MU-NLPC/Calc-aqua_rat huggingface dataset:
Rahul went to a shop and bought things worth Rs. 27, out of which 30 Paise went on sales tax on taxable purchases. If the tax rate was 6%, then what was the cost of the tax free items?
Choose the most appropriate option:  A) Rs 15  B) Rs 12.10  C) Rs 21.70  D) Rs 16.80  E) None of these

Solution: Explanation :   Let the cost of the tax items = x   Given that tax rate = 6%   Rs 21.70ost of tax items, x*(6/100) = 30/100   x = 5 rs   Now non taxable item = total cost - cost for taxable item - tax   = 27 - 5 - 0.30= 
27 - 5 - 0.30 = 21.7
21.70   Answer : Rs 21.70
Answer: C
Manu, Manju and Maya can do a work in 90, 30 and 45 days respectively. If they work together, in how many days will they complete work?	Answers:  A) 15  B) 10  C) 20  D) 25  E) 30

Solution: Manu’s one day’s work = 1/90   Manju’s one day’s work = 1/30   Maya’s one day’s work = 1/45   Manu, Manju and Maya together can do the work = 1/90 + 1/30 + 1/45   = (1+3+2)/90   = 1/15   So, They will complete the work in 15 days.   15NSWER:15
Answer: A
X can do a piece of work in 20days. He works at it for 10days and then Y finished it in 12days. How long will Y take to complete the work?
Choose the most appropriate option.
A) 10 B) 12 C) 24 D) 29 E) 30

Solution: Work done by X in 10days = 10*1/20 = 1/2   Remaining work = 1 - 1/2 = 1/2   1/2 work is done by Y in 12days   Whole work will be done by Y in 12*2= 
12*2 = 24
24days   Answer is 24
Answer: C
In one year, the population, of a village increased by 10% and in the next year, it decreased by 10%. If at the end of 2nd year, the population was 7920, what was it in the beginning?
Choices:
A) 2277
B) 8000
C) 2688
D) 1266
E) 1912

Solution: x*110/100 * 90/100 = 7920   X*0.99=7920   X=7920/0.99= 
7920/0.99 = 8_000
> 8000   Answer: 8000
Answer: B
The length of a train and that of a platform are equal. If with a speed of 90 k/hr, the train crosses the platform in one minute, then the length of the train (in meters) is:
Pick.
A) 377  B) 267  C) 268  D) 750  E) 271

Solution: Speed = [90 * 5/18] m/sec = 25 m/sec; Time = 1 min. = 60 sec.   Let the length of the train and that of the platform be x meters.   Then, 2x/60 = 25 è x = 25 * 60 / 2= 
25 * 60 / 2 = 750
750 .Answer: 750
Answer: D
What is the smallest integer k for which 64^k > 4^22?  Select.
A) 4	B) 5	C) 6	D) 7	E) 8

Solution: 64^k > 4^22   4^(3k) > 4^22   3k > 22   k = 8   The answer is 8.
Answer: E
Out of 10 persons working on a project, 4 are graduates. If 3 are selected, what is the probability that there is at least one graduate among them?
Choose the correct choice from the following choices.
A) 5/7
B) 9/6
C) 5/9
D) 5/6
E) 3/6

Solution: Explanation:   P(at least one graduate) = 1 - P(no graduates) =   1 - ⁶C₃/¹⁰C₃ = 1 - (6 * 5 * 4)/(10 * 9 * 8) = 5/6   Answer: Option 5/6
Answer: D
Laxmi and Prasanna set on a journey. Laxmi moves northwards at a speed of 22 kmph and Prasanna moves southward at a speed of 24 kmph. How far will be Prasanna from Laxmi after 60 minutes ?  Choose the correct choice from the following
A) 44 B) 50 C) 28 D) 27 E) 18

