Important Formulas: Simplification & Approximation | SSC CGL Tier 2 - Study Material, Online Tests, Previous Year PDF Download

Simplification & Approximation

The simplification and approximation topic is one of the easiest in the numerical ability section and only efficient calculation can help a candidate solve questions from this section easily.
The main idea behind asking questions from the approximation and simplification topic is to test the ability of a candidate to work with numbers and basic calculations.
Questions are made to confuse the candidates with long decimal numbers and calculations which may seem complicated but this topic is one where a candidate can score most without making errors. 

The simplification questions can be asked in two ways:

• Missing numbers – An equation can be given in the paper and candidates need to fill the blank in that equation, given either in LHS (Left-hand side) or RHS (Right-hand side).
  For example, 252 – _____ + 100 = 5 × 45 + 275. 
• Simplifying the equation –  The second way in which the simplification questions may be asked is the direct way of giving an equation and solving it to find the answer. For example: 252 – 225 + 100 = ?. In such questions, candidates have to answer what comes in place of the question mark (?)

Solve Simplification/ Approximation Questions

To ensure that the candidate does not lose marks in this topic, there are some basic tips and tricks which may be used to solve the approximation and simplification questions. Refer to the tips given below:

• Always solve the Approximation or simplification questions following the BODMAS rule. 
• Numbers which are given in a decimal format, use a rounded-off value for those numbers. For example, 45.62 can be taken as 46, 22.10 can be taken as 22, etc. 
• Learning tables till at least 20 can be of great help for the candidates and help them save some time
• Remember the basic important formulas which can be used in such question:
  • (a+b)² = a² + b² + 2ab
  • (a-b)² = a² + b² – 2ab
  • a² – b² = (a+b) (a-b)
  • a³ + b³ = (a+b) (a² – ab + b²)
  • (a+b)³ = a³ + b³ + 3ab (a+b)
  • (a-b)³ = a³ – b³ – 3ab (a-b)
• Do not overcomplicate the questions and make sure that long calculations need to be skipped in order to solve the equations within the shorter time period

The image given below shows what is the BODMAS rule as mentioned in the first point of tips:

Example 1: 98/3 % of 769.002 + 24% of 160.89 – 67.9900=?
(a) 220
(b) 224
(c) 225
(d) 226
(e) 227
Ans: (d)
Divide the question into parts,
(98/3 % of 769.002) + (24% of 160.89) – 67.9900
⇒ 98/3 % of 769.002 = 33% × 769 = 254.77 = 255 —– (1)
⇒ 24% of 160.89 = 24% × 161 = 38.64 = 39 —– (2)
Finally,
255 + 39 – 68 = 294 – 68 = 226

Example 2: What shall come in place of question mark (?)
794.89 ÷ 15.001+ 767.99 ÷ 12.001 – 1273.012 ÷ 18.9968=?
(a) 42
(b) 35
(c) 50
(d) 55
(e) 47
Ans: (c)
As per BODMAS,
The division needs to be done first.
794.89 ÷ 15.001 = 795 ÷ 15 = 53
767.99 ÷ 12.001 = 768 ÷ 12 = 64
1273.012 ÷ 18.9968 = 1273 ÷ 19 = 67
So, 53 + 64 – 67 = 117 – 67 = 50