Basic Quantitative Aptitutude And Reasoning 20 April
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Basic quantitative aptitutude and reasoning AFTERSCHO☻OL – DEVELOPING CHANGE MAKERS CENTRE FOR SOCIAL ENTREPRENEURSHIP PGPSE PROGRAMME – World’ Most Comprehensive programme in social entrepreneurship & spiritual entrepreneurship OPEN FOR ALL FREE FOR ALL
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Basic quantitative aptitutude and reasoning Dr. T.K. Jain.
AFTERSCHO☺OL Centre for social entrepreneurship Bikaner M: 9414430763 [email protected] www.afterschool.tk, www.afterschoool.tk
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How many prime factors are there in 60? • • • • •
60 divided by 2 30, divided by 2 15 divided by 3 5 divided by 5 Prime factors : 2,3,5 (three) answer
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What is the minimum fraction divisible by 2/3, 4/5 and 3/7? • We have to calculate here LCM (least common multiple) of these three fractions.. • Every fraction has two parts : • 1. numerator (2,4,3) • 2. denominator (3,5,7) • Calculate LCM of numerators • Calculate HCF of denominators • LCM of numerator = 12 • HCF of denominator = 1 (3,5,7 are prime numbers) • Write it as fraction : 12/ 1 (this is the answer) . www.afterschoool.tk
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What is the square root of 15625? • • • • • • • •
Let us divide it by 5, we get : 3125 Now again divide by 5 = 625 Now again divide by 5 = 125 Now again divide by 5 = 25 Now again divide by 5 = 5 Again divide by 5 = nil. Thus we have 5^6 =15625 Thus square root is 5^3 = 5*5*5 = 125 .
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What is the square root of .25? • • • • • •
We can write it as 25/100 Factors of 25 = 5*5 = 5^2 Square root of 25 = 5^1 Factors of 100 = 10^2 Square root of 100 = 10^1 Thus answer = 5/10 = .5 answer
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What is the square root of .09? • • • • • •
We can write it as 9/100 Factors of 9 = 3*3 = 3^2 Square root of 9 = 3^1 Factors of 100 = 10^2 Square root of 100 = 10^1 Thus answer = 3/10 = .3 answer
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What is the square root of .04? • • • • • •
We can write it as 4/100 Factors of 4 = 2*2 = 2^2 Square root of 4 = 2^1 Factors of 100 = 10^2 Square root of 100 = 10^1 Thus answer = 2/10 = .2 answer
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What is cubic root of 64? • • • • • • • • •
Let us find the factors of 64 Divide 64 by 2 = 32 Divide by 2 again = 16 Divide by 2 again = 8 Divide by 2 again = 4 Divide by 2 again = 2 Divide by 2 again = nil We can say 2^6 = 64, divide the power by 3 Cubic root = 2^2 = 4 ans
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What is cubic root of .064? • • • •
We can write it as : 64/ 1000 Cubic root of 64 = 4 Cubit root of 1000 = 10 Thus answer = 4/10 = .4 answer
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What is cubic root of .ooooo8? • • • •
We can write it as : 8/ 1000000 Cubic root of 8 = 2 Cubit root of 1000000 = 100 Thus answer = 2/100 = .02 answer
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What is cubic root of .o27? • • • •
We can write it as : 27/1000 Cubic root of 27 = 3 Cubit root of 1000 = 10 Thus answer = 3/10 = .3 answer
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What is the LCM of 60,64,68? • LCM (least common multiple) is always bigger than these numbers. • Find factors of these numbers: • 60 = 2*2*3*5 • 64 = 2^6 • 68= 2*2 *17 • Taking highest powers = 2^6*3^1*5^1*17^1 = 16320 answer. www.afterschoool.tk
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What is the HCF of 64, 160,128? • HCF (highest common factor) is always less than these numbers • Let us find the factors of these numbers: • 64 = 2^6 • 160 = 2*2*2*2*2*5 • 128 = 2^7 • Now pick up the factors which is there in each of these with minimum power : =2^5 www.afterschoool.tk
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What is HCF of 140,180 and 210? • • • •
Factors of 140 = 2*2*5*7 Factors of 180 = 2*2*3*3*5 Factors of 210 = 2*3*5*7 Now we can find that 2*5 is there in each of these numbers, so HCF is 10. answer.
