MU-NLPC/Calc-aqua_rat huggingface dataset:
----------------YES---------NO----UNSURE
Subject M----500--------200-----100
Subject R----400--------100-----300
A total of 800 students were asked whether they found two subjects, M and R, interesting. Each answer was either yes or no or unsure, and the numbers of students who gave these answers are listed in the table above. If 180 students answered yes only for subject M, how many of the students did not answer yes for either subject?
Choose the correct choice from the following answers.
A) 100	B) 220	C) 300	D) 400	E) 500

Solution: Since 180 students answered yes only for subject M, then the remaining 320 students who answered yes for subject M, also answered yes for subject R. So, 320 students answered yes for both subjects.   If 320 students answered yes for both subjects, then 400-320= 
400-320 = 80
80 students answered yes only for subject R.   So, we have that:   200 students answered yes only for subject M;   80 students answered yes only for subject R;   300 students answered yes for both subjects;   Therefore 800-(200+80+300)= 
800-(200+80+300) = 220
220 students did not answer yes for either subject.   Answer: 220.
Answer: B
when i was married 10 years ago,my wife was the 6th member in the family.today,my father died,and a baby was born to me.the average age in my family today is what it was when i was married.how old was my father when he died?  Choices
A) 50yrs
B) 60yrs
C) 70yrs
D) 80yrs
E) indeterminate

Solution: 10 years ago the family members there were 6 members with age= I+Father+Wife+3 others   Now 6 members with age= (I+10)+(Wife +10)+ (3 others+3*10) + (baby=0).   I+Father+Wife+3 others=(I+10)+(Wife +10)+ (3 others+3*10) + (baby=0)   Father =50+0= 
50+0 = 50
50= Father's age 10 year ago   So now father's age=50 +10= 
50 +10 = 60
60.   ANSWER:60yrs
Answer: B
A can do a piece of work in 7 days and B can do it in 6 days how long will they both work together to complete the work?  Choose the correct choice from the following answers:
A) 6/11 B) 8/13 C) 3/13 D) 9/11 E) 10/13

Solution: Explanation:   A’s one day work = 1/5   B’s one day work = 1/6   (A+B)’s one day work = 1/7 + 1/6 = 13/42 => time = 42/13 = 3 3/13 days   Answer: Option 3/13
Answer: C
At a certain university, 65% of the professors are women, and 70% of the professors are tenured. If 90% of the professors are women, tenured, or both, then what percent of the men are tenured?  Choose the correct option
A) 25 B) 37.5 C) 50 D) 62.5 E) 75

Solution: total women = 65%   total men = 40%   total tenured = 70% (both men and women)   therefore, women tenured + women professors + men tenured = 90%   men tenured = 25%   but question wants to know the percent of men that are tenured   25%/40% = 62.5%   62.5
Answer: D
The marks obtained by Vijay and Amith are in the ratio 4:5 and those obtained by Amith and Abhishek in the ratio of 3:2. The marks obtained by Vijay and Abhishek are in the ratio of?	Answers
A) 6:8
B) 6:2
C) 6:5
D) 6:4
E) 6:2

Solution: 4:5   3:2   -------   12:15:10   12:10   6:5   Answer: 6:5
Answer: C
Rs.2500 is divided into two parts such that if one part be put out at 5% simple interest and the other at 6%, the yearly annual income may be Rs.145. How much was lent at 5%?
Options.
A) 2333  B) 2777  C) 2688  D) 500  E) 2871

Solution: (x*5*1)/100 + [(2500 - x)*6*1]/100 = 145   X = 500   Answer: 500
Answer: D
Calculate the number of bricks, each measuring 25 cm x 15 cm x 8 cm required to construct a wall of dimensions 10 m x 4 m x 5 m when 10% of its volume is occupied by concrete ?  Pick one:  A) 6000  B) 5400  C) 3800  D) 4700  E) 2500

