MU-NLPC/Calc-aqua_rat huggingface dataset:
In a camp, there is a meal for 140 men or 200 children. If 150 children have taken the meal, how many
men will be catered to with the remaining meal ?
Select:
A) 38 men  B) 32 men  C) 35 men  D) 30 men  E) None of these

Solution: Explanation:   There is meal for 200 children. 150 children have taken the meal.   Remaining meal is to be catered to 50 children.   Now, 200 children = 140 men   So, 50 35 menhildren = 140/200 * 50= 
140/200 * 50 = 35
35 men   Answer: 35 men
Answer: C
When 21 is divided by positive integer j, the remainder is 6. For how many values of j is this true?	Choose the correct option.
A) 1
B) 3
C) 5
D) 7
E) 9

Solution: When 21 is divided by j, the remainder is 6 i.e. 6 dragonfruit left over after grouping, so j is greater than 6.   It also means that 15 is completely divisible by j.   Factors of 15 are 1, 3, 5, and 15.   Out of these j could be 12.   1nswer (1)
Answer: A
A is thrice as good a work man as B and together they finish a piece of work in 12 days.The number of days taken by A alone to finish the work is :
Options
A) 28 days.  B) 14 days.  C) 12 days.  D) 16 days.  E) 18 days.

Solution: Solution   (A’s 1 day’s work): (B’s 1 day’s work)= 3 : 1.   (A + B)'s 1 day’s work = 1/12   Divide 1/14 in the ratio 3 : 1.   ∴ A’s 1 day’s work = (1/12 x2/3)= 1/16   Hence,A alone can finish the work in 16 days.   Answer 16 days.
Answer: D
A alone can finish a work in 10 days which B alone can finish in 15 days. If they work together and finish it, then out of a total wages of Rs.3100, A will get:
Choose the correct option
A) Rs.1200
B) Rs.1500
C) Rs. 1860
D) Rs.2000
E) None of these

Solution: Explanation:   Ratio of working days of A : B = 10 : 15   Therefore, their wages ratio = reverse ratio = 15 : 10   Therefore, A will get 15 units of ratio   Total ratio = 25   1 unit of ratio =3100/25= 
3100/25 = 124
124   So, A’s amount= 124 × 15 = Rs.1860.   Answer: Option Rs. 1860
Answer: C
A man in a train travelling at 24km/hr notices that a train going in the opposite direction passes him in 10 sec.If the length of this train is 220m find its speed .	Pick one:
A) 30 km/hr
B) 40 km/hr
C) 55 km/hr
D) 60 km/hr
E) 70 km/hr

Solution: relative speed of trains = 220/10 mtrs/sec = 220*18/(10*5)= 79 km/hr   speed of 2nd train = 79-24= 
79-24 = 55
55 km/hr   ANSWER:55 km/hr
Answer: C
Given f(x) = 2x – 3, for what value of x does 2*[f(x)] – 21 = f(x – 4) ?	Pick:
A) 0	B) 2	C) 4	D) 6	E) 8

Solution: 2(2x-3)-21 = 2(x-4) - 3   2x = 16   x = 8   The answer is 8.
Answer: E
In division sum, the remainder is 0. As student mistook the divisor by 12 instead of 21 and obtained 3 as quotient. What the correct quotient?
Pick:	A) 0	B) 12	C) 13	D) 20	E) None of these

Solution: Number = (12*35)= 
(12*35) = 420
420   Correct Quotient=420/21= 
420/21 = 20
20   Correct Option: 20
Answer: D
Pipe A can fill a tank in 5 hours, pipe B in 10 hours and pipe C in 30 hours. If all the pipes are open, in how many hours will the tank be filled? Choose the correct choice from the following.
A) 6 hours
B) 8 hours
C) 3 hours
D) 1 hours
E) 2 hours

