MU-NLPC/Calc-aqua_rat huggingface dataset:
A placed three sheets with two carbons to get two extra copies of the original. Then he decided to get more carbon copies and folded the paper in such a way that the upper half of the sheets were on top of the lower half. Then he typed. How many carbon copies did he get?	Choose the correct choice.
A) 1 B) 2 C) 3 D) 4 E) 5

Solution: Explanation:   Since the number of carbons is 2, only two copies can be obtained.   Answer: 2
Answer: B
Two fair die with sides numbered 1 to 6 are tossed. What is the probability that the sum of the exposed faces on the die is a prime number?	Choose the correct choice from the following options
A) 5/11	B) 5/12	C) 5/21	D) 2/9	E) 5/36

Solution: Two dices are thrown ! So we may get 1+1 or 1+2 ... or 1+6.. or 2+6 or 3+6 etc   Therefore the total different sum values we can get are :2,3,4,5,6,7,8,9,10,11,12[Sample space] ----------------(1)   Out of these values, 5 numbers are primes i.e.2,3,5,7,11[Favorable events] --------------------(2)   From (1)(2)   The answer is5/11!!   Option 5/11
Answer: A
1,345
1,354
1,435
.....
....
+5,431
The addition problem above shows four of the 24 different integers that can be formed by using each of the digits 1,3,4,5 exactly once in each integer. What is the sum of these 24 integers?	Answers:	A) 78,690	B) 82,240	C) 86,658	D) 90,240	E) 94,426

Solution: In each of the units, tens, hundreds, and thousands place, each digit will appear 6 times.   Then the sum equals 6(1111)+6(3333)+6(4444)+6(5555) = 86,658   The answer is 86,658.
Answer: C
A batsman makes a score of 65 runs in the 17th inning and thus increases his average by 3. Find his average after 17th inning.
Select the correct option.
A) 17	B) 39	C) 42	D) 45	E) None of the above

Solution: Let the average after 17th inning = x.   Then, average after 16th inning = (x – 3).   ∴ 16(x – 3) + 65 = 17x or x = (65 – 48) = 17.   17nswer 17
Answer: A
The actual price of an article was Rs. 6000/- the successive discount on 10% and 20% then Finds the selling price Choose the correct choice from the following options.
A) Rs.3240/-	B) Rs. 4320/-	C) Rs.4230/-	D) Rs.4200/-	E) None of these

Solution: Explanation:   Note: Selling price = MRP * (100 - d1)/100 * (100 - d2)/100 * -------------   MRP = 6000/- , d1 = 10, d2 = 20   Selling price = 6000 * (100 - 10)/100 * (100-20)/100 ==> 6000 * 90/100 * 80/100   => 48 * 90 = Rs. 4320/-   Answer: Option Rs. 4320/-
Answer: B
If a(a + 5) = 6 and b(b + 5) = 6, where a ≠ b, then a + b =  Choose the most appropriate option:	A) −5	B) −2	C) 2	D) 46	E) 48

Solution: a(a + 5) = 6 and b(b + 5) = 6   => a, b must be integers and if a is -6 or 1, b will be 1 and -6 respectively   => a+b = -5   −5ns: −5
Answer: A
John and Peter are among the eight players a volleyball coach can choose from to field a six-player team. If all six players are chosen at random, what is the probability of choosing a team that includes John and Peter?  Pick: A) 7/15 B) 11/20 C) 14/25 D) 15/28 E) 16/35

Solution: The total possible ways of selecting a 6-member team is 8C6 = 28   The possible ways which include John and Peter is 6C4 = 15   The probability of choosing both John and Peter is 15/28   The answer is 15/28.
Answer: D
If 15 Horses eat 15 bags of gram in 15 days, in how many days will one horse eat one bag of Grain?  Choose the correct choice from the following
A) 15 days
B) 1/15 days
C) 1 day
D) 30 days
E) 225 days