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What is the LCM of 8, 10 , 12? • • • •
Factors of 8 = 2^3 Factors of 10 = 2*5 Factors of 12 = 2*2*3 Let us combine all these with highest powers : • 2^3 *3*5 = 120 answer
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What is the mean (simple average) of 20, 30,40,50? • • • •
Add them all We get : 140 There are 4 digits, so divide 140 by 4, We get 140/4 = 35 answer.
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What is the geometric mean of 20 and 30? • • • •
Let us multiply these two numbers: We get : 600 Now we will get square root of 600 = 24.5 answer.
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What is the difference between simple mean and geometric mean of 9 and 16? • • • • •
Simple mean = (9 + `16) / 2 = 12.5 Geometric mean = sqrt( 9 * 16) = sqrt (144) = 12 Thus the difference of simple mean and geometric mean is .5 only.
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What is harmonic mean of 20 and 30? • Let us convert 20 into 1/20 and 30 into 1/30 • Now add these : 1/20 + 1/30 = ( 50 / 600), this is equal to 1/12 • Now multiply this by ½ • 1/12 * ½ = 1/24 • Now convert it into 24. • This is answer. www.afterschoool.tk
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The average of 5 quantities is 6. The average of 3 of them is 8. What is the average of the remaining two numbers?
• • • •
Total of 5 = 6 * 5 = 30 Total of 3 = 8 * 3 = 24 Thus remaining two have total of 6 Thus their average is = 6/2 = 3 answer.
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The average age of a group of 10 students was 20. The average age increased by 2 years when two new students joined the group. What is the average age of the two new students who joined the group?
• • • • •
Total of the old group = 10 * 20 = 200 New average = 22 New total = 12 * 22 = 264 Total of the new : 264 – 200 = 64 Average of new ones = 64/2 = 32 ans.
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The average weight of a group of 30 friends increases by 1 kg when the weight of their football coach was added. If average weight of the group after including the weight of the football coach is 31kgs, what is the weight of their football coach in kgs?
• New average = 31, total = 31*31 = 961 • Old average = 30. old total = 30 * 30 = 900 • Thus the weight of coach = 961-900 = 61. www.afterschoool.tk
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If the mean of numbers 28, x, 42, 78 and 104 is 62, then what is the mean of 128, 255, 511, 1023 and x?
• • • • •
There are 5 numbers, 5 * 62 = 310 X = 310 – (28 + 42+78+104) = 58 Average of : 128,255,511,1023,58 = ? Total of : (128+255+511+1023+58) = 1975 Average = 1975/5=395 answer.
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DATA SUFFICIENCY QUESTION…
Is m divisible by 6? • (1) m is divisible by 3 • (2) m is divisible by 4 •
• • • •
ANSWER : We cant get from 1st alone We cant get from 2nd alone We can get from both the statement together.
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Data sufficiency question • • • • • • •
Is y an integer? (1) y^3 is an integer (2) 3y is an integer Answer : Answer cant be drawn from 1st statement Answer cant be drawn from 2nd statement Answer can be drawn from both the statement together
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Explanation…. • Suppose Y = 3 ^(1/3), then , here y^3 is integer, but not y, • Suppose for 2nd statement, Y = 1/3, here 3Y is integer, but Y is not integer, so we are not able to decide. • But if both the conditions are taken together, then we have to take y as an interger itself, thus we can say that Y will definitely be integer. www.afterschoool.tk
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Average age of 5 friends increase by 1 kg when Chiku joins them. Their new average is 64 kg. What is the weight of Chiku?
• Total of 6 = 64*6 = 384 • Total of 5 = 63*5 = 315 • Weight of Chiku = 69 answer.
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What is HCF of 312, 351 and 650? • Let us take HCF of any two of these. • Let us divide 650 by 312, remainder is 26. let us divide 312 by 26, we get zero as remainder. Now let us take 26 and divide 351 by 26, we get : 13 as remainder. Now divide 26 by 13, we get zero as remainder. • Thus 13 is the answer.
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DATA SUFFICIENCY QUESTION • WHAT IS THE VALUE OF Y? • 1. V is 10 multiplied 5. • 2. if we devide 1000 by 20, we get V? • Answer cant be obtained from 1st • Answer cant be obtained from 2nd • Andwer cant be obtained at all. www.afterschoool.tk
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Out of two positive numbers, which mean out of harmonic mean, geometric mean, arithmetic mean will be highest and lowest?
• Arithmetic mean (simple average) is highest and harmonic mean is the least of all these three values.
