Basic Number System

1. NUMBER SYSTEM
QUANTITATIVE APTITUDE

2. Introduction
• Real Numbers : Decimals (fractions),
Integers (No Decimals)
• Decimals : RATIONAL – Finite (Terminating
Decimal 2.7, 3.4)
Infinite (Non Terminating
Repeating Decimal 2.1212, 2.66)
IRRATIONAL – Non terminating
Non repeating decimal 2.5813, ∏

3. Introduction
• Integers : Negative, Zero, Positive
• Natural Numbers : Positive Integers 1,2,3,4..
• Whole Numbers : Includes 0.. 0,1,2,3…
• 1 = Neither prime Nor Composite

4. Introduction
• Face Value : 1, 2, 3 is face value. In 34562 the
face value of 2 and 3 is 2 and 3 respectively.
• Place Value : In 34562 the place value of 2
and 3 is 2 and 30000 respectively and 5 is 500.

5. Formulae
• Sum of first N natural numbers :
Sn = n(n+1) / 2
• Sum of squares first N natural numbers :
Sn = n(n+1)(2n +1) / 6
• Sum of cubes first N natural numbers :
Sn = [n(n+1) / 2]2

6. • Sum of first N odd natural numbers :
Sn = [n]2
• Sum of first N even natural numbers :
Sn = n(n+1)
Formulae

7. Tips
• (xn – an) is completely divisible by (x + a) when n is
even number.
• (xn + an) is completely divisible by (x + a) when n is
odd number.
• What is the remainder when 17200 is divided by
18?
(17200 – 1200) is completely divisible by (17 + 1) as
200 is even number. So when 17200 is divided by
18 remainder is 1.

8. Contd..
• If 232 + 1 is completely divisible by a whole
number, which number is completely divisible
by this number?
• Lets assume 232 + 1 = x + 1
296 + 1 = {(232 ) 3 + 1} = (x 3 + 1)
= (x + 1)(x2 – x + 1)

9. Contd..
• What is the common factor of (22121 + 19121 )
and (22231 + 19231 )
• Answer will be 22+19 = 41.
• Since 121 and 231 are odd.

10. Some shortcuts
• Multiplication with base 100 :
• 98*115 =?
• -2*15=-30
• 115-2=98+15=113
• (113*100)-30 = 11300 – 30 = 11270

11. Some shortcuts
• Multiplication with base 300 :
• 297*292 =?
• -3*-8=24
• 297-8=292-3=289
• (289 * 300) + 24 = 86700 + 24 = 86724

12. Some shortcuts
• Multiplication with base 1000 :
• 997*983 =?
• -3*-17=51
• 997-17=983-3=980
• (980*1000)+51 = 980000 + 51 = 980051

13. Problem
• What will be the remainder when (6767 + 67)
is divided by 68?
• (xn + an) is completely divisible by (x + a) when
n is odd number.
• So (6767 + 1) + 66 is when divided by 67+1 (68)
• So remainder will be 66 as (6767 + 1) is
completely divided by 68.