactly 2) - 2*(# in 3 sets)   59 = 22+27+28 - (6) - 2x   so, # In 3 sets = 6=6
Answer: C
A manufacture of printer toner adjusts its price of color toner from $33 to $35 a cartridge and the price of standard black ink toner from $29 to $30 a cartridge if a document printing center spends an average of $1555 a month for toner of which 3/5 is for color cartridges how much more per month will the printing center spent?
Answers.
A) 78
B) 79
C) 60
D) 80
E) 90

Solution: Total money spend per month = 1555   Money spend on color toner cartridges = 3/5*1555= 
3/5*1555 = 933
933   Money spend on black ink toner cartridges= 2/5*1555= 
2/5*1555 = 622
622   Number of color toned cartridges bought= 933/33   Number of black ink toned cartridges bought = 622/29   New price of color toned cartridges bought = 933/33*35   New price of black ink toned cartridges bought = 622/29*30   Total price = 1632.993   78dditional money spend = Rs77.993   78NSWER:78
Answer: A
Dany bought a total of 20 game cards some of which cost $0.25 each and some of which cost $0.15 each. If Dany spent $4.2 to buy these cards, how many cards of each type did he buy?
Choose the correct choice from the following answers
A) 6 B) 7 C) 8 D) 9 E) 10

Solution: Let X be the number of cards that cost $0.25 each and Y the number of cards that cost $0.15 each. The total number of cards is 20. Hence   X + Y = 20   If X is the number of cards at $0.25, then the X cards cost   0.25 X   If Y is the number of cards at $0.15, then the Y cards cost   0.15 Y   The total cost of the X cards and the the Y cards is known to be $4.2 and also given by   0.25 X + 0.15 Y = 4.2   We now need to solve the system of equations   X + Y = 20   0.25 X + 0.15 Y = 4.2   The first equation gives Y = 20 - X. Substitute y by 20 - x in the second equation and solve   0.25 X + 0.15 (20 - X) = 4.2   X(0.25 - 0.15) + 3 = 4.2   0.1 X = 1.2   X = 12 and Y = 20 - 12= 
20 - 12 = 8
8   correct answer 8
Answer: C
A certain sum is invested at simple interest at 18% p.a. for two years instead of investing at 12% p.a. for the same time period. Therefore the interest received is more by Rs. 300. Find the sum?	Choose the correct choice from the following options.
A) 7000  B) 2500  C) 2778  D) 2800  E) 2791

Solution: Let the sum be Rs. x.   (x * 18 * 2)/100 - (x * 12 * 2)/100 = 300 => 36x/100 - 24x/100 =300   => 12x/100 = 300 => x = 2500.Answer:2500
Answer: B
A man can row with a speed of 15 kmph in still water. If the stream flows at 5 kmph, then the speed in downstream is?  Choose one:
A) 22	B) 28	C) 20	D) 10	E) 17

Solution: M = 15   S = 5   DS = 15 + 5= 
15 + 5 = 20
20   Answer:20
Answer: C
What is the smallest positive integer x, such that 1,152x is a perfect cube?  Choose the correct choice.
A) 4	B) 6	C) 8	D) 12	E) 18

Solution: We need to make 1152x a perfect cube, hence we need to have the powers a multiple of 3   1152 = 2^7*3^2   The minimum value of x for which 1152x is a perfect cube = 2^2*3 = 12   Correct Option: 12
Answer: D
How many minutes does it take Dorathy to type 16 words if she types at the rate of 4 words per minute?  Select the correct option:
A) 7
B) 3
C) 6
D) 2
E) 4

Solution: time*rate=job --> time*4=16 --> time=16/4=2.   Answer: 4.
Answer: E
Two persons start running simultaneously around a circular track of length 300 m from the same point at speeds of 15 km/hr and 25 km/hr. When will they meet for the first time any where on the track if they are moving in opposite directions? Select the correct option:
A) 22	B) 74	C) 77	D) 27	E) 29