Solution: Explanation:   Let 'B' be the nuber of bricks.   => 10 x 4/100 x 5 x 90/100 = 25/100 x 15/100 x 8/100 x B   => 10 x 20 x 90 = 15 x 2 x B   => B = 6000   6000NSWER IS 6000
Answer: A
A number is said to be prime saturated if the product of all the different positive prime factors of g is less than the square root of g. What is the greatest two digit prime saturated integer ?  Choose the most appropriate option:  A) 99  B) 98  C) 97  D) 96  E) 95

Solution: g=96 = 3 * 32 = 3 * 2^5   Answer is 96.
Answer: D
David and Rachel are getting married. The extended family wants to have its picture taken, but David's father is unwilling to stand next to Rachel's mother. How many options does the photographer have to arrange the 13 family members in a row for the picture? Select the correct option:
A) 14!
B) 12×11!
C) 11×12!
D) 13!/2!
E) 13!

Solution: The number of ways to arrange 13 people is 13!   We need to subtract the arrangement when these two people are together.   Let's think of these two people as a single unit so there are 12 units.   The number of ways to arrange 12 units is 12!   We need to multiply this by 2 since these two people could switch places.   The total number of valid arrangements is 13! - 2*12! = 12!*(13-2) = 11x12!   The answer is 11×12!.
Answer: C
At a certain stage of a soccer tournament, the score ratio of teams A, B and C was 3:4:5. Eventually, the score ratio of A to B has doubled while the score ratio of A to C has halved. If the final score of team C was 40, what was the final score A of team B?
Choose the correct choice:
A) 1)8 B) 2)10 C) 3)20 D) 4)40 E) 5)80

Solution: A to B = 3 : 4   So, on doubling we get 6 : 4   A to C = 3 : 5   So, on halving we get 1.5 : 5 or 3 : 10 or 6 : 20   So final ratio = 6 : 4 : 20.   If 20x = 40   4x = 8   Hence, answer is 1)8
Answer: A
a is the hundreds digit of the three digit integer x, b is the tens digit of x, and c is the units digit of x. a = b = 3c, and a > 0.
What is the difference between the two greatest possible values of x?
Tip: Dont stop till you have exhausted all answer choices to arrive at the correct one. Choose the correct answer:
A) 112	B) 213	C) 331	D) 511	E) 745

Solution: Ratio of a:b:c= 3:3:1   Two possible greatest single digit values for a are 9 and 6   if a is 9, then x= 993   if a is 6, then x= 662   difference= 993-662= 
993-662 = 331
331   331 is the answer
Answer: C
. A car covers a distance of 810 km in 5 hours. Find its speed?  Choose the correct choice from the following:
A) 104	B) 55	C) 162	D) 174	E) 2761

Solution: 810/5= 
810/5 = 162
162 kmph   Answer: 162
Answer: C
Set E consists of all the prime numbers between 10 and 25. What is the range of set E?	Choose the correct choice from the following answers:  A) 12  B) 13  C) 16.6  D) 17  E) 23

Solution: 12nswer of set E is 12=12
Answer: A
If 7<x<9<y<15, then what is the greatest possible positive integer difference of x and y? Choose the correct choice from the following answers:	A) 7	B) 4	C) 5	D) 6	E) 3

Solution: Let x=7.1 and y=14.1   Greatest possible difference=14.1-7.1= 
14.1-7.1 = 7
7   7nswer 7
Answer: A
The average age of 32 students in a group is 10 years. when teacher's age is included to it, the average increases by one.What is the teacher's age in years?
Choose the correct choice from the following
A) 45	B) 43	C) 51	D) 53	E) 57

Solution: age of the teacher=(33*11-32*10)= 
(33*11-32*10) = 43
43 years.   ANSWER:43
Answer: B
Three candidates contested in an election and received 2136, 7636, 11628 votes respectively. What is the percentage of the total votes did the winning candidate get? Pick one:	A) 45%	B) 49%	C) 57%	D) 54%	E) 62%

Solution: Total number of votes polled = 2136+7636+11628= 
2136+7636+11628 = 21_400
21400   Required percentage= 11628*100/21400 = 54%   Answer is 54%
Answer: D
If xy+4z = x(y+z), which of the following must be true?	Choose the correct choice from the following choices:
A) 1. x=0 and z=0  B) 2. x=1 and y=1  C) 3. y=1 and z=0  D) 4. x=1 or y=0  E) 5. x=4 or z=0