Solution: Horse*days=bags   15*15=15 and 1*days=1   (15*15)/(1*days)=15/1= 
15/1 = 15
15   15 daysNSWER:15 days
Answer: A
An urn contains 10 balls, numbered from 1 to 10. If 2 balls are selected at random with replacement from the urn, what is the probability P that the sum of the 2 numbers on the balls will be even? Select
A) 25%	B) 37.5%	C) 50%	D) 62.5%	E) 75%

Solution: Correct Answer: C   Since there are 5 even numbered balls and 5 odd numbered balls, the probability of selecting either an even or an odd is 5/10= 1/2. In order for the sum of the numbers on the two balls to be even, either both numbers must be even or both numbers must be odd; one even and one odd number would add to an odd number. The probability of selecting two even numbers is:   1/2 * 1/2= 1/4   The probability of selecting two odd numbers is also:   1/2 * 1/2= 1/4   Adding both probabilities gives P=1/4+1/4= 1/2 , or 50%, as the probability that the sum of the numbers will be even. Thus, the correct answer is (50%).
Answer: C
The speed of a boat in still water is 60kmph and the speed of the current is 10kmph. Find the speed downstream and upstream?  Choose the correct choice.
A) 87 kmph B) 40 kmph C) 50 kmph D) 15 kmph E) 18 kmph kmph

Solution: Speed downstream = 60 + 10= 
60 + 10 = 70
70 kmph   Speed upstream= 60 - 10= 
60 - 10 = 50
50 kmph   Answer:50 kmph
Answer: C
A die is thrown three times. Events X and Y are defined as below:
X : 4 on the third throw
Y : 6 on the first and 5 on the second throw
What is the probability of X given that Y has already occurred. Choices:
A) 1/6
B) 1/7
C) 1/11
D) 1/13
E) 1/15

Solution: The sample space has 216 outcomes.   Now X =   (1,1,4) (1,2,4) ... (1,6,4) (2,1,4) (2,2,4) ... (2,6,4)   (3,1,4) (3,2,4) ... (3,6,4) (4,1,4) (4,2,4) ...(4,6,4)   (5,1,4) (5,2,4) ... (5,6,4) (6,1,4) (6,2,4) ...(6,5,4) (6,6,4)   Y = {(6,5,1), (6,5,2), (6,5,3), (6,5,4), (6,5,5), (6,5,6)}   and X n Y = {(6,5,4)}.   Now P(Y) = 6/216   and P (X n Y) = 1/216   Then P(X|Y) = (1/216)/(6/216) = 1/6   1/6)
Answer: A
In a pet shop there are 120 eyes and 172 legs. How many birds and puppies are included in these?
Pick
A) Birds=34 , Puppies=26	B) Birds=36 , Puppies=26	C) Birds=34 , Puppies=20	D) Birds=32 , Puppies=24	E) Birds=38 , Puppies=24

Solution: Let there are x birds and y puppies.   Each bird and puppy has 2 eyes. Each bird has 2 legs and each puppy has 4 legs.   Then   2x+2y = 120 => x+y = 60----------(1)   2x+4y = 172 => x+2y = 86-----------(2)   Solving (i) and (ii) we get   y = 26 & x = 34   So birds are 34 and puppies are 26. Birds=34 , Puppies=26nswer : Birds=34 , Puppies=26
Answer: A
Two boats are heading towards each other at constant speeds of 4 miles/hr and 20 miles/hr respectively. They begin at a distance 20 miles from each other. How far are they (in miles) one minute before they collide ?	Choose the correct choice from the following answers
A) 1/12  B) 6/15  C) 1/6  D) 1/3  E) 1/5

Solution: The question asks: how far apart will they be 1 minute=1/60 hours before they collide?   Since the combined rate of the boats is 4+20=25 mph then 1/60 hours before they collide they'll be rate*time=distance --> 24*1/60=6/15miles apart.   Answer: 6/15.
Answer: B
In a room with 6 people, 4 people have exactly 1 friend in the room and 3 people have exactly 2 friends in the room (Assuming that friendship is a mutual relationship, i.e. if Jane is Paul's friend, Paul is Jane's friend). If two individuals are selected from the room at random, what is the probability that those two individuals are NOT friends?	Choose the most appropriate option.
A) 5/21
B) 3/7
C) 4/7
D) 5/7
E) 16/15

