MU-NLPC/Calc-aqua_rat huggingface dataset:
Every day, the value of a stock rises by exactly two dollars in the morning, and
then falls by exactly one dollar in the afternoon. If the stock's value at the start of the rst
day is $100, on what day will the stock's value rst reach $200?  Choose the correct choice from the following answers.
A) 50	B) 99	C) 100	D) 101	E) 200

Solution: Note that each day the stock is worth $1 more than on the previous day, and that   on the rst day it rises to $102 and then falls to $101. Therefore, on the nth day, the stock's   value rises to n + 101 dollars in the morning and falls to n + 100 dollars in the afternoon.   The solution is therefore the smallest n for which n+101 = 200, or n = 99. In particular,   the stock will be $200 in the middle of day 99, although not at the end of this day.   correct answer 99
Answer: B
A person purchased a TV set for Rs. 16000 and a DVD player for Rs. 6250. He sold both the items together for Rs. 31150. What percentage of profit did he make?	Choose the correct choice from the following answers
A) 323  B) 88  C) 40  D) 99  E) 81

Solution: The total CP = Rs. 16000 + Rs. 6250 = Rs. 22250 and SP = Rs. 31150   Profit(%) = (31150 - 22250)/22250 * 100= 
(31150 - 22250)/22250 * 100 = 40
40%   Answer: 40
Answer: C
The ratio of two numbers is 5:9. If each number is decreased by 5, the ratio becomes 5:11. Find the numbers.	Choose the correct choice from the following: A) 30, 19 B) 21, 37 C) 15, 34 D) 15, 27 E) None of these

Solution: Explanation:   Let the two numbers be 5x and 9x.   (5x-5)/(9x-5) = 5:11   (5x-5)*11 = (9x-5)*5   55x – 55 = 45x – 25   10x = 30   x = 3   Therefore, the numbers are 15 and 27.   ANSWER: 15, 27
Answer: D
A number is increased by 20 % and then decreased by 20 %. Find the net increase or decrease per cent. Choose the correct choice from the following.
A) 9%  B) 8%  C) 7%  D) 3%  E) 4%

Solution: Let the number be 100.   Increase in the number = 20 % = 20 % of 100   = (20/100 Ã— 100)   = 20   Therefore, increased number = 100 + 20= 
100 + 20 = 120
120   This number is decreased by 20 %   Therefore, decrease in number= 20 % of 120   = (20/100 Ã— 120)   = 2400/100= 
2400/100 = 24
24   Therefore, new number= 120 - 24= 
120 - 24 = 96
96   Thus, net decreases= 100 - 96= 
100 - 96 = 4
4   Hence, net percentage decrease= (4/100 Ã— 100) %   = (400/100)= 
(400/100) = 4
4 %   Answer:4%
Answer: E
In an election only two candidates contested. A candidate secured 70% of the valid votes and won by a majority of 184 votes. Find the total number of valid votes?	Pick:	A) 430	B) 438	C) 436	D) 434	E) 460

Solution: Let the total number of valid votes be x.   70% of x = 70/100 * x = 7x/10   Number of votes secured by the other candidate = x - 7x/100 = 3x/10   Given, 7x/10 - 3x/10 = 184 => 4x/10 = 184   => 4x = 1840 => x = 460.   Answer:460
Answer: E
A rectangular field is to be fenced on three sides leaving a side of 20 feet uncovered. If the area of the field is 210 sq. feet, how many feet of fencing will be required?  Choose the correct option: A) 34 B) 41 C) 68 D) 88 E) None

Solution: EXPLANATION   We have: l = 20 ft and lb = 210 sq. ft.   So, b = 10.5 ft.   Length of fencing = (l + 2b) = (20 + 21)= 
(20 + 21) = 41
41 ft.   Answer 41
Answer: B
Two trains A and B are 200 m and 150 m long and are moving at one another at 54 Km/hr and 36 Km/hr respectively. Arun is sitting on coach B1 of train A. Calculate the time taken by Arun to completely cross Train B.	Choose the correct choice
A) 10 s  B) 6 s  C) 14 s  D) 8 s  E) 12 s