Solution: xy+4z=x(y+z)   xy+4z=xy+xz   4z=xz   it means x=4 or z=0   Answer 5. x=4 or z=0
Answer: E
If 5x = 6y and xy ≠ 0, what is the ratio of 1/3*x to 1/5*y ? Choose the correct option.
A) 25/6  B) 36/25  C) 2  D) 5/6  E) 25/36

Solution: 5x = 6y => x/y = 6/5   1/3*x to 1/5*y = x/y * 5/3 = (6/5)*(5/3)= 
(6/5)*(5/3) = 2
2   Ans: 2
Answer: C
Excluding stoppages, the speed of a bus is 54 kmph and including stoppages, it is 45 kmph. For how many minutes does the bus stop per hour?  Choose the correct choice from the following choices:
A) 7 min
B) 8 min
C) 9 min
D) 10 min
E) 11 min

Solution: Due to stoppages, it covers 9 km less.   Time taken to cover 9 km =(9/54)x60 = 10 min   answer : 10 min
Answer: D
In an examination the number of successful students was 4 times the numbr of unsuccessful students If there were 35 less students nd the numbr of unsuccessful students were 9 more,then the ratio of their numbr would have been 2:1 . Find the total numbr of students
Choose the correct choice from the following answers.
A) 155	B) 145	C) 135	D) 125	E) 112

Solution: successful students 4x,unsuccessful student x.total 5x   now,total students become 5x-35 & unsuccessful students x+9 then successful students 4x-44   ratio 4x-44 / x+9=2 / 1   x=31 then total student 5x=155   155NSWER:155
Answer: A
A box contains 20 green balls, 15 red balls and 25 white balls. A ball is drawn at random from the box. What is the probability that the ball drawn is either red or green?
Choose the correct choice from the following.
A) 6/7	B) 5/11	C) 3/8	D) 1/13	E) 7/12

Solution: Total number of balls = 20+15+25= 
20+15+25 = 60
60   n(s)=60   7/121 = event of drawing a red ball = 15/60 = 1/4   7/122 = event of drawing a green ball = 20/60 = 1/3   P(7/121)+P(7/122) = (1/4)+(1/3) = 7/12   Answer is 7/12
Answer: E
5 OUT OF 1000 PARTS OF EARTH IS SULPHUR. WHAT IS THE PERCENTAGE OF SULPHUR IN EARTH  Answers.
A) 11/50	B) 2/9	C) 1/2	D) 2/45	E) NONE OF THESE

Solution: REQUIRED PER1/2ENTAGE=(5/1000*100)%=1/2%   1/2ORRE1/2T OPTIONS: 1/2
Answer: C
For any number d, d* is defined as the greatest positive even integer less than or equal to d. What is the value of 5.2 – 5.2*?
Choose the correct choice from the following answers: A) 0.2 B) 1.2 C) 1.8 D) 2.2 E) 4.0

Solution: Since d* is defined as the greatest positive even integer less than or equal to d, then 5.2* = 4 (the greatest positive even integer less than or equal to 5.2 is 4).   Hence, 5.2 – 5.2* = 5.2 - 4= 
5.2 - 4 = 1.2
1.2   Answer: 1.2.
Answer: B
On a clock, how many times a day do the minute and hour hand overlap?  Pick
A) 10
B) 11
C) 20
D) 22
E) 24

Solution: 22 times: 12:00:00, 1:05:27, 2:10:55, 3:16:22, 4:21:49, 5:27:16, 6:32:44, 7:38:11, 8:43:38, 9:49:05, 10:54:33. Each twice a day.
Answer: D
The average age of husband, wife and their child 3 years ago was 27 years and that of wife and the child 5 years ago was 20 years. The present age of the husband is
Choose the correct choice
A) 22  B) 40  C) 38  D) 21  E) 11

