MU-NLPC/Calc-aqua_rat huggingface dataset:
Two brothers Ram and Ravi appeared for an exam. The probability of selection of Ram is 6/7 and that of Ravi is 1/5. Find the probability that both of them are selected.  Choose the correct choice from the following answers.
A) 2/35  B) 2/3  C) 6/35  D) 5/7  E) 7/5

Solution: Let A be the event that Ram is selected and B is the event that Ravi is selected.   P(A) = 6/7   P(B) = 1/5   Let C be the event that both are selected.   P(6/35) = P(A) x P(B) as A and B are independent events:   = 6/7 x 1/5 = 6/35   ANSWER:6/35
Answer: C
If a/b= 1.25, then b is what percent of a?	Choose the correct choice:
A) 0.008
B) 0.08
C) 0.8
D) 8
E) 80

Solution: You are given , a/b=1.25 ---> b< a but only 'just'. This eliminates A-C as you are asked % and as such these values will be further reduced by 1/100, making them even smaller.   Also, as b iscloseto 'c', eliminate D and mark E as the correct answer.   Alternatively, 1.25 = 5/4 ---> a/b=5/4 --> b= 4/5 (b) = 0.8a ---> b= 80% of a. 80 is the correct answer.
Answer: E
Find the length of the longest pole that can be placed in a room 12 m long, 8 m broad and 9 m high.  Choose one:
A) 10 m
B) 12 m
C) 17 m
D) 19 m
E) None

Solution: Solution   Length of longest pole = Length of the diagonal of the room   =√(12)2 + 82 + 92   ‹=›√289   = 17 m.   Answer 17 m
Answer: C
If the diagonal of a rectangle is 17 cm long and its perimeter is 46 cm, find the area of the rectangle.
Options
A) 127 cm^2 B) 125 cm^2 C) 120 cm^2 D) 102 cm^2 E) None of them

Solution: Let length = x and breadth = y. Then,   2 (x + y) = 46 or x + y = 23 and x^2 + y^2 = (17)^2 = 289.   Now, (x + y)^2 = (23)^2 <=> (x^2 + y^2) + 2xy = 529 <=> 289 + 2xy = 529 =xy=120   Area = xy = 120 cm^2   Answer is 120 cm^2.
Answer: C
Two pipes A and B can fill a tank in 30 and 40 minutes respectively. If both the pipes are used together, then how long it will take to fill the tank ?
Select
A) 16 1/7
B) 17 1/7 mins.
C) 15 1/7
D) 14 1/7
E) 18 1/7

Solution: Explanation:   In this type of questions we first get the filling in 1 minute for both pipes then we will add them to get the result, as   Part filled by A in 1 min = 1/30   Part filled by B in 1 min = 1/40   Part filled by (A+B) in 1 min = 1/30 + 1/40   = 7/120   So both pipes can fill the tank in 17 1/7 mins.   Option 17 1/7 mins.
Answer: B
John makes $60 a week from his job. He earns a raise and now makes $80 a week. What is the % increase?  Choose the most appropriate option
A) 16%  B) 16.66%  C) 18%  D) 21%  E) 33.33%

Solution: Increase = (20/60)*100 = 33.33%.   33.33%
Answer: E
ABCD is a square where AB =âˆš4004. Let X be a point on AB and Y be a point on CD such that AX = CY . Compute the area of trapezoid AXYD.
Choose the correct choice from the following
A) 3008  B) 2002  C) 1008  D) 2016  E) 3000

Solution: Note that trapezoids AXY D and BXY C are congruent, so the area of AXY D is   always   4004/2= 
4004/2 = 2_002
2002 .   correct answer 2002
Answer: B
A horse is tethered to one corner of a rectangular grassy field 46 m by 20 m with a rope 17 m long. Over how much area of the field can it graze?  Choose the correct choice: A) 154 cm2 B) 308 m2 C) 227 m2 D) 407 m2 E) None of these

Solution: Area of the shaded portion   = 1⁄4 × π × (17)2 = 227 m2   Answer 227 m2
Answer: C
.It was calculated that 75 men could complete a piece of work in 20 days. When work was scheduled to commence, it was found necessary to send 25 men to another project. How much longer will it take to complete the work?  Choose the correct choice from the following options:
A) 20 days.
B) 23 days.
C) 30 days.
D) 92 days.
E) 97 days.