Solution: Explanation:   We know 60 min = 1 hr   Total northward Laxmi's distance = 22kmph x 1hr = 22 km   Total southward Prasanna's distance = 24kmph x 1hr = 24 km   Total distance between Prasanna and Laxmi is = 22 + 24 = 44 km.   44nswer: 44
Answer: A
GINGER has 3 pairs of pants, 4 different colored dress shirts 3 sports jackets, 9 ties, and 1 pairs of dress shoes in his closet. How many different outfits can he select?  Options.
A) 324  B) 312  C) 290  D) 115  E) 352

Solution: no. of ways he can select a pant = 3   no. of ways he can select a shirt= 4   number of ways he can select a pant = 3   number of ways he can select a shirt= 4   similarly, he can select jacket by 3 ways, tie by 9 ways and shoe by 1 way   number of ways to select different outfits = 3*4*3*9*1= 
3*4*3*9*1 = 324
324   324nswer:324
Answer: A
In a lottery, there are 10 prizes and 30 blanks. A lottery is drawn at random. What is the probability of getting a prize?	Choose the correct choice from the following answers.
A) 1/10	B) 2/5	C) 2/7	D) 1/4	E) None

Solution: Solution   P(getting a prize)	= 10 / (10+30)   ‹=› 10 / 40   ‹=› 1 / 4.   Answer 1/4
Answer: D
James takes a trip and drives 7 hours from Town A to Town C at a rate of 30 miles per hour. On his way back, James drives 60 miles per hour and stops in Town B which is midway between Town A and Town C. How many hours does it take James to drive from Town C to Town B? Choose the most appropriate option.
A) 1.25
B) 1.75
C) 1.51
D) 1.55
E) 2.12

Solution: distance from A to C =7 hr* 30 mph= 210 miles   hence distance from Y to C= 1/2*210= 
1/2*210 = 105
105   time=105/60= 
105/60 = 7/4 = around 1.75
1.75 hrs   IMO: 1.75
Answer: B
The expression (11.98 x 11.98 + 11.98 x x + 0.02 x 0.02) will be a perfect square for x equal to:
Choose the correct choice from the following options.
A) 0.4	B) 0.004	C) 0.04	D) 0.0004	E) None of them

Solution: Given expression = (11.98)(power 2) + (0.02)(power 2) + 11.98 x x.   For the given expression to be a perfect square, we must have   11.98 x (x) = 2 x 11.98 x 0.02 or   x = 0.04   Answer is 0.04.
Answer: C
Students at a school were on average 180 cm tall. The average female height was 170 cm, and the average male height was 186 cms. What was the ratio of men to women?
Select the correct option
A) 5:2	B) 5:1	C) 5:3	D) 4:1	E) 3:1

Solution: We're given a few facts to work with:   1) The average height of the females is 170cm   2) The average height of the males is 186cm   3) The average of the GROUP is 180cm   We're asked for the RATIO of men to women.   W = number of Women   M = number of Men   (170W + 186M)/(W+M) = 180   170W + 186M = 180W + 180M   6M = 10W   3M = 5W   M/W = 5/3   The ratio of men to women is 5 to 3.   5:3
Answer: C
Find the one which does not belong to that group ? Choose the correct choice from the following choices: A) 117 B) 121 C) 727 D) 188 E) 122

Solution: Explanation:   343 = 73, 121 = 112, 1331 = 113, 2197 = 133 and 125 = 53.   343, 1331, 2197 and 125 are perfect cubes, but not 121.   Answer: 121
Answer: B
Kamal started a business investing Rs. 9000. After five months, Sameer joined with a capital of Rs. 8000. If at the end of the year, they earn a profit of Rs. 6970, then what will be the share of Sameer in the profit?	Choose the correct choice from the following options:
A) 2388	B) 2380	C) 2385	D) 2383	E) 2381

