## Test of Quantitative Aptitude

The Quantitative  Aptitude Section of Success Bureau Study Material covers the complete syllabus and includes  Often Asked Questions ( OAQs) in the Competitive Examinations .

Hence, you are advised to properly learn and practice  the contents .  You should not waste time in learning out dated  books .

Below is given a small Sample of the Study Material provided to the students along with the Quizzes .

We have included the following two Chapters  in our Sample Study Material  :

• Square Root & Cube Root
• Percentage

## Square Root & Cube Root​

SQUARE – If a number is multiplied by itself , the product is called the Square of  the number.

SQUARE ROOT ( Vargmool ) of a number is that number which when multiplied by itself is equal the given number. Thus , 3 is the square root of 9 and 4 is the square root of 16 .

The Square root of a number is indicated by the symbol   √     Or    √¯ .     Thus, √9 = 3 , √16 = 4 ,  √25 = 5 .

Similarly, √9  = √3×3 = 3 ; √16 = √4×4 = 4 ; √25 = √5×5 = 5 etc .

Note  :  The square root of 1 is 1.

## TABLE - 1

Numbers & Their Squares

 1 1 2 4 3 9 4 16 5 25 6 36 7 49 8 64 9 81 10 100 11 121 12 144 13 169 14 196 15 225 16 256 17 289 18 324 19 361 20 400 21 441 22 284 23 529 24 576 25 625 26 676 27 729 28 784 29 841 30 900

## TABLE – 2

Numbers & Their Cubes

 1 1 ( ie. 1 x 1 x 1  ) 2 8 3 27 4 64 5 125 6 216 7 343 8 512 9 729 10 1000 11 1331 12 1728 13 2197 14 2744 15 3375 16 4096 17 4913 18 5032 19 6859 20 8000 21 9261 22 10648 23 12167 24 13824 25 15625 26 17576 27 19683 28 21952 29 24389 30 27000

## Under Roots & Their Values

 √2  = 1.41421 √5  = 2.23607 √3  = 1.73205 √7  = 2.65 √10  = 3.16 √15  = 3.873

## A Fraction, whose Denominator is 100, is called the Percentage or Rate Percentage and the Numerator of the Fraction is Denoted by % .

For example, 25% means 25 out of 100 This can be expressed  as 25 / 100  =  1/ 4

Similarly, 100%  means 100 / 100 = 1.

## Percentage Rule - 2

(A)    Multiply by 100 if you want to Show a Certain Number in % .

(B)    Divide by 100 if you want to  Remove % Sign from a Certain Number .

Examples :  Q.1      2 / 10 as a rate per cent is  ?

Solution :  2 / 10 x 100 = 20% .

Q.2    3.793 as a rate per cent is  ?

Solution : 3.793 x 100 = 379.3 %

Q.3     20% =  ?

Solution :  20 / 100 = 1 / 5

Q.4    3.768 % =  ?

Solution :  3.768 / 100 = 0.03768

## Percentage Rule - 3

In Competitive Examinations, the Questions Based on the Following Relationship of A, B and C, are Often Asked :

 A  %  of  B  = C

In such problems, You  are  required to find out the Value of Any of the Three ( i.e. A, B or C ) on the basis of the Given Values of any Two .

These Problems can be Easily Solved in the following way  :

 A = C x  100 / B B = C x 100 / A C = A x B / 100

Examples :  Q.1   Find out the value of X if X % of 200 is equal to 50 .

Solution :    X = 50 x 100 / 200 = 25

Q.2   20 is what % of 80 or X % of 80 is 20 ?

Solution  :  X = 20 x 100 / 80 = 25 %

Q.3       40% of 600 is equal to what ?

Solution :    Suppose, 40% of 600 = X .  Hence , X = 40 x 600 / 100 = 240

Memories the following relationships given in the Chart below. It will help you in solving  the percentage questions quickly  :

## CHART - 1

 5 % = 1/20 55  % = 11/20 10 % = 1/10 65 % = 13/20 15 % = 3/20 85 % = 17/20 20 % = 1/5 75 % = 3/4 25 % = 1/4 50 % = 1/2 35 % = 7/20 100 % = 1 40 % = 2/5 45 % = 9/20

From the above chart we can see that for obtaining 5% of a certain number, we have to divide the number by 20 and so on .

## CHART - 2

 100  %  =  1  i.e. Whole of anything 200 %  =  two times of anything Similarly,50 % = 1 / 2   of anything 25 % = 1 / 4  of anything 20 % = 1 / 5   of anything 10 % = 1 / 10  of anything 100 % of 10 will be 10  x  1  =  10 200 % of 10 will be 10  x  2  =  20 400 % of 10 will be 10  x  4  =  40 50 % of 10 will be   10 x 1 / 2 = 5 25 % of 10 will be  10 x 1 / 4  = 25 10 % of 10 will be 10 x 1 / 10 = 1

Examples :

Q.1      5% of 80 = ?

Solution  : 80 x 1/20 = 4

Q.2       20% of 400 = ?

Solution  : 400 x 1/5 = 80

Q.3   35% of 900 = ?

Solution  :  900 x 7/20 = 315

Q.4   12.5% of 200 = ?

Solution  :  200 X 1/8  = 25

Q.5. Two numbers are respectively 20% and 40% more than a third number. What is the ratio of the two numbers ?

Solution :  Suppose the third number is 100 .

Hence, the Ist and IInd numbers would naturally be 120 and 140 respectively. Ratio = 120 : 140 = 6 : 7.

Q.6. A Regiment lost in an engagement 25% of its men and still had 300 men left . What was the original number of men in the regiment ?

Solution :  75% ( or 3/4th ) of original men    =  300   .   Hence , Original men = 300 x 4/3   =  400

Q.7. The number of seats for admission for a vocational course is increased by 15% every year. If the number of students in 2017 is 800, what is the expected number of students in 2019 ?

Solution :  The no. of seats increases by 15% ever year.       So,   800 x 115 / 100 x 115 / 100  =  1058

Q.8. 30% of A’ s salary is equal to the 20% of 3/5th of B’ s salary. If B’s salary is Rs. 24,000/- , what is A’s salary ?

Solution :         Suppose A’s salary is  Rs. X.

Then, 3X / 10 = 1 / 5 x 3 / 5 x 24000/-       ( 30% = 3/10  ,  20% = 1/5 )      Or      X = Rs. 9600/-

Q.9. In a library, 40% of the total number of books are in English, 80% of the rest in Hindi and the balance 300 books are in other languages. What is the total number of books in the library ?

Solution  : Suppose total number of books = X

Hence, 40% of  X + 80% of ( X – 40% ) + 300 = X  Or 2X / 5 + 4 / 5 ( X – 2X / 5 ) + 300 = X  Or    X = 2500

Q.10. After deducting 20% from a certain sum and then 25% from the remainder, there are Rs.1200/- left .  Find the original sum .

Solution : Suppose the original sum was Rs. X.   After deducting 20%, 80% of X is left .

Then after deducting 25% of the remainder 75% of it would be left which is equal to Rs. 1200/-

The whole process can be shown like this : 4X / 5 x 3 / 4 = 1200  ( 80% = 4 / 5 , 75%  = 3 / 4

Or    X  =  Rs. 2000

## SPECIAL NOTE

The Quantitative Aptitude  Section of Success Bureau Study Material covers the complete syllabus and includes  Often Asked Questions

( OAQs)  in the Competitive Examinations .

Hence, you are advised to properly learn the Study Material and practice  .  You should  not waste time in learning out dated  books .

The above is given a small Sample of the Study Material provided to the students along with the Quizzes .