Solution: Part filled by A + B + C in 1 hour   = 1/5 + 1/10 + 1/30 = 1/3   All the three pipes together will fill the tank in 3 hours.   Answer: 3 hours
Answer: C
The speed of a boat in still water is 80kmph and the speed of the current is 20kmph. Find the speed downstream and upstream?  Answers.
A) kmph
B) kmph
C) kmph
D) kmph
E) kmph

Solution: Speed downstream = 80 + 20= 
80 + 20 = 100
100 kmph   Speed upstream= 80 - 20= 
80 - 20 = 60
60 kmph   Answer:kmph
Answer: D
A train 385 meters long is running with a speed of 60 kmph. In what time will it pass a man who is running at 6 kmph in the direction opposite to that in which the train is going? Answers:	A) 5	B) 6	C) 21	D) 8	E) 9

Solution: Speed of train relative to man = (60 + 6) km/hr = 66 km/hr   [66 * 5/18] m/sec = [55/3] m/sec.   Time taken to pass the man = [385 * 3/55= 
385 * 3/55 = 21
21 sec   Answer: 21
Answer: C
The H.C.F of two numbers is 23 and the other two factors of their L.C.M are 13 and 14. The larger of the two numbers is:	Pick one:
A) 276  B) 299  C) 322  D) 345  E) 355

Solution: Clearly, the numbers are (23 * 13) and (23 * 14). Larger number = (23 * 14)= 
(23 * 14) = 322
322.   ANSWER:322
Answer: C
When a Mobile is sold for Rs. 7200, the owner loses 20%. At what price must that Mobile be sold in order to gain 20%? Choose the correct choice from the following answers.
A) 10,400
B) 10,600
C) 10,800
D) 11,000
E) 11,200

Solution: 80 : 7200 = 120 : x   x = (7200 x 120)/80 = 10800.   Hence, S.P. = Rs. 10,800.   Answer: Option 10,800
Answer: C
When you multiply a number by 4 and
then subtract 8, the result is the same as
if you first subtracted 11 from the same
number and then multiplied by 8. What
is the number?  Choose the correct choice from the following answers:
A) A)23
B) B)13
C) C)19
D) D)31
E) E)20

Solution: Let x equal the number and then change the words into an equation and solve for x:   4x – 8 = 8(x – 11)   4x – 8 = 8x – 88   80 = 4x   20 = x   correct answer 20)20
Answer: E
Of the goose eggs laid at a certain pond, 1/4 hatched and 4/5 of the geese that hatched from those eggs survived the first month. Of the geese that survived the first month, 2/5 did not survive the first year. If 120 geese survived the first year and if no more than one goose hatched from each egg, how many goose eggs were laid at the pond?  Select
A) 600	B) 700	C) 800	D) 900	E) 1000

Solution: Let x be the number of eggs that were laid.   (3/5)(4/5)(1/4)x = 120   (12/100)x = 120   x = 1000   The answer is 1000.
Answer: E
x, a, z, and b are single digit positive integers. x = ¼ a. z = ¼ b. (10a + b) – (10x + z) could be equal to
Choose the correct choice:  A) 32  B) 36  C) 45  D) 64  E) 65

Solution: 1) firstly we are not given that all are different integers..   2) since each is a positive single digit integer and x=a/4... a can take only 4 and 8 as value, and x can take 1 and 2..   3) same as 2) for b and z.   so in (10a + b) – (10x + z) ..   10a+b can be   44,48,84,88..   10x+z can be   11,12,21,22..   Ans :36
Answer: B
Seth opened a shop investing Rs.6000. Taylor joined him after one year, investing Rs.10000. They earned a profit of Rs.1100 after completion of two years. What will be Taylor's share of profit?  Select the correct option
A) 600 B) 700 C) 500 D) 800 E) 450

Solution: SoL = ~s- So Anju’s share = [5/11] x 1100 = 500   Answer: 500
Answer: C
A train speeds past a pole in 15 seconds and a platform 100 m long in 25 seconds. Its length is?	Choose the correct choice from the following answers.
A) 288 m
B) 267 m
C) 888 m
D) 150 m
E) 278 m

