MU-NLPC/Calc-aqua_rat huggingface dataset:
A two digit number, digits interchange places and the new number is added to the original number, then the resulting number will be divisible by?	Select:
A) 10
B) 11
C) 13
D) 15
E) 16

Solution: Let the ten's digit be x and unit's digit be y.   Then, number = 10x + y.   Number obtained by interchanging the digits = 10y + x.   (10x + y) + (10y + x) = 11(x + y), which is divisible by 11.   11
Answer: B
if 5 boys take two hours to water the garden, then how long should 10 boys take to water the same type of garden?  Select.
A) 80 min	B) 50 min	C) 30 min	D) 65 min	E) 60 min

Solution: if 5 boys take an hour to water the garden, then   10 boys will take  5*120/10= 
 5*120/10 = 60
60 mins to water the same type of garden.   ANSW60 minR:60 min
Answer: E
A train 125 m long passes a man, running at 6 km/hr in the same direction in which the train is going, in 10 sec. The speed of the train is? Choose the correct choice from the following options.
A) 40
B) 50
C) 51
D) 79
E) 80

Solution: Speed of the train relative to man = 125/10 = 25/2 m/sec.   = 25/2 * 18/5= 
25/2 * 18/5 = 45
45 km/hr   Let the speed of the train be x km/hr. Then, relative speed= (x - 6) km/hr.   x - 6 = 45 => x = 51 km/hr.   Answer: Option 51
Answer: C
Eight family members are seated around their circular dinner table. If only arrangements that are considered distinct are those where family members are seated in different locations relative to each other, and Michael and Bobby insist on sitting next to one another, then how many distinct arrangements around the table are possible?	Choose the correct choice from the following choices:
A) 1040
B) 1240
C) 1440
D) 1640
E) 1840

Solution: Let's consider Michael and Bobby as one unit.   There are 7! possible arrangements of 7 units.   Around a table, there would be repetitions of each arrangement, so we divide by 7.   Then there are 6! arrangements around a circular table.   For each arrangement, Michael and Bobby can switch places, so we multiply by 2.   The number of arrangements is 6!*2 = 1440.   The answer is 1440.
Answer: C
Two trains of equal lengths take 10 sec and 15 sec respectively to cross a telegraph post. If the length of each train be 160 m, in what time will they cross other travelling in opposite direction?  Choose the correct choice.
A) 17 sec B) 12 sec C) 16 sec D) 15 sec E) 18 sec

Solution: Speed of the first train = 120/10= 
120/10 = 12
12 m/sec.   Speed of the second train= 120/5 = 8 m/sec.   Relative speed = 12 + 8= 
12 + 8 = 20
20 m/sec.   Required time= (160 + 160)/20= 
(160 + 160)/20 = 16
16 sec.   Answer:16 sec
Answer: C
Excluding stoppages, the speed of a train is 50 kmph and including stoppages it is 30 kmph. Of how many minutes does the train stop per hour?  Options.
A) 82  B) 17  C) 12  D) 24  E) 18

Solution: Explanation:   T = 20/50 * 60= 
20/50 * 60 = 24
24   Answer: Option 24
Answer: D
How many arrangements can be made out of the letters of the word 'ENGINEERING' ?	Choose the correct choice from the following:
A) 277200 B) 92400 C) 69300 D) 23100 E) 45380

Solution: The word 'ENGINEERING' contains 11 letters, namely 3E, 3N, 2G, 2I and 1R.   ∴ Required number of arrangements = 11!/(3!)(3!)(2!)(2!)(1!) = 277200.   277200nswer is 277200
Answer: A
From January 1, 1991, to January 1, 1993, the number of people enrolled in health maintenance organizations increased by 10 percent. The enrollment on January 1, 1993, was 45 million. How many million people, to the nearest million, were enrolled in health maintenance organizations on January 1, 1991 ?
Choose the correct choice from the following answers.
A) 38  B) 39  C) 40  D) 41  E) 42