Solution: One day work = 1 / 20   One man’s one day work = 1 / ( 20 * 75)   Now:   No. Of workers = 50   One day work = 50 * 1 / ( 20 * 75)   The total no. of days required to complete the work = (75 * 20) / 50= 
(75 * 20) / 50 = 30
30   Answer:30 days.
Answer: C
The total price of a kilogram each of Shimla apples and Red Delicious apples is 250 rupees more than the total price of a kilogram each of Red Delicious apples and Fuji apples. Fuji apples is how much cheaper than Shimla apples? Choose one
A) 250	B) 125	C) 500	D) 100	E) 80

Solution: (Shimla + Red Delicious) - (Red Delicious + Fuji) = 250   Shimla - Fuji = 250   250nswer: 250
Answer: A
On a class test there are 5 questions. One question has been taken from each of four chapters. The first two chapters have 3 questions each, the last two chapters have 6 questions each. The fourth question can be picked from any of the four chapters. How many different question papers could have been prepared?
A.
B.
C.
D.
E.  Pick
A) 540
B) 1260
C) 2268
D) 4000
E) 4860

Solution: nIf 2 questions are picked from the first chapter: C23∗3∗6∗6C32∗3∗6∗6;   If 2 questions are picked from the second chapter: 3∗C23∗6∗63∗C32∗6∗6;   If 2 questions are picked from the third chapter: 3∗3∗C26∗63∗3∗C62∗6;   If 2 questions are picked from the third chapter: 3∗3∗6∗C263∗3∗6∗C62.   Total = 2,268.   ANS:2268
Answer: C
In a group of ducks and cows, the total number of legs are 32 more than twice the no. of heads. Find the total no.of buffaloes.
Choose the correct choice from the following.
A) 11  B) 12  C) 14  D) 16  E) 18

Solution: Let the number of buffaloes be x and the number of ducks be y   => 4x + 2y = 2 (x + y) + 32   => 2x = 32 => x = 16   16
Answer: D
If 16 percent of the students at a certain school went to a camping trip and took more than $100, and 75 percent of the students who went to the camping trip did not take more than $100, what percentage of the students at the school went to the camping trip?	Choose the correct choice from the following choices
A) 95
B) 90
C) 85
D) 80
E) 64

Solution: Let x be the number of students in the school. 0.16x students went to the trip and took more than 100$. They compose   (100-75)= 
  (100-75) = 25
25% of all students who went to the trip. Therefore the toal of 0.16x/0.25=0.64x students went to the camping which is 64%.   The answer is 64  0.16 /0.25= 
  0.16 /0.25 = 0.64
0.64x students went to the camping which is 64%.   The answer is 64
Answer: E
In a box of 11 pencils, a total of 2 are defective. If a customer buys 3 pencils selected at random from the box, what is the probability that neither pencils will be defective?	Options: A) 1/25 B) 28/55 C) 2/35 D) 2/55 E) 1/75

Solution: First, there are 9C3 ways you can select 3 good pencils from 4 good ones.   Second, there are 11C3 ways you select 3 pencils from 6 ones in the box.   Then, the probability that neither pen will be defective is: 9C3/11C3=84/165 = 28/55   Answer is 28/55
Answer: B
A, B, C subscribe Rs. 50,000 for a business, A Subscribes Rs. 4000 more than B and B Rs. 5000 more than C. Out of a total profit of Rs. 70,000, A receives :
Options
A) 14700 B) 24703 C) 29400 D) 33777 E) 34778