Solution: Kamal : Sameer = (9000 * 12) : (8000 * 7)   = 108:56 = 27:14   Sameer's share = 6970 * 14/41 = Rs. 2380.   Answer:2380
Answer: B
A cylinder has a diameter of 20 meters and a height of 15 meters. If it is filled to capacity with oil and the content is poured into smaller cylinders of 4 meter radius and 10 meter height, how many smaller cylinders will be filled to capacity?	Choose the correct choice from the following choices
A) 11	B) 5	C) 2	D) 2	E) 3

Solution: Calculate the volume of the larger cylinder and divide it by the volume of the smaller cylinder.   volume of cylinder =πr2h   larger cylinder volume=1570.8   smaller cylinder volume=502.65   therefore the number of cylinders B that can be filled to capacity=1570.8/502.65=3.1   Answer is 3 only 3 smaller cylinders can be filled to capacity.
Answer: E
Jamshid and Irwin decided to make up their own version of basketball. In addition to being able to score 2-point baskets, they created ways to score 5-, 11-, and 13-point baskets. If at halftime the product of the point values of Irwin’s baskets was 2,420, how many 11-point baskets did Irwin score?  Choose the most appropriate option:
A) 0
B) 1
C) 2
D) 3
E) 4

Solution: First thing I noticed was that all these numbers are prime...   Prime factorization gives the following   Step 1:2*1210   Step 2:2*11*110   Step 4:2*11*11*10   Step 5:2*11*11*2*5   So he scored 2 11-point baskets in my opinion.   Answer 2
Answer: C
I had Rs. 10,000 with me. Out of this, money I lent some money to A for 2 years at 15% simple interest. I lent the remaining money to B for an equal number of years at 18% simple interest. After 2 years, I found that A had given me Rs. 360 more as interest as compared to(b) the amount of money which I had lent to B must have been	Choose one.
A) 2,000 B) 3,000 C) 4,000 D) 5,000 E) 6,000

Solution: Explanation:   Total amount = Rs. 10,000   Let money lent A =Rs. x and money lent to B = Rs. (10,000 x)   x = Rs. 6,000. So the amount of money lent to B = Rs. 4,000   Answer: 4,000
Answer: C
A man can row his boat with the stream at 16 km/h and against the stream in 12 km/h. The man's rate is?	Options:	A) 8 kmph	B) 9 kmph	C) 2 kmph	D) 4 kmph	E) 1 kmph

Solution: DS = 16   US = 14   S = ?   S = (16 - 2)/2 = 2 kmph   Answer:2 kmph
Answer: C
Which of the following integers is a divisor of(15!+10)? Choose the correct choice.
A) 15	B) 4	C) 3	D) 10	E) 9

Solution: When we say 15!, it just means 1*2*3*4*5*...*13*14*15   So you need to find the integer which is a divisor of   (1*2*3*4*5*...*13*14*15 + 10) = 10 (1*2*3*4*5*..*9*11*12*13*14*15 + 1) We obtain this by taking 10 common.   Hence 10 is definitely a divisor of (15! + 10).   Ans 10
Answer: D
The cost of producing x tools by a company is given by
C(x) = 1800 x + 5500 (in $)
a) What is the cost of 100 tools?
Answers.
A) 185500 $  B) 185800 $  C) 185900 $  D) 186500 $  E) 182500 $

Solution: Solution   C(100) = 1800*100 + 5500= 
1800*100 + 5500 = 185_500
185500 $   185500 $nswer 185500 $
Answer: A
The mean of 30 values was 180. It was detected on rechecking that one value 155 was wrongly copied as 135 for the computation of the mean. Find the correct mean.	Select the correct option
A) 151	B) 149	C) 152	D) 148	E) 180.67

Solution: Corrected mean = 180×30−135+155/30   = 5400−135+155/30   =5420/30=180.67   Answer 180.67
Answer: E
If x and y are integers, what is the least positive number of 24x+21y?	Pick one.
A) 3 B) 5 C) 6 D) 8 E) 9