Solution: 1.10x=45 --> 11/10*x=45 --> x=45*10/11=450/11=~41.   Answer: 41.
Answer: D
On a map, 1 centimeter represents 17 kilometers. Two cities 663 kilometers apart would be separated on the map by how many centimeters?	Choose the correct choice from the following choices
A) 15  B) 27  C) 39  D) 270  E) 480

Solution: X=663/17= 
663/17 = 39
39   Answer: 39
Answer: C
In a group of 68 students, each student is registered for at least one of three classes – History, Math and English. Twenty-one students are registered for History, twenty-six students are registered for Math, and thirty-four students are registered for English. If only three students are registered for all three classes, how many students are registered for exactly two classes?	Pick one
A) 13 B) 10 C) 9 D) 8 E) 7

Solution: A U B U C = A + B + C - AB-BC-AC + ABC   68 = 21 + 26+ 34 -AB-BC-AC +3 => AB+BC+AC = 16   7xactly Two classes = AB+BC+AC - 3ABC = 16 -3*3= 
16 -3*3 = 7
7   Hence 7
Answer: E
The average marks scored by Ganesh in English, Science, Mathematics and History is less than 18 from that scored by him in English, History, Geography and Mathematics. What is the difference of marks in Science and Geography scored by him? Choose one:  A) 72  B) 50  C) 60  D) Data inadequate  E) None of these

Solution: E+H+G+M/4âˆ’E+S+M+H/4=18   â‡’ G - S = 72   72nswer 72
Answer: A
Which is longest: a foot, a yard or an inch?
Choose the correct choice from the following answers: A) a yard B) inch C) foot D) feet E) cm

Solution: 3 feet = 1 yard   12 inches = 1 foot   answer a yard
Answer: A
If p and q are integers, such that p < 3 < q, and s is a nonnegative integer, which of the following must be true?	Choices:	A) p^2 < q^2	B) p + q = 0	C) sp < sq	D) sp ≠ sq	E) p/q < s

Solution: We're told that P < 0 < Q and that S is a NON-NEGATIVE INTEGER. We're asked which of the following MUST be true.   P = -2   Q = 2   S = 0   Answer A: P^2 < Q^2.... 4 < 1 NOT TRUE   Answer B: P+Q=0... -2+1 = -1 NOT TRUE   Answer C: SP < SQ... 0 < 0 NOT TRUE   Answer D: SP ≠ SQ... 0 = 0 NOT TRUE   Answer E: P+Q=0 This IS TRUE   p + q = 0
Answer: B
A grocer stacked apples in a pile. The bottom layer was rectangular with 3 rows of 5 apples each. In the second layer from the bottom, each apple rested on 4 apples from the bottom layer, and in the third layer, each apple rested on 4 apples from the second layer. Which of the following is the maximum number of apples that could have been in the third layer?  Choose one
A) 5  B) 3  C) 6  D) 2  E) 1

Solution: 3ottom Layer = 5 x 3 = 15   IInd Layer = (5-1) x (3-1) = 8   IIIrd Layer = (4-1) x (2-1) = 3   Answer = 3 = 3
Answer: B
The radius of a sphere is increased by 50%. The increase in surface area of the sphere is : Choose the correct option:	A) 168	B) 125	C) 186	D) 197	E) 191

Solution: Explanation:   Take radius 100. Then surface area is 4 × ππ × 100 × 100.   After increase radius by 50% the radius becomes100 + 50% of 100 = 150   Then new surface area is 4 × ππ × 150 × 150   Then put the values into formula of percentage = 4π1502−4π10024π1002×1004π1502−4π10024π1002×100 = 125%   Answer: 125
Answer: B
If a man lost 4% by selling oranges at the rate of 12 a rupee at how many a rupee must he sell them to gain 44%?  Options
A) 9  B) 8  C) 7  D) 6  E) 65

Solution: 96% ---- 12   144% ---- ?     96/144 * 12= 
  96/144 * 12 = 8
8   Answer: 8
Answer: B
How much is 80% of 40 is greater than 2/5 of 25?	Choose the correct option:
A) 22
B) 27
C) 18
D) 12
E) 81

