MU-NLPC/Calc-aqua_rat huggingface dataset:
Tom, working alone, can paint a room in 12 hours. Peter and John, working independently, can paint the same room in 6 hours and 2 hours, respectively. Tom starts painting the room and works on his own for two hour. He is then joined by Peter and they work together for two hour. Finally, John joins them and the three of them work together to finish the room, each one working at his respective rate. What fraction of the whole job was done by Peter?
Options:
A) 5/3 B) 1/3 C) 7/3 D) 4/9 E) 3/5

Solution: Let the time when all three were working together be t hours. Then:   Tom worked for t+4 hour and has done 1/12*(t+4) part of the job;   Peter worked for t+2 hour and has done 1/6*(t+2) part of the job;   John worked for t hours and has done 1/2*t part of the job:   1/12*(t+4)+1/6*(t+2)+1/2*t=1 --> multiply by 12 --> (t+4)+(2t+2)+6t=12 --> t=2/3;   Hence Peter has done 1/6*(2/3+2)=1/6 *8/3=8/18=4/9   Answer: 4/9
Answer: D
A cistern has a leak which would empty the cistern in 20 minutes. A tap is turned on which admits 5 liters a minute into the cistern, and it is emptied in 24 minutes. How many liters does the cistern hold?  Choose the correct option: A) 480 B) 487 C) 481 D) 729 E) 600

Solution: 1/x - 1/20 = -1/24   x = 120   120 * 5 = 480   Answer:600
Answer: E
Rs.1500 is divided into two parts such that if one part is invested at 6% and the other at 5% the whole annual interest from both the sum is Rs.85. How much was lent at 5%?  Select:
A) 298  B) 287  C) 202  D) 500  E) 279

Solution: (x*5*1)/100 + [(1500 - x)*6*1]/100 = 85   5x/100 + 90 – 6x/100 = 85   x/100 = 5   => x =500   Answer:500
Answer: D
If both 7^2 and 3^4 are factors of the number a*4^3*6^2*13^11, then what is the smallest possible value of a?
Choose the correct choice from the following answers:  A) 120  B) 256  C) 343  D) 441  E) 512

Solution: The number a must include at least 3^2*7^2 = 441   The answer is 441.
Answer: D
The average of first twelve prime numbers which are odd is?	Choose the correct choice from the following answers
A) 15.5 B) 19.7 C) 15.2 D) 15.8 E) 15.1

Solution: Sum of first 12 prime no. which are odd = 236   Average = 236/12 = 19.7   Answer:19.7
Answer: B
The difference between two numbers is 1365. When the larger number is divided by the smaller one, the quotient is 6 and the remainder is 15. The smaller number is : Choose the correct option:  A) 240  B) 270  C) 295  D) 360  E) None

Solution: Solution   Let the numbers be x and (x + 1365).   Then, x + 1365 = 6x + 15 ⇔ 5x = 1350 ⇔ x = 270.   Answer 270
Answer: B
16,25,36,72,144,196,225 Choose one:
A) 36
B) 196
C) 225
D) 144
E) 72

Solution: Each of the numbers except 72 is a perfect square.   answer :72
Answer: E
Of the 3,600 employees of Company X, 12/25 are clerical. If the clerical staff were to be reduced by 1/4, what percent of the total number of the remaining employees would then be clerical? Select the correct option.
A) 40%	B) 22.2%	C) 20%	D) 12.5%	E) 11.1%

Solution: Let's see, the way I did it was   12/25 are clerical out of 3600 so 1728 are clerical   1728 reduced by 1/4 is 1728*1/4   so it reduced 432 people , so there is 1296 clerical people left   but since 432 people left, it also reduced from the total of 3600 so there are 3168 people total   since 1296 clerical left / 3168 people total   you get (40%) 40%
Answer: A
Train W leaves New York at 7:00 am traveling to Boston at 80mph. Train B leaves Boston at 7:45 am traveling to New York at 70 mph on a parallel track. If the distance between New York and Boston is 210 miles, at what time will the two trains pass each other?  Choose the most appropriate option.
A) 8:15 am	B) 8:45 am	C) 9:00 am	D) 9:30 am	E) Cannot be determined from the information given