Solution: Let the length of the train be x meters and its speed be y m/sec.   They, x / y = 15 => y = x/15   x + 100 / 25 = x / 15   x = 150 m.   Answer: 150 m
Answer: D
In an election between two political leaders 10% of the voters did not cast their vote. 10% of the votes polled were found invalid. The successful political leader got 54% of the valid, votes and won by a majority of 3240 votes. The number of voters enrolled on the voters list was :
Choose one:
A) 30000	B) 50000	C) 33000	D) 40000	E) 45000

Solution: Explanation :   Solution: Let the number of voters be x. then, votes polled = 90% of x.   Valid votes = 90% of(90% of x)   .'. 54% of[90% of(90% of x)] - 46% of[90% of(90% of x)] = 3240.   8% of[90% of(90% of x)] = 3240.   8/100 * 90/100 * 90/100 * x = 3240   x = (3240*100*100*100)/(8*90*90)= 
(3240*100*100*100)/(8*90*90) = 50_000
50000   Answer : 50000
Answer: B
A jogger running at 9 km/hr along side a railway track is 240 m ahead of the engine of a 100 m long train running at 45 km/hr in the same direction. In how much time will the train pass the jogger?
Choose the correct choice from the following options:
A) 19 sec
B) 87 sec
C) 36 sec
D) 34 sec
E) 11 sec

Solution: Speed of train relative to jogger = 45 - 9= 
45 - 9 = 36
36 km/hr.= 36 * 5/18= 
36 * 5/18 = 10
10 m/sec.   Distance to be covered= 240 + 100= 
240 + 100 = 340
340 m.   Time taken= 340/10= 
340/10 = 34
34 sec.   Answer: 34 sec
Answer: D
Two passenger trains start at the same hour in the day from two different stations and move towards each other at the rate of 18 kmph and 21 kmph respectively. When they meet, it is found that one train has traveled 60 km more than the other one. The distance between the two stations is?	Pick.
A) 11	B) 444	C) 468	D) 287	E) 221

Solution: 1h ----- 5   ? ------ 60   12 h   RS = 18 + 21= 
18 + 21 = 39
39   T= 12   D = 39 * 12= 
39 * 12 = 468
468   Answer:468
Answer: C
A man sells a horse for Rs.800 and loses something, if he had sold it for Rs.980, his gain would have been double the former loss. Find the cost price of the horse?  Choose the correct choice: A) 227 B) 299 C) 277 D) 860 E) 771

Solution: CP = SP + 1CP = SP - g   800 + x = 980 - 2x   3x = 180 => x = 60   CP = 800 + 60= 
800 + 60 = 860
860   Answer: 860
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 110? Choose the correct choice:  A) 10  B) 25  C) 55  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=110/2= 
110/2 = 55
55   Answer is 55
Answer: C
The average weights for Tom,Jack,Rose was 90kg. The average weights for Jack,Rose,John was 100kg. If the weight of John be 50kg, what was the weight of Tom?	Options:
A) 20	B) 44	C) 37	D) 42	E) None of these

Solution: Explanation:   T + J + R = 90 × 3 = 270   J+R+J = 100× 3 = 300   20lso, weight of John = 50   Weight of Tom = 270+50-300= 
270+50-300 = 20
20kg   20nswer: Option 20
Answer: A
If e is an even integer and e/18 is an odd integer, which of the following is NOT an even integer? Choose the correct choice from the following answers:	A) (e^2)/54	B) (e^2)/12	C) (e^2)/9	D) (e^2)/6	E) (e^2)/2

