MU-NLPC/Calc-aqua_rat huggingface dataset:
A train travelled from station P to Q in 8 hours and came back from station Q to P is 6 hours. What would be the ratio of the speed of the train while traveling from station P to Q to that from station Q to P? Options:
A) 3 : 4 B) 4 : 3 C) 1 : 4 D) 2 : 3 E) 4 : 5

Solution: Since S # 1/t   S1 : S2 = 1/t1 : 1/t2 = 1/8 : 1/6 = 3 : 4   3 : 4nswer : 3 : 4
Answer: A
The three digits of a number add up to 20. The number is divisible by 5. The leftmost digit is double the middle digit. What is the product of the three digits?  Select
A) 175 B) 250 C) 78 D) 225 E) 125

Solution: Say the three-digit number is abc.   The leftmost digit is double the middle digit --> a=2b;   The number is divisible by 5 --> c is either 0 or 5;   The three digits of a number add up to 20 --> a+b+c=20   So, either a+b+c=2b+b+0=20 or a+b+c=2b+b+5=20. The first equation does not give an integer value of b, so it's not the case. From the second we get that b=5 --> a=10 and c=5 --> a*b*c=250.   Answer: 250.
Answer: B
During a Pizza buffet where A eats more times 2.5 than B, and B eats 7 times less than C.find the least number of times all the three has to eat	Options.
A) 50	B) 60	C) 70	D) 80	E) 85

Solution: A eats more than B if B eats 1 times than the ratio of A and B is A:B is 2.5:1 or 5:2 and as B eat 7 times less the C the the ratio of B : C is 2:14 the the least number of times all three has eat is the LCM of A,B,C that is 70 ..   ANSWER:70
Answer: C
A sum of Rs.5000 was divided into 30 persons such that each man gets Rs.200 and each woman gets Rs.150. Find the number of women.
Choose the correct choice from the following options:
A) 20 B) 15 C) 18 D) 24 E) 26

Solution: m+w=30,   200m+150w=5000   By solving we get men=10,women=20   20NSWER:20
Answer: A
What least number must be added to 3000 to obtain a number exactly divisible by 19 ?	Choose the most appropriate option: A) 2 B) 1 C) 4 D) 18 E) 17

Solution: On dividing 3000 by 19, we get 17 as remainder.   Number to be added = (19 - 17)= 
(19 - 17) = 2
2.   2NSWER 2 2
Answer: A
A boat moves upstream at the rate of 1 km in 20 minutes and down stream 1 km in 9 minutes. Then the speed of the current is :  Choose the correct choice from the following: A) 1 kmph B) 2 kmph C) 3 kmph D) 2.5 kmph E) 1.85 kmph

Solution: Rate upstream = (1/20 *60)= 
(1/20 *60) = 3
3 kmph   Rate dowm stream= 1/9 * 60 = 6.7 kmph   Rate of the current = ½ (6.7-3) = 1.85 kmph   ANSW1.85 kmphR:1.85 kmph
Answer: E
A vessel has 300 ml of pure milk. 30 ml of milk is removed and 30 ml of water is added into the vessel. If this operation is repeated another 2 times, what is the % of milk in the vessel at the end?.  Choose the correct choice from the following answers:
A) 50
B) 60
C) 70
D) 80
E) 90

Solution: Total MIlk Removed= 30+30+30= 
30+30+30 = 90
90 ml   Remaining Milk= 300-90= 
300-90 = 210
210 ml   % of Milk= 210/300=7/10=70%   ANSWER:70
Answer: C
There is a rectangular prism made of 1 in cubes that has been covered in tin foil. There are exactly 128 cubes that are not touching any tin foil on any of their sides. If the width of the figure created by these 128 cubes is twice the length and twice the height, what is the p measure in inches of the width of the foil covered prism?	Choose the correct choice from the following choices:
A) 4
B) 6
C) 8
D) 9
E) 10