Solution: 24x+21y = 3(8x+7y) which will be a minimum positive number when 8x+7y = 1.   8(1) + 7(-1) = 1   Then 3(8x+7y) can have a minimum positive value of 3.   The answer is 3.
Answer: A
What is the sum of all possible 3-digit numbers that can be constructed using the digits 1, 2, and 4 if each digit can be used only once in each number?
Choose the correct choice from the following options:
A) 1210  B) 1221  C) 1332  D) 1443  E) 1554

Solution: There are 6 possible arrangements of the three numbers.   Then each number will be in the hundreds, tens, and ones place two times each.   The sum is 2(111) + 2(222) + 2(444) = 1554   The answer is 1554.
Answer: E
Find the greatest number that will divide 40, 60 and 120 so as to leave the same remainder in each case.  Choose the most appropriate option:
A) 2 B) 3 C) 4 D) 5 E) 6

Solution: Required number = H.C.F. of (60 - 40), (120 - 60) and (120-40)   = H.C.F. of 20, 60 and 80 = 2.   2NSWER :2
Answer: A
A committee of three people is to be chosen from four married couples. What is the number of different committees that can be chosen if two people who are married to each other cannot both serve on the committee?  Pick
A) 16
B) 24
C) 26
D) 30
E) 32

Solution: The committee could have   0 men and 3 women = 4 possibilities ( 4c3 )   1 man and 2 women = 12 possibilities ( no couple should be in the team : 4 * 3c2 )   2 men and 1 woman = 12 possibilities ( no couple should be in the team : 4c2 *2c1 )   3 men and 0 women = 4 possibilities ( 4c3 )   Therefore  4+12+12+4= 
 4+12+12+4 = 32
32   Answer 32 32
Answer: E
find out how many positive integers less than 60 are equal to the product of a positive multiple of 5 and an even number?
Choose the correct choice from the following answers
A) 4
B) 5
C) 9
D) 10
E) 11

Solution: Number of positive multiples of 5 less than 60 = 11   5*1= 
5*1 = 5
5   5*2= 
5*2 = 10
10   5*3= 
5*3 = 15
15   5*4= 
5*4 = 20
20   5*5= 
5*5 = 25
25   5*6= 
5*6 = 30
30   5*7= 
5*7 = 35
35   5*8= 
5*8 = 40
40   5*9= 
5*9 = 45
45   5*10= 
5*10 = 50
50   5*11= 
5*11 = 55
55   Only 5 of the above are a product of a positive multiple of 5 and an even number - 10,20,30,40,50   Answer 5
Answer: B
A side of beef lost 35 percent of its weight in processing. If the side of beef weighed 580 pounds after processing, how many pounds did it weigh before processing?  Choose the correct answer.
A) 191	B) 355	C) 737	D) 892	E) 1,560

Solution: Let weight of side of beef before processing = x   (65/100)*x = 580   => x = (580 * 100)/65 = 892   Answer 892
Answer: D
Cindy has her eye on a sundress but thinks it is too expensive. It goes on sale for 15% less than the original price. Before Cindy can buy the dress, however, the store raises the new price by 25%. If the dress cost $78.2 after it went on sale for 15% off, what is the difference between the original price and the final price? Select
A) $0.00  B) $5.75  C) $3.40  D) $5.00  E) $6.80

Solution: 0.85*{Original Price} = $78.2 --> {Original Price} = $92.   {Final Price} = $78.2*1.25 = $97.75.   The difference = $97.75 - $92 = $5.75   Answer: $5.75.97.75 -  92= 
97.75 -  92 = 5.75
$5.75   Answer: $5.75.
Answer: B
The area of a triangle is with base 4m and height 5m?	Choose the correct choice from the following answers:
A) 10  B) 20  C) 30  D) 15  E) 11