Solution: train W will cover 60 kms in 45 min at 7:45, the time when train B starts...   distance left to cover is 210-60=150..   combined speed=80+70=150..   so the trains meet in 1 hour i.e. 7:45 + 1 hr=8:45   8:45 am
Answer: B
A car covers a distance of 10km in 12 minutes. If its speed is decreased by 5km/hr, the time taken by the car to cover the same distance will be?	Choose one
A) 10min 12sec	B) 15min 45sec	C) 13min 20sec	D) 20min 4sec	E) 30min 13sec

Solution: Speed = 10*60/12= 
10*60/12 = 50
50km/hr   New speed= 50-5= 
50-5 = 45
45 km/hr   Time taken= 10/45 = 60*2/9 = 13min 20sec   Answer is 13min 20sec
Answer: C
Two cars cover the same distance at the speed of 50 and 62 kmps respectively. Find the distance traveled by them if the slower car takes 1 hour more than the faster car. Choose the correct choice.
A) 250 km	B) 214 km	C) 224 km	D) 216 km	E) 204 km

Solution: 50(x + 1) = 62x   X = 4.16   60 * 4.16 = 250 km   250 kmNSWER:250 km
Answer: A
The side of a rhombus is 26 m and length of one of its diagonals is 20 m. The area of the rhombus is?	Options:
A) 289
B) 269
C) 207
D) 480
E) 271

Solution: 262 – 102 = 242   d1 = 20 d2 = 48   1/2 * 20 * 48= 
1/2 * 20 * 48 = 480
480   Answer: 480
Answer: D
A man walking at the speed of 4 kmph crosses a square field diagonally in 3 minutes. The area of the field is:	Pick one.
A) 18000m2
B) 20000m2
C) 19000m2
D) 25000m2
E) 15000m2

Solution: Length of the diagonal= Distance covered in 3 min. at 4 km/hr.   = (4000/ 60 *3)= 
(4000/ 60 *3) = 200
200m.   Therefore, Area of the field= 1/2 * diagonal2   = ½ * 200*200 = 20000 m2   ANSWER:20000m2
Answer: B
During 2003, a company produced an average of 1,000 products per month. How many products will the company need to produce from 2004 through 2007 in order to increase its monthly average for the period from 2003 through 2007 by 200% over its 2003 average?	Choose the correct choice from the following choices
A) 132,000 B) 235,000 C) 175,000 D) 200,000 E) 250,000

Solution: Company produced 12*1000 = 12,000 products in 2003. If company produces X products from 2004 to 2007, then total amount of product produced in 4 years (2003 through 2007) is X+12,000. The gives the average of (X+12,000)/4.   This average needs to be 200% higher than that in 2003. In math terms, 12,000+200%(12,000) = 36,000. So:   (X+12,000)/4 = 36,000   X+12,000 = 144,000   X = 132,000   The answer is 132,000.
Answer: A
Of the families in City X in 1992, 60 percent owned a personal computer. The number of families in City X owning a computer in 1993 was 50 percent greater than it was in 1992, and the total number of families in City X was 3 percent greater in 1993 than it was in 1992. what percent of the families in City X owned a personal computer in 1993?
Choose the correct answer
A) 68.99% B) 66.55% C) 91.23% D) 77.77% E) 87.37%

Solution: Say a 100 families existed in 1994 then the number of families owning a computer in 1994 - 60   Number of families owning computer in 1998 = 60 * 150/100= 
60 * 150/100 = 90
90   Number of families in 1998= 103   The percentage = 90/103 * 100 = 87.37%.   ANSW87.37%R:87.37%
Answer: E
In digging a pond 20 m * 10 m * 5 m the volumes of the soil extracted will be?	Pick one:
A) 3387
B) 1000
C) 2866
D) 2787
E) 1121