Solution: If the width is w, then length and height would be w/2.   So, w*w/2*w/2 = 128 => w^3 = (2^3)*64 = (2^3) * (4^3)   => w = 2*4= 
2*4 = 8
8 in.   Along the width of the cuboid, 8 cubes don't touch the tin foil. So the actual width will be non-touching cubes + touching cubes= 8 +2 =p=10   Ans 10.
Answer: E
A certain number of men can do a work in 65 days working 6 hours a day. If the number of men are decreased by one-fourth, then for how many hours per day should they work in order to complete the work in 40 days?  Choose the correct choice from the following answers:
A) 11
B) 13
C) 66
D) 77
E) 88

Solution: Let the number of men initially be x. we have M1 D1 H1= M2 D2 H2   So, x * 65 * 6 = (3x)/4 * 40 * h2   => h2 = (65 * 6 * 4)/(3 * 40)= 
(65 * 6 * 4)/(3 * 40) = 13
13.   Answer: 13
Answer: B
Four people are to be selected to receive a modeling contract from a group of 10 men, 5 women and 2 children. How many ways are possible in which 2 men, one woman and one child will receive a contract?  Choose the correct choice from the following choices
A) 90	B) 180	C) 225	D) 450	E) 900

Solution: We need to select   M M W C = four people   M - 10C2 = 45   W = 5C1 = 5   C = 2C1 = 2   Now  45*5*2= 
 45*5*2 = 450
450   ANS option 450
Answer: D
If a man can cover 16 metres in one second, how many kilometres can he cover in 3 hours 45 minutes?
Choose the correct option:
A) 118 km
B) 162 km
C) 216 km
D) 1887 km
E) 177 km

Solution: 16 m/s = 16 * 18/5 kmph   3 hours 45 minutes = 3 3/4 hours = 15/4 hours   Distance = speed * time = 16 * 18/5 * 15/4= 
16 * 18/5 * 15/4 = 216
216 km.   Answer: 216 km
Answer: C
A class of 40 students has an average height of 120 cm. four students whose average height is 160 cm, left the class and four others whose average height is 124 cm, joined. Calculate the new average height of the students of the class (in cm) is?
Select
A) 292.4 cm  B) 296.4 cm  C) 206.4 cm  D) 294.4 cm  E) 236.4 cm

Solution: Total height = 120 * 40= 
120 * 40 = 4_800
4800 cm.   Total height of those who left= 160 * 4= 
160 * 4 = 640
640   Total height of those who joined= 124 * 4= 
124 * 4 = 496
496   New average= [12000 - 640 + 496 ] / 40 = 11856/40 cm.   = 296.4 cm   Answer:296.4 cm
Answer: B
At an election 2 candidates are participated and a candidate got 30% of votes and defeated by 1000. and 100 votes are invalid. Find the total polled votes? Select the correct option.
A) 2150	B) 2600	C) 3120	D) 1500	E) 1895

Solution: Winner votes = 100-30= 
100-30 = 70
70   polled votes= [(100*1000)/2*70-100]+100 = 2600   Answer is 2600
Answer: B
A class has a ratio of 3:6:7 of children with red hair, blonde hair and black hair respectively. If the class has 9 kids with red hair, how many kids are in the class?	Choose the correct choice from the following answers
A) 99 B) 48 C) 16 D) 22 E) 60

Solution: Since there are 9 children with red hair, and the class exists in a 3:6:7 ratio, there are 3 times more children than the unit ratio. Therefore   9 red-haired children   3*(6) blonde-haired children   3*(7) black-haired children   9+18+21= 
9+18+21 = 48
48   Alternatively, a part-to-whole ratio can be set up. Since the whole is   3+6+7= 
  3+6+7 = 16
16,   9/3=X/16   3*16= 
3*16 = 48
48   Answer: 48)
Answer: B
A palindrome is a number that reads the same front-to-back as it does back-to-front (e.g. 202, 575, 1991, etc.) p is the smallest integer greater than 400 that is both a prime and a palindrome. What is the sum of the digits of p?  Answers:
A) 3 B) 4 C) 5 D) 6 E) 7