Solution: Explanation:   Sum of the present ages of husband, wife and child = (27 x 3 + 3 x 3) years = 90 years.   Sum of the present ages of wife and child (20 x 2 + 5 x 2) years = 50 years.   Husband's present age = (90 - 50)= 
(90 - 50) = 40
40 years.   Answer: 40
Answer: B
If the cost of A metres of wire is C rupees, then what is the cost of E metres of wire at the same rate?	Choose the correct answer
A) Rs. (EC/A)  B) Rs. (EC)  C) Rs. (C/A)  D) Rs. (E/A)  E) Rs. (AC/E)

Solution: cost of A metres of wire = Rs.C   cost of 1 metre of wire = Rs.(C/A)   cost of E metre of wire = Rs.(E×C/A)=Rs. (EC/Rs. (EC/)   Rs. (EC/NSWER:Rs. (EC/
Answer: A
Which one of the following is not a prime number?
Pick
A) 31  B) 61  C) 71  D) 91  E) None of these

Solution: Explanation:   91 is divisible by 7. So, it is not a prime number.   ANSWER IS 91
Answer: D
Let y = 2g + x^2 and g = 5x + 1.
If g^2 = 121, then which of the following can be a value of 2y + 3g?
Choose the correct choice from the following options
A) 81
B) 130
C) 141
D) 142
E) 160

Solution: 800score Official Solution:   First note that g can either be 11 or -11. We are going to have to use both to find all solutions before we can choose a final answer. We begin by substituting g = 11 and then g = -11. If g = 11, then x = 2. If g = -11, then x = -12/5. Since all of our solutions are whole numbers, we can dismiss -12/5. We use g = 11 and x = 2 to determine the value of y: y = 2(11) + 4 = 24. Finally, we substitute the values for y and g into the last expression to determine its value : 2(24) + 3(11) = 48 + 33= 
48 + 33 = 81
81;the correct answer is (81).
Answer: A
If Jan 1, 2006 was a Monday, What was the day of the week Jan 1, 2010?
Select the correct option
A) Friday
B) Thursday
C) Tuesday
D) Saturday
E) None of these

Solution: Explanation :   Given that Jan 1 2006 was a Monday   Number of odd days in the period 2006-2009   = 3 normal years + 1 leap year   = 3 x 1 + 1 x 2 = 5 (note that we have taken the complete year 2006 because the period in 2006 is from 01-Jan-2006 to 31-Dec-2006, which is the whole year 2006. Then the complete years 2007, 2008 and 2009 are also involved)   Hence Jan 1 2010 = (Monday + 5 odd days) = Saturday.. Answer : Option Saturday
Answer: D
The present ratio of students to teachers at a certain school is 50 to 1. If the student enrollment were to increase by 50 students and the number of teachers were to increase by 5, the ratio of students to teachers would then be 25 to 1. What is the present number of teachers?  Select.
A) 3 B) 8 C) 10 D) 12 E) 15

Solution: We are given that the ratio of students to teacher is 50 to 1. We can rewrite this using variable multipliers.   students : teachers = 50x : x   We are next given that student enrollment increases by 50 and the number of teachers increases by 5. With this change the new ratio becomes 25 to 1. We can put all this into an equation:   Students/Teachers  25/1 = (30x + 50)/(x + 5)   If we cross multiply we have:   25(x + 5) = 50x + 50   25x + 125 = 50x + 50   3 = x   Since x is the present number of teachers, currently there are 3 teachers.   3nswer 3.
Answer: A
A man can hit the target once in two. If he fires four shots in succession, what is the probability that he will hit the target?	Select the correct option.
A) 1	B) 1/16	C) 81/16	D) 15/16	E) 185/256

Solution: In four shots he can hit once,twice,thrice,all hit   the probability of hitting the target is p(1hit out of 4)+P(2hit out of 4)+p(3hit out of 4)+p(All hit)   it is total probability-probability of not hitting the target   =>1-(1/2*1/2*1/2*1/2)   =>15/16   ANSWER:15/16
Answer: D
A certain ball team has an equal number of right- and left-handed players. On a certain day, two-thirds of the players were absent from practice. Of the players at practice that day, two-third were left handed. What is the ratio of the number of right-handed players who were not at practice that day to the number of lefthanded players who were not at practice?	Choose the correct choice from the following answers:	A) 1/3	B) 2/3	C) 5/7	D) 7/5	E) 3/2