Solution: 20 * 10 * 5= 
20 * 10 * 5 = 1_000
1000   Answer: 1000
Answer: B
If b does not equal zero, and ab = b/5, what is the value of a?	Choose the correct choice from the following options
A) A)1/5 B) B)1/4 C) C)1/3 D) D)1/2 E) of the above

Solution: Explanation:   To solve for a, divide both sides of the equation by b: ab = b/5   (ab)/b = (b/5)/b   a = (b/5)*1/b   a = 1/5   1/5nswer: (1/5).
Answer: A
476 ** 0 is divisible by both 3 and 11. The non-zero digits in the hundred's and ten's places are respectively
Choose the correct choice
A) 7 and 4 B) 7 and 5 C) 8 and 4 D) 8 and 5 E) None

Solution: Let the given number be 476 xy 0.   Then (4 + 7 + 6 + x + y + 0) = (17 + x + y) must be divisible by 3.   And, (0 + x + 7) - (y + 6 + 4) = (x - y -3) must be either 0 or 11.   x - y - 3 = 0 y = x - 3   (17 + x + y) = (17 + x + x - 3) = (2x + 14)   x= 2 or x = 8.   x = 8 and y = 5.   Option 8 and 5
Answer: D
In a class of 69 students 41 are taking French, 22 are taking German. Of the students taking French or German, 9 are taking both courses. How many students are not enrolled in either course? Choose the correct choice from the following answers:
A) 6	B) 15	C) 24	D) 33	E) 54

Solution: Formula for calculating two overlapping sets:   A + 15 - both + NOT(A or 15) = Total   so in our task we have equation:   41 (french) + 22 (german) - 9 (both) + NOT = 69   54 + NOT = 69   NOT = 69 - 54= 
69 - 54 = 15
15   So answer is 15
Answer: B
Find the simple interest on $3000 for 3 years at 10% per annum?	Choose the correct choice from the following choices
A) $900	B) $300	C) $500	D) $600	E) $1000

Solution: SI = PTR/100   = 3000*3*10/100= 
3000*3*10/100 = 900
$900   $900nswer is $900
Answer: A
How many different positive integers are factors of 36 ?  Choose the correct choice from the following choices:	A) 10	B) 2	C) 7	D) 3	E) 2

Solution: 36=2*18   3*12   4*9   6*6   Answer : 7
Answer: C
A certain sum is invested at simple interest at 15% p.a. for two years instead of investing at 10% p.a. for the same time period. Therefore the interest received is more by Rs. 840. Find the sum?  Choose the correct answer
A) s. 8400  B) s. 9000  C) s. 14000  D) s. 17000  E) s. 27000

Solution: Let the sum be Rs. x.   (x * 15 * 2)/100 - (x * 10 * 2)/100 = 840   => 30x/100 - 20x/100 =840   => 10x/100 = 840   => x = 8400.   s. 8400NSWER:s. 8400
Answer: A
Car Z travels 48 miles per gallon of gasoline when driven at a constant rate of 45 miles per hour, but travels 20 percent fewer miles per gallon of gasoline when driven at a constant rate of 60 miles per hour. How many miles does car Z travel on 10 gallons of gasoline when driven at a constant rate of 60 miles per hour? Pick one.
A) 320 B) 384 C) 400 D) 408.3 E) 440

Solution: The question stem asks us for the distance possible with 10 gallons of fuel at a constant speed of 60 miles per hour. We therefore first calculate the fuel efficiency at that speed.   The stem tells us that at 45 miles/hour, the car will run 48 miles/gallon and at 60 miles/hour, that distance decreases by 20%. We can therefore conclude that the car will travel 38.4 miles/gallon at a constant speed of 60 miles/gallon. With 10 gallons of fuel, the car can therefore travel 38.4 miles/gallon * 10 gallons = 384 miles.   Answer 384.
Answer: B
In a consumer survey, 85% of those surveyed liked at least one of three products: 1, 2, and 3. 50% of those asked liked product 1, 30% liked product 2, and 20% liked product 3. If 7% of the people in the survey liked all three of the products, what percentage of the survey participants liked more than one of the three products? Choose the correct choice from the following answers
A) 5	B) 8	C) 15	D) 20	E) 25