Solution: Explanation:   Let C = x. Then, B = x + 5000 and A = x + 5000 + 4000 = x + 9000.   So, x + x + 5000 + x + 9000 = 50000 <=> 3x = 36000 <=>   x = 12000.   A : B : C = 21000 : 17000 : 12000 = 21 : 17 : 12.   A's share = Rs. (70000 * 21/50 ) = Rs. 29,400.   Answer: 29400)
Answer: C
Among 600 students, 56% study sociology, 44% study mathematics and 40% study biology. If 30% of students study both mathematics and sociology, what is the largest possible number of students who study biology but do not study either mathematics or sociology?
Pick one
A) 30  B) 90  C) 120  D) 172  E) 180

Solution: I would just like to add a bit of explanation after the step where you calculate that the number of students studying both M and S = 180   Using your analysis:   We see that the total number of students who study either Maths or Sociology = 264 + 336 - 180= 
264 + 336 - 180 = 420
420   So, in the image we know that the number of students in the zone with the black boundary= 420   Let's assume the number of students who studyonlybiology to beb(this is the number that we have to maximize)   And, let's assume the number of students who study none of the three subjects, that is the number of students in the white space =w   Since the total number of students = 600, we can write:   420 +b+w= 600   Or,b+w= 600 - 420= 
600 - 420 = 180
180   That is,b= 180 -w   So, the maximum value ofbwill happen forw= 0   This is how we get, the maximum value ofb= 180   180
Answer: E
Rahul went to a shop and bought things worth Rs. 29, 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 correct choice from the following answers:  A) Rs 15  B) Rs 12.10  C) Rs 23.70  D) Rs 26.80  E) None of these

Solution: Explanation :   Let the cost of the tax items = x   Given that tax rate = 6%   Rs 23.70ost of tax items, x*(6/100) = 30/100   x = 5 rs   Now non taxable item = total cost - cost for taxable item - tax   = 29 - 5 - 0.30= 
29 - 5 - 0.30 = 23.7
23.70   Answer : Rs 23.70
Answer: C
A certain family has 3 sons: Richard is 6 years older than David, and David is 8 years older than Scott. If in 8 years, Richard will be twice as old as Scott, then how old was David 5 years ago?	Select the correct option:
A) 9 B) 10 C) 12 D) 14 E) 16

Solution: Let's say   Age of Richard isR   Age of David isD   Age of Scott isS   Now   Richard is 6 years older than David,   i.e. R = D +6   David is 8 years older than Scott   i.e. D = S +8   If in 8 years, Richard will be twice as old as Scott   i.e. R+8 = 2x(S+8)   i.e. R+8 = 2S + 16   i.e. R = 2S+8   But R = D+6 = (S+8)+6 = S+14   therefore, 2S + 8 = S +14   i.e. S = 6   i.e. R = 20   i.e. D = 14   Now,   how old was David 5 years ago?   i.e. D-5 = 14-5= 
14-5 = 9
9 years   9nswer: Option   9
Answer: A
A rectangular field has area equal to 150 sq m and perimeter 50 m. Its length and breadth must be?  Answers:
A) 15 m,17 m B) 85 m,10 m C) 15 m,80 m D) 15 m,10 m E) 15 m,14 m

Solution: lb = 150   2(l + b) = 50 => l + b = 25   l – b = 5   l = 15 b = 10   Answer:15 m,10 m
Answer: D
A can do a piece of work in 12 days and B can do it in 15 days and C can do it 20 days. They started the work together and A leaves after 2 days and B leaves after 4 days from the beginning. How long will work lost?
Choose the correct choice from the following choices:
A) 15 1/3
B) 16 1/3
C) 17 1/3
D) 18 1/3
E) 25 1/3

Solution: 2/12 + 4/15 + x/20 = 1   x = 46/3 = 15 1/3   15 1/3NSWER:15 1/3
Answer: A
If q and r are both odd numbers, which of the following must also be odd? Answers.
A) q – r  B) (q + r)^2  C) q(q + r)  D) (qr)^2  E) q/r