Solution: DETAILED SOLUTION   Speed of A = 54∗1000/60∗60 = 15 m/s   Speed of B = 36∗1000/60∗60 = 10 m/s   Relative speed = S1 + S2 = 15 + 10 m/s = 25 m/s   The length that needs to be crossed = length of train B = 150 m. Therefore time taken = 150/25= 
150/25 = 6
6s.   What is the time taken for trains to completely cross each other? The length that needs to be crossed= 200 + 150= 
200 + 150 = 350
350 m. Time taken= 350/25= 
350/25 = 14
14 s.   14 sORRE14 sT ANSWER 14 s.
Answer: C
An amount of money is to be divided between P, Q and R in the ratio of 3:7:12. If the difference between the shares of P and Q is Rs.2400, what will be the difference between Q and R's share?
Choose the most appropriate option
A) 2788 B) 3000 C) 7282 D) 2782 E) 2729

Solution: 4 --- 2000   5 --- ? => 3000   Answer:3000
Answer: B
A company D has 15 percent of the employees are secretaries and 10 percent are salespeople. If there are 120 other employees of Company D, how many employees does Company D have?
Choose the correct choice
A) 200  B) 160  C) 180  D) 152  E) 250

Solution: Let the total number of employees in the company be x   % of secretaries = 15%   % of salespeople = 10%   % of of employees other than secretaries and salespeople = 100 - 25= 
100 - 25 = 75
75%   160ut this number is given as 120   so 75% of x= 120   x = 160   Therefore there a total of 160 employees in the company D   Correct answer - 160
Answer: B
Oak trees line both sides of a street for a length of 6/8 of a kilometer. If there is 16 meters of space between the trees, and each tree is 1 meter wide, how many trees are there along the street?	Select
A) a)	22 B) b)	23 C) c)	24 D) d)	45 E) e)	46

Solution: There is a gap of 16 m between every 2 trees , each tree is 1 m wide.   6/8of 1 km = 750 m   Lets assume that x trees are planted So equation is   x*1 +(x-1)*16 = 750   Solve for x and we get x = 45, answer is d)	45
Answer: D
Mary passed a certain gas station on a highway while traveling west at a constant speed of 50 miles per hour. Then, 15 minutes later, Paul passed the same gas station while traveling west at a constant speed of 60 miles per hour. If both drivers maintained their speeds and both remained on the highway for at least 3 hours, how long after he passed the gas station did Paul catch up with Mary?	Pick one
A) 1.5  B) 1.3  C) 1.25  D) 1.6  E) 2

Solution: d = rt   M: r = 50mph, t = t + 1/4hr   d = 50 (t + 1/4)   P: r = 60, t = t   d = 60t   since they went the same distance:   50t + 50/4 = 60t   10t = 50/4   t = 1.25 or 1 hr, 15min   1.25
Answer: C
If the compound interest on a sum of Rs.5000 at the rate of 10% per annum is Rs.1050, then time period is (Interest compounded yearly)	Select.
A) 1 YRS	B) 21/2 YRS	C) 3 YRS	D) 2 YRS	E) 4 YRS

Solution: amount=5000+1050= 
5000+1050 = 6_050
6050   C.I=P(1+R/100)^n   6050=5000(1+10/100)^n   6050/5000=(11/10)^n   121/100=(11/10)^n   (11/10)^2=(11/10)^n   n=2 yrs .   ANSWER:2 YRS
Answer: D
Fom the integer n, if n*n*n is odd, then what is true from below options? Choose one:
A) n is odd	B) n is odd and n*n is even	C) n is even	D) n*n is odd	E) n*n is even

Solution: n is odd and n*n is even   Option n is odd and n*n is even
Answer: B
The value of (4.7 × 13.26 + 4.7 × 9.43 + 4.7 × 77.31) is :
Pick
A) 0.47	B) 47	C) 470	D) 4700	E) None of these