Solution: Say the total number of players is 18, 9 right-handed and 9 left-handed.   On a certain day, two-thirds of the players were absent from practice --> 12 absent and 6 present.   Of the players at practice that day, one-third were left-handed --> 6*2/3=4 were left-handed and 2 right-handed.   The number of right-handed players who were not at practice that day is 9-2 --  6*2/3= 
 --  6*2/3 = 4
4 were left-handed and 2 right-handed.   The number of right-handed players who were not at practice that day is  9-2= 
 9-2 = 7
7.   The number of left-handed players who were not at practice that days is   9-4= 
  9-4 = 5
5.   The ratio= 7/5.   Answer: 7/5
Answer: D
If x is chosen at random from the set {1, 2, 3, 4} and y is to be chosen at random from the set {5, 6, 7}, then what is the probability that xy will be even?  Choices:
A) 5/6
B) 2/6
C) 2/3
D) 1/2
E) 1/4

Solution: S = {(1,5), (1,6), (1,7), (2,5), (2,6), (2,7), (3,5), (3,6), (3,7), (4,5), (4,6), (4,7)}   Total element n(S) = 12   xy will be even when even x or y or both will be even.   Events of xy being even is E.   E = {(1,6), (2,5), (2,6), (2,7), (3,6), (4,5), (4,6), (4,7)}   n(E) = 8   P(E) = n(E)/n(S)   = 8/12   = 2/3   ANSWER:2/3
Answer: C
If 5% more is gained by selling an book for $ 350 than by selling it for $ 340, the cost of the book is:
Choose the most appropriate option:	A) 500	B) 400	C) 200	D) 300	E) 100

Solution: C   200   Let C.P. be $ x.   Then, 5% of x = 350 - 340= 
350 - 340 = 10
10   x/20= 10 => x = 200
Answer: C
One of the number is odd, Which one ?
Choose the correct choice from the following:
A) 4377
B) 3954
C) 9862
D) 9862
E) 9862

Solution: 9862   9862   Sum of digits of all other numbers is 21 , but sum of digits of 9862 is 25
Answer: E
If 0 < x ≤ 4, then which one of the following is the maximum value of (x – 1)^2 + x ?
Choose one
A) 13	B) –1	C) 0	D) 1	E) 2

Solution: the maximum value of (x – 1)^2 + x for 0 < x ≤ 4 is when x=4 --> (x – 1)^2 + x = 13   13nswer 13
Answer: A
Three persons invested Rs.9000 in a joint business. The second person invested Rs.1000 more than the first and the third Rs.1000 more than second. After two years, they gained Rs.5400. How much third person will get?	Choose the correct choice from the following choices.
A) 2400  B) 2429  C) 2428  D) 2421  E) 2408

Solution: First persons investment = x   Second persons investment = x + 1000   Third persons investments = x + 2000   x + x + 1000 + x + 2000 = 9000   3x = 6000   x = 2000   Ratio = 2000 : 3000 : 4000   2:3:4   4/9 * 54000 = 2400   2400nswer:2400
Answer: A
A rectangular lawn of dimensions 80 m * 60 m has two roads each 10 m wide running in the middle of the lawn, one parallel to the length and the other parallel to the breadth. What is the cost of traveling the two roads at Rs.3 per sq m?	Choose one:
A) 3929 B) 3998 C) 3128 D) 3900 E) 3920

Solution: Area = (l + b – d) d   (80 + 60 – 10)10 => 1300 m2   1300 * 3 = Rs.3900   Answer: 3900
Answer: D
If 1/a^3 + a^3 represents the diameter of circle O and 1/a + a = 3, which of the following best approximates the circumference of circle O?
Pick one:
A) 28  B) 22  C) 20  D) 16  E) 12