Solution: Given that p is smallest integer greater than 400 - assume there is a 3-digit that satisfies the above conditions. Let the number be xyx ; question asks us the values of 2x+y   We can straight away cross out options 3) and D) - sum of digits 3 or 6 implies it is divisible by 3 ---> we know that p is a prime number   Coming to option B) 2x + y = 4 --> only x = 2 and y = 0 satisfy this equation ( x> 2 will never give sum of digits = 4) ; but 202 is divisible by 2 ; we know that p is a prime number   Similarly option C) 2x+y = 5 --> only x = 2 and y = 1 satisfy this equation ( x> 2 will never give sum of digits = 5) ; but 212 is divisible by 2 ; we know that p is a prime number   Therefore answer option should be E ---> can be verified by taking 2x+y = 7 ---> x = 3 and y = 1 ; gives 313   3
Answer: A
300 liters of a mixture contains milk and water in the ratio 3:2 If 15 liters of this mixture be replaced by 15 liters of milk, the ratio of milk to water in the new mixture would be?	Pick:
A) 12:8 B) 12:4 C) 13:8 D) 14:5 E) 13:5

Solution: Quantity of milk in 300 liters if mix = 300*3/5= 
300*3/5 = 180
180 liters   Quantity of milk in 315liters of new mix= 180+15= 
180+15 = 195
195 liters   Quantity of water in it= 315-195= 
315-195 = 120
120 liters   Ratio of milk and water in new mix= 90:20 = 13:8   Answer is13:8
Answer: C
12 points lie on a circle. How many cyclic quadrilaterals can be drawn by using these points?
Choose the most appropriate option.
A) 334	B) 377	C) 495	D) 766	E) 261

Solution: Explanation:   For any set of 4 points we get a cyclic quadrilateral. Number of ways of choosing 4 points out of 12 points is \inline {\color{Black}12C_4{}} = 495.   Therefore, we can draw 495 quadrilaterals   Answer: 495) 495
Answer: C
Jones covered a distance of 50 miles on his first trip. On a later trip he traveled 300 miles while going three times as fast. His new time compared with the old time was Choose the correct choice from the following:  A) three times as much  B) twice as much  C) the same  D) half as much  E) a third as much

Solution: Let speed of the 1st trip x miles / hr. and speed of the 2nd trip 3x / hr.   We know that   Speed = Distance/Time.   Or, Time = Distance/Speed.   So, times taken to covered a distance of 50 miles on his first trip = 50/x hr.   And times taken to covered a distance of 300 miles on his later trip = 300/3x hr.   = 100/x hr.   So we can clearly see that his new time compared with the old time was: twice as much.   Answer: (twice as much)
Answer: B
Two dice are thrown together .What is the probability that the sum of the number on the two faces is divided by 4 or 6  Choose the correct option
A) 7/9 B) 5/4 C) 15/4 D) 2/5 E) 7/18

Solution: Clearly n(S)=6*6= 
6*6 = 36
36   Let E be the event that the sum of the numbers on the two faces is divided by 4 or 6.Then   E={(1,3),(1,5),(2,2),(2,4),(2,6),(3,1),(3,3),(3,5),(4,2),(4,4),(5,1),(5,3),(6,2),   (6,6)}   n(E)=14.   Hence p(e)=n(e)/n(s)=14/36=7/18   Ans:7/18
Answer: E
By weight, liquid X makes up 2 percent of solution P and 7.5 percent of solution Q. If 400 grams of solution P are mixed with 600 grams of solution Q, then liquid X accounts for what percent of the weight of the resulting solution?
Choose the most appropriate option.
A) 4.5%
B) 4.7%
C) 4.9%
D) 5.1%
E) 5.3%

Solution: The number of grams of liquid X is 2(400)/100 + 7.5(600)/100 = 8 + 45= 
8 + 45 = 53
53 grams.   53 / 1000= 5.3%   The answer is 5.3%.
Answer: E
If (|p|!)^p=|p|!, which of the following could be the value(s) of p ?
Options
A) -1 B) 0 C) 1 D) -1 and 1 E) -1, 0, and 1