Solution: Solution   Given expression = 4.7 × ( 13.26 + 9.43 + 77.31) = 4.7 × 100 = 470 . Answer 470
Answer: C
What will come in place of the x in the following Number series? 12, 38, 116, 350, 1052, x  Choose the correct option:	A) 2400	B) 2600	C) 2435	D) 3000	E) 3158

Solution: 12   12 × 3 + 2 = 38   38 × 3 + 2 = 116   116 × 3 + 2 = 350   350 × 3 + 2 = 1052   1052 × 3 + 2 = 3158   3158
Answer: E
A box contains ten bulbs out of which 5 are defective. If four bulbs are chosen at random, find the probability that exactly two bulbs are good?
Choose the most appropriate option
A) 7/21 B) 10/21 C) 9/21 D) 8/21 E) 5/21

Solution: Required probability = (5C2 . 5C2)/10C4 = (10 * 10)/210   = 10/21   Answer:10/21
Answer: B
Evaluate: 1234562- 12*3*2 = ?	Select:  A) 32435453  B) 1234554  C) 76768786  D) 97979797  E) 75868656

Solution: According to order of operations, 12?3?2 (division and multiplication) is done first from left to right   12**2 = 4* 2= 
4* 2 = 8
8   Hence   1234562 - 12*3*2= 1234562 - 8= 
1234562 - 8 = 1_234_554
1234554   correct answer 1234554
Answer: B
Reena took a loan of $. 1200 with simple interest for as many years as the rate of interest. If she paid $ 972 as interest at the end of the loan period, what was the rate of interest?	Choose the correct choice from the following answers
A) 3.6	B) 6	C) 18	D) Cannot be determined	E) None of these

Solution: Let rate = R% and time = R years.   Then,1200 x R x R/100= 972   12R2 = 972   R2 = 81   R = 9.   Answer:None of these
Answer: E
What is the area of square field whose side of length 18 m?	Choose the correct choice:
A) 225
B) 777
C) 266
D) 288
E) 324

Solution: 18 * 18= 
18 * 18 = 324
324 sq m   Answer: 324
Answer: E
A train running at the speed of 60 km/hr crosses a pole in 9 sec. What is the length of the train?	Choose the correct choice from the following choices
A) 298 m	B) 150 m	C) 208 m	D) 988 m	E) 299 m

Solution: Speed = 60 * 5/18 = 50/3 m/sec   Length of the train = speed * time = 50/3 * 9= 
50/3 * 9 = 150
150 m   Answer:150 m
Answer: B
The perimeter of one face of a cube is 40 cm. Its volume will be:
Choose the most appropriate option
A) 125cm3 B) 400cm3 C) 250cm3 D) 1000cm3 E) None of these

Solution: Explanation:   Edge of cude = 40/4= 
40/4 = 10
10 cm   Volume= a*a*a = 10*10*10= 
10*10*10 = 1_000
1000 cm cube   Option 1000cm3
Answer: D
A rectangular grass field is 75 m * 55 m, it has a path of 2.5 m wide all round it on the outside. Find the area of the path and the cost of constructing it at Rs.7 per sq m?
Choose the correct choice:
A) 4350
B) 4725
C) 4328
D) 4329
E) 4829

Solution: Area = (l + b +2d) 2d   = (75 + 55 +2.5 * 2) 2*2.5 => 675   675 * 7 = Rs.4725   Answer:4725
Answer: B
The ratio of male to female in a class is 2:3. the career preference of the students in the class are to be represented in a circle graph. If the area of the graph allocated to each career preference is to be proportional to the number of students who have that career preference, how many degrees of the circle should be used to represent a career that is preferred by one fourth of the males and 3/4th of the females in the class?
Choose the correct choice from the following answers:
A) a)160 degree B) b) 198 degree C) c)191 degree D) d)192 degree E) e)204 degree