Solution: Since q and r are odd numbers we can put q and r as q=2*Q+1 and r=2*R+1, for some integers Q, R.   A. q-r2* +1= 
2* +1 = 2
2*R+1, for some integers Q, R.   A. q-r=(2*Q+1)-(2*R+1)=2*(Q-R) ---> must be an even number.   B. (q + r)^2 =(2Q+2R+2)^2= 4*(Q+R+1)^2 ---> must be an even number.   C. q(q+r) = (2Q+1)(2Q+2R+2)= 2*(2Q+1)(Q+R+1) ---> must be an even number.   D. (qr)^2 = ((2Q+1)(2R+1))^2 = (4QR +2Q +2R +1)^2   by putting 2QR+Q+R = T we have (2T+1)^2= 4T^2 + 4T +1=2(2T^2 +2T)+1 ---> must be an odd number.   E. q/r cannot be an integer   The answer is, therefore, ((qr)^2)
Answer: D
Find out the wrong term in the series 2, 3, 4, 4, 6, 8, 9, 12, 16
Answers
A) 9 B) 8 C) 7 D) 6 E) 2

Solution: Explanation:   The given sequence is a combination of three series:   i)1st, 4th, 7th terms i.e, 2, 4, 9   ii)2nd, 5th, 8th terms i.e, 3, 6, 12   iii)3rd, 6th, 9th terms i.e, 4, 8, 16   In each one of i, ii, iii, each term is twice the preceding term.   So, 9 is wrong and must be replaced by  (4*2)= 
 (4*2) = 8
8   9nswer: 9) 9
Answer: A
A box contains 3 blue marbles, 4 red, 6 green marbles and 2 yellow marbles. If three marbles are picked at random, what is the probability that they are all blue?	Choose the correct answer:
A) 1/455
B) 1/429
C) 1/408
D) 1/421
E) 1/420

Solution: Given that there are three blue marbles, four red marbles, six green marbles and two yellow marbles.   Probability that all the three marbles picked at random are blue   = ³C₃/¹⁵C₃ = (1 * 3 * 2 * 1)/(15 * 14 * 13)   = 1/455   1/455nswer: 1/455
Answer: A
If a function f is defined by f(x)= -1/x for all non zero numbers x. If f(a) = -1/2 and f(ab) = 1/4 then b= ? Choose the correct choice from the following
A) -1/2
B) 1/2
C) 2
D) -2
E) 8

Solution: f(a) = -1/2 = -1/a, and thus a = 2   f(ab) = 1/4, and thus ab = -4   2b = -4   b = -2   The answer is -2.
Answer: D
If the area of circle O is 16π, what is the length of an arc on the circle formed by a central angle measuring 35 degrees?	Answers:
A) π
B) 3π/2
C) 2π
D) 5π/2
E) 7π/9

Solution: Area = 16π   Radius = 4   Circumference = 2 x 4 x π = 8π   Angle forming the arc = 35 degrees. 35/360 = 7/72.   Therefore length of arc = 7/72 * 8π = 7π/9 - Answer choice 7π/9.
Answer: E
The perimeter of a triangle is 35 cm and the inradius of the triangle is 4.5 cm. What is the area of the triangle?	Options.
A) 22	B) 75	C) 78	D) 54	E) 23

Solution: Area of a triangle = r * s   Where r is the inradius and s is the semi perimeter of the triangle.   Area of triangle = 4.5 * 35/2= 
4.5 * 35/2 = 78.75
78.75 cm2   Answer:78
Answer: C
In a camp, there is a meal for 160 men or 220 children. If 160 children have taken the meal, how many men will be catered to with remaining meal?	Choose one:
A) 20
B) 43
C) 50
D) 10
E) 40

Solution: There is a meal for 220 children. 160 children have taken the meal.   Remaining meal is to be catered to 60 children.   Now, 220 children 160 men.   60 children (160/220)	* 60 = 43 men   Answer is 43.
Answer: B
A batsman played seven games and scored an average of 80 runs per game. If, in his first five games, he scored 75, 69, 81, 90, and 73 runs, what was the average (arithmetic mean) number of runs scored over the last two games?
Choose the correct choice from the following answers.
A) 65  B) 81  C) 82  D) 86  E) Cannot be determined from the information given.