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Calculate the simple mean, harmonic mean and geometric mean of 40 and 60? • • • • •
Simple mean = 100 / 2 = 50 Harmonic mean = 1/40 + 1/60 = 100/2400 Multiply by ½ = 1/48 ans = 48 Geometric mean = sqrt (40 * 60 ) =48.9 Answer.
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Calculate the simple mean, harmonic mean and geometric mean of 20,40 and 60?
• • • • • • •
Simple mean = (120) / 3 = 40 Harmonic mean : 1/20 + 1/40 + 1/60 =11/120 multiply it by 1/3 = 11/360 Reverse it : 360/11 = 32.7 Geometric mean : Cubic root (20 * 40 * 60) = 36.34 answer.
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When do we always use harmonic mean? • For finding average of speed,
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Afterschooolian Ram comes to afterschoool at the speed of 50 km per hour, but goes back to home at the speed of 80 km per hour, what is the average speed?
• • • • • •
We will calculate harmonic mean here : 1/50 + 1/80 = 130 / 4000 Now multiply it by ½ = 130 / 8000 Reverse it : 8000/130 = 61.5 answr.
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What is BODMAS? • • • • • •
B= bracket O = of D = division M = multiply A = addition S = subtraction
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What will be outcome of : 9- 9 * 9 / 9 + 9 *9 -9? • • • • •
First solve / 9 – 9 *1 + 9*9 – 9 Now solve * 9 – 9 + 81 – 9 =72 answer.
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What will be outcome of : 9- 9 * 9 / 9 + 9 *9 -9? If it is given that – actually means /, / actually means +, + actually means * and * actually means -?
• • • •
9/ 9 - 9 +9 * 9 -9 /9 First solve for / =1 – 9 +9 *9 – 1 Now solve for * = 1 – 9 +81 – 1 We get = 72 answer.
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What is the HCF of 1938 and 2736? • Use division method. • Divide 2736 by 1938, we get 798 as remainder. Now divide 1938 by 798, we get 342 as remainder. Now divide 798 by 342, we get 114 as remainder, now divide 342 by 114, we get nil as remainder. Thus HCF is 114.
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What is the HCF of 370 and 592? • Divide 592 by 370, we get 222 as the remainder. Now divide 370 by 222, we get 148 as the remainder, now divide 222 by 148, we get 74 as the remainder. Now divide 148 by 74, the remainder is nil. • Thus HCF is 74 answer.
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what is the least number of square tiles required for a room of size 1440 inch by 2000 inch. The tiles are in square inch.
• • • • • • •
Step 1. find HCF of 1440 and 2000 = HCF = 80 Area of room = 1440 * 2000 Area of tile = 80 * 80 Number of tiles require = (1440*2000) / (80*80) =450 answer
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what is the least number of square tiles required for a room of size 15.17 m X 9.02 m. . The tiles are in square cm.
• 814 answer.
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If you have exactly 3 times as many oranges as apples in your fruit-bowl, which of the following CANNOT be the number of oranges and apples in your fruit bowl?
• • • • • •
(1)68 (2) 72 (3)54 (4) 44 SOLUTION: (3) only 54 is not divisible by 4.
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A certain company retirement plan has a “rule of 70” provision that allows an employee to retire when the employee’ s age plus years of employment with the company total at least 70. In what year could a female employee hired in 1986 on her 30 birthday first be eligible to retire under this provision?
• • • •
(1) 2026 (2) 2006 (3) 2016 (4) 2020
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Solution… • 70 – 30 = 40 • 40/2 = 20 • Let us add 20 to 1986 (year of appointment), we get 2006 as the year of her retirement.
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What is the smallest integer n for which 25^n> 5^12.?
• • • • • •
(1) 7 (2) 6 (3) 8 (4) 9 Solution: (1), as it will be equal at 6.
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What is the units digit of (l3)^4 (17)^2(29)^3? • • • • • •
(1) 1 (2) 2 (3) 3 (4) 4 Solution (1)
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The present ratio of students to faculty at a certain B-School is 30 to 1. If the student enrollment were to increase by 50 students, the number of faculty were to increase by 5, the ratio of students to faculty would then be 25 to 1. What is the present number of faculty?
• • • •
(1) 15 (2) 6 (3)40 (4) 8
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Solution… • • • • •
Let us assume the number of students = x (30x + 50) / (x+ 5)= 25/1 30x + 50 = 25x + 125 5x = 75 X = 15 answer.