Solution: let the common ratio be x.. so M=2x and F=3x and Total=5x   1/4 of M= 2x/4 and 3/4 of F= 9/4x..   Total preferring that carrer = x/2+9x/4=11x/4   Now 5x= 360, so x=360/5=72..   so 72*11/4= 
72*11/4 = 198
198   ans 198   b) 198 degree
Answer: B
A strain of bacteria reproduces @ 25% every 12 min. In how much time will it triple itself ??
Select the correct option.
A) 96 min
B) 72 min
C) 60 min
D) 48 min
E) 40 min

Solution: The original question is:   A strain of bacteria reproduces at the rate of 25% every 12 min. In how much time will it triple itself ?   1.25^x = 3 --> x = ~5 --> five 12 minute periods = 60 minutes.   Answer: 60 min.
Answer: C
Two trains of equal are running on parallel lines in the same direction at 46 km/hr and 36 km/hr. The faster train passes the slower train in 36 sec. The length of each train is?	Answers
A) 50  B) 86  C) 85  D) 25  E) 28

Solution: Let the length of each train be x m.   Then, distance covered = 2x m.   Relative speed = 46 - 36= 
46 - 36 = 10
10 km/hr.= 10 * 5/18 = 25/9 m/sec.   2x/36 = 25/9 => x =50.   50nswer: 50
Answer: A
A certain culture of bacteria quadruples every hour. If a container with these bacteria was half full at 7:00 a.m., at what time was it one-eighth full?
Options
A) 9:00 a.m.
B) 7:00 a.m.
C) 6:00 a.m.
D) 4:00 a.m.
E) 2:00 a.m.

Solution: To go from one-eighth (1/8) full to half (1/2) full culture of bacteria should quadruple: 1/8*4=1/2, as it quadruples every hour then container was one-eighth full at 7:00 a.m -1 hour = 6:00 a.m.   Answer: 6:00 a.m..
Answer: C
A basketball team composed of 12 players scored 100 points in a particular contest. If none of the individual players scored fewer than 7 points, what is the greatest number of points W that an individual player might have scored?
Answers:
A) 7 B) 13 C) 16 D) 21 E) 23

Solution: General rule for such kind of problems:   to maximize one quantity, minimize the others;   to minimize one quantity, maximize the others.   Thus to maximize the number of points of one particular player minimize the number of points of all other 11 players.   Minimum number of points for a player is 7, so the minimum number of points of 11 players is 7*11= 
7*11 = 77
77.   Therefore, the maximum number of points W for 12th player is  100-77= 
 100-77 = 23
23.   Answer: 23.
Answer: E
What least value should be replaced by * in 223431* so the number become divisible by 5	Answers:
A) 0
B) 4
C) 5
D) 6
E) 7

Solution: Explanation:   Trick: Number is divisible by 5, if last digit is 0 or 5   so that least number is 0.   0nswer: Option 0
Answer: A
If x is the sum of a consecutive positive integers. y is the sum of b consecutive positive integers. For which of the following values of a and b is it impossible that x = y?	Choices.
A) a = 2; b = 6
B) a = 3; b = 6
C) a = 7; b = 9
D) a = 10; b = 4
E) a = 10; b = 7

Solution: I approached this in a different way, although may be longer but it's certainly more intuitive   It is impossible that x = y if one of them is necessarily even while the other is necessarily odd   for two consecutive integers the sum is necessarily odd   for six consecutive integers the sum is necessarily odd (sum of 3two consecutive integerswhich are all odd)   Thus A is incorrect.   The sum of 3 consecutive integers can be even or odd (an odd integer from the first 2 + an additional integer which can be even or odd). Thus B is incorrect. You can do a similar approach for C and E (it follows that the sum of a specified odd number of consecutive integers can be odd or even).   Leaving us with D to be the only not-wrong answer. To confirm, you can easily deduce that the sum of 4 consecutive integers (sum of 2 odd integers) is necessarily even while the sum of 10 consecutive integers (sum of 5 odd integers) is necessarily odd. Thus a = 10; b = 4 is the right answer.
Answer: D
How many four letter words are formed using the letters of the word PRESS?  Answers:
A) A)30
B) B)60
C) C)90
D) D)120
E) E)150