Solution: Use the forumla ;   Total = Group1 + Group2 + Group3 - (sum of 2-group overlaps) - 2*(all three) + Neither   100 = 50 + 30 + 20 - ( sum of 2) -2(7) +15   100 = 101-( sum of 2)   1 = sum of 2   so more than 1 = 8   8
Answer: B
The ratio of the volumes of two cubes is 729 : 1331. What is the ratio of their total surface areas?	Choose one.
A) 81:121
B) 81:128
C) 81:126
D) 81:124
E) 81:122

Solution: Ratio of the sides = ³√729 : ³√1331   = 9 : 11   Ratio of surface areas = 92 : 112   = 81:121   81:121nswer: 81:121
Answer: A
Which of the following points is closest to line y=x Choose one
A) (2, -1)
B) (2, 4)
C) (1, 1)
D) (2, -1)
E) (-2, 0)

Solution: Attachment:   m12-20.pngAs you can see point (1, 1) is the closest to line y=x.   Answer: (1, 1).
Answer: C
x and y are positive integers. If x is a prime factor of y^2 , which of the following MUST be true?
Choose the correct choice from the following:
A) x is even
B) x=y^2
C) y/x is even
D) x/y <=1
E) x+1 is also the prime factor of y^2

Solution: A. x is even --> not necessarily true: x=3=odd and y=3   B. x=y2--> never true, as x=primex=prime then it can not equal to square of another integer;   C. yx is even --> not necessarily true: if x=3x=3 and y=3y=3 then yx=1=odd   D. xy≤1 is less than or equal to 1 --> always true as shown above or by POE;   E. x+1 is also a prime factor of y2--> not necessarily true: if x=2 and y=2 then x+1=3 and 3 is not a factor of y2=4   Answer: x/y <=1.
Answer: D
How many numbers with 2 different digits can be formed using only the odd digits? Answers
A) 10	B) 20	C) 40	D) 60	E) 120

Solution: Odd digits are 1, 3, 5, 7, 9.   We want 3 different digits.   First digit can be chosen in 5 ways.   Second digit can be chosen in 4 ways.   Total ways = 5*4= 
5*4 = 20
20   Hence option (20).
Answer: B
What is the least number of digits (including repetitions) needed to express 10^600 in decimal notation?  Select the correct option
A) a) 4 B) b) 601 C) c) 101 D) d) 1000 E) e) 1001

Solution: 10^n is a decimal number with a 1 followed by n zeros.   So 10^600 will include 600 0's + 1 digit for 1 = 601   So the answer is b) 601
Answer: B
In a 2000 m race, A beats B by 100 meters or 40 seconds. Find the speed of B?
Choose the correct choice from the following answers
A) 10m/s B) 2.5m/s C) 5m/s D) 7m/s E) 3m/s

Solution: Since A beats B by 100 m or 40 seconds,   it implies that B covers 100 m in 40 seconds.   Hence speed of B = 100/40= 
100/40 = 5/2 = around 2.5
2.5 m/s.   Answer: 2.5m/s
Answer: B
It takes 2 tons of copper ore and 4 tons of iron ore to make one ton of alloy A. How many tons of alloy A can be made from 60 tons of copper ore and 90 tons of iron ore?  Choose the correct choice from the following options:	A) 18	B) 18 3/4	C) 20	D) 22 1/2	E) 50