Solution: (80/100) * 40 â€“ (2/5) * 25   32 - 10= 
32 - 10 = 22
22   22nswer:22
Answer: A
Given two sets A = {1,1,2,2,7,7} and B = {0,1}, if one number is chosen from each set at random, what is the probability that the sum of both numbers is an even number Choose the correct answer
A) 1/5
B) 1/6
C) 1/2
D) 1/3
E) 1/4

Solution: One way to look at it:   The number from set A can be ANYTHING.   The number selected from set B will determine whether the sum is odd or even.   For example, if a 2 is selected from set A, we need a 0 from set B to get an even sum.   If a 7 is selected from set A, we need a 1 from set B to get an even sum.   And so on.   So, P(sum is even) = P(select ANY number from set AANDselect the number from set B that makes the sum even)   = P(select ANY number from set A)xP(select the number from set B that makes the sum even)   = 1x1/2   = 1/2   = 1/2
Answer: C
Of the three-digit integers greater than 700, how many have distinct digits? Pick: A) 216 B) 82 C) 80 D) 45 E) 36

Solution: Three digit number can have only following 3 patterns:   A. all digits are distinct;   B. two digits are alike and third is different;   C. all three digits are alike.   We need to calculate B. B=Total - A - C   Total numbers from 700 to 999 = 299 (3-digit numbers greater than 700);   A. all digits are distinct = 3*9*8= 
3*9*8 = 216
216   216nswer: 216
Answer: A
Find the compound interest on $ 10,000 in 2 years at 4% per annum, the interest being compounded half-yearly  Pick.
A) 824
B) 824.36
C) 824.32
D) 824.24
E) 824.26

Solution: Principal = $ 10000; Rate = 2% per half-year; Time = 2 years = 4 half-years.   Amount = $ [10000 * (1+(2/100))4] = $(10000 * (51/50) * (51/50) * (51/50) * (51/50))   = $ 10824.32.   :. C.I. = $ (10824.32 - 10000) = $ 824.32.   Answer 824.32.
Answer: C
There are n cities. What is the number of airlines that connected 5 different cities (airline from city A to city B is different with airline from city B to city A)? Choose the correct option:  A) n(n-1)  B) n(n+1)  C) n(n-1)/2  D) n(n-3)  E) n2

Solution: First of all, the possible number of airlines is n. Then, the possible number of airlines departing from one city to another becomes (n-4). Hence, the answer is n(n-4), which makes A an answer choice.   n(n-3)
Answer: D
What is the probability that a two digit number selected at random is a multiple of 3 and not a multiple of 5 ?
Choose the correct choice from the following choices.
A) 1/15  B) 2/15  C) 4/15  D) 7/15  E) None of these

Solution: Explanation :   Since every third number starting from 10 will be divisible by 3, so total number of numbers divisible by 3 are   90/3= 
  90/3 = 30
30   Numbers which are divisible by 3 and 5 both are numbers which are multiple of 15.   For the range 10 to 99, 15 is the first number divisible by 15 and 90 is the last number.   So total number of numbers divisible by 15 are: (90-15)/15 + 1= 5 + 1= 
5 + 1 = 6
6   Number of numbers which are divisible by 3 are 30 and number of numbers which are divisible by 3 and 5 both are 6. So number of numbers divisible by 3 and not by 5 are: 30-6= 
30-6 = 24
24   So total probability= 24/90 = 4/15   Answer : 4/15
Answer: C
The sale price of a trolley bag including the sale tax is Rs. 280. The rate of sale tax is 12% . If the shopkeeper has made a profit of 25%, the cost price of the trolley bag is:	Choose the correct choice from the following answers.
A) Rs 200  B) Rs 220  C) Rs 260  D) Rs 280  E) None of these