Solution: The number of letters in the given word is five.   The number of three letter words that can be formed using these four letters is 5P4   = 5 *4 * 3*2= 
5 *4 * 3*2 = 120
120.   Answer:120
Answer: D
If a<0, which of the following represents a positive number?  Choose the correct choice from the following: A) a/ |a| B) -a|a| C) a|a| D) |a|/a E) |a|a

Solution: Answer : -a|a|
Answer: B
A sum of money becomes double itself in 8 years at simple interest. How many times will it become 10 years at the same rate?	Answers
A) 10 years
B) 11 years
C) 77 years
D) 88 years
E) 55 years

Solution: P ---- 2P ---- 8 years   2 1/4 P ---- 10 years   10 yearsnswer:10 years
Answer: A
ABCD is a square. F and E are the midpoints of sides AD and CD, respectively. The area of triangle FED is 2 square inches. What is the area of square ABCD (in square inches)? Choose the correct choice from the following choices:
A) 4 B) 8 C) 16 D) 32 E) 64

Solution: Area of FED = 2 sq inches = 1/2*DE*FD = 1/2*DE^2   Because the sides of a square are equal, hence half of the sides will also be equal.   DE^2 = 4   DE = FD = 2   Hence the side of the square = 4   Area if the square = 4*4= 
4*4 = 16
16   16orrect Option: 16
Answer: C
What is the difference between the largest number and the least number written with the digits 9, 2, 1, 5?  Choose the correct choice from the following answers
A) 6084  B) 3788  C) 2077  D) 8262  E) 1812

Solution: Explanation:   1259   9521   ------------   8262   Answer:8262
Answer: D
A tradesman by means of his false balance defrauds to the extent of 25%? in buying goods as well as by selling the goods. What percent does he gain on his outlay?
Choices.
A) 17%
B) 77%
C) 44%
D) 56.25%
E) 47%

Solution: g% = 25 + 25 + (25*25)/100= 
25 + 25 + (25*25)/100 = 225/4 = around 56.25
56.25%   Answer: 56.25%
Answer: D
33 1/3% of 36?	Options:  A) 16  B) 21  C) 18  D) 12  E) 18

Solution: Explanation:   33 1/3 % = 1/3   1/3 * 36= 
1/3 * 36 = 12
12   Answer: Option 12
Answer: D
The population of locusts in a certain swarm doubles every two hours. If 4 hours ago there were 1,000 locusts in the swarm, in approximately how many hours will the swarm population exceed 256,000 locusts? Choose the most appropriate option:
A) 12 B) 14 C) 16 D) 15 E) 11

Solution: - 4 hours: 1,000   -2 hours: 2,000   Now: 4,000   + 2 hours: 8,000   + 4 hours: 16,000   + 6 hours: 32,000   + 8 hours: 64,000   + 10 hours: 128,000   + 12 hours: 256,000   12nswer : 12
Answer: A
If the price of a TV is first decreased by 20% and then increased by 30%, then the net change in the price will be :  Choices
A) 4% increase
B) 10% increase
C) 10% decrease
D) 6% increase
E) None of these

Solution: Explanation :   Solution: let the original price be Rs. 100.   New final price = 130% of(80% of 100) =Rs. 130/100 * 80/100 * 100 = Rs. 104.   .'. Increase = 4%   4% increasenswer : 4% increase
Answer: A
If two numbers are in the ratio 2:3. If 10 is added to both of the numbers then the ratio becomes 3:4 then find the smallest number?  Choose the correct choice from the following choices
A) 10	B) 20	C) 30	D) 40	E) 50