Solution: Yes, you need copper ore:iron ore in the ratio 2:4. Total 6 tons of the mix in this ratio will give 1 ton of alloy A.   If you have 60 tons of copper ore, it is enough for 60/2= 
60/2 = 30
30 tons of alloy A.   If you have 90 tons of iron ore, it is enough for 90/4= 22 1/2 tons of alloy A.   Since iron ore is available for only 22 1/2 tons of alloy A, you can make only 22 1/2 tons of alloy A.   The leftover copper ore alone cannot make any alloy A and hence will be leftover only.   Answer must be 22 1/2.   (22 1/2)
Answer: D
If a fair coin is flipped seven times in a row, what is the probability that there will be at least one head and one tail?
Select the correct option.
A) 3/4	B) 11/12	C) 15/16	D) 31/32	E) 63/64

Solution: The number of possible outcomes is 2^7 = 128   There is one way to get no heads and one way to get no tails.   Thus there are 126 outcomes with at least one head and one tail.   P(at least one head and one tail) = 126/128 = 63/64   The answer is 63/64.
Answer: E
A watch was sold at a loss of 10%. If it was sold for Rs.196 more, there would have been a gain of 4%. What is the cost price? Choose the correct answer:  A) s:1000  B) s:1067  C) s:1278  D) s:1028  E) s:1400

Solution: 90%   104%   --------   14% ---- 196   100% ---- ? =>   Rs:1400   Answer: s:1400
Answer: E
A WORKS TWICE AS FAST AS B. IF B CAN COMPLETE A WORK IN 12 DAYS INDEPENDENTLY, THE NUMBER OF DAYS IN WHICH A AND B CAN TOGETHER FINISH THE WORK IS:
Select
A) 4 DAYS  B) 6 DAYS  C) 8 DAYS  D) 18 DAYS  E) NONE OF THESE

Solution: RATIO OF RATES OF WORKING OF A AND B = 2:1. SO, RATIO OF TIME TAKEN = 1:2   A'S 1 DAY'S WORK = 1/6, B'S 1 DAY'S WORK = 1/12   (A+B)'S 1 DAY'S WORK = (1/6+1/12)=3/12=1/4   SO, A AND B TOGETHER CAN FINISH THE WORK IN 4 DAYS.   CORRECT OPTION: 4 DAYS
Answer: A
John traveled 80% of the way from Yellow-town to Green-fields by train at an average speed of 80 miles per hour. The rest of the way John traveled by car at an average speed of v miles per hour. If the average speed for the entire trip was 70 miles per hour, what is v in miles per hour?  Choose the correct option:
A) 30
B) 40
C) 50
D) 55
E) 60

Solution: HiBunuel   THe question seems incorrect. it should not be 80% at the speed of 80. However if it's 20% at the speed of 80, Answer comes out 55.   The question is correct. Here's the explanation:   Let distance be D. We can find the total timeequate it, which comes as:   0.8D / 80 + 0.2D / v = D / 70 => v = 60 (Option 60).
Answer: E
An amount of money is to be divided between P, Q and R in the ratio of 3:7:12. If the difference between the shares of P and Q is Rs.4000, what will be the difference between Q and R's share?
Choose the correct choice.
A) 2788 B) 5000 C) 7282 D) 2782 E) 2729

Solution: 4 --- 4000   5 --- ? => 5000   Answer:5000
Answer: B
In the next Worldcup of cricket there will be 12 teams, divided equally in 2groups. Teams of eachgroup will play a match against each other. From each group 3 top teams will qualify for the next round. In this round each team will play against each others once. 4top teams of this round will qualify for the semifinal round, where they play the best of 3matches. The Minimum number of matches in the next World cup will be
Pick:
A) 48 B) 49 C) 53 D) 55 E) 58

Solution: The number of matches in first round,   = 6C2 +6C2;   Number of matches in next round,   = 6C2;   Number of matches in semifinals,   = 4C2;   Total number of matches,   = 6C2 +6C2+6C2+4C2+2.   = 53.   53
Answer: C
find the number, difference between number and its 3/5 is 62. Choose the correct choice: A) 150 B) 153 C) 154 D) 155 E) 156