Solution: (4/6)(5/5) + (3/6)(4/5) if you choose one of the 4 with one other friend, then you have a 5/5 chance of not picking their friend 2nd. If you choose one of the 3 with 2 friends, you have a 4/5 chance of not picking one of their friends second. Add them up.   20/30 + 12/30   32/30 = 16/15   E. 16/15
Answer: E
A box contains TWELVE bulbs out of which 3 are defective. If THREE bulbs are chosen at random, find the probability that atleast one bulb is good?  Choose the most appropriate option.
A) 250/251	B) 265/265	C) 241/242	D) 256/257	E) 219/220

Solution: Required probability=1-3C3/12C3= 1 - 1/220= 219/220Answer:219/220
Answer: E
Buses leave town B at 3 pm and every 10 hours after that. Buses leave town C at 4pm and every 15 hours after that. If the buses follow this schedule beginning on a Monday, what is the earliest day D on which the buses leave at the same time.	Answers:  A) D=Tuesday  B) D=Wednesday  C) Thursday  D) Sunday  E) D=The busses will never leave at the same time

Solution: The answer is E.   I think the best way to do it is to look at the times on a 24 hour clock. Town B busses start at 15:00, and Town C start at 16:00. If you think about it that way, then for Town B you'd add 10 hours each time, and the number will always end in a 5. Town C you'd add 15 hours each time, and the numbers would always end in a 1 or 6. So you can see they'd never coincide.   Alternatively, you could see that if they left at the same time, they'd coincide every 30 hours, but since C is one hour ahead of B, every 30 hours C will still be one hour ahead of B.D=The busses will never leave at the same time
Answer: E
find the ratio of 8th and 4th term of sequence 3.1, 6.2, 12.4, .....? Choices:
A) 16
B) 12
C) 4
D) 8
E) 20

Solution: a= first term = 3.1   r = common ratio = 6.2/3.1= 
6.2/3.1 = 2
2====> 4th term = a * r^(4-1) = 3.1 * (2)^3 = 24.8 and 8th term = 3.1 * (2)^7 = 396.8   Ratio of a8/a4 = 396.8/24.8= 
396.8/24.8 = 16
16 ------16ns- 16
Answer: A
A wire in the form of a circle of radius 3.5 m is bent in the form of a rectangule, whose length and breadth are in the ratio of 6 : 5. What is the area of the rectangle?	Choose the correct option:
A) 70 cm2  B) 30 cm2  C) 66 cm2  D) 55 cm2  E) 54 cm2

Solution: The circumference of the circle is equal to the permeter of the rectangle.   Let l = 6x and b = 5x 2(6x + 5x) = 2 * 22/7 * 3.5   => x = 1   Therefore l = 6 cm and b = 5 cm Area of the rectangle = 6 * 5= 
6 * 5 = 30
30 cm2   Answer: 30 cm2
Answer: B
Eight friends met for lunch at an expensive restaurant, and everyone decided to contribute equally to the total bill of $680. If one of the friends had a coupon for 12% off the total bill, and if each friend still contributed equally after the coupon was applied to the bill, how much did each friend pay?	Select: A) $90 B) $74 C) $45 D) $37 E) $35

Solution: 680 * 0,12 = 81   680 - 81= 
680 - 81 = 599
599   599 / 8= 74   Answer $74
Answer: B
A train crosses a platform of 150 m in 15 sec, same train crosses another platform of length 250 m in 20 sec. then find the length of the train? Select: A) 150 B) 2787 C) 277 D) 279 E) 271

Solution: Length of the train be ‘X’   X + 150/15 = X + 250/20   4X + 600 = 3X + 750   X = 150m   150nswer: 150
Answer: A
P and Q started a business with respective investments of Rs. 4 lakhs and Rs. 10 lakhs. As P runs the business, his salary is Rs. 5000 per month. If they earned a profit of Rs. 2 lakhs at the end of the year, then find the ratio of their earnings?	Pick.
A) 1:8 B) 1:6 C) 2:1 D) 1:1 E) 1:7