Solution: Explanation :   112% of S.P. = 280   S.P. = Rs.(280x 100/112) = Rs.250.   C.P. = Rs (100/125x 250) = Rs 200   Rs 200nswer : Rs 200
Answer: A
How many factors of 990 are odd numbers greater than 1?
Choose the correct answer.
A) 13
B) 14
C) 15
D) 16
E) 17

Solution: When factorized, 990 has 5 prime factors. Of these prime factors 4 are odd and 1 is even. Hence total number of odd factors is 2*2*2*2(16), which includes 1. The total number of odd factors greater than 1 are 15.(option 15)
Answer: C
A sum of Rs.1420 is divided into 13 students so that each boy gets Rs.120 while each girl gets Rs.100. Find the number of boys and number of girls
Choose the correct choice from the following answers.
A) 8B, 5G
B) 5B, 8G
C) 4B, 9G
D) 9B, 4G
E) 6B, 7G

Solution: 120B+100G=1420-----i   B+G=13-------ii   from i   100B+20B+100G=1420   100(B+G)+20B=1420   100(13)+20B=1420   By simplifing we get   B=6;G=7   ANSW6B, 7GR:6B, 7G
Answer: E
For some integer p, p^2 - 5 is divisible by all of the following EXCEPT
Options:
A) 30
B) 38
C) 41
D) 29
E) 31

Solution: Hint: p^2-5 (p is an integer) is never multiple of 3 (try to prove this), hence 30 is out.   30nswer: 30
Answer: A
The length of a room is 5.5 m and width is 3.75 m. Find the cost of paving the floor by slabs at the rate of Rs. 1200 per sq. metre.  Choose the correct answer
A) Rs. 15000	B) Rs. 15550	C) Rs. 24750	D) Rs. 16500	E) None of these

Solution: Solution   Area of the floor = (5.5 × 3.75) m2 = 20.625 m2   ∴ Cost of paving = Rs. (1200 × 20.625) = 24750. Answer Rs. 24750
Answer: C
How many seconds will a 500 meter long train take to cross a man walking with a speed of 3 km/hr in the direction of the moving train if the speed of the train is 63 km/hr Choices
A) 25 Seconds	B) 28 Seconds	C) 30 Seconds	D) 35 Seconds	E) 40 Seconds

Solution: Explanation:   Relative Speed = 63-3= 
63-3 = 60
60 Km/hr= 60 *(5/18) = 50/3 m/sec   Time taken to pass the man will be   500âˆ—3/50=30seconds   ANSWER IS 30 Seconds
Answer: C
What is the length of the longest pole which can be kept in a room 12 m long, 4 m broad and 3 m high?  Choose the correct choice from the following answers: A) 16 B) 4 C) 11 D) 12 E) 13

Solution: d^2 = 12^2+4^2+3^2   d^2 = 122 + 42 + 32 = 13   Answer: 13
Answer: E
A number is doubled and 5 is added. If the resultant is trebled, it becomes 105. What is that number?	Choose the correct choice from the following:
A) 12
B) 29
C) 27
D) 15
E) 99

Solution: Explanation:   Let the number be x.   Therefore,   3(2x + 5) = 105   6x + 15 = 105   6x = 90   x = 15   ANSWER:15
Answer: D
The Present worth of Rs.2310 due years hence ,the rate of interest being 15% per annum, is :  Choose the correct choice from the following options.
A) Rs.1440  B) Rs.1750  C) Rs.1680  D) Rs.1840  E) None of these

Solution: Explanation:   P.W.=Rs.[100×2310/100+(15×52)]=Rs.1680.   Answer: Rs.1680
Answer: C
All even numbers from 2 to 98 inclusive, except those ending in 0, are multiplied together what is the rightmost digit (the units digit) of the product? Choose the correct choice from the following:	A) 0	B) 2	C) 4	D) 6	E) 8