Solution: Explanation:   2:3   2x + 10 : 3x + 10 = 3 : 4   4[2x + 10] = 3[3x + 10]   8x + 40 = 9x + 30   9x - 8x = 40 - 30= 
40 - 30 = 10
10   Then smallest number is= 2   2x = 20   Short cut method:   a:b = 2:3   c:d = 3:4   1.Cross multiplication with both ratios   a * d ~ b * c = 2 * 4 ~ 3 * 3 = 8 ~ 9 = 1   2. If 10 is added both the number means   10 * 3= 
  10 * 3 = 30
30 and   10 * 4= 
  10 * 4 = 40
40,   Then 30 ~ 40= 10   ===> 1 -----> 10   ===> 2 -----> 20   Answer: Option 20
Answer: B
286, 462, 362, 527, 671, 253  Pick:
A) 286	B) 462	C) 352	D) 537	E) 671

Solution: In each number except 537, the middle digit is the sum of other two.   Answer: Option 537
Answer: D
In a family 15 people eat only vegetarian, 8 people eat only non veg., 11 people eat both veg and non veg.. How many people eat veg in the family?
Choose the correct choice from the following answers
A) 20
B) 11
C) 23
D) 26
E) 21

Solution: Total people eat veg = only veg + both veg and non veg   Total= 15+11= 
15+11 = 26
26   Answer= 26
Answer: D
The H.C.F. of two numbers is 23 and the other two factors of their L.C.M. are 13 and 14. The larger of the two numbers is:	Choose the correct choice from the following.
A) 276  B) 299  C) 322  D) 345  E) 375

Solution: Explanation:   Clearly, the numbers are (23 x 13) and (23 x 14).   Larger number = (23 x 14) = 322.   ANSWER IS 322
Answer: C
If a 10 percent deposit that has been paid toward the purchase of a certain product is $130, how much more remains to be paid?  Pick
A) $880  B) $990  C) $1,000  D) $1,170  E) $1,210

Solution: 10/100P = 130 >> p= 130*100/10= 
130*100/10 = 1_300
1300   1300 - 130= 
1300 - 130 = 1_170
1170   ANSWER:$1,170
Answer: D
College T has 1000 students. Of the 180 students majoring in one or more of the sciences,120 are majoring in Chemistry and 120 are majoring in Biology. If at least 20 of the students are not majoring in either Chemistry or Biology, then the number of students majoring in both Chemistry and Biology could be any number from?
Choose the correct choice from the following answers.
A) 50 to 120
B) 60 to 130
C) 50 to 100
D) 70 to 110
E) 60 to 120

Solution: Total = Chemistry + Biology - Both + Neither   180= 120 + 120 - Both + N   We know that N (Neither) must be at least 20, so set N=20 and solve:   180 = 120 + 120 - Both + 20   200 = 260 - Both   Both = 60   Even if you're not sure whether 60 is the highest or lowest Both could possibly be, it doesn't matter, because you know it's a boundary point of the range,   Both can not be greater than 120, because even if every chemistry major was also a biology major, there are only 120 chemistry majors total. 60 to 120 the solution.
Answer: E
A sells a bicycle to B and makes a profit of 20%. B sells the same bicycle to C at a profit of 25%. If the final S.P. of the bicycle was Rs. 225, find out the cost price of the bicycle for A. Select the correct option:
A) 237 B) 126 C) 971 D) 611 E) 150

Solution: 150xplanation:   ANSW150R: 150
Answer: E
What is the smallest positive integer which when increased by 1 is divisible by 22, 36, 26 and 21?	Choose the correct choice from the following answers.
A) 7271	B) 36035	C) 122149	D) 22362621	E) 4109

Solution: 22 = 2*11   36 = 2 * 2 * 3 * 3   26 = 2 * 13   21 = 3 * 7   So the answer is   (2 * 2 * 3 * 3 * 7 * 11 * 13) - 1= 
  (2 * 2 * 3 * 3 * 7 * 11 * 13) - 1 = 36_035
36035, which is option 36035.
Answer: B
A wall photo 2 inches wide is placed around a rectangular paper with dimensions 8 inches by 12 inches. What is the area of the wall photo, in square inches?
Pick one.
A) 96	B) 86	C) 108	D) 144	E) 118