Solution: Ratio of investments of P and Q is 2 : 5   Total salary claimed by P = 12 * 5000 = Rs. 60000   Total profit = Rs. 2 lakhs.   Profit is to be shared = Rs. 140000   Share of P = (2/7) * 140000 = Rs. 400000   Share of Q = Rs. 100000   Total earnings of P = (60000 + 40000) = Rs. 100000   Ratio of their earnings = 1:1   Answer:1:1
Answer: D
If the area of circle is 520 sq cm then its circumference?	Choose the correct answer:
A) 11  B) 81  C) 99  D) 266  E) 12

Solution: 22/7 r2 = 520 => r = 12.9   2 * 22/7 * 12.9 = 81 Answer: 81
Answer: B
CP of two houses are Rs.1.995 lakhs each. On one gains 5% and on the other, loses 5%. What is the gain or loss percent in the whole transaction?  Answers:
A) .23%  B) .25%  C) .30%  D) .50%  E) 1%

Solution: If a person sells two items at the same price; one at a gain of x % and another at a   loss of x %, then the seller always incurs a loss expressed as   Loss%=(Common Loss and Gain%10)2=(x10)2So in this case, he will have a loss. Loss%=(510)2=(12)2=(14)=.25%   .25%
Answer: B
Rs.1070 is divided so that 4 times the first share, thrice the 2nd share and twice the third share amount to the same. What is the value of the third share?  Select.
A) Rs.190	B) Rs.260	C) Rs.493	D) Rs.393	E) Rs.593

Solution: A+B+Rs.493 = 1070   4A = 3B = 2Rs.493 = x   A:B:Rs.493 = 1/4:1/3:1/2 = 3:4:6   6/13 * 1070 = Rs.493   ANSWER:Rs.493
Answer: C
If an object travels at six feet per second, how many feet does it travel in one hour? Select.
A) 30
B) 21600
C) 720
D) 1800
E) 18000

Solution: Speed = 6 feet per second.   1 Hour= 60X60 Seconds = 3600 Seconds.   Total no of feet traveled in 1 hour = 3600X6 = 2160X10 =21600   Answer 21600
Answer: B
Three friends Alice, Bond and Charlie divide $1260 amongs them in such a way that if $10, $20 and $30 are removed from the sums that Alice, Bond and Charlie received respectively, then the share of the sums that they got will be in the ratio of 10 : 20 : 30. How much did Charlie receive? Choose one:  A) $490  B) $630  C) $500  D) $510  E) $520

Solution: A+$630+C = 1260   Given ratio 10:20:30   Let us say the shares of A,$630,C deducting 10,20,30 be a,b,c   a+b+c = 1260-60= 
1260-60 = 1_200
1200= 60K   c share = (1200X30)/60 = 600   C = charlie share = 600+30= 
600+30 = 630
630   Option $630
Answer: B
In a drawer of shirts 8 are blue, 6 are green and 4 are magenta. If Mason draws 2 shirts at random, what is the probability Q at least one of the shirts he draws will be blue?  Choose one:
A) 25/153	B) 28/153	C) 5/17	D) 4/9	E) Q=12/17

Solution: P(at least one blue) = 1- P(0 blue) = 1 - 10/18*9/17 =Q= 12/17.   Answer: Q=12/17.
Answer: E
A walks at 4 kmph and 4 hours after his start, B cycles after him at 10 kmph. How far from the start does B catch up with A?	Choices: A) 62.6 km B) 26.7 km C) 22.8 km D) 19.5 km E) None

Solution: Sol.   Suppose after x km from the start B catches up with A. Then, the difference in the time taken by A to cover x km and that taken by B to cover x km is 4 hours.   ∴ x/4 - x/10 = 4 or x = 26.7 km.   Answer 26.7 km
Answer: B
What least value must be assigned to * so that th number 197*5462 is divisible by 9?  Choose the correct answer: A) 2 B) 4 C) 6 D) 1 E) 3