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In a group of 120 members, one fifth are adult men, one-fourth are adult women and the rest are children. The average age of women is fivesixth of the average age of men. The average age of children is one-fourth of the average age of men. If the average age of men is 60 years, then the average of 120 members is ?
• • • •
(1) (2) (3) (4)
32.50 years 32.75 years 32.85 years 32.95 years
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Solution… • • • • • • • •
No. of men : 120/5 = 24 No. of women 120/4 = 30 Children = 66 Age of man = 60 *24 Age of woman = 50*30 Age of children = 15*66 Total age of all : 3930 of 120 persons Average = 32.75 answer.
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If x is equal to the sum of the even integers from 40 to 60 inclusive, and y is the number of even integers from 40 to 60 inclusive, what is the value of x+y? • • • •
(1) 572 (2) 561 (3)560 (4) 551
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Solution… • • • • •
=40+42+44+46+48+50+52+54+56+58+60 X = 550 Y = 11 =total of x+y = 561 Answer : (2)
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The number of diagonals of a regular decagon will be —
• • • •
(1) 10 (2) 120 (3) 45 (4) 35
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The odds in favour of Team India winning of a Test in 3-series Test-Cricket are 7:4 against the Australian team. If three games are to be played in the 3-series Test-Cricket, what are the odds in favour of the Team India’s winning at least one game?
• • • •
(1) 21: 12 (2) 1267 : 64 (3) 1:3 (4) 64 : 131
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Solution… • • • • • •
India can loose in all the games as : 4 / 11 * 4/11 * 4/11 =64 / 1331 Thus probability of at least one game : 1- 64/1331 = 1267 / 1331 Thus odds in favour of at least one victory is : 1267: 64 answer.
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The figure below shows the lengths of the sides of an equi-angular polygon. What is the area of the polygon?
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Solution…. • The sides are either 1 or sqrt(2). We know that diagonal is sqrt(2) * side. Thus the cross sides have actual side of 1 each if we consider it a square. Thus we have 2 squares of 1 side each. Deducted from an area of 3*3 = 9 – (2) = the area is 7 answer.
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In the figure below, ABC is an equilateral triangle having each side 4cm. ABC is formed by joining the centres A, B and C of the three circles where the radius of each circle is 2 cm. The area of the shaded portion is —
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Solution… • • • • •
Each angle of the triangle is 60 degree. Let us find area of circle : Pi * radius * radius =22/7*2*2= 12.57 The area of side of square taken by triangle is : 12.57 * 60/360 = 2.095 • Thus area of shaded region = • (sqrt(3)/4 *4*4) – (3*2.095) = .643 answer. • (instead of taking this exercise, you may take half circle as the area of un-shaded region of the trinagle). www.afterschoool.tk
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In how many ways can 5 boys and 3 girls be arranged in a row so that no two girls may sit together side by side?
• • • •
(1) 120 (2) 14400 (3) 126 (4) 3360
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Solution… • • • • •
There are 6 places for girls. 6p3 * 5! 6!/(3!) *5! =14400 answer. GBGBGBGBGBG
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In a certain B-School, of 110 students only 30 students have enrolled in Computer Science; 35 students have enrolled in Marketing; and only 20 students have enrolled in the courses in the first term. How many students of 110 have not enrolled in any of these two courses?
• • • • • •
(1) 45 (2) 65 (3) 15 (4) 25 Solution (4)
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The price of a commodity is increased by 20% and its consumption is decreased by 10%. Then the net % change in expenditure of a person will be
• Option: (1) 10% increase (2) 8% increase (3) 10% decrease (4) none of these • Solution…. • There is 8% increase in the consumption … www.afterschoool.tk
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Basic quantitative aptitutude and reasoning Dr. T.K. Jain.
AFTERSCHO☺OL Centre for social entrepreneurship Bikaner M: 9414430763 [email protected] www.afterschool.tk, www.afterschoool.tk
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How many prime factors are there in 60? • • • • •
60 divided by 2 30, divided by 2 15 divided by 3 5 divided by 5 Prime factors : 2,3,5 (three) answer
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What is the minimum fraction divisible by 2/3, 4/5 and 3/7? • We have to calculate here LCM (least common multiple) of these three fractions.. • Every fraction has two parts : • 1. numerator (2,4,3) • 2. denominator (3,5,7) • Calculate LCM of numerators • Calculate HCF of denominators • LCM of numerator = 12 • HCF of denominator = 1 (3,5,7 are prime numbers) • Write it as fraction : 12/ 1 (this is the answer) . www.afterschoool.tk
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What is the square root of 15625? • • • • • • • •
Let us divide it by 5, we get : 3125 Now again divide by 5 = 625 Now again divide by 5 = 125 Now again divide by 5 = 25 Now again divide by 5 = 5 Again divide by 5 = nil. Thus we have 5^6 =15625 Thus square root is 5^3 = 5*5*5 = 125 .