Solution: This question is an example of a 'punch out' question - we have to find the area of EVERYTHING, then 'punch out' the part that we don't want.   We're told that a wall photo 2 inches wide is placed around a rectangular paper with dimensions 8 inches by 12 inches. We're asked for the area of the wall photo, in square inches.   Area of a rectangle = (length)(width)   So the area of the wall photo is... (8)(12) = 96   The wall photo 'adds' 2 inches to the top, bottom, left and right 'sides' of the picture, so the area of EVERYTHING is...   (8+2+2)(12+2+2) = (12)(16) = 196   When we 'punch out' the area of the paper, we'll be left with the area of the wall photo:     192 - 96= 
  192 - 96 = 96
96   Final 96nswer:   96
Answer: A
What was the day of the week on 17th June, 1998?
Choose the correct option
A) Sunday	B) Tuesday	C) Friday	D) Wednesday	E) Suturday

Solution: Explanation:   17th June, 1998 = (1997 years + Period from 1.1.1998 to 17.6.1998)   Odd days in 1600 years = 0   Odd days in 300 years = (5 x 3) 1   97 years has 24 leap years + 73 ordinary years.   Number of odd days in 97 years ( 24 x 2 + 73) = 121 = 2 odd days.   Jan. Feb. March April May June   (31 + 28 + 31 + 30 + 31 + 17)= 
(31 + 28 + 31 + 30 + 31 + 17) = 168
168 days   168 days= 24 weeks = 0 odd day.   Total number of odd days = (0 + 1 + 2 + 0)= 
(0 + 1 + 2 + 0) = 3
3.   Given day is Wednesday   Answer: Wednesday) Wednesday
Answer: D
In a class of 25 students, 3 students did not borrow any books from the library, 11 students each borrowed 1 book, 6 students each borrowed 2 books, and the rest borrowed at least 3 books. If the average number of books per student was 2, what is the maximum number of books any single student could have borrowed?  Choose the correct choice from the following answers:  A) 12  B) 13  C) 14  D) 15  E) 16

Solution: The total number of books the students borrowed is 25*2= 
25*2 = 50
50.   The students who borrowed zero, one, or two books borrowed   11*1+6*2= 
  11*1+6*2 = 23
23 books.   The 5 students who borrowed at least three books borrowed   50-23= 
  50-23 = 27
27 books.   If 4 of these students borrowed exactly 3 books, then the maximum that one student could have borrowed is  27-12= 
 27-12 = 15
15 books.   The answer is 15.
Answer: D
Two trains 180m and 360m long run at the speed of 60kmph and 30kmph in opposite directions in parallel tracks. The time which they take to cross each other is?	Options.
A) 21.6sec
B) 8.9sec
C) 10.8sec
D) 12.6sec
E) 15sec

Solution: Relative speed = 60+30= 
60+30 = 90
90kmph * 5/18= 25 m/s   Distance covered in crossing each other = 180+360= 
180+360 = 540
540m   Required time= 540*1/25= 
540*1/25 = 108/5 = around 21.6
21.6 sec   21.6secnswer is 21.6sec
Answer: A
The difference between the compound interest compounded annually and simple interest for 2 years at 20% per annum is Rs.144. Find the principal?  Choose the most appropriate option:
A) 2888	B) 2669	C) 3600	D) 1279	E) 1271

Solution: P = 144(100/5)2 => P = 3600.Answer:3600
Answer: C
Calculate the largest 4 digit number which is exactly divisible by 98?
Choose the correct choice
A) 9800  B) 9898  C) 9702  D) 9604  E) 9996

Solution: Largest 4 digit number is 9999   After doing 9999 ÷ 98 we get remainder 3   Hence largest 4 digit number exactly divisible by 98 = 9999 - 3= 
9999 - 3 = 9_996
9996   9996
Answer: E