The topic on Mathematical Operations is an important part of the Reasoning syllabus of various competitive exams like- SSC CHSL, SSC CGL, SBI PO, IBPS PO and many others.
In Mathematical Operations, the questions are based on the basic mathematical functions. Here, the four basic operations like- addition, subtraction, multiplication and division, and also statements such as ‘less than’, ‘greater than’, ‘equal to’, ‘not equal to’, etc. are indicated by symbols, which are different from the usual ones. The questions on this topic are set using artificial symbols.
For solving questions on Mathematical Operations accurately, you must understand the BODMAS rule really well.
Numerical Operation
In such types of questions, a mathematical equation is given with arithmetic notification.
Candidates are required to solve such questions as per the BODMAS rule.
For example-
Q1) If + stands for ‘division’, × stands for ‘addition’, – stands for ‘multiplication’ and ÷ stands for subtraction, then which of the following equations is correct?
(a) 36 × 6 + 7 ÷ 2 – 6 = 20
(b) 36 + 6 – 3 × 5 ÷ 3 = 24.
(c) 36 ÷ 6 + 3 × 5 – 3 = 45.
(d) 36 -6 + 3 × 5 ÷ 3 = 74.
Answer: (d)
Explanation:
36 – 6 + 3 × 5 ÷ 3
→ 36 × 6 ÷ 3 + 5 – 3.
→ 36 × 2 + 5 – 3 = 74.
→ 72 + 5 – 3 = 74.
Symbolic Operation
Here, a mathematical equation is given with symbolic notification.
Candidates are required to replace the given symbols according to the given instructions, so that the equation makes perfect sense.
For example-
Q1) Example. If P denotes ‘+’, Q denotes ‘–‘, R denotes ‘×’ and S denotes ‘÷’, then which of the following statements is correct ?
(a) 16 R 12 P 49 S 7 Q 9 = 200
(b) 32 S 8 R 9 = 160 Q 12 R 12
(c) 8 R 8 P 8 S 8 Q 8 = 57
(d) 36 R 4 S 8 Q 7 P 4 = 10
Answer: (c)
Explanation:
= 8 × 8 + 8 ÷ 8 – 8
= 8 × 8 + (8/8) – 8
= 64 +1 – 8 = 57.
Sample Questions on Mathematical Operations
Q1) If × stands for -, ÷ stands for +, + stands for ÷ and – stands for ×, which one of the following equations is correct?
15 – 5 ÷ 5 × 20 + 16 = 6
8 ÷ 10 – 3 + 5 × 6 = 8
6 × 2 + 3 ÷ 12 – 3 = 15
3 ÷ 7 – 5 × 10 + 3 = 10
Answer: (b)
Explanation:
Using the proper signs, we get:
Expression in (a) = 15 × 5 + 5 – 20 ÷ 10 = 15 × 5 + 5 – 2 = 75 + 5 – 2 = 78
Expression in (b) = 8 + 10 × 3 ÷ 5 – 6 = 8 + 10 × 3/5 – 6 = 8 + 6 – 6 = 8
Expression in (c) = 6 – 2 ÷ 3 + 12 × 3 = 6 – 2/3 + 36 = 42 – 2/3=124/3
Expression in (d) = 3 + 7 × 5 – 10 ÷ 3 = 3 + 7 × 5 – 10/3=3+35-10/3=104/3
Therefore, statement (b) is true.
Q2) If ‘+’ means ‘÷’, ‘–‘ means ‘×’, ‘×’ means ‘+‘, ‘÷’ means ‘– ‘, given the value of 45 + 9 – 3 × 15 ÷ 2.
a. 40
b. 36
c. 56
d. 28
Answer: (d)
Explanation:
Conversion according to question.
→ 45 ÷ 9 × 3 + 15 – 2.
= 5 × 3 + 15 – 2.
= 15 + 15 – 2 = 28.
Q3) If ‘R’ stands for ‘–‘, ‘A’ stands for ‘+’, ‘B’ stands for ‘÷’ and ‘C’ stands for ‘×’, then what is the value of the given equation ?(BODMAS rule will not be applicable).
25 A 37 C 2 B 4 R 1 = ?
a. 32
b. 35
c. 30
d. 27
Answer: (c)
Explanation:
According to the question, after putting signs
= 25 + 37 × 2 ÷ 4 – 1
= 62 × 2 ÷ 4 – 1
= 124 ÷ 4 – 1
= 31 – 1 = 30
Q4) If > denotes +, < denotes -, + denotes ÷, – denotes =, = denotes ‘less than’ and × denotes ‘greater than’, find which of the following is a correct statement.
3 + 2 > 4 = 9 + 3 < 2
3 > 2 > 4 = 18 + 3 < 1
3 > 2 < 4 × 8 + 4 < 2
3 + 2 < 4 × 9 + 3 < 3
Answer: (c)
Explanation:
Using proper notations, we have:
(a) Given statement is 3 ÷ 2 + 4 < 9 ÷ 3 – 2 or 11/2 < 1, which is not true
(b) Given statement is 3 + 2 + 4 < 18 ÷ 3 – 1 or 9 < 5, which is not true
(c) Given statement is 3 + 2 – 4 > 8 ÷ 4 – 2 or 1 > 0, which is true
(d) Given statement is 3 ÷ 2 – 4 > 9 ÷ 3 – 3 or -5/2 > 0, which is not true
So, Statement (c) is true.
Conclusion
The topic on Mathematical Operations is asked to test the analytical abilities of the candidates. To score well on this topic, you must practice enough questions and understand the concept behind it. You can expect around 5 questions in competitive exams.