Solution: Test Values   A. -1 ==> |−1|−1=|−||! ==> 1/1= 
1/1 = 1
1==> -1 is valid   B. 0 ==> |0|!0=|0|! ==> 1^0 ==> 1=1 ==> 0 is valid   C. 1 ==> 1^1 ==> 1 is valid   D. -1 and 1   E. -1, 0, and 1   Answer:-1, 0, and 1
Answer: E
The probability that a convenience store has no iced tea is 50%. If Karl is stopping by 4 convenience stores on his way to work, what is the probability thatat least oneof the stores will not have a can of iced tea?  Select the correct option:
A) 1/8	B) 1/4	C) 1/2	D) 3/4	E) 15/16

Solution: p=1-1/2^4(all stores have iced tea)=15/16   15/16
Answer: E
A man gains 20% by selling an article at a certain price. If the sells it at double the price, the percentage of profit will be? Choose the correct choice from the following choices
A) 288%  B) 882%  C) 388%  D) 140%  E) 382%

Solution: Let C.P. = Rs. x.   Then, S.P. = Rs. (12% of x) = Rs. 6x/5   New S.P. = 2 * 6x/5 = Rs. 12x/5   Profit = 12x/5 - x = Rs. 7x/5   Profit = 7x/5 * 1/x * 100 = 140%.   Answer:140%
Answer: D
A rectangular circuit board is designed to have width w inches, perimeter p inches, and area M square inches. Which of the following equations must be true?	Choose the correct choice from the following options
A) w^2 + pw + M = 0  B) w^2 - pw + 2M = 0  C) 2w^2 + pw + 2M = 0  D) 2w^2 - pw - 2M = 0  E) 2w^2 - pw + 2M = 0

Solution: Notice that we can discard options A, and C right away. The sum of 3 positive values Cannot be 0.   Now, assume:   Width =w = 1 inchand length = 1 inch;   Perimeter =p = 4 inches;   Area =M = 1 square inches.   Plug the values of w, p, and M into the answer choices: only for E 2w^2 - pw  + 2= 
 + 2 = 2
2 - 4 + 2= 
2 - 4 + 2 = 0
0.   Answer: 2w^2 - pw + 2M= 0.
Answer: E
In a factory, there are 30% technicians and 70% non-technicians. If the 30% of the technicians and 70% of non-technicians are permanent employees, then the percentage of workers who are temporary is?	Choose the correct choice:	A) 62%	B) 57%	C) 52%	D) 22%	E) 48%

Solution: Total = 100   T= 30 NT= 70   30*(70/100)= 
30*(70/100) = 21
21 70*(30/100)=21   21 + 21= 
21 + 21 = 42
42=> 100 - 42= 
100 - 42 = 58
58%   Answer:48%
Answer: E
The probabilities of solving a question by 3students A, B & C are 1/2,1/3 &1/4, respectively. The probability that the problem will be solved is?  Answers:
A) 1/5 B) 3/4 C) 3/7 D) 3/5 E) 3/7

Solution: Sol. First, we find the probability of not solving the problem x PTO x = (1 — D x - D x - D   1 2 3 1 =iXiX71=4;   1 3 Required probability 3/4   3/4
Answer: B
Find the percentage gain if a shop owner sells 40 mtr of fabric and gains Cost Price of 15 meters?
Choices:	A) 38.50%	B) 39.50%	C) 27.50%	D) 37.50%	E) 17.90%

Solution: Let cost of each metre be Rs. 100.   Therefore, cost price of 15m cloth = 15*100= 
15*100 = 1_500
1500   cost price of 40m cloth= 40*100= 
40*100 = 4_000
4000   Since the trader made the CP of 15m from the sale of 40m therefore   Profit on sale of 40m= cost price of 15 m cloth = 1500   Selling price of 40m = 4000+1500= 
4000+1500 = 5_500
5500   Profit %= 37.50%   37.50%
Answer: D
Approximately how many cubic feet of water are needed to fill a circular swimming pool that is 40 feet across and 7 feet deep? Select the correct option:
A) 700
B) 1500
C) 3000
D) 5000
E) 9000