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What is the square root of .25? • • • • • •
We can write it as 25/100 Factors of 25 = 5*5 = 5^2 Square root of 25 = 5^1 Factors of 100 = 10^2 Square root of 100 = 10^1 Thus answer = 5/10 = .5 answer
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What is the square root of .09? • • • • • •
We can write it as 9/100 Factors of 9 = 3*3 = 3^2 Square root of 9 = 3^1 Factors of 100 = 10^2 Square root of 100 = 10^1 Thus answer = 3/10 = .3 answer
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What is the square root of .04? • • • • • •
We can write it as 4/100 Factors of 4 = 2*2 = 2^2 Square root of 4 = 2^1 Factors of 100 = 10^2 Square root of 100 = 10^1 Thus answer = 2/10 = .2 answer
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What is cubic root of 64? • • • • • • • • •
Let us find the factors of 64 Divide 64 by 2 = 32 Divide by 2 again = 16 Divide by 2 again = 8 Divide by 2 again = 4 Divide by 2 again = 2 Divide by 2 again = nil We can say 2^6 = 64, divide the power by 3 Cubic root = 2^2 = 4 ans
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AFTERSCHO☺OL's MATERIAL FOR PGPSE PARTICIPANTS
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What is cubic root of .064? • • • •
We can write it as : 64/ 1000 Cubic root of 64 = 4 Cubit root of 1000 = 10 Thus answer = 4/10 = .4 answer
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What is cubic root of .ooooo8? • • • •
We can write it as : 8/ 1000000 Cubic root of 8 = 2 Cubit root of 1000000 = 100 Thus answer = 2/100 = .02 answer
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What is cubic root of .o27? • • • •
We can write it as : 27/1000 Cubic root of 27 = 3 Cubit root of 1000 = 10 Thus answer = 3/10 = .3 answer
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What is the LCM of 60,64,68? • LCM (least common multiple) is always bigger than these numbers. • Find factors of these numbers: • 60 = 2*2*3*5 • 64 = 2^6 • 68= 2*2 *17 • Taking highest powers = 2^6*3^1*5^1*17^1 = 16320 answer. www.afterschoool.tk
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What is the HCF of 64, 160,128? • HCF (highest common factor) is always less than these numbers • Let us find the factors of these numbers: • 64 = 2^6 • 160 = 2*2*2*2*2*5 • 128 = 2^7 • Now pick up the factors which is there in each of these with minimum power : =2^5 www.afterschoool.tk
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What is HCF of 140,180 and 210? • • • •
Factors of 140 = 2*2*5*7 Factors of 180 = 2*2*3*3*5 Factors of 210 = 2*3*5*7 Now we can find that 2*5 is there in each of these numbers, so HCF is 10. answer.
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What is the LCM of 8, 10 , 12? • • • •
Factors of 8 = 2^3 Factors of 10 = 2*5 Factors of 12 = 2*2*3 Let us combine all these with highest powers : • 2^3 *3*5 = 120 answer
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What is the mean (simple average) of 20, 30,40,50? • • • •
Add them all We get : 140 There are 4 digits, so divide 140 by 4, We get 140/4 = 35 answer.
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What is the geometric mean of 20 and 30? • • • •
Let us multiply these two numbers: We get : 600 Now we will get square root of 600 = 24.5 answer.
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What is the difference between simple mean and geometric mean of 9 and 16? • • • • •
Simple mean = (9 + `16) / 2 = 12.5 Geometric mean = sqrt( 9 * 16) = sqrt (144) = 12 Thus the difference of simple mean and geometric mean is .5 only.
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What is harmonic mean of 20 and 30? • Let us convert 20 into 1/20 and 30 into 1/30 • Now add these : 1/20 + 1/30 = ( 50 / 600), this is equal to 1/12 • Now multiply this by ½ • 1/12 * ½ = 1/24 • Now convert it into 24. • This is answer. www.afterschoool.tk
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The average of 5 quantities is 6. The average of 3 of them is 8. What is the average of the remaining two numbers?