Solution: since e is an even integer and e/18 is an odd integer. thus maximum power of 2 in a is one. why ?? because if the power of 2 in the expression has been 2 or greater, then the e/18 must have been an even integer. (18=2*3^2. as 18 contain only one 2 in the expression)   now, any expression in which we have 4 at the denominator will be odd. out of the given options only 12 is a multiple of 4. hence answer should be (e^2)/12
Answer: B
The elevator in an eleven-story office building travels at the rate of one floor per 1/4 minute, which allows time for picking up and discharging passengers. At the main floor and at the top floor, the operator stops for 1 minute. How many complete trips will an operator make during a 3-hour period?	Answers
A) 88 B) 56 C) 42 D) 25 E) 64

Solution: Complete trip = 10 floors up and 10 floors down = 20 floors = 20*1/4= 
20*1/4 = 5
5 minutes plus 2 minutes= 7 minutes.   3 hour = 180 minutes.   In 180 minutes operator can make 180/7=25 trips.   Answer: 25.
Answer: D
List A consists of 12 consecutive integers. If -4 is the least integer in list A, what is the range of positive integers in list A? Choose the most appropriate option: A) 5 B) 6 C) 7 D) 11 E) 12

Solution: Since -4 is the least integer in list A, then 7 is the largest integer in that list. Thus the range of the positive integers in the list is   7-1= 
  7-1 = 6
6.   Answer: 6.
Answer: B
What profit percent is made by selling an article at a certain price, if by selling at 4/5rd of that price, there would be a loss of 20%? Choose the correct choice from the following answers: A) 0% B) 29% C) 70% D) 27% E) 28%

Solution: SP2 = 4/5 SP1   CP = 100   SP2 = 80   4/5 SP1 = 80   SP1 = 100   100 --- 100= 
100 --- 100 = 0
> 0%   0%nswer: 0%
Answer: A
Three-twentieths of the members of a social club are retirees who are also bridge players, six-twentieths of the members are retirees, and one-half of the members are bridge players. If 130 of the members are neither retirees nor bridge players, what is the total number of members in the social club?	Choose the correct choice from the following options
A) 240	B) 300	C) 200	D) 400	E) 480

Solution: {Total} = {Retirees} + {Bridge players} - {Both} + {Neither}   x = 6/20*x + x/2 - 3/20*x + 130   20x = 6x + 10x - 3x + 130*20 (multiply by 20)   13x = 130*20   x = 200.   Answer: 200
Answer: C
In how many ways, a committee of 5 members can be selected from
6 men and 5 ladies, consisting of 3 men and 2 ladies?	Select.
A) 200	B) 450	C) 350	D) 500	E) 430

Solution: (3 men out 6) and (2 ladies out of 5) are to be chosen.   Required number of ways = (6c3x5c2)   = [6x5x4/3x2x1] x [5x4/2x1] = 200.   200NSWER 200
Answer: A
Zack has 3 red fish, 5 yellow fish and 7 green fish. How many fish does he have in all? Select
A) 8 B) 5 C) 15 D) 1 E) 18

Solution: 3+5+7= 
3+5+7 = 15
15. Answer is 15
Answer: C
The product of n consecutive positive integers is always divisible by? Choose the correct choice from the following.
A) n^2 -1  B) (n+1)!  C) 2n +1  D) n^2 + 1  E) n!

Solution: Plug in some vlues and check -   Product of first 2 number is 2*1   Product of first 3 number is 3*2*1   Product of first 4 number is 4*3*2*1   Product of first 5 number is 5*4*3*2*1   So, The product of first n natural numbers is always divisible by n! , answer will be (n^2 + 1)
Answer: D
he average weight of 8 persons increases by 2.5 kg when a new person comes in place of one of them weighing 70 kg. What might be the weight of the new person ? Choices:
A) 90 kg
B) 55 kg
C) 45 kg
D) 85 kg
E) 25 kg

Solution: Explanation:   Total weight increased = (8 x 2.5) kg = 20 kg.   Weight of new person = (70 + 20)= 
(70 + 20) = 90
90 kg.   90 kgnswer: 90 kg
Answer: A
What is the remainder when 1201 × 1202 ×1204 × 1205 is divided by 6?
Options.
A) 1
B) 2
C) 3
D) 4
E) 5