Solution: Answer Should be E.   V= \pir^2h= \pi*20^2*7= approximately 9000
Answer: E
Ramu bought an old car for Rs. 38000. He spent Rs. 12000 on repairs and sold it for Rs. 64900. What is his profit percent? Choose the correct choice
A) 17%
B) 19%
C) 18%
D) 14%
E) 29.8%

Solution: Total CP = Rs. 38000 + Rs. 12000   = Rs. 50000 and SP   = Rs. 64900   Profit(%) = (64900 - 50000)/50000 * 100= 
(64900 - 50000)/50000 * 100 = 149/5 = around 29.8
29.8%   Answer: 29.8%
Answer: E
In 1990 the budgets for projects Q and V were $540,000 and $780,000, respectively. In each of the next 10 years, the budget for Q was increased by $30,000 and the budget for V was decreased by $10,000. In which year was the budget for Q equal to the budget for V ?
Select
A) 1992 B) 1993 C) 1994 D) 1995 E) 1996

Solution: Let the no of years it takes is x.   540+30x = 780-10x --> 40x = 240 and x=6.   Thus, it happens in 1996.   1996.
Answer: E
If s is the product of the integers from 30 to 40 inclusive, and if t is the product of the integers from 30 to 41 inclusive, what is 1/s + 1/t in terms of t?
Choose the most appropriate option:
A) 40/t
B) 42/t
C) 38/t
D) 36/t
E) 34/t

Solution: Similarly in the actual problem   s =t/41. 1/s = 1/(t/41) or 1/s = 41/t   1/s + 1/t = 41/t + 1/t = 42/t   42/t
Answer: B
How many seconds will a train 100 meters long take to cross a bridge 130 meters long if the speed of the train is 36 kmph? Choose the correct choice from the following:
A) 26
B) 72
C) 25
D) 23
E) 27

Solution: Explanation:   23 = 100 + 130= 
100 + 130 = 230
230   S= 36 * 5/18= 
36 * 5/18 = 10
10 mps   T= 230/10= 
230/10 = 23
23 sec   Answer: Option 23
Answer: D
Sam has forgotten his friend’s seven-digit telephone number. He remembers the following: the first three digits are either 635 or 674, the number is odd, and the number nine appears once. If Sam were to use a trial and error process to reach his friend, what is the minimum number of trials he has to make before he can be certain to succeed ?
Choose the correct choice from the following choices:
A) 1000
B) 2430
C) 3402
D) 3006
E) None of these

Solution: Explanation :   Let's check the number of ways for the first telephone number.   6 3 5 - - - -   a) 6 3 5 9 - - -   4 choices for last digit (1,3,5,7).   9 * 9 choices for 5th and 6th digits together.   So, 9 * 9 * 4 choices = 324 ways.   Similarly,   b.) 6 3 5 - 9 - - = 324 ways.   c.) 6 3 5 - - 9 - = 324 ways.   d.) 6 3 5 - - - 9 = 9 * 9 * 9= 
9 * 9 * 9 = 729
729 ways.   Total= (324 + 324 + 324 + 729)= 
(324 + 324 + 324 + 729) = 1_701
1701.   It will be also the case with the phone number starting with 674.   Hence, the minimum number of trial required is 2 x 1701= 3402.   Answer : 3402
Answer: C
A contractor undertook to finish a job in 150 days and employed 200 men. After 50 days he found that only 1/4 of work was finished. How many extra days are needed if he employs 50 more men? Choose the correct answer.
A) 20	B) 25	C) 30	D) 35	E) 45