Solution: Let the missing digit be x   Sum of digits = (1+9+7+x+5+4+6+2)=34+x   For 34+x to be divisible by 9 , x must be replaced by 2   The digit in place of x must be 2.   2NSWER 2 2(1+9+7+ +5+4+6+2)= 
(1+9+7+ +5+4+6+2) = 34
34+x   For 34+x to be divisible by 9 , x must be replaced by 2   The digit in place of x must be 2.   2NSWER 2 2
Answer: A
Find the value of x from this equation? 7(x - 1) = 21  Answers
A) 2
B) 3
C) 4
D) 6
E) 7

Solution: 1. Divide both sides by 7:   2. Simplify both sides:   x - 1 = 3   3. Add 1 to both sides:   x - 1 + 1 = 3 + 1   4. Simplify both sides:   x = 4   4
Answer: C
What is his percentage profit made by Felix if he purchased 21 dozen t-shirts at Rs. 12 per dozen. He sold 7 dozens at 15% profit and the remaining 14 dozens with 18% profit?  Choose the correct choice from the following options
A) 18%	B) 17%	C) 15%	D) 13%	E) 14%

Solution: Explanation :   C.P of 21 dozen = Rs.(12 x 21) = Rs.252   C.P of 7 dozen = Rs. (12 x7) = Rs. 84.   C.P of 14 dozen =Rs. (12 x14) = Rs. 168   profit on 7 dozen at 15% = 15/100*84= 
15/100*84 = 63/5 = around 12.6
12.6   profit on 14 remaining dozen at 18%= 18/100*168= 
18/100*168 = 756/25 = around 30.24
30.24   total profit= 12.6 + 30.24= 
12.6 + 30.24 = 42.84
42.84   % profit= ?/100*252 = 42.84   = 17%   Answer : 17%
Answer: B
A certain manufacturer of cake, muffin, and bread mixes has 100 buyers, of whom 50 purchases cake mix, 40 purchase muffin mix, and 15 purchase both cake mix and muffin mix. If a buyer is to be selected at random from the 100 buyers, what is the probability that the buyer selected will be one who purchases neither cake mix nor muffin mix?  Pick:	A) 1/10	B) 3/10	C) 1/4	D) 7/10	E) 9/10

Solution: C+M+B-CM-MB-CB-2CMB = 100   C - cake buyers, M - muffin and B - Bread buyers. CM,MB,CB and CMB are intersecting regions.   the question asks for people who have bought only bread mixes = B-CB-MB-2CMB has to be found out.   50 + 40 + B-CB-MB-15-2CMB = 100   B-CB-MB-2CMB = 25   hence the probability = 25/100 = 1/4.   1/4
Answer: C
In an island, there are four men for every three women and five children for every three men. How many children are there in the island if it has 531 women ?  Choose the correct answer: A) 454 B) 1180 C) 1070 D) 389 E) 983

Solution: The ratio of Women : Men = 3 : 4   Men : Children = 3 : 5   The combined ratio,   Women : Men : Children = 9 : 12 : 20   In this ratio, 9 ==> 531 Women   Thus, 20 ==> 1180 Children   ANSWER:1180
Answer: B
How many number of 3 digits can be formed with the digits 1,2,3,4,5 if repetition of digits is not allowed?
Choose the correct choice from the following answers.
A) 60 B) 120 C) 30 D) 240 E) 48

Solution: n = number of digits = 5   r = number of places to be filled up = 3   Required number = 5P3 = 5!/2! = 60   60nswer is 60
Answer: A
A father is 30 years older than his son however he will be only thrice as old as the son after 5 years what is father's present age ?  Options.
A) 40 yrs
B) 30 yrs
C) 50 yrs
D) 60 yrs
E) none of these

Solution: Son's age: x   Father's age: x + 30   In 5 years:   Son's age: x + 5   Father's age: x + 35   In 5 years the father is thrice as old as his son so:   3(x + 5) = x + 35   x = 10   Current father's age is 40.   40 yrsNSWER:40 yrs
Answer: A
If t and b are positive numbers, and t^3 + b^3 = 75, then the greatest possible value of t is between:
Select:
A) 0 and 3	B) 3 and 5	C) 4 and 5	D) 5 and 7	E) 6 and 9