Solution: The first thing to recognize is that to find the average, you take the sum and divide by the number of inputs (games, in this case) you have. Here were have 7 inputs, or games. Therefore, I approach this problem by first writing the following:   (A+B+C+D+E+F+G)/7 = 80   Plug in the sum of the first 5 games (388) for (A+B+C+D+E)   [(388+F+G)/7]= 80   Multiply both sides by 7   388+F+G = 560   Subtract 388 on both sides   F+G = 172   Since the answer asks for the average of the last two games, F and G, all you need to do is take 172 and divide it by 2, giving 86.   The answer is 86.
Answer: D
A math teacher has 32 cards, each of which is in the shape of a geometric figure. Half of the cards are rectangles, and a third of the cards are rhombuses. If 8 cards are squares, what is the maximum possible number of cards that re circles.
Select
A) 9	B) 10	C) 11	D) 12	E) 15

Solution: a square is a special kind of rhombus (sides are perpendicular)   a square is a special kind of rectangles (sides with same length)   Among the 32 cards with have:   15 rectangles   10 rhombus   8 squares   Among the 15 rectangles, there could be 8 special ones (with sides of same length) that are squares. That lets at least 7 rectangles that are not square.   Among the 10 rectangles, there could be 8 special ones (with sides perpendicular) that are squares. That lets at least 2 rhombus that are not square.   We have 8 squares.   So the minimum different cards that represent a square, a rhombus or a rectangle is   2 + 7 + 8= 
  2 + 7 + 8 = 17
17   Which means that the maximum number of circles that you could have is  32 - 17= 
 32 - 17 = 15
15   Answer (15)
Answer: E
Lori deposits $10,000 in a savings account at 10% annual interest, compounded annually.
After 3 years, what is the balance on the account?	Choose the correct choice from the following choices.
A) 13310	B) 13410	C) 13510	D) 13610	E) 13710

Solution: The deposit of $10,000 increases by 10% every year. So use the formula for amount in case of CI.   13310mount = P*(1 + r/100)^n   13310mount = 10,000 * (1 + 10/100)^3   13310mount = 10,000*(1.1)^3   13310mount = 13310   13310NSWER:13310
Answer: A
A 600 meter long train crosses a signal post in 15 seconds. How long will it take to cross a 3 kilometer long bridge, at the same speed?
Answers:  A) 4 min  B) 2 min  C) 8 min  D) 9 min  E) 1.5 min

Solution: S = 600/15= 
600/15 = 40
40 mps   S= 3600/40= 
3600/40 = 90
90 sec= 1.5 min   Answer: 1.5 min
Answer: E
If cost of 15 eggs be 90 rupees, then find out the cost of 5 dozen eggs.  Choose the correct option:	A) 300	B) 400	C) 500	D) 600	E) 360

Solution: Cost of 15 eggs = 90 rupees   Cost of 1 egg = 90/15= 
90/15 = 6
6 rupees,   Cost of 5 dozens, i.e. 6 x 12= 72 x 5 = 360   Answer : 360
Answer: E
Attorneys are questioning 11 potential jurors about their ability to serve on a jury and decide a case fairly. Seven individuals will be selected to serve on the jury. If each potential juror has an equal chance of being selected, what is the probability that Tamara and Inga are chosen for the jury?
Pick one:
A) 2/11	B) 2/7	C) 21/55	D) 4/11	E) 34/55