Solution: work part 20=25% and work part B= 75%   25% work done by 200 people in 50 days   if only one employee works then he takes  200*50= 
 200*50 = 10_000
10000 days   and if work(B) is triple more ten he will take=10000*3= 
10000*3 = 30_000
30000 days   if employees are 250 then days= 30000/250= 
30000/250 = 120
120days   then total days= 50+120= 
50+120 = 170
170 days   how many extra days taken= 170-150= 
170-150 = 20
20 days   20NSWER:20
Answer: A
Murali travelled from city A to city B at a speed of 40 kmph and from city B to city C at 60 kmph. What is the average speed of Murali from A to C given that the ratio of distances between A to B and B to C is 4 : 2?  Answers: A) 16 B) 45 C) 277 D) 92 E) 11

Solution: Let the distances between city A to B and B to C be 4x km and 2x km respectively.   Total time taken to cover from A to C   = (4x)/40 + (2x)/60 = (4x + 12x)/120 = 16x/120 = 2x/15 Average speed = (4x + 2x)/(x/10) = 45 kmph.   Answer:45
Answer: B
14, 35, 56, 91, 126, 238
In the sequence above, each term is related with the others. Which of the following could not be a term in the sequence? Answers:
A) 161
B) 250
C) 322
D) 686
E) 847

Solution: Simplifying the question into easier words we just need to find which of the numbers is not divisible by 7   clearly the answer is 250 because if we divide 250 by 7 we get a remainder of 1   Correct answer - 250
Answer: B
Balls of equal size are arranged in rows to form an equilateral triangle. the top most row consists of one ball, the 2nd row of two balls and so on. If 789 balls are added, then all the balls can be arranged in the shape of square and each of the sides of the square contain 8 balls less than the each side of the triangle did. How many balls made up the triangle? Answers.
A) 1711	B) 2209	C) 2878	D) 1210	E) 1560

Solution: As expected, this question boils down to 2 equation,   Consider total number of Balls in Triangle = T and number of balls in last row = x.   1+2+3+...+x = T   x(x+1)/2 = T ----(a)   As mentioned in the question, side of a square will be (x-8) and total number of Balls in square will be (T+789)   (x-8)^2 = T+789 -----(b)   Now the hardest part of the question will be to solve these 2 equations and this looks like time consuming BUT the easy way will be plug and play. Also, we've to find a value of T (from 5 optiosn given below) which can make a square of a a number. One we know this, it will be a cake walk.   We can see that option A fits this criteria in eq (b). Add - 1711+789 = 2500 = 50^2 = (x-8)^2 Hence, x = 58.   Cross check by putting in eq (a) = x(x+1)/2 = T = > 58*59/2= 
58*59/2 = 1_711
1711   Hence, answer is 1711.
Answer: A
The price of 5 kilograms of Wheat was $3 in 1995. In 2015, the price had increased to $5. What was the percent increase in the price of the 5 kilograms of Wheat?	Choose the most appropriate option:
A) 66.6%
B) 76.4%
C) 67.7%
D) 38.3%
E) 78%

Solution: Increase = 5 - 3= 
5 - 3 = 2
2   % increase= 2*100/3 = 66.6%   66.6%nswer: option 66.6%
Answer: A
Joe invested a certain sum of money in a simple interest bond whose value grew to $400 at the end of 3 years and to $500 at the end of another 5 years. What was the rate of interest in which he invested his sum?	Choose the correct option
A) 4.76%  B) 5.88%  C) 6.33%  D) 7.75%  E) 8.33%

Solution: In 5 years, the value grew $100, so the simple interest was $20 per year.   In 3 years, the total interest was 3*$20 = $60   The principal is $400 - $60 3* 20= 
3* 20 = 60
$60   The principal is $400 - $60 = 340.   The interest rate is $20/$340 400 -  60= 
400 -  60 = 340
340.   The interest rate is $20/$340= 1/17 which is about 5.88%   The answer is 5.88%.
Answer: B
Which of the following numbers is two more than the square of an odd integer?  Choose the correct choice from the following answers
A) 14,173	B) 14,361	C) 15,627	D) 15,737	E) 15,981