Solution: Yes the question is ambiguous, and the answer is certainly not C between 4 and 5 .   The question stated: t and b are positive numbers but not positive integers.   so fractions are allowed to be a part of calculation.   So if the answer is C then the value 4.5 = 9/2 must comply the equation.   (9/2)^3 + b^3 = 75   so, b^3 = -129/8 , which is not possible according to the question.   Moreover the question didn't mentioninclusive or not, so we can't assume that b is 4 .   hi asif,   question is correct IMO.   Sincemaximumvalues areuniqueso you cant take any value and make it satisfy with equation   question is asking that maximum value ofa(means that unique value ofa) is between...   its not saying all value of that range will satisfy.
Answer: C
Two trains are running in opposite directions with the same speed. If the length of each train is 120 m and they cross each other in 12 sec, then the speed of each train is? Select the correct option:
A) 78	B) 89	C) 36	D) 34	E) 23

Solution: Let the speed of each train be x m/sec.   Then, relative speed of the two trains = 2x m/sec.   So, 2x = (120 + 120)/12 => x = 10   Speed of each train = 10 m/sec.   = 10 * 18/5 =- 36 km/hr.   Answer: Option 36
Answer: C
The area of a square is 4900 sq cm. Find the ratio of the breadth and the length of a rectangle whose length is same the side of the square and breadth is 20 cm less than the side of the square?
Select
A) 5:8 B) 5:10 C) 5:13 D) 5:7 E) 5:16

Solution: Let the length and the breadth of the rectangle be l cm and b cm respectively. Let the side of the square be a cm.   a2 = 4900   a = (4900)^1/2 = 70   l = a and b = a - 20   b : l = a - 20 : a = 50 : 70 = 5:7   Answer: 5:7
Answer: D
What percent of a day is ten hours?	Select the correct option
A) 41.67%	B) 16x1/2%	C) 18x2/3%	D) 22x1/2%	E) None of these

Solution: Explanation :   Required percentage = (10/24100)%.   = 41.67%.   41.67%nswer : 41.67%
Answer: A
What is the difference between the place value of 4 in the numeral 7449? Select the correct option:
A) 150 B) 360 C) 180 D) 190 E) 210

Solution: 400 - 40= 
400 - 40 = 360
360   360
Answer: B
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 2 : 3? Answers.
A) 22	B) 50	C) 88	D) 25	E) 12

Solution: Let the distances between city A to B and B to C be 2x km and 3x km respectively.   Total time taken to cover from A to C   = (2x)/40 + (3x)/60 = (6x + 6x)/120 = 12x/120 = x/10 Average speed = (2x + 3x)/(x/10) = 50 kmph.   Answer: 50
Answer: B
What annual installment will discharge a debt of Rs. 1344 due in 3 years at 12% simple interest?  Choose the correct choice from the following options:
A) 315
B) 345
C) 325
D) 335
E) 400

Solution: Let each Installment be Rs. x   Then, ( x+ ((x*12*1)/100)) + (x+ ((x*12*2)/100) ) + x = 1344   =((28x/25) + (31x/25) + x) = 1344 ïƒ› (28x+31x+25x)=(1344*25)   x= (1344*25)/84 = Rs.400.   Therefore,	Each installment = Rs. 400.   Answer is 400.
Answer: E
A man's speed with the current is 12 km/hr and the speed of the current is 2 km/hr. The man's speed against the current is
Choose the correct answer
A) 8	B) 10	C) 11	D) 12	E) 13

Solution: Man's rate in still water = (12 - 2) km/hr = 10 km/hr.   Man's rate against the current = (10 - 2) km/hr = 8 km/hr.   8nswer:8
Answer: A
Irin, Ingrid and Nell bake chocolate chip cookies in the ratio of 9.18: 5.17: 2.05. If altogether they baked a batch of 148 cookies, what percent of the cookies did Irin bake?
Choose the correct choice from the following answers.
A) 0.125%
B) 1.25%
C) 56%
D) 125%
E) 0.152%