Solution: The remainders when dividing each number by six are: 1, 2, 4, and 5.   The product is 1*2*4*5= 
1*2*4*5 = 40
40   The remainder when dividing 40 by 6 is 4.   The answer is 4.
Answer: D
The population of a village is 15540. It increases annually at the rate of 28% p.a. What will be its population after 2 years?  Select: A) 10000 B) 25460 C) 26709 D) 14000 E) 14400

Solution: Formula :   ( After =100 denominator   Ago = 100 numerator)   15540 × 128/100 × 128/100 = 25460   25460
Answer: B
If the perimeter of a rectangular garden is 600 m, its length when its breadth is 120 m is? Choose the most appropriate option:
A) 286 m
B) 180 m
C) 200 m
D) 166 m
E) 187 m

Solution: 2(l + 120) = 600 => l   = 180 m   Answer: 180 m
Answer: B
What is the average of xx, 2x2x, and 66?
Choose the correct choice from the following choices.
A) x+2
B) x+2x
C) x+2x+2
D) 2x+2
E) x

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
A sum of money deposited at C.I. amounts to Rs.2420 in 2 years and to Rs.2662 in 3 years. Find the rate percent? Pick
A) 28
B) 10
C) 21
D) 17
E) 11

Solution: Explanation:   2420 --- 242   100 --- ? => 10%   Answer: Option 10
Answer: B
If there are 200 questions in a 3 hr examination. Among these questions are 25 type A problems, which requires twice as much as time be spent than the rest of the type B problems. How many minutes should be spent on type A problems? Choose the correct choice from the following answers:
A) 40 min B) 62 min C) 70 min D) 74 min E) 76 min

Solution: x=time for type B prolems   2x=time for type 40 min problem   total time=3hrs=180min   175x+25*2x=180   x=180/225= 
180/225 = 4/5 = around 0.8
0.8   time taken for type 40 min problem=25*2*0.8= 
25*2*0.8 = 40
40min   40 minNSWER:40 min
Answer: A
Find the simple interest on Rs. 3000 at 6 1/4% per annum for the period from
4th Feb., 2005 to 18th April, 2005.
Choose the correct choice from the following choices
A) Rs.36.50
B) Rs.37.50
C) Rs.35.50
D) Rs.32.50
E) Rs.33.50

Solution: Time = (24+31+18)= 
(24+31+18) = 73
73 days= 73/365 years = 1/5 years.   P = Rs.3000 and R = 6 ¼ %p.a = 25/4%p.a   S.I. = Rs.(3,000*(25/4)*(1/5)*(1/100))= Rs.37.50.   Remark : The day on which money is deposited is not counted while the day on which money is withdrawn is counted   Answer is Rs.37.50.
Answer: B
Two trains 140 m and 160 m long run at the speed of 60 km/hr and 40 km/hr respectively in opposite directions on parallel tracks. The time which they take to cross each other is?	Choose one:
A) 6.3 B) 5.2 C) 4.9 D) 10.8 E) 10.5

Solution: Answer: Option D   Relative speed = 60 + 40= 
60 + 40 = 100
100 km/hr.= 100 * 5/18 = 250/9 m/sec.   distance covered in crossing each other = 140 + 160= 
140 + 160 = 300
300 m.   Required time= 300 * 9/250 = 54/5= 
54/5 = 54/5 = around 10.8
10.8 sec.
Answer: D
Arabica coffee costs $0.4 per ounce while Robusta coffee costs $0.3 per ounce. If the blend of Arabica and Robusta costs $0.34 per ounce, what is the share of Arabica in this blend?	Choose the correct option:
A) 20%
B) 24%
C) 30%
D) 33%
E) 40%