Solution: Given that (1/a)+a =3   Square both sides of the equation:   We get,   [(1/a)^2 + a^2 + 2*(1/a)*a] = 9   => (1/a)^2 + a^2 + 2 = 9   => (1/a)^2 + a^2 = 7 ----------------- (1)   Diameter D = (1/a)^2 + a^2   = 7 (From (1))   So Radius = D/2 = 7/2   20ircumference = 2*Pi*r   = 2*(22/7)*(7/2)   =20   So the answer should be 20
Answer: C
The curved surface area of a cylindrical pillar is 264 sq.m and its volume is 924 cub.m. Find the ratio of its diameter to its height
Choose the correct choice from the following choices:
A) 7:9  B) 7:3  C) 7:7  D) 7:6  E) 7:1

Solution: Explanation:   {\color{7:3lack} \frac{\prod r^{2}h}{2\prod rh}=\frac{924}{264}}   {\color{7:3lack} \Rightarrow r=\frac{924}{264}\times 2=7m}   {\color{7:3lack}And\; \; 2\prod rh =264 \Rightarrow h=(264\times \frac{7}{22}\times \frac{1}{2}\times \frac{1}{7})=6m}   {\color{7:3lack}\therefore } Required Rato ={\color{7:3lack}\frac{2r}{h} } ={\color{7:3lack}\frac{14}{6}=7:3 }   Answer: 7:3) 7 : 3
Answer: B
In how many ways can 5 GIRLS and 3 BOYS be seated on 8 chairs so that no two BOYS are together? Choose the correct option
A) A)5760 B) B)14400 C) C)480 D) D)56 E) E)40320

Solution: Consider the following arrangement:   *G*G*G*G*G   Now, if BOYS occupy the places of 6 stars no BOYS will be together.   # of ways 3 14400OYS can occupy the places of these 6 stars is C36=20;   # of ways 3 14400OYS can be arranged on these places is 3!=6   # of ways 5 GIRLS can be arranged is 5!=120   So total # of ways to arrange 3 14400OYS and 5 GIRLS so that no 14400OY are together is 20∗6∗120=14,400   ANS:14400
Answer: B
S is a set of 45 consecutive multiples of 5. If the smallest number in S is 55, then the greatest number in S is
Choose the correct choice from the following:
A) 198
B) 275
C) 299
D) 402
E) 205

Solution: last term =first term +(total no. of terms-1)consecutive difference   S is a set of 45 consecutive multiples of 5. If the smallest number in S is 55, then the greatest number in S is   first term = 55 ; total terms =45 ; difference = 5   55+(44)5 = 275   Ans 275
Answer: B
A salesman commission is 10% on all sales upto $5000 and 5% on all sales exceeding this. He remits $15000 to his parent company after deducting his commission. Find the total sales?
Choose the correct choice from the following.
A) 15456 B) 14758 C) 15789 D) 13250 E) 12450

Solution: Let his total sales be x   Total sales - commission = $15000   x - [(10% of 5000)+5% of (x-5000)] = 15000   95x/100 = 15000   x = 15789 approximately   Answer is 15789
Answer: C
The product of all the prime numbers less than 24 is closest to which of the following powers of 10?
Choose the correct choice from the following answers:  A) 10^9  B) 10^8  C) 10^7  D) 10^6  E) 10^5

Solution: OA: 10^8
Answer: B
If the cost price of 12 pens is equal to the selling price of 11 pens, the gain percent is: Choose the correct choice from the following.
A) 80%  B) 90%  C) 9%  D) 40%  E) 10%

Solution: Explanation:   Let C.P. of each pen be Re. 1.   Then, C.P. of 11 pens = Rs. 11; S.P. of 11 pens = Rs. 12.   Gain % = 1/11 * 100 = 9%   Answer:9%
Answer: C
One boy can eat 100 chocolates in half a minute, and another can eat half as many in twice the length of time. How many chocolates can both boys eat in 15 seconds? Pick:
A) 61.5 chocolates
B) 63.5 chocolates
C) 62.5 chocolates
D) 64.5 chocolates
E) 65.5 chocolates