Solution: First person to be chosen one of the two girls - 2/11   Second person to be chosen to be the other girl - 1/10   The probability to chose both girls - (2/11)*(1/10) = 1/55.   The two girls can be chosen anywhere in the list of the 7 jurors, therefore the final probability is (1/55)*7C2 = (1/55)*(7*6/2) = 21/55.   Combinatorial approach:   Total number of possibilities to choose the 7 jurors - 11C7 = 11*10*9*8/(2*3*4) = 11*10*3.   Number of possibilities to have the two girls among the final 7 jurors - 9C5 = 9*8*7*6/(2*3*4) = 9*2*7 (the two girls must be in, therefore we need to choose 5 more people from the remaining 9).   Required probability 9*2*7/(11*10*3) = 21/55.   (I prefer not to multiply before I express the final probability as a ratio, I always try to reduce a fraction whenever possible.)   Answer 21/55.
Answer: C
List R contains five numbers that have an average value of 60. If the median of the numbers in the list is equal to the mean and the largest number is equal to 20 more than two times the smallest number, what is the smallest possible value in the list?	Choose the correct choice:
A) 25
B) 28
C) 31
D) 34
E) 37

Solution: The middle number is 60.   Let the smallest number be x. Then the largest number is 2x+20.   To make x as small as possible, let's make the remaining numbers as large as possible.   So the second largest = the largest = 2x+20.   The second smallest should be equal to the median.   The numbers are x, 60, 60, 2x+20, 2x+20.   x + 60 + 60 + 2x + 20 + 2x + 20 = 5*60= 
5*60 = 300
300   5x= 140   x = 28   The answer is 28.
Answer: B
Machine A can make 350 widgets in 1 hour, and machine B can make 250 widgets in 1 hour. If both machines work together, how much time will it take them to make a total of 1200 widgets?  Choose the correct choice from the following answers.
A) 2 hour and 20 minutes
B) 2 hour and 24 minutes
C) 2 hour and 30 minutes
D) 2 hour and 36 minutes
E) 2 hour and 00 minutes

Solution: (350+250)t=1200   600t=1200   t=2   t=2 hour and 00 minutes   Answer: 2 hour and 00 minutes
Answer: E
The sum of the first 50 positive even integers is 2550. What is the sum of the even integers from 202 to 300 inclusive?	Options
A) 5,150 B) 7,550 C) 10,150 D) 12,550 E) 20,150

Solution: 2 + 4 + 6 + 8 +...+ 100 = 2550   202 + 204 + ... + 300 = 50(200) + (2+4+...+100) = 10,000 + 2550 = 12,550   The answer is 12,550.
Answer: D
A tank contains 10,000 gallons of a solution that is 7 percent sodium chloride by volume. If 2,500 gallons of water evaporate from the tank, the remaining solution will be approximately what percent sodium chloride?	Choose the most appropriate option.
A) 1.25%  B) 3.75%  C) 9.33%  D) 10.67%  E) 11.7%

Solution: The remaining solution will be approximately what percent sodium chloride?means:what percent of the remaining solution is sodium chloride. Now, since the remaining solution is 10,000-2,500=7,500 gallons and sodium chloride is 700 gallons (7% of initial solution of 10,000 gallons) then sodium chloride is 700/7,500*100=~9.33% of the remaining solution of 7,500 gallons.   Answer: 9.33%.
Answer: C
Barbata invests $2200 in the National Bank at 5%. How much additional money must she invest at 8% so that the total annual income will be equal to 6% of her entire investment?	Select the correct option.
A) 1100  B) 3000  C) 1000  D) 3600  E) 2400

Solution: Let the additional invested amount for 8% interest be x;   Equation will be;   2200+0.05*2200+x+0.08x = 2200+x+0.06(2200+x)   0.05*2200+0.08x = 0.06x+0.06*2200   0.02x = 2200(0.06-0.05)   x = 2200*0.01/0.02= 
2200*0.01/0.02 = 1_100
1100   1100ns: "1100"
Answer: A
The average age of the mother and her 6 children is 12 years which is reduced by 5 years if the age of the mother is excluded. How old is the mother?	Options.
A) 42 years	B) 40 years	C) 48 years	D) 50 years	E) None of these