Solution: 9.18x+5.17x+2.05x = 16.4x 9.18 +5.17 +2.05= 
9.18 +5.17 +2.05 = 16.4
16.4x= 150 cookies   x= 150/16.4 = 9.14 (approx)   So, Irin baked 9.14*9.18 cookies or 84 cookies (approx)   % share = 84/150 = 56 approx   Hence, answer is 56%.
Answer: C
The third proportional to 2 and 8 is?	Choose the correct answer.
A) 18 B) 17 C) 42 D) 52 E) 32

Solution: (8*8)/2= 
(8*8)/2 = 32
32   Answer:32
Answer: E
Which of the following leads to the correct mathematical solution for the number of ways that the letters of the word ELECTRIC could be arranged to create a eight-letter code?	Select the correct option.
A) 6!	B) 6! − (3! + 2!)	C) 6! − (3! × 2!)	D) 8!/(2! x 2!)	E) 9!/(3! × 2!)

Solution: Number of letters in word 'ELECTRIC' = 8.   The letters 'E' and 'C' appear 2 times and 2 times respectively in the word 'ELECTRIC'.   Therefore the mathematical solution for number of ways that the letters of the word ELECTRIC can be arranged to create eight-letter code   = 8!/(2!*2!)   Answer:8!/(2! x 2!)
Answer: D
What approximate value should come in place of question mark (?) in the following equation?
33 1⁄3% of 768.9 + 25% of 161.2 – 66.12 = ?
Choose the correct choice from the following choices.
A) 230  B) 225  C) 232  D) 220  E) 240

Solution: ? = 33 1⁄3% of 768.9 + 25% of 161.2 – 66.12   = 1⁄3 of 768.9 + 1⁄4 of 161.2 – 66.12   = 256.3 + 40.3 – 66.12 ≈ 232   Answer 232
Answer: C
Find the greatest number that will divide 28, 128 and 147 leaving 10, 2 and 3 as remainders respectively	Pick:
A) 19	B) 17	C) 13	D) 9	E) 18

Solution: 18xplanation:   Answer will be HCF of (28-10, 128-2, 147-3)   HCF of (18, 126, 144) = 18   Option 18
Answer: E
Machine A can process 6000 envelopes in 3 hours. Machines B and C working together but independently can process the same number of envelopes in 2.5 hours. If Machines A and C working together but independently process 3000 envelopes in 1 hour, then how many hours would it take Machine B to process 5600 envelopes.	Options.
A) 2	B) 3	C) 4	D) 6	E) 60/7

Solution: You can either take the amount of work done as the same as Karishma has done or take the work done by each in the same time. I will do the latter   1. Work done in 1 hr by A is 2000 envelopes   2. Work done in 1 hr by A and C is 3000 envelopes   3. So work done in 1 hr by C is 1000 envelopes   4. Work done in 1 hr by B and C is 2400 envelopes   5. So work done in 1 hr by B is 1400 envelopes   6. So to process 5600 envelopes B will take   5600/1400= 
  5600/1400 = 4
4 hrs   So the answer is choice 4
Answer: C
When the no.7y86038 is exactly divisible by 11, then the smallest whole no.in place of y? Select the correct option:
A) 1	B) 2	C) 3	D) 4	E) 6

Solution: The given number =7y86038   Sum of the odd places =8+0+8+7= 
8+0+8+7 = 23
23   Sum of the even places= 3+6+y   (Sum of the odd places)- (Sum of even places) = Number (exactly divisible by 11)   23-(9+y) = divisible by 11   14 � y = divisible by 11.   Y must be 3, to make given number divisible by 11.   3
Answer: C
If the price of gasoline increases by 25% and a driver intends to spend only 5% more on gasoline, by how much percent should the driver reduce the quantity of gasoline that he buys? Answers:
A) 20%
B) 16%
C) 15%
D) 12%
E) 10%

Solution: Let x be the amount of gasoline the driver buys originally.   Let y be the new amount of gasoline the driver should buy.   Let P be the original price per liter.   (1.25*P)y = 1.05(P*x)   y = (1.05/1.25)= 
(1.05/1.25) = 0.84
0.84x which is a reduction of 16%.   The answer is 16%.
Answer: B