Solution: The area of a triangle=1/2*bh   =1/2 * 4 * 5= 
1/2 * 4 * 5 = 10
10 m^2   10NSWER:10
Answer: A
Three coworkers P , J , R meet for Dinner. P had 5 sandwiches, J had 3 and R had none. Both PJ share their sandwiches with R such that each one got the same amount. If R paid $ 8 to PJ, how much of $ 8 should P get? Assume both sandwiches and Dollars can be split. Choose the correct answer.
A) a) 5$
B) b) 3 $
C) c) 7 $
D) d) 4 $
E) e) 5.5 $

Solution: we got total 8 sandwiches ....we are dividing equally in 3 people.   per person: 8/3   initially   p:8   J:3   r:0   now since r ate 8/3 so he is paying 8 dollars for 8/3 sandwiches.   now p also ate 8/3 of his 5 sandwiches = so he gave 5-8/3 to r ==>7/3 to r   ok we have 8 dollars for 8/3 sandwich   therefore for 7/3 sandwich we will get 7 dollars.   hence p should get 7 dollars.   hence c) 7 $
Answer: C
A certain league has two divisions. The respective divisions had 7 and 9 teams qualify for the playoffs. Each division held its own double-elimination tournament -- where a team is eliminated from the tournament upon losing two games -- in order to determine its champion. The four division champions then played in a single-elimination tournament -- where a team is eliminated upon losing one game -- in order to determine the overall league champion. Assuming that there were no ties and no forfeits, what is the maximum number of games that could have been played in order to determine the overall league champion?
Choose the correct choice from the following choices:
A) 30  B) 31  C) 34  D) 36  E) 38

Solution: Overall, there can be 31 minuses. Tus, it is 31.
Answer: B
Jill is dividing her eight-person class into two teams of equal size for a basketball game. If no one will sit out, how many different match-ups between the two teams are possible?
Answers
A) 10 B) 35 C) 126 D) 252 E) 630

Solution: With 8 players, the process of figuring out how many groups of 4 can be formed is pretty straight-forward....   8C4 = 8!/(4!4!) = 70 possible groups of 4   Once forming that first group of 4, the remaining 4 players would all be placed on the second team by default.   The 'twist' is that the two teams of 4 canshow upin either order:   35
Answer: B
Ram can do a piece of work in 8 days which Shyam can finish in 12 days. If they work at it on alternate days with Ram beginning, in how many days, the work will be finished?	Choose the correct choice from the following choices
A) 9 1/3
B) 9 1/2
C) 9 1/4
D) 10 1/3
E) 11 1/3

Solution: (ram+shyam)'s 2 days work = (1/8+1/12) = 5/24   work done in 4 pair of days = (5/24)*4 = 5/6; remaining work = 1-(5/6) = 1/6   work done by ram on 9th day = 1/8; Remaining work = (1/6)-(1/8)= 1/24   On 10th day it is shyam's turn   1/12 work is done by shyam in 1 day   1/24 work is done by shyam in 12*(1/24) = 1/2   total time = (9 + 1/2) day   ANSWER:9 1/2
Answer: B
A boat having a length 3 m and breadth 2 m is floating on a lake. The boat sinks by 1.8 cm when a man gets on it. The mass of man is  Select:  A) 12 kg  B) 60 kg  C) 108 kg  D) 96 kg  E) None

Solution: Solution   Volume of water displaced	= (3 x 2 x 0.018)m3   = 0.108m3.   Mass of man	=Volume of water displaced ×Density of water   = (0.108×1000) kg   = 108 kg.   Answer 108 kg
Answer: C
John has on his shelf four books of poetry, four novels, and three reference works. Suppose from these ten books, we were to pick two books at random. What is the probability that we pick one novel and one reference work? Pick:  A) 1/2  B) 12/55  C) 3/10  D) 7/20  E) 8/45

Solution: When we are picking two books, one novel and one reference work, we could either pick a novel first and then a reference book or pick a reference book and then a novel. Therefore the answer is 4/11*3/10 + 3/11*4/10 = 12/55.   Answer: 12/55.
Answer: B
What is the sum of all 5 digit numbers which can be formed with the digits 0,1,2,3,4 without repetation?	Choose the correct choice from the following choices:
A) 2599980	B) 235500	C) 923580	D) 765432	E) 765434