Solution: Explanation:   Let the number = x,   Then, x-(3/5)x = 62,   => (2/5)x = 62 => 2x = 62*5,   => x = 155   Answer: Option 155
Answer: D
A team bought a total of 198 balls. If each player on the team bought at least 17 balls, then what is the greatest possible number of players on the team?	Choose the correct choice from the following options.
A) 21 B) 11 C) 23 D) 24 E) 25

Solution: 198/17=11 plus remainder.   The answer is 11.
Answer: B
Every month Rani gives 65% of her salary to her mother. She spends 15% of her salary and saves the remainder. She saves $130 more than what she spends. What is her monthly salary? Choose the correct answer.
A) 2200 B) 2400 C) 2600 D) 2800 E) 3000

Solution: Total Salary given+Spent+Saving= 100%   65%+15%+Savings =100%   80%+Savings=100%   Savings=100%-80%=20%   Savings%-Spent%100 -80= 
100 -80 = 20
20%   Savings%-Spent%=$130   20-15= 
20-15 = 5
5%   5%of Salary=$130   5/100 * Salary = 130   Salary =130*100/5= 
130*100/5 = 2_600
$2600   answer : 2600
Answer: C
If you select two cards from a pile of cards numbered 1 to 10, what is the probability that the sum of the numbers is less than 4?  Pick:
A) 1/45
B) 4/45
C) 1/15
D) 1/10
E) 1/5

Solution: The number of ways to choose two cards is 10C2=45.   There is only one way to get a sum less than 4.   P(sum less than 4)=1/45   The answer is 1/45.
Answer: A
The difference between a discount of 35% and two successive discounts of 20% and 20% on a certain bill was 22. Find the amount of the bill.	Pick one:
A) 1,100	B) 200	C) 2,200	D) Data inadequate	E) None of these

Solution: Successive discount = 20%+20×80/100   = 20 + 16= 
20 + 16 = 36
36%   Difference in discount= 36 – 35 = 1%   \ Bill amount = 22 × 100 = 2200   Answer 2,200
Answer: C
A boy goes to his school from his house at a speed of 3 km/hr and returns at a speed of 2 km/hr. If he takes 5 hours in going and coming. The distance between his house and school is? Select:
A) 3 km B) 2 km C) 8 km D) 6 km E) 9 km

Solution: D   Average speed = (2 * 3 * 2) / (3 + 2) = 12/5 km/hr.   Distance traveled = 12/5 * 5= 
12/5 * 5 = 12
12 km.   6 kmistance between house and school= 12/2= 
12/2 = 6
6 km.
Answer: D
Rahim bought 27 books for Rs.581 from one shop and 20 books for Rs.594 from another. What is the average price he paid per book ? Select the correct option.
A) 28
B) 18
C) 27
D) 25
E) 21

Solution: Average price per book   = (581+ 594) / (27 + 20)   = 1175 / 47   = Rs.25   Answer:25
Answer: D
Two pipes A and B can separately fill a tank in 2 minutes and 15 minutes respectively. Both the pipes are opened together but 4 minutes after the start the pipe A is turned off. How much time will it take to fill the tank?
Select.
A) 22
B) 10
C) 88
D) 566
E) 222

Solution: 4/12 + x/15 = 1   x = 10.Answer: 10
Answer: B
In a race of length L metres, Johnson beats Lewis by M metres and Greene by N metres, By how many metres does Lewis beat Greene in the same race ? (M<N) Select the correct option:
A) L(L-N) / L-M B) L(N-M) / L-M C) L-N D) M-N E) M+

Solution: the ans is quite simple N-M but since the ans is not given, the best way to 'find' the correct option is to plug in the numbers. For my work, i took the following numbers:   L = 300   M = 10   N =20.   So basically, L beat G by 10 meters. Now whatever options comes close to the figure 10 is the right ans..   looking the the opion C to E, one can make out that they are incorrect, leaving us with just ..L(L-N) / L-M   Out of which, i choose L(L-N) / L-M.
Answer: A
By selling 16 pencils for a rupee a man loses 5%. How many for a rupee should he sell in order to gain 15%?	Choose the correct choice from the following:
A) 12.95 B) 19 C) 17.56 D) 16.56 E) 15