Solution: first multifly all numbers ending with 2 those are 2*12*22*32*42.......*92=2^10=4 is last digit   multify all numbers ending with 4=4^10=6 last digit   multify all numbers ending with 6=6^10= 6 last digit   multifly all numbers ending with 8=8^10=4 last digit   so 4*6*6*4=6 last digit   ANSWER:6
Answer: D
A basket contains 5 apples of which one is rotten. If Henry is to select 2 apples from the basket simultaneously and at random what is the probability that the 2 apples selected will include the rotten apple?	Choose one:
A) 1/5 B) 3/10 C) 2/5 D) 1/2 E) 3/5

Solution: Direct probability approach:   P=15∗44+45∗14=25P=15∗44+45∗14=25: probability of {first apple rotten, second apple good} plus the probability of {first apple good, second apple rotten}.   Reverse probability approach:   Again 1- the probability of the opposite event --> P=1−45∗34=25P=1−45∗34=25.   Answer: 2/5
Answer: C
What is the units digit of 29! + 50! + 3! + 3!?  Answers:
A) 0	B) 2	C) 4	D) 6	E) 8

Solution: For all N greater than 4, the units digit of N! is 0.   The sum of the four units digits is 0 + 0 + 6 + 6= 
0 + 0 + 6 + 6 = 12
12   The units digit is 2.   The answer is 2.
Answer: B
If the milk and water ware added in the ratio 5:4 then how much more water should be added so he gets the ratio of 6:7.
Pick
A) 11/6 B) 11/7 C) 11/8 D) 6/11 E) 7/11

Solution: let quantity of water should added be x then   11/6/Q   5/(4+x)= 6/7   => 35=24+6x   => x=11/6   11/6NSWER:11/6
Answer: A
if 5 tomatoes are worth 8 oranges,5 oranges are worth 4 apples, 7 apples are worth 3 pineapples and 7 pineapples cost rs.203,then he approx price of each tomato is Choices
A) 16 B) 5 C) 19 D) 20 E) none of these

Solution: 7 pineapples cost rs.203 means one pineapple cost is 29   7 apples are worth 3 pineapples means 7 apple cost 29*3. 1 Apple cost (29*3)/7   5 oranges are worth 4 apples. 1 orange cost is (29*3*4)/(7*5)   5 tomatoes are worth 8 oranges. 1 tomato cost is (29*3*4*8)/(7*5*5) = 2784/175 = 15.9   16NSWER:16
Answer: A
A school’s annual budget for the purchase of student computers increased by 60% this year over last year. If the price of student computers increased by 20% this year, then the number of computers it can purchase this year is what percent greater than the number of computers it purchased last year?	Pick one.
A) 33.33%	B) 40%	C) 42%	D) 48%	E) 60%

Solution: If last year, the budget was B and the price of one computer was P, then B/P was the number of purchased computers.   This year, 1.6B/(1.2P) = 4/3(B/P) = 1.33(B/P) computers can be purchased, which is 33.33% greater than the number of computers purchased last year.   33.33%nswer 33.33%.
Answer: A
An unbiased cubic die is thrown.What is the probabiltiy of getting a multiple of 3 or 4? Choose the most appropriate option
A) 1/9	B) 1/12	C) 1/2	D) 3/4	E) 3/8

Solution: Explanation :   Total numbers in a die=6P(mutliple of 3) = 2/6 = 1/3P(multiple of 4) = 1/6P(multiple of 3 or 4) = 1/3 + 1/6 = 1/2   Answer : 1/2
Answer: C
In a class there are 55 pupil, out of them 10 are in debate only and 18 in singing only. Then how many in both?
Choose one
A) 132  B) 26  C) 17  D) 11  E) 12

Solution: Explanation:Total pupil = 55   Debate + Singing = 10 + 18= 
10 + 18 = 28
28   The intersection for two= 55 â€“ 10 â€“ 28 = 17 play both games.   Answer: 17
Answer: C
Anna left for city A from city B at 5.20 a.m. She traveled at the speed of 80 km/hr for 2 hrs 15 min. After that the speed was reduced to 60 km/hr. If the distance between two cities is 350 kms, at what time did Anna reach city A?
Choose one
A) 9.20 a.m B) 9.25 a.m C) 9.35 a.m D) 10.05 a.m E) None of these