Solution: a= amount of arabica coffee   1-a = amount of robusta coffee. because if you subtract a from the 1 ounce, the remaining amount is robusta   therefore:   .4a + .3(1-a) = .34   .4a + .3 - .3a = .34   a= .4   therefore: .4/1 ounce = 40%. Therefore, the answer should be 40%
Answer: E
Vijay bought 160 shirts at the rate of Rs. 225 per shirt. The transport expenditure was Rs. 1400. He paid an octroi at the rate of Rs. 1.75 per shirt and labour charges were Rs. 320. What should be the selling price of one shirt, if he wants a profit of 20%?  Select the correct option.
A) Rs.275  B) Rs.216  C) Rs.208  D) Rs.285  E) Rs.281

Solution: Total CP per shirt = 225 + 1400/160 + 1.75 + 320/160 = Rs. 237.5   SP = CP[(100 + profit%)/100]   = 237.5 * [(100 + 20)/100] = Rs.285.   Answer:Rs.285
Answer: D
Two digits in father's age are the same as the digit in the son's age, but in reverse order. In five years father will be twice as old as son will be then. what is the difference in their current age ?  Pick one.
A) 18	B) 16	C) 34	D) 25	E) 12

Solution: Father's age= 10x+y   so son's age= 10y+x..   after 5 years , 10x+y+5=2*(10y+x+5)....   so 5+19y=8x... check for odd values of y, y=1 satisfies the eqn with x=3... so ages are 31 and 13 and ans as found correctly by u is 18..18
Answer: A
If a1 = 1 and an+1= 2an + 5, n = 1, 2 .. , then a20 is equal to ?	Choose the correct answer.
A) a. 5*2^99-6	B) b.6 * 2^19 - 5	C) c. 6*2^99+5	D) d. 6*2^99-5	E) e. 6*2^99-6

Solution: Here is my solution:   an+1=2an+5............(1)   lets ADD 5 to both sides....   so (an+1) + 5= 2 (an+5)....................taking 2 as common factor   now a1=1. so for n=1, an+5=6.......   putting n=1. we get both sides as,   a2 + 5= 2 * 6 ..............as ( an+5=6 .......(for n=1)..)   a2= 2 *6 - 5   a2= 2 * 2 *3 - 5   a2= 2^2 *3 - 5................. so with same progression   a20= 2^20 * 3 - 5   a20=2 * 2^19 * 3 - 5   a100= 6 * 2^19 - 5   b.6 * 2^19 - 5
Answer: B
The total number of digit used in numbering the pages of a book having 366 pages, is :	Select:
A) 732	B) 990	C) 1098	D) 1305	E) None of these

Solution: Solution   Total number of digits =( No. of digits in 1-digits page nos. + No. of digits in 2-digits page nos. + No. of digits i 3-digits page nos.)   = (1 * 9 + 2 * 90 + 3 * 267) = (9 + 180 + 801)= 
(9 + 180 + 801) = 990
990 .   Answer 990
Answer: B
If 15% of 30% of 50% of a number is 126, then what is the number? Choose the correct choice from the following answers:  A) 5000  B) 5600  C) 5400  D) 4500  E) None of these

Solution: Let the number be a   Given, 15/100 * 30/100 * 50/100 * a = 126   => 3/20 * 3/10 * 1/2 * a = 126   => a = 10 * 20 * 10 * 2 = 5600.   ANSWER:5600
Answer: B
Roja and Pooja start moving in the opposite directions from a pole. They are moving at the speeds of 2 km/hr and 3 km/hr respectively. After 4 hours what will be the distance between them?	Choices.
A) 22 km B) 20 km C) 65 km D) 18 km E) 16 km

Solution: Distance = Relative Speed * Time   = (2 + 3) * 4= 
(2 + 3) * 4 = 20
20 km   [ They are travelling in the opposite direction, relative speed= sum of the speeds].   Answer: 20 km
Answer: B
If the LCM of two numbers a and b is 1104 and their HCF is 4, which of the following MUST be true?
I. a * b = 4416
II. a and b are both divisible by 8
III. a : b = 48 : 23
Select:
A) I only  B) II only  C) I and III only  D) II and III only  E) I, II, and III