Solution: Time taken to meet for the first time anywhere on the track   = length of the track / relative speed   = 300 / (15 + 25)5/18 = 300* 18 / 40 * 5 = 27 seconds.   Answer: 27
Answer: D
40 litres of diesel is required to travel 600 km using a 800 cc engine. If the volume of diesel required to cover a distance varies directly as the capacity of the engine, then how many litres of diesel is required to travel 800 km using 1200 cc engine?  Select.
A) 80 litres
B) 90 litres
C) 120 litres
D) 170 litres
E) None of these

Solution: Explanatory Answer   To cover a distance of 800 kms using a 800 cc engine, the amount of diesel required = 800/600*40 = 53.33 litres.   However, the vehicle uses a 1200 cc engine and the question states that the amount of diesel required varies directly as the engine capacity.   i.e., for instance, if the capacity of engine doubles, the diesel requirement will double too.   Therefore, with a 1200 cc engine, quantity of diesel required = 1200/800*53.33 = 80 litres.   80 litresnswer 80 litres
Answer: A
A person covered one-fourth of the total distance at 12 kmph and remaining distance at 24 kmph. What is the average speed for the total distance?
Choose the correct choice from the following answers:
A) 19 (1/8)kmph
B) 19 (1/5)kmph
C) 21 (7/3)kmph
D) 27 (1/3)kmph
E) 21 (1/8)kmph

Solution: Let the total distance be x km   total time taken = (x/4)/12 + (3x/4)/24 = x/48+ x/32 = 5x/96   Average speed = x/(5x/96) = 96/5 kmph   = 19 1/5 kmph.   Answer:19 (1/5)kmph
Answer: B
A rower can row upstream at 7 km/hr and downstream at 11 km/hr. What is the rower's rate in still water?
Choose the correct choice from the following options.
A) 7.5 km/hr  B) 8.0 km/hr  C) 8.5 km/hr  D) 9.0 km/hr  E) 9.5 km/hr

Solution: The rate in still water is 1/2 * (11 + 7)= 
1/2 * (11 + 7) = 9
9 km/hr   The answer is 9.0 km/hr.
Answer: D
A man is 34 years older than his son. In two years, his age will be twice the age of his son. The present age of the son is?	Select the correct option:
A) 16	B) 19	C) 15	D) 32	E) 40

Solution: Let the son's present age be x years.   Then, man's present age = (x + 24) years.   (x + 34) + 2 = 2(x + 2)   x + 36 = 2x + 4   => x =32 .   Answer: 32
Answer: D
A and B together can complete a work in 12 days. A alone can complete it in 20 days. If B does the work only for half a day daily, then in how many days A and B together will complete the work?
Options
A) 22  B) 88  C) 15  D) 66  E) 81

Solution: B's 1 day work = (1/12 - 1/20) = 1/30   Now, (A + B)'s 1 day work = (1/20 + 1/60) = 1/15   So, A and B together will complete the work in 15 days.   Answer: 15
Answer: C
A fruit seller had some apples. He sells 40% apples and still has 420 apples. Originally, he had:  Choices:
A) 700
B) 650
C) 850
D) 800
E) 900

Solution: Explanation :   Suppose originally he had x apples.   Then, (100 - 40)% of x = 420.   => 60% of x = 420   => 60 * x /100 = 420   => x = (420 * 100) / 60   => x = 700   Hence 700 is the answer   700nswer : 700
Answer: A
A computer is programmed to multiply consecutive even integers 2*4*6*8*…*n until the product is divisible by 1419, What is the value of n?	Select the correct option
A) 86	B) 38	C) 62	D) 122	E) 672

Solution: Factorise 1419.. 3*11*43..   So n has to be a multiple of largest prime number,61..   So n=2*43=86..   86ns :86
Answer: A
Let A be the event that a randomly selected two digit number is divisible by 2 and let B be the event that a randomly selected two digit number is divisible by 5. What is P(A and B)?	Choose the correct answer
A) 1/18	B) 1/10	C) 1/5	D) 1/3	E) 1/2