Solution: Total age of the mother and six children = 12 × 7 = 84 years.   Total age of six children = 7 × 6 = 42 years. (since average is reduced by 5)   Mother is 42 years old.   42 yearsNSWER:42 years
Answer: A
In a certain company, a third of the workers do not have a retirement plan. 40% of the workers who do not have a retirement plan are women, and 40% of the workers who do have a retirement plan are men. If 120 of the workers of that company are men, how many of the workers are women?  Choose the correct choice from the following choices.
A) 80 B) 95 C) 105 D) 120 E) 137

Solution: Set up equation:   x = total number of workers   120 = 0,4 * 2/3 * x + 0,6 * 1/3 * x   120 = 14/30 x   x = 257   257 - 120= 
257 - 120 = 137
137   Answer 137
Answer: E
When 1/10 percent of 3,000 is subtracted from 1/10 of 3,000, the difference is	Select
A) 2970 B) 297 C) 2997 D) 300 E) 30

Solution: (1/10)*3000 - (1/10)%*3000 =   300 - (1/1000)*3000 =   300 - 3= 
300 - 3 = 297
297   The answer is 297.
Answer: B
A student is ranked 13th from right and 8th from left.how many are there?  Options
A) 18 B) 19 C) 20 D) 21 E) 22

Solution: 13th from right means = x + 12   8th from left means = 7 + x   Total = 12+7+1= 
12+7+1 = 20
20   ANSWER:20
Answer: C
John must arrange 3 different physics books and 5 different mathematics books on one shelf. If the first book on the leftmost side is a mathematics book and no physics book is next to another physics book. How many different arrangements exist? Choose the correct choice from the following
A) 6
B) 9
C) 36
D) 120
E) 720

Solution: First Place, is reserved for Math book. There are 3 Math books which can be arranged in3 ways   Restriction comes into playhysics book cannot be together. Hence, the maththe physics books take alternate places   Second Place, Physics Book - in 3 ways   Third Place, Math Book - in 2 ways (only 2 books left)   Fourth Place, Physics - in 2 ways (only 2 Physics book left)   Rest two places can be arranged in one way only.   Total no of ways = 5*4*3*3*2*2*1*1= 
5*4*3*3*2*2*1*1 = 720
720 ways   720
Answer: E
How many five-digit numbers are there, if the two leftmost digits are even, the other digits are odd and the digit 4 cannot appear more than once in the number?	Answers:  A) 1375  B) 8451  C) 1546  D) 2375  E) 3215

Solution: Total five-digit numbers with two even leftmost digits and with three odd last digits: EEOOO - 4*5*5*5*5=4*5^4 (notice that we have only 4 choices for the first digit since we cannot use zero);   Total five-digit numbers with two 4's as leftmost digits and with three odd last digits: 44OOO - 5*5*5=5^3;   So, the answer is 4*5^4-5^3=5^3(4*5-1)=125*19= 
125*19 = 2_375
2375.   Answer: 2375.
Answer: D
A man buys Rs. 20 shares paying 9% dividend. The man wants to have an interest of 12% on his money. The market value of each share is:
Choices:
A) 15
B) 10
C) 20
D) 25
E) 30

Solution: Dividend on rs 20 = (9/100*20) = 9/5   =>9/5 is an income on Rs   (100/12 * 9/5)= 
  (100/12 * 9/5) = 15
15   15NSWER 15
Answer: A
Find number which is 60% less than 80.  Choose the correct choice from the following options:
A) 18
B) 32
C) 28
D) 26
E) 98

Solution: Explanation:   60% less is 40% of the given number   Therefore, 40% of 80 is 32.   ANSWER: 32
Answer: B
The average weight of 6 persons increases by 1.5 kg. If a person weighing 65 kg is replaced by a new person, what could be the weight of the new person?
Choose the correct option:  A) 74 kg  B) 77 kg  C) 76.5 kg  D) Data inadequate  E) None of these

Solution: total weight increases = 6 × 1.5 = 9 kg   so the weight of new person = 65 + 9= 
65 + 9 = 74
74 kg   74 kgnswer 74 kg
Answer: A