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Mathematical Operations :Verbal Reasoning Questions

Mathematical operations  

Mathematical operations are basically the  simplification of an expression containing  numbers and different Mathematical  operations.  In this chapter, we deal with questions  having four fundamental Mathematical  operations– addition (+), subtraction (–),  multiplication (×) and division (÷) and also  statements such as ‘less than (<)’, ‘greater  than (>)’, ‘equal to (=)’, ‘not equal to (≠)’, etc.  All these operations are represented by  symbols, different from usual ones. The  candidate is required to substitute the real  signs in place of artificial symbols to solve the  questions.  We need to follow the BODMAS rule for  simplification of Mathematical operations.  

B – Brackets, O – Order of powers or roots, D – Division, M – Multiplication A – Addition, and S – Subtraction. Mathematical expressions with multiple operators need to be solved from left to right in the order of BODMAS.

There are four types of questions based on  mathematical operations which are usually  asked in various competitive examinations.

Type 1 : Problem Solving by Substitution 

In this type of questions, you have substitutes  for various mathematical symbols or numerals  followed by a question involving calculation of  an expression or choosing the correct/incorrect  equation. 

Example1: If ‘÷’ means ‘+’, ‘–’ means ‘÷’, ‘×’ means ‘–’ and ‘+’ means ‘×’ then, 62 ÷ 8 – 4 × 12 + 4 =
(A)16
(B)36
(C)1/6
(D)26
Answer : (A) Given expression, 62 ÷ 8 – 4 × 12 + 4 = ?
According to question, after replacement of mathematical sign
62 + 8 ÷ 4 – 12 × 4 = ?
= 64 – 48 = 16

Example 2. If ‘–‘ stands for ‘÷’, ‘+’ stands for ‘×’, ‘÷’ stand for ‘–‘ and ‘×’ stands for ‘+’, which one of the following question is correct?
(A) 30 – 6 + 5 × 4 ÷ 2 = 27.
(B) 30 + 6 – 5 ÷ 4 × 2 = 30.
(C) 30 × 6 ÷ 5 – 4 + 2 = 32.
(D) 30 ÷ 6 × 5 + 4 – 2 = 40.

Answer (A)
30 ÷ 6 × 5 + 4 – 2 = 27
→ 5 × 5 + 4 – 2 = 27.
→ 29 – 2 = 27.
→ 27 = 27.


Type 2:Interchanging the Signs  and Numbers  Type

In this type of questions, certain signs or  numbers interchange among each other. The  candidate is required to change the given  signs or numbers with each other and select  the equation which is correct from the given  alternatives.  It can also be asked to find the correct pair of  signs and numbers to be interchanged from  the alternatives to make the given equation correct. 

Example 3:If signs ‘+’ and ‘−’ and numbers  4 and 8 interchange between each other, then  which one of the following four equations  would be correct?  
(A) 4- 8+ 12  =0
(B)8 − 4 ÷ 12 = 8 
(C)4 ÷ 8 − 12 = 16
(D) 8 ÷ 4 − 12 = 24 

Answer (A) Given, 4 -8 +12= 0    On interchanging signs ‘+’ and ‘−’ and numbers 4  and 8 in option (A), we get  8+ 4- 12 =0   ⇒12 -12  =  0 

Example 4: Which one of the four  interchanges in signs and numbers would  make the given equation correct?                    
                             6× 4+2 =16

(A) + and ×, 2 and 4
(B) + and ×, 4 and 6 
(C) + and ×, 2 and 6
(D)None of these

Answer (B):Given, 6× 4+2 =16 On interchanging signs ‘+’ and ‘×’ and number 4 and 6 
4 +6 ×2 =4 +12= 16

Replacement of signs by alphabets or symbols

 In this type of questions signs are replaced by alphabets or symbols. You have to substitute corresponding signs and find the solution of the given equation. 

Example5 :If ‘R’ stands for ‘–‘, ‘A’ stands for ‘+’, ‘B’ stands for ‘÷’ and ‘C’ stands for ‘×’, then what is the value of the given equation ?
25 A 37 C 8 B 4 R 1 = ?

(A) 99
(B) 100
(C) 98
(D) 199

Answer (C)= 25 + 37 × 8 ÷ 4 – 1

Example 6. If P denotes ‘÷’, Q denotes ‘×’, R denotes ‘+’  and S denotes ‘−’,
 then  18 Q 12 P 4 R 5 S 6 =?
(A) 95 
(B) 53 
(C) 51 
(D) 57 

Answer:(B)
18 ×12÷ 4+  5− 6      = 53  (Apply BODMAS rule)
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