Solution: Explanation:   Distance covered in 2 hrs 15 min i.e., 2 1/4 hrs = 80 * 9/4= 
80 * 9/4 = 180
180 hrs.   Time taken to cover remaining distance= (350 - 180)/60 = 17/6 hrs   = 2 5/6 = 2 hrs 50 min   Total time taken = (2 hrs 15 min + 2 hrs 50 min) = 5 hrs 5 min.   So, Anna reached city A at 10.25 a.m.   ANSWNone of theseR IS None of these
Answer: E
If point A coordinates are (-6, -3) point B coordinates are (8 ,4 ) if C is along the line A-B so that AC = 1/2 CB. What are the coordinates of point C. Pick one:
A) (-2, - 2/3)	B) (2, -2/3)	C) (2/3, -2)	D) (0, 2)	E) (2, 2/3)

Solution: Look at the diagram below:   Line segment.pngSince, AC= 1/2 CB, then AC = 1/3 AB. This implies that point C is closer to A than to B, which on the other hand implies that the x-coordinate of C must be less than (-6+8)/2=0.5. Only D and A fits, but as (0 , 2) is clearly not on line segment AB, then the answer must be B.   Answer: (2, -2/3).
Answer: B
Of the 420 members at a health club, 260 use the weight room and 300 use the pool. If at least 60 of the members do not use either, then the number of members using both the weight room and the pool must be between:	Choose the correct choice:
A) 200 to 260  B) 160 to 260  C) 220 to 260  D) 220 to 300  E) 40 to 100

Solution: W=260   P=300   200 to 260LL=420   N(NEITHER)=200 to 260T LE200 to 260ST 60   BOTH=?   W+P-BOTH+N=200 to 260LL   260+300-BOTH+60=420   BOTH=200   now pay attention to the fact, that both at most can be 260, since W=260   so, the answer is 200 to 260
Answer: A
A seller of used cars has 10 cars to sell and each of his clients selected 2 cars that he liked most. If each car was selected exactly thrice, how many clients visited the garage?
Choose one: A) 8 B) 10 C) 15 D) 14 E) 16

Solution: IfNo caris selected more than once then the number of clients = 10/2= 
10/2 = 5
5   But since every car is being selected three times so No. of 15lients must be thrice as well=5*3= 
5*3 = 15
15   Answer: option 15
Answer: C
A man sells a car to his friend at 13% loss. If the friend sells it for Rs.54000 and gains 20%, the original C.P.of the car was :	Choose one.
A) Rs.21724.14 B) Rs.31724.14 C) Rs.51724.14 D) Rs.61724.14 E) None of these

Solution: Explanation:   S.P = Rs.54,000. Gain earned = 20%   C.P = Rs.[100/120Ã—54000]   =Rs. 45000   This is the price the first person sold to the second at at loss of 13%.   Now S.P = Rs.45000 and loss = 13%   C.P. Rs.[100/87Ã—45000]= Rs.51724.14.   Rs.51724.14orrect Option : Rs.51724.14
Answer: C
Three people each took 6 tests. If the ranges of their scores in the 6 practice tests were 17, 28 and 35, 42 what is the minimum possible range in scores of the three test-takers?	Choices:
A) a 17  B) b) 28  C) c) 35  D) d) 45  E) e) 80

Solution: It is finding the minimum range between all their scores, if all test taker scores are between 0 and maximum range we will have:   A- 0 and 17   B- 0 and 28   C- 0 and 35   D-0 and 42   therefore the minimum range is 42, it cant be any lower however you play with the numbers.   d) 45
Answer: D
A room 5.44m long and 3.74m broad is to be paved with square tiles. The least number of square tiles required to cover the floor is:
Choose the correct choice from the following choices:	A) 176	B) 192	C) 184	D) 162	E) 172