• • • •
Total of 5 = 6 * 5 = 30 Total of 3 = 8 * 3 = 24 Thus remaining two have total of 6 Thus their average is = 6/2 = 3 answer.
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The average age of a group of 10 students was 20. The average age increased by 2 years when two new students joined the group. What is the average age of the two new students who joined the group?
• • • • •
Total of the old group = 10 * 20 = 200 New average = 22 New total = 12 * 22 = 264 Total of the new : 264 – 200 = 64 Average of new ones = 64/2 = 32 ans.
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AFTERSCHO☺OL's MATERIAL FOR PGPSE PARTICIPANTS
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The average weight of a group of 30 friends increases by 1 kg when the weight of their football coach was added. If average weight of the group after including the weight of the football coach is 31kgs, what is the weight of their football coach in kgs?
• New average = 31, total = 31*31 = 961 • Old average = 30. old total = 30 * 30 = 900 • Thus the weight of coach = 961-900 = 61. www.afterschoool.tk
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If the mean of numbers 28, x, 42, 78 and 104 is 62, then what is the mean of 128, 255, 511, 1023 and x?
• • • • •
There are 5 numbers, 5 * 62 = 310 X = 310 – (28 + 42+78+104) = 58 Average of : 128,255,511,1023,58 = ? Total of : (128+255+511+1023+58) = 1975 Average = 1975/5=395 answer.
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DATA SUFFICIENCY QUESTION…
Is m divisible by 6? • (1) m is divisible by 3 • (2) m is divisible by 4 •
• • • •
ANSWER : We cant get from 1st alone We cant get from 2nd alone We can get from both the statement together.
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Data sufficiency question • • • • • • •
Is y an integer? (1) y^3 is an integer (2) 3y is an integer Answer : Answer cant be drawn from 1st statement Answer cant be drawn from 2nd statement Answer can be drawn from both the statement together
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Explanation…. • Suppose Y = 3 ^(1/3), then , here y^3 is integer, but not y, • Suppose for 2nd statement, Y = 1/3, here 3Y is integer, but Y is not integer, so we are not able to decide. • But if both the conditions are taken together, then we have to take y as an interger itself, thus we can say that Y will definitely be integer. www.afterschoool.tk
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Average age of 5 friends increase by 1 kg when Chiku joins them. Their new average is 64 kg. What is the weight of Chiku?
• Total of 6 = 64*6 = 384 • Total of 5 = 63*5 = 315 • Weight of Chiku = 69 answer.
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What is HCF of 312, 351 and 650? • Let us take HCF of any two of these. • Let us divide 650 by 312, remainder is 26. let us divide 312 by 26, we get zero as remainder. Now let us take 26 and divide 351 by 26, we get : 13 as remainder. Now divide 26 by 13, we get zero as remainder. • Thus 13 is the answer.
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DATA SUFFICIENCY QUESTION • WHAT IS THE VALUE OF Y? • 1. V is 10 multiplied 5. • 2. if we devide 1000 by 20, we get V? • Answer cant be obtained from 1st • Answer cant be obtained from 2nd • Andwer cant be obtained at all. www.afterschoool.tk
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Out of two positive numbers, which mean out of harmonic mean, geometric mean, arithmetic mean will be highest and lowest?
• Arithmetic mean (simple average) is highest and harmonic mean is the least of all these three values.
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Calculate the simple mean, harmonic mean and geometric mean of 40 and 60? • • • • •
Simple mean = 100 / 2 = 50 Harmonic mean = 1/40 + 1/60 = 100/2400 Multiply by ½ = 1/48 ans = 48 Geometric mean = sqrt (40 * 60 ) =48.9 Answer.
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Calculate the simple mean, harmonic mean and geometric mean of 20,40 and 60?
• • • • • • •
Simple mean = (120) / 3 = 40 Harmonic mean : 1/20 + 1/40 + 1/60 =11/120 multiply it by 1/3 = 11/360 Reverse it : 360/11 = 32.7 Geometric mean : Cubic root (20 * 40 * 60) = 36.34 answer.
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When do we always use harmonic mean? • For finding average of speed,
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Afterschooolian Ram comes to afterschoool at the speed of 50 km per hour, but goes back to home at the speed of 80 km per hour, what is the average speed?