Solution: If a square has an odd unit's digit, then its ten's digit must be even.   Only 15,627-2 = 15,625 satisfies this condition.   The answer is 15,627.
Answer: C
In an exam, Bright scored 60 percent, Bivi scored 65 percent and Lisa 45 percent. The maximum score awarded in the exam is 900. Find the average mark scored by all the three boys?	Choose the correct choice from the following choices:
A) 490  B) 530  C) 520  D) 500  E) 510

Solution: Average mark scored by all the three boys =   [60/100 (900) + 65/100 (900) + 45/100 (900)] / 3   (540+585+405)/3= 
(540+585+405)/3 = 510
510   Answer: 510
Answer: E
What is value of (P + Q)/(P - Q) if P/Q = 7 ?  Choose the correct option.
A) 1/3 B) 2/3 C) 4/3 D) 5/3 E) None of these

Solution: Explanation:   (P + Q)/(P - Q) = (P/Q+1)/(P/Q - 1) = (7 +1)/(7 - 1) = 4/3.   Answer: 4/3
Answer: C
97 students take part in a test and the median score is 85. Which of the following descriptions must be correct?
I. At least 49 students’ score are equal to or more than 87.
II At least 49 students’ score are equal to or more than 85.
III. At most 49 students’ score are equal to or more than 85.
Options
A) I
B) II
C) III
D) III
E) IIII

Solution: If we order the scores increasingly, then on the 49th place we have the score of 85. There must be 48 scores (those on the right of the 85 score) greater or equal to 85. So, I is necessarily correct.   The scores on the left of the 49th place, all have to be equal or less than 85. Since we can have the extreme case of all the scores 85, neither II, nor III is correct. The question asks for descriptions thatmustbe correct.   Answer II.
Answer: B
At the end of three years what will be the compound interest at the rate of 10% p.a. on an amount of Rs.10000?	Select the correct option.
A) 6620	B) 3310	C) 2776	D) 2997	E) 2718

Solution: A = 10000(11/10)^3   = 13310   = 10000   ----------   3310. Answer: 3310
Answer: B
In a box of 9 pens, a total of 3 are defective. If a customer buys 2 pens selected at random from the box, what is the probability that neither pen will be defective?  Choose the correct choice from the following:	A) 3/10	B) 4/11	C) 5/12	D) 6/13	E) 7/15

Solution: P(neither pen is defective) = 6/9*5/8 = 5/12   The answer is 5/12.
Answer: C
Light glows for every 32 seconds . How many max. times did it glow between 1:57:58 and 3:20:47 am.  Choose the correct choice from the following:
A) 180 times
B) 381 times
C) 155 times
D) 392 times
E) 150 times

Solution: Time difference is 1hr,22min,49sec=4969sec. So, light glows floor(4969/32)=15582 times.   ANSWER:155 times
Answer: C
If 30! × 30!/30^n is an integer, what is the largest possible value of n? Choose the correct choice from the following: A) 20 B) 14 C) 8 D) 4 E) 1

Solution: 30! × 30!/30^n is an integer.   Or 30! × 30!/(3^2n*5^n)   This means we need to find the power of 5 in the numerator. We can safely say that the number of powers of 5 will be lower than the number of powers of 4 in the numerator.   Largest power of 5 in 30! = [30/5] + [30/25] = 7   Since there are 2 20!'s, power of 7 in the numerator = 2*7= 
2*7 = 14
14   Hence the largest value of b for which 30! × 30!/30^n is integer= 14   Correct Option : 14
Answer: B
While working alone at their constant rates, computer X can process 240 files in 8 hours, and computer Y can process 240 files in 6 hours. If all files processed by these computers are the same size, how many hours would it take the two computers, working at the same time at their respective constant rates, to process a total of 240 files?	Choose one.
A) 3	B) 3.4	C) 3.8	D) 4	E) 4.5

Solution: Both computers together process files at a rate of 240/8 + 240/6 = 30+40= 
30+40 = 70
70 files per hour.   The time required to process 240 files is 240/70 which is about 3.4 hours   The answer is 3.4.
Answer: B