Solution: 10(11111)*4! - 10(1111)3! = 2599980   2599980NSWER:2599980
Answer: A
The arithmetic mean of set P is zero. If Q = {-2.22; -1.96; -1.68; 1.62; 1.94; 2.16} is the subset of P consisting of all those elements in P which are more than two but less than three standard deviations away from the arithmetic mean of P, what could be equal to the standard deviation of P?	Choose the correct choice from the following choices:
A) 0.54
B) 0.77
C) 0.82
D) 0.97
E) 1.62

Solution: This is a fairly straightforward question that can be solved quickly by just applying the options   We are provided with Mean, m= 0   and Q = {-2.22; -1.96; -1.68; 1.62; 1.94; 2.16} is the subset of P   Q consists of all those elements in P that are more than 2 but less than 3 SDs away from the arithmetic mean of P   If an element is 1 PD away from the mean, we can write it as either m + PD or m - PD   Similarly, if an element is 2 PDs away from the mean, we can write it as either m + 2*PD or m - 2*PD   So, if these elements lie within 2 and 3 PDs of mean, m=0   we can find which one of these values of PD satisfies each value within Q   Only PD = 0.77 does   Answer : 0.77
Answer: B
A train 360 m long passed a pole in 30 sec. How long will it take to pass a platform 780 m long? Choose the correct choice:
A) 76 sec
B) 89 sec
C) 87 sec
D) 95 sec
E) 16 sec

Solution: Speed = 360/30= 
360/30 = 12
12 m/sec.   Required time= (360 + 780)/12= 
(360 + 780)/12 = 95
95 sec.   Answer:95 sec
Answer: D
The following questions are based on the information given below:
1)A cuboid shaped wooden block has 4 cm length, 3 cm breadth and 5 cm height.
2)Two sides measuring 5 cm x 4 cm are coloured in red.
3)Two faces measuring 4 cm x 3 cm are coloured in blue.
4)Two faces measuring 5 cm x 3 cm are coloured in green.
5)Now the block is divided into small cubes of side 1 cm each.
How many small cubes will have will have three faces coloured ?	Choose the most appropriate option.
A) 14  B) 8  C) 10  D) 12  E) 16

Solution: Such cubes are related to the corners of the cuboid and in the cuboid there are 8 corners.   Hence, the required number of small cubes is 8.   Answer :8
Answer: B
A fort of 2000 soldiers has provisions for 50 days. After 10 days some of them left and the food was now enough for the same period of 40 days as before. How many of them left?  Choose the correct choice from the following:
A) 100	B) 0	C) 200	D) 400	E) 500

Solution: 2000 ---- 50   2000 ---- 40   x ----- 40   x*40 = 2000*40   x=2000   2000   -------   0   ANSWER:0
Answer: B
If the order of the letter in the English alphabet is reversed which letter will be the seventh to right of the twelfth letter from the right?  Select
A) E B) V C) F D) U E) T

Solution: Lkjihgfedcba   So ans wiil be   E   ENSWER:E
Answer: A
The proportion of copper and zinc in the brass is 3:7. How much zinc will there be in 100 kg of brass?	Select the correct option:	A) 70	B) 50	C) 40	D) 270	E) 170

Solution: 7/10 * 100= 
7/10 * 100 = 70
70   70NSWER:70
Answer: A
A meal cost $ 36.50 and there was no tax. If the tip was more than 10 pc but less than 15pc of the price, then the total amount paid should be:  Choose one
A) 40-42
B) 39-41
C) 38-40
D) 37-39
E) 36-37

Solution: 10%(36.5) = 3.65   15%(36.5) = 5.475   total amount could have been 36.5+3.65 and 36.5+5.475   => could have been between 40.15 and 41.975   => approximately between 40 and 42   40-42nswer is 40-42.
Answer: A
If a square mirror has a 20-inch diagonal, what is the approximate perimeter Q of the mirror, in inches?
Choose the correct choice from the following answers:
A) 40  B) 60  C) 80  D) 100  E) 120