Solution: LCM (x,y)=1104   HCF (x,y)=4   The product of two numbers is equal to product of their LCM and HCF.   x * y =1104 * 4= 
1104 * 4 = 4_416
4416 so statement I only is true   Since HCF (x,y) is 4 hence maximum common number with which x and y are divisible by is 4   so statement B is false   Now the ratio between x and y may be either 48:23 or 23:48   so statement C is false   Hence answer is 1   I onlyNSWER:I only
Answer: A
A big beautiful cube is formed by rearranging the 160 coloured and 56 non-coloured similar cubes in such a way that the exposure of the coloured cubes to the outside is minimum. The percentage of exposed area to the coloured is :  Answers:
A) 25.9%
B) 44.44%
C) 35%
D) 61%
E) None of these

Solution: Well the big cube which has the side built with 6 little cubes (6^3) will haveinsidethe cube which has the side built with 4 little cubes (6-2 edges), so 4^3. .. Similarly, the cube which has the side built with 4 little cubes (4^3) will haveinsidethe cube which has the side built with 2 little cubes, (4-2 edges), so 2^3... answer is 44.44%
Answer: B
Three men sit at a table. One dollar is placed in front of each of them. When a buzzer sounds, the first man to touch the money in front of him keeps the money that is in front of him, while the other two receive nothing. If none of the three men touches the money in front of them, then the amount of money doubles for the next round. After eight rounds of this activity, what is the maximum amount of money that any one man could receive?	Pick one.
A) $4 B) $5 C) $101 D) $115 E) $128

Solution: The Optimized scenario   After 1st Round - $1. Let nobody touches the amount will double in next round.   After 2nd Round - $2. Let nobody touches the amount will double in next round.   After 3rd Round - $4. Let nobody touches the amount will double in next round.   After 4th Round - $8. Let nobody touches the amount will double in next round.   After 5th Round - $16. Let nobody touches the amount will double in next round.   After 6th Round - $32. Let nobody touches the amount will double in next round.   After 7th Round - $64. Let Man A touches it and get$64   After 8th Round - $64. Let the same Man A touches it and get another$64.   So, after 8th round, the maximum amount a man receives is $128.   Answer ($128)
Answer: E
A question paper consists of five problems, each problem having three internal choices. In how many ways can a candidate attempt one or more problems?  Options:  A) 1546  B) 1054  C) 1023  D) 1608  E) 1065

Solution: Given that, the question paper consists of five problems. For each problem, one or two or three or none of the choices can be attempted.   Hence, the required number of ways = 45 - 1.   = 210 - 1 = 1024 - 1= 
1024 - 1 = 1_023
1023   Answer:1023
Answer: C
If P represents the product of the first 13 positive integers, which of the following must be true?
I. P is an odd number
II. P is a multiple of 16
III. P is a multiple of 27 Choose the correct choice from the following answers
A) I only	B) II only	C) III only	D) None of the above	E) All of the above

Solution: Answer = II only) II only
Answer: B
The sum of two number is 25 and their difference is 13. Find their product.	Choose the correct choice from the following options:
A) 104 B) product=114 C) 315 D) 325 E) None

Solution: EXPLANATION   Let the numbers be x and y.   Then, x + y = 25 and x – y = 13.   4xy = (x + y)2 – (x– y)2   = (25)2 – (13)2   = (625 – 169)   = 456   xy = 114.   Answer product=114
Answer: B
Two pipes can fill a tank in 20 minutes and 12 minutes. An outlet pipe can empty the tank in 10 minutes. If all the pipes are opened when the tank is empty, then how many minutes will it take to fill the tank?  Choose the correct choice from the following options:
A) 24  B) 26  C) 28  D) 30  E) 32

Solution: Let V be the volume of the tank.   The rate per minute at which the tank is filled is:   V/20 + V/12 - V/10 = V/30 per minute   The tank will be filled in 30 minutes.   The answer is 30.
Answer: D