• • • • • •
We will calculate harmonic mean here : 1/50 + 1/80 = 130 / 4000 Now multiply it by ½ = 130 / 8000 Reverse it : 8000/130 = 61.5 answr.
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What is BODMAS? • • • • • •
B= bracket O = of D = division M = multiply A = addition S = subtraction
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What will be outcome of : 9- 9 * 9 / 9 + 9 *9 -9? • • • • •
First solve / 9 – 9 *1 + 9*9 – 9 Now solve * 9 – 9 + 81 – 9 =72 answer.
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What will be outcome of : 9- 9 * 9 / 9 + 9 *9 -9? If it is given that – actually means /, / actually means +, + actually means * and * actually means -?
• • • •
9/ 9 - 9 +9 * 9 -9 /9 First solve for / =1 – 9 +9 *9 – 1 Now solve for * = 1 – 9 +81 – 1 We get = 72 answer.
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What is the HCF of 1938 and 2736? • Use division method. • Divide 2736 by 1938, we get 798 as remainder. Now divide 1938 by 798, we get 342 as remainder. Now divide 798 by 342, we get 114 as remainder, now divide 342 by 114, we get nil as remainder. Thus HCF is 114.
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What is the HCF of 370 and 592? • Divide 592 by 370, we get 222 as the remainder. Now divide 370 by 222, we get 148 as the remainder, now divide 222 by 148, we get 74 as the remainder. Now divide 148 by 74, the remainder is nil. • Thus HCF is 74 answer.
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what is the least number of square tiles required for a room of size 1440 inch by 2000 inch. The tiles are in square inch.
• • • • • • •
Step 1. find HCF of 1440 and 2000 = HCF = 80 Area of room = 1440 * 2000 Area of tile = 80 * 80 Number of tiles require = (1440*2000) / (80*80) =450 answer
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what is the least number of square tiles required for a room of size 15.17 m X 9.02 m. . The tiles are in square cm.
• 814 answer.
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If you have exactly 3 times as many oranges as apples in your fruit-bowl, which of the following CANNOT be the number of oranges and apples in your fruit bowl?
• • • • • •
(1)68 (2) 72 (3)54 (4) 44 SOLUTION: (3) only 54 is not divisible by 4.
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A certain company retirement plan has a “rule of 70” provision that allows an employee to retire when the employee’ s age plus years of employment with the company total at least 70. In what year could a female employee hired in 1986 on her 30 birthday first be eligible to retire under this provision?
• • • •
(1) 2026 (2) 2006 (3) 2016 (4) 2020
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Solution… • 70 – 30 = 40 • 40/2 = 20 • Let us add 20 to 1986 (year of appointment), we get 2006 as the year of her retirement.
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What is the smallest integer n for which 25^n> 5^12.?
• • • • • •
(1) 7 (2) 6 (3) 8 (4) 9 Solution: (1), as it will be equal at 6.
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What is the units digit of (l3)^4 (17)^2(29)^3? • • • • • •
(1) 1 (2) 2 (3) 3 (4) 4 Solution (1)
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The present ratio of students to faculty at a certain B-School is 30 to 1. If the student enrollment were to increase by 50 students, the number of faculty were to increase by 5, the ratio of students to faculty would then be 25 to 1. What is the present number of faculty?
• • • •
(1) 15 (2) 6 (3)40 (4) 8
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Solution… • • • • •
Let us assume the number of students = x (30x + 50) / (x+ 5)= 25/1 30x + 50 = 25x + 125 5x = 75 X = 15 answer.
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In a group of 120 members, one fifth are adult men, one-fourth are adult women and the rest are children. The average age of women is fivesixth of the average age of men. The average age of children is one-fourth of the average age of men. If the average age of men is 60 years, then the average of 120 members is ?
• • • •
(1) (2) (3) (4)
32.50 years 32.75 years 32.85 years 32.95 years
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Solution… • • • • • • • •
No. of men : 120/5 = 24 No. of women 120/4 = 30 Children = 66 Age of man = 60 *24 Age of woman = 50*30 Age of children = 15*66 Total age of all : 3930 of 120 persons Average = 32.75 answer.