Solution: if you draw the square and diagonal inside the square. u can see square becomes part of two triangles opposite to each other.   And We know the property of the triangle, addition of two sides of triangle must be greater than its diagonal in order to complete the triangle. And each side must be less than 20 and perimeter Q must be less than 80, so we can eliminate answer choice C, D and E.   so Side 1 + side 2 > 20, that means Side 1 or Side 2 must be > 10. so we can eliminate the answer choice A.   Now we are left with is 60
Answer: B
The cost price of a radio is Rs.2550 and it was sold for Rs.2130, find the loss %?
Choose the correct option:
A) 18  B) 10  C) 15  D) 66  E) 41

Solution: 2550 ---- 400   100 ---- ? => 15%   Answer: 15
Answer: C
Walking across campus, a student interviewed a group of students. 25% of the students took a finance class last semester, 50% took a marketing class last semester, and 40% took neither a finance nor a marketing class last semester. What percent of the students in the group took both a finance and a marketing class?	Choose one:
A) 60% B) 50% C) 25% D) 15% E) 10%

Solution: {Total} = {finance} + {marketing} - {both} + {neither}   100 = 25 + 50 - {both} + 40   {both} = 15%.   Answer: 15%.
Answer: D
n is a whole number which when divided by 4 gives 3 as remainder. What will be the remainder when 2n is divided by 4? Choose the correct choice
A) 3  B) 2  C) 1  D) 0  E) None of these

Solution: Let n=4q+3.   2n=8q+6=4(2q+1)+2   Thus, when 2n is divided by 4, the remainder is 2.   Correct Option: 2
Answer: B
The area of a rectangular plot is 21 times its breadth. If the difference between the length and the breadth is 10 metres, what is its breadth?  Choose the correct choice from the following options:  A) 10 metres  B) 5 metres  C) 11 metres  D) Data inadequate  E) None of these

Solution: L × B = 21 × B   ∴ L = 21 m   and L – B = 10   ∴ B = 21 – 10 = 11 m   Answer 11 metres
Answer: C
Dacid obtained 76, 65, 82, 67 and 85 marks (out of 100) in English, Mathematics, Physics, Chemistry and Biology. What are his average marks?  Choose the correct choice from the following:
A) 29	B) 38	C) 39	D) 37	E) 75

Solution: Average = (76 + 65 + 82 + 67 + 85)/5   = 375/5= 
375/5 = 75
75.   Answer: 75
Answer: E
Find the remainder when 6^50 is divided by 215	Options:
A) 36 B) 99 C) 27 D) 99 E) 17

Solution: 36ns: 650=(63)16.62=21616.62650=(63)16.62=21616.62   So this expression gives a remainder of 36   36nswer:36
Answer: A
Lionel left his house and walked towards Walt's house, 48 miles away. Four hours later, Walt left his house and ran towards Lionel's house. If Lionel's speed was 3 miles per hour and Walt's 6 miles per hour, how many miles had Lionel walked when he met Walt? Options: A) 12 B) 16 C) 20 D) 24 E) 28

Solution: In the first 4 hours Lionel at the rate of 3 miles per hour covered distance=rate*time=4*3= 
4*3 = 12
12 miles. So, the distance between him and Walt was 48-12= 
48-12 = 36
36 miles when Walt left his house. Now, their combined rate to cover this distance was 3+6= 
3+6 = 9
9 miles per hour, hence they will meet (they will cover that distance) in time=distance/rate=36/9= 
36/9 = 4
4 hours. Total time that Lionel was walking is 4+4= 
4+4 = 8
8 hours, which means that he covered in that time interval distance=rate*time=3*8= 
3*8 = 24
24 miles.   Answer: 24.
Answer: D