Solution: 1st boy eats 100 chocos / 30 sec   so he can eat 50 in 15 sec   2nd boy can eat one-half of 100 in twice of 30 sec   so he can eat 50 in 60 sec   or that is 12.5 in 15 sec   so, together they can eat   50 + 12.5 or   62.5 chocolates in 15 seconds.   ANSWER:62.5 chocolates
Answer: C
Robert is traveling on his cycle and has calculated to reach point A at 2 p.m. if he travels at 10 km/hr; he will reach there at 12 noon if he travels at 15 km/hr. At what speed must he travel to reach A at 1 p.m.?
Choose the correct choice from the following choices:
A) 12 kmph	B) 18 kmph	C) 19 kmph	D) 15 kmph	E) 11 kmph

Solution: Let the distance traveled be x km.   Then, x/10 - x/15 = 2   3x - 2x = 60 => x = 60 km.   Time taken to travel 60 km at 10 km/hr = 60/10= 
60/10 = 6
6 hrs.   So, Robert started 6 hours before 2. p.m. i.e., at 8 a.m.   Required speed= 60/5= 
60/5 = 12
12 kmph.   12 kmphnswer:12 kmph
Answer: A
Given three boxes I, II and III, each containing two coins. In box I, both coins are 1 rupee
coins, in box II, both are 2 rupee coins and in the box III, there is one 1 rupee and one 2 rupee coin.
A person chooses a box at random and takes out a coin. If the coin is of 1 rupee, what is the
probability that the other coin in the box is also of 1 rupee?	Choose the correct choice from the following
A) 1/5	B) 2/3	C) 2/7	D) 3/7	E) 2/5

Solution: Let E1, E2 and E3 be the events that boxes I, II and III are chosen, respectively.   Then P(E1) = P(E2) = P(E3) = 1/3   Also, let A be the event that ‘the coin drawn is of 1 rupee'   Then P(A|E1) = P(a 1 rupee coin from bag I) = 2/2= 
2/2 = 1
1   P(A|E2)= P(a 1 rupee coin from bag II) = 0   P(A|E3) = P(a 1 rupee coin from bag III) = 1/2   the probability that the other coin in the box is of 1 rupee   = the probability that 1 rupee coin is drawn from the box I.   = P(E1|A)   from 2/3ayes' theorem, we know that   P(E1|A) = [P(E1 )P(A|E1 )]/ [P(E1 )P(A|E1 )+P(E2 )P(A|E2 )+P(E3 )P(A|E3 )]   = (1/3 × 1)/(1/3 × 1 + 1/3 × 0 + 1/3 × 1/2)   = (1/3)/(1/3 × 1 + 1/3 × 0 + 1/3 × 1/2)   = (1/3)/(1/3 × 1/6) = (1/3)/(3/6) = (1/3)/2 = 2/3   2/3
Answer: B
The difference between a number and its two-fifth is 510. What is 20% of that number?	Answers.
A) 58  B) 170  C) 95  D) 100  E) 120

Solution: Let the number be x. Then,   x - 2/5 x = 510   x = (510 * 5)/3= 
(510 * 5)/3 = 850
850   20% of 850= 170.   Answer:170
Answer: B
Seats for Mathematics, Physics and Biology in a school are in the ratio 5:7:8. There is a proposal to increase these seats by 40%, 50% and 75% respectively. What will be the ratio of increased seats?	Pick
A) 2:3:4  B) 2:3:8  C) 2:3:0  D) 2:3:1  E) 2:3:9

Solution: Originally, let the number of seats for Mathematics, Physics and Biology be 5x, 7x and 8x respectively. Number of increased sears are (140% of 5x), (150% of 7x) and (175% of 8x)   i.e., (140/100 * 5x), (150/100 * 7x) and (175/100 * 8x)   i.e., 7x, 21x/2 and 14x   Required ratio = 7x:21x/2:14x   = 14x : 21x : 28x = 2:3:4   2:3:4nswer: 2:3:4
Answer: A