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If x is equal to the sum of the even integers from 40 to 60 inclusive, and y is the number of even integers from 40 to 60 inclusive, what is the value of x+y? • • • •
(1) 572 (2) 561 (3)560 (4) 551
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Solution… • • • • •
=40+42+44+46+48+50+52+54+56+58+60 X = 550 Y = 11 =total of x+y = 561 Answer : (2)
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The number of diagonals of a regular decagon will be —
• • • •
(1) 10 (2) 120 (3) 45 (4) 35
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The odds in favour of Team India winning of a Test in 3-series Test-Cricket are 7:4 against the Australian team. If three games are to be played in the 3-series Test-Cricket, what are the odds in favour of the Team India’s winning at least one game?
• • • •
(1) 21: 12 (2) 1267 : 64 (3) 1:3 (4) 64 : 131
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Solution… • • • • • •
India can loose in all the games as : 4 / 11 * 4/11 * 4/11 =64 / 1331 Thus probability of at least one game : 1- 64/1331 = 1267 / 1331 Thus odds in favour of at least one victory is : 1267: 64 answer.
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The figure below shows the lengths of the sides of an equi-angular polygon. What is the area of the polygon?
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Solution…. • The sides are either 1 or sqrt(2). We know that diagonal is sqrt(2) * side. Thus the cross sides have actual side of 1 each if we consider it a square. Thus we have 2 squares of 1 side each. Deducted from an area of 3*3 = 9 – (2) = the area is 7 answer.
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In the figure below, ABC is an equilateral triangle having each side 4cm. ABC is formed by joining the centres A, B and C of the three circles where the radius of each circle is 2 cm. The area of the shaded portion is —
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Solution… • • • • •
Each angle of the triangle is 60 degree. Let us find area of circle : Pi * radius * radius =22/7*2*2= 12.57 The area of side of square taken by triangle is : 12.57 * 60/360 = 2.095 • Thus area of shaded region = • (sqrt(3)/4 *4*4) – (3*2.095) = .643 answer. • (instead of taking this exercise, you may take half circle as the area of un-shaded region of the trinagle). www.afterschoool.tk
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In how many ways can 5 boys and 3 girls be arranged in a row so that no two girls may sit together side by side?
• • • •
(1) 120 (2) 14400 (3) 126 (4) 3360
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Solution… • • • • •
There are 6 places for girls. 6p3 * 5! 6!/(3!) *5! =14400 answer. GBGBGBGBGBG
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In a certain B-School, of 110 students only 30 students have enrolled in Computer Science; 35 students have enrolled in Marketing; and only 20 students have enrolled in the courses in the first term. How many students of 110 have not enrolled in any of these two courses?
• • • • • •
(1) 45 (2) 65 (3) 15 (4) 25 Solution (4)
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The price of a commodity is increased by 20% and its consumption is decreased by 10%. Then the net % change in expenditure of a person will be
• Option: (1) 10% increase (2) 8% increase (3) 10% decrease (4) none of these • Solution…. • There is 8% increase in the consumption … www.afterschoool.tk
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About AFTERSCHO☺OL • PGPSE - World’s most comprehensive programme on social entrepreneurship – after class 12th • Flexible – fast changing to meet the requirements • Admission open throughout the year • Complete support from beginning to the end – from idea generation to making the project viable. www.afterschoool.tk
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Branches of AFTERSCHO☺OL • PGPSE programme is open all over the world as free online programme. • Those who complete PSPSE have the freedom to start branches of AFTERSCHO☺OL • A few branches have already started one such branch is at KOTA (Rajasthan).
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Workshop on social entrepreneurship
• We conduct workshop on social entrepreneurship – all over India and out of India also - in school, college, club, association or any such place - just send us a call and we will come to conduct the workshop on social entrepreeurship. • These workshops are great moments of learning, sharing, and commitments. www.afterschoool.tk
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FREE ONLINE PROGRAMME • AFTERSCHO☺OL is absolutely free programme available online – any person can join it. The programme has four components : • 1. case studies – writing and analysing – using latest tools of management • 2. articles / reports writing & presentation of them in conferences / seminars • 3. Study material / books / ebooks / audio / audio visual material to support the study • 4. business plan preparation and presentations of those plans in conferences / seminars www.afterschoool.tk
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100% placement / entrepreneurship
• AFTERSCHO☺OL has the record of 100% placement / entrepreneurship till date • Be assured of a bright career – if you join AFTERSCHO☺OL
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Pursue professional courses along with PGPSE
• AFTERSCHO☺OL permits you to pursue distance education based professional / vocational courses and gives you support for that also. Many students are doing CA / CS/ ICWA / CMA / FRM / CFP / CFA and other courses along with PGPSE. • Come and join AFTERSCHO☺OL
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