Solution: 176rea of the room= 544*374 sq.cm   Size of largest square tile= HCF of 544 cm & 374cm   176rea of 1 tile= 34*34 sq.cm   Therefore, number of tiles= (544*374/34*34)= 176   176NSWER:176
Answer: A
A textile manufacturing firm employees 125 looms. It makes fabrics for a branded company. The aggregate sales value of the output of the 125 looms is Rs 5,00,000 and the monthly manufacturing expenses is Rs 1,50,000. Assume that each loom contributes equally to the sales and manufacturing expenses are evenly spread over the number of looms. Monthly establishment charges are Rs 75000. If one loom breaks down and remains idle for one month, the decrease in profit is:  Choose the correct choice from the following answers:	A) 13000	B) 7000	C) 10000	D) 2800	E) None of these

Solution: Explanation :   Profit = 5,00,000âˆ’(1,50,000+75,000) =Rs. 2,75,000.   Since, such loom contributes equally to sales and manufacturing expenses.   But the monthly charges are fixed at Rs 75,000.   If one loan breaks down sales and expenses will decrease.   New profit :-   =>500000Ã—(124/125)âˆ’150000Ã—(124/125)âˆ’75000.   =>Rs 2,72,200.   Decrease in profit   =>2,75,000âˆ’2,72,200   =>Rs. 2,800.   Answer : 2800
Answer: D
P, Q and R started a business by investing Rs.120000, Rs.135000 and Rs.150000 respectively. Find the share of each, out of the annual profit of Rs.56700.
Choose the correct answer:
A) 17850, 18900, 21000 B) 16800, 18900, 21000 C) 17850, 18900, 22000 D) 18900, 17850, 21000 E) 21000, 18900, 17850

Solution: P : Q : R = 120000:135000:150000   =120:135:150=24:27:30=8:9:10   Share of P   =56700×8/27=2100×8=16800   Share of Q   =56700×9/27=2100×9=18900   Share of R   =56700×10/27=2100×10=21000   Answer is 16800, 18900, 21000.
Answer: B
In a class of 40 students, 5 students did not borrow any books from the library, 15 students each borrowed 1 book, 10 students each borrowed 2 books, and the rest of the students each borrowed at least 3 books. If the average (arithmetic mean) number of books borrowed per student was 2, what is the maximum number of books that any single student could have borrowed ?  Select the correct option:
A) 3
B) 5
C) 8
D) 13
E) 18

Solution: The average number of books per student was 2means that total of   2*40= 
  2*40 = 80
80 books were borrowed;   5+15+10= 
5+15+10 = 30
30 students borrowed total of  5*0+15*1+10*2= 
 5*0+15*1+10*2 = 35
35 books;   So  80-35= 
 80-35 = 45
45 books are left to distribute among 40-30= 
40-30 = 10
10 students, these 10 arethe rest who borrowed at least 3 books;   Tomaximizethe number of books one student from above 10 could have borrowed we shouldminimizethe number of books other 9 students from 10 could have borrowed. Minimum these 9 students could have borrowed is 3 books per student, so total number of books they could have borrowed is 9*3= 
9*3 = 27
27 books. So the 10th student could have borrowed is  45-27= 
 45-27 = 18
18 books.   Answer: 18.
Answer: E
What least number must be subtracted from 427398 so that remaining no.is divisible by 14	Choose the most appropriate option.
A) 3  B) 5  C) 6  D) 7  E) 8

Solution: Explanation:   On dividing 427398 by 14 we get the remainder 6, so 6 should be subtracted   Answer: Option 6
Answer: C
If the perimeter of a rectangular stadium is 800 m, its length when its breadth is 300 m is?	Choose the most appropriate option
A) 500
B) 400
C) 300
D) 200
E) 100

Solution: 2(l + 300) = 800 => l = 100 m Answer: 100
Answer: E
The average of 10 numbers is calculated as 15. It is discovered later on that while calculating the average, one number namely 36 was wrongly read as 26. The correct average is?
Choose the most appropriate option
A) 28 B) 27 C) 16 D) 29 E) 24

Solution: 10 * 15 + 36 – 26   = 160/10= 
160/10 = 16
16   Answer:16
Answer: C