Solution: P(A and 1/10) = 1/2*1/5 = 1/10   The answer is 1/10.
Answer: B
Find the number of square tiles to cover the floor of a room measuring 4 m * 9 m leaving 0.25 m space around the room. A side of square tile is given to be 25 cms?	Pick one.
A) 366
B) 476
C) 296
D) 176
E) 191

Solution: 3 1/2 * 8 1/2   = 1/4 * 1/4 * x => x   = 476   476
Answer: B
In an election between two candidates, the winner has a margin of 10% of the votes polled. If 1500 people change their mind and vote for the loser, the loser would have won by a margin of 10% of the votes polled. Find the total number of votes polled in the election?	Choose the correct choice from the following answers:
A) 30,000 B) 15,450 C) 45,000 D) 60,000 E) 15,000

Solution: Total # of votes cast = 100x, out of these, let the # of votes won by the winner = w, and for the loser(l) = 100x-w. Given that w-(100x-w) = 10% of total votes cast = 10x   Thus, 2w-100x = 10x →→ w = 55x and l = 100x-55x = 45x.   According to the new condition, if the loser had won 45x+1500 votes, then , (45x+1500)-(55x-1500) 100 -55= 
100 -55 = 45
45x.   According to the new condition, if the loser had won 45x+1500 votes, then , (45x+1500)-(55x-1500)= 10 % of total votes cast = 10x   Thus, 3000 = 20x and 100x = 15000   ANSW15,000R:15,000
Answer: E
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?	Options
A) 20 min
B) 30 min
C) 40 min
D) 35 min
E) 37 min

Solution: A   20 min   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: A
If P represents the product of the first 13 positive integers, which of the following must be true?
I. P is an even number
II. P is a multiple of 17
III. P is a multiple of 60
Pick one: A) I only B) II only C) I & III only D) None of the above E) All of the above

Solution: The correct answer is I and III   I & III only
Answer: C
Which of the following is an integer?
I. 10! / 6!
II. 10! / 8!
III. 10! / 7!5!
Pick.
A) I only  B) II only  C) III only  D) I and II only  E) I, II and III

Solution: 10!/6! = 10*9*8*7 which is an integer.   10!/8! = 10*9 which is an integer.   10!/7!5! = 10*9*8 / 5*4*3*2 = 3*2 which is an integer.   The answer is I, II and III.
Answer: E
In an election between 2 candidate one have got 53% votes and
won by 1057 votes, how many votes were there ?	Choose the correct choice from the following.
A) 17616	B) 27616	C) 37616	D) 15616	E) 12616

Solution: other got=100-53= 
100-53 = 47
47   they won bye 1057 votes so that is their difference   so,53-47=6   then,6-->1057   100-->?   ( 1057*100)/6   =17616   17616NSWER:17616
Answer: A
Set R includes elements {8, 2, 11, x, 3, y} and has a mean of 7 and a median of 5.5. If x < y, then which of the following is the maximum possible value of x?
Choose the correct choice from the following answers:
A) 0	B) 1	C) 2	D) 3	E) 4

Solution: First, reach to the point of getting the equation R : x + y = 18   It should take about 20 seconds.   Then Substitute the answer choices into the equation.   I don't know what the answer choices in this case are.   But I'm sure, you would be able to eliminate at least 2 or 3 answer choices. (about 10 seconds).   Say you are left with 2 answer choices. (If you are short on time, guess One of the two and you'll have a 50% probability of getting it right.)   The Median (of 6 numbers) = 5.5. See if the AVERAGE of any two numbers among (2,3,8,11) results in the median. In this case, it does for 3 and 8. (15 seconds).   Once you know that the numbers that contribute towards Median are 3 and 8, and not x or y, then given x < y, x≤3. (about 10 seconds)=3
Answer: D