Solution: 85% --- 16   105% --- ?   85/105 * 16 = 8   12.95nswer: 12.95
Answer: A
Four friends go to see a movie at the local movie theater and sit in a row together. If there are two friends who refuse to sit next to each other, how many 4-person seating arrangements are possible? Choose the correct choice from the following
A) 6 B) 8 C) 10 D) 12 E) 24

Solution: The number of ways to arrange 4 people in a row is 4!   From this we want to subtract all the arrangements where the two friends are next to each other. If we consider them as one unit, then the number of arrangements of this 2-person unit and the 2 other friends is 3! And the number of arrangements of the two friends within this unit are 2 because the two friends can switch places. So the total number of arrangements of the 4 friends with the 2-person unit together is 3!*2   The total number of permutations where these two friends are not seated next to each other is 4! - 3!*2 = 24-12= 
24-12 = 12
12   The answer is 12.
Answer: D
Tough and Tricky questions: Exponents.
If 2^(3x+2)*3^(2y-3) = 32^x*9^y, then x + y = Choose the correct option.
A) -3 B) -1 C) 0 D) -5 E) -2

Solution: Here is my solution.   2^(3x+2)*3^(y-3) = 32^x*9^y   Here RHS 32^x*9^y= 2^(5x)*3^(2y)   -2quating powers on both sides-->   3x+2=5x , thus x 3 +2= 
 3 +2 = 5
5x , thus x=1 and   y-3=2y giving y=-3   So, x+y=-2   Option: -2
Answer: E
Let us say that a table tennis tournament was going on with knock out terms which means the one who loses the match is out of the tournament. 120 players took part in that tournament.
How many matches were played?
Choose the correct choice: A) 99 matches. B) 88 matches. C) 77 matches. D) 66 matches. E) 119 matches.

Solution: Solution:   119 matches.   The number of matches will always sum up to one less than the number of players in a knock out tournament. You may calculate it in any manner. Thus 119 matches were played.   Answer 119 matches.
Answer: E
A, B and C invests Rs.2000, Rs.3000 and Rs.4000 in a business. After 2 year A removed his money; B and C continued the business for two more year. If the net profit after 3 years be Rs.4000, then A's share in the profit is? Choose the correct choice:
A) 460
B) 289
C) 220
D) 400
E) 640

Solution: 2*24 : 3*36 : 4*36   4: 9: 12   4/25 * 4000= 
4/25 * 4000 = 640
640   Answer: 640
Answer: E
What is the probability of rolling a total of 8 with a single roll of two fair six-sided dice, each with the distinct numbers 1 through 6 on each side?
Choose the correct choice from the following answers
A) 1/12
B) 1/6
C) 2/7
D) 5/36
E) 1/2

Solution: Totalsample spacefrom two fair six-sided dice is 36.   There are six possible ways to be 8 i.e. (2+6), (3+5), (4+4), (5+3), (6+2)   So, total probability is 5/36.   Answer is 5/36.
Answer: D
What is the smallest positive integer K such that the product of 2205 x K is a perfect square?
Choose the correct option: A) 5 B) 9 C) 15 D) 25 E) 63

Solution: A perfect square, is just an integer that can be written as the square of some other integer. For example 16=4^2, is a perfect square.   Now, 2205 = 3^2 * 7^7 * 5, so if k=5 then 2205 k = (3 * 7 * 5)^2, which is a perfect square (basically the least positive value of k must complete only the power of 7 to even power as powers of other primes are already even).   5nswer: 5.
Answer: A
Which of the following will divide evenly into 347,456,520?	Answers
A) 3  B) 9  C) 11  D) 13  E) none of these

Solution: Rule:   3: Sum of the digits should be divisible by 3   Given number : 3+4+7+4+5+6+5+2+0= 
3+4+7+4+5+6+5+2+0 = 36
36 which is divisible by 3   3nswer: 3
Answer: A