Simplification – Aptitude Questions and Answers

Simplification questions hold a significant position in the Quantitative Aptitude section of various government exams. These questions are designed to test the candidate’s ability to solve complex mathematical problems in a simplified manner. Scoring well in this topic can prove to be a game-changer, as it can help candidates secure a significant number of marks in a short time. This article will discuss the importance of simplification questions, and their weightage in government exams, and provide tips and tricks to help aspirants master this topic.

Practice Quiz:

Practice Simplification Quiz Questions

Simplification Rules

There are several simplification rules that can be applied to solve quantitative aptitude questions efficiently. Some of the most commonly used simplification rules are:

V	Vinculum
B	Remove Brackets  The order is: ( ), { }, [ ]
O	Of
D	Division
M	Multiplication
A	Addition
S	Subtraction

Tips and Tricks to Solve Simplification Questions

• When attempting to solve questions that involve, simplification, it is important to remember the VBODMAS rule. 
• Keep in mind the following formulas to solve the questions accurately:
• (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)
• Always put on a timer while solving questions so that you can solve questions on time.

Simplification Questions are generally presented in two ways – 

1. Missing numbers: Missing numbers are when an equation is given and the candidate must fill in the blanks.

Example: 

Q. What is the missing number in the following expression? (5 + 2) ÷ 7 – 3 x 2 = 1 + ?

Solution: First, simplify the expression on the left-hand side: (5 + 2) ÷ 7 – 3 x 2 = 1 7 ÷ 7 – 6 = 1 1 – 6 = -5 Therefore, the missing number is -5.

2. Simplifying equations: Simplifying equation questions present an equation directly and ask the candidate to find its solution. 

Example:

Q. Simplify the following expression: (4x – 3y + 2z) – (2x + 4y – z) + (5y + z)

Solution: Distribute the negative sign in the second term: = 4x – 3y + 2z – 2x – 4y + z + 5y + z Combine like terms: = 2x – 2y + 8z

Therefore, the simplified expression is 2x – 2y + 8z.

Sample Questions on Simplification

Q1. Simplify the expression 12/3 + 5(2 – 1). 

Solution: 

We can simplify by first evaluating the expressions inside the parentheses: 12/3 + 5(2 – 1) = 4 + 5(1) Then, we can multiply and add: 5(1) = 5 4 + 5 = 9 Therefore, 12/3 + 5(2 – 1) simplifies to 9.

Q2. Simplify the expression 2(4 + 6) – 3(2 + 5). 

Solution:

We can simplify by first evaluating the expressions inside the parentheses: 2(4 + 6) – 3(2 + 5) = 2(10) – 3(7) Then, we can multiply and subtract: 2(10) = 20 and 3(7) = 21 20 – 21 = -1 Therefore, 2(4 + 6) – 3(2 + 5) simplifies to -1.

Q3. Simplify the expression (3x – 7) + (2x + 5) 

Solution:

Combine like terms: (3x – 7) + (2x + 5) = (3x + 2x) + (-7 + 5) = 5x – 2 Therefore, the simplified expression is 5x – 2.

Q4. Simplify the expression 2(3x + 4) – 5x + 2(2x – 3) 

Solution:

Distribute the coefficients: 2(3x + 4) = 6x + 8 2(2x – 3) = 4x – 6 Combining like terms: 6x + 8 – 5x + 4x – 6 = (6x – 5x + 4x) + (8 – 6) = 5x + 2 Therefore, the simplified expression is 5x + 2.

Q5. Simplify the expression (2x + 3y)^2 – (2x – 3y)^2 

Solution: 

Using the difference of squares formula: (a^2 – b^2) = (a + b)(a – b) (2x + 3y)^2 – (2x – 3y)^2 = [(2x + 3y) + (2x – 3y)][(2x + 3y) – (2x – 3y)] = (4x)(6y) = 24xy Therefore, the simplified expression is 24xy.

Q6. Simplify: 5(2x + 3) – 2(3x – 1) + 4x

Solution:

Distribute the coefficients and combine like terms: = 10x + 15 – 6x + 2 + 4x = 8x + 1.

Q7. Simplify: (3a – 2b)² – 4(a + b)²

Solution:

First, square the terms inside the parentheses: = (9a² – 12ab + 4b²) – 4(a² + 2ab + b²) Distribute the negative sign: = 9a² – 12ab + 4b² – 4a² – 8ab – 4b² Combine like terms: = 5a² – 20ab

Q8. Simplify the fraction 3/4 + 1/6.

Solution:

Find a common denominator: 3/4 + 1/6 = (3 x 3)/(4 x 3) + (1 x 2)/(6 x 2) = 9/12 + 2/12 = 11/12. Therefore, the simplified fraction is 11/12.

Q9. Simplify the decimal 0.875.

Solution:

Express the decimal as a fraction: 0.875 = 875/1000. Find the greatest common factor of 875 and 1000: 875 = 5 x 5 x 7 x 2 x 5 1000 = 2 x 2 x 5 x 5 x 5 The greatest common factor is 125. Divide both numerator and denominator by 125: 875/1000 = (875 ÷ 125)/(1000 ÷ 125) = 7/8. Therefore, the simplified decimal is 7/8.

Q10. Simplify the fraction (2/3)/(4/5).

Solution:

Invert the denominator and multiply: (2/3)/(4/5) = (2/3) x (5/4) = 10/12. Reduce the fraction: 10/12 = (10 ÷ 2)/(12 ÷ 2) = 5/6. Therefore, the simplified fraction is 5/6.

Test your knowledge of Simplification in Quantitative Aptitude with the quiz linked below, containing numerous practice questions to help you master the topic:-

<< Practice Simplification Aptitude Questions >>

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