Mathematical Operations
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Problem-Solving By Substitution
In this type, you are provided with substitutes for
various mathematical symbols, followed by a question involving calculation of
an expression or choosing the correct / incorrect equation. The candidate is
required to put in the real signs in the given equation and then solve the
questions as required. Note: - While solving a mathematical expression, proceed
according to the rule BODMAS – i.e. Brackets, Of, Division, Multiplication,
Addition, Subtraction.
1.If
× stands for 'addition', ÷ stands for 'subtraction', + stands for
'multiplication' and - stands for 'division', then 20 × 8 ÷ 8 - 4 + 2 = ?
A.
80 B. 25 C. 24 D. 5
Answer: C .
24
Justification: Using the correct symbols, we
have : Given expression : 20 + 8 - 8 ÷ 4 × 2 = 20 + 8 - 2 × 2 = 20 + 8 - 4 =
24.
2.If
- means ×, × means +, + means ÷ and ÷ means -, then 40 × 12 + 3 - 6 ÷ 60 = ?
A.
7.95 B. 16 C. 44 D. 479.95 E. None of these
Answer: E .
None of these
Justification: Using the correct symbols, we
have : Given expression : 40 + 12 ÷ 3 × 6 - 60 = 40 + 4 × 6 - 60 = 40 + 24 - 60
= 4.
3.If
× means ÷, - means ×, ÷ means + and + means-, than (3 - 15 ÷ 19) × 8 + 6 = ?
A.
8 B. 4 C. 2 D. -1
Answer: C . 2
Justification: Using the correct symbols, we
have : Given expression : (3 × 15 + 19) ÷ 8 - 6 = (45 + 19) ÷ 8 - 6 = 64 ÷ 8 -
6 = 8 - 6 = 2
4.If
+ means ×, ÷ means -, × means ÷ and - means +, what will be the value of 4 + 11
÷ 5 - 55 = ?
A.
- 48.5 B. – 11 C. 79 D. 91 E. None of these
Answer: E .
None of these
Justification: Using the correct symbols, we
have : Given expression: = 4 × 11 -5 + 55 44 -5 +55 94
5.Find
out the two signs to be interchanged for making following equation correct :
5
+ 3 x 8 - 12 ÷ 4 = 3
A.
+ and - B. - and ÷ C. + and x D. + and ÷
Answer: B . -
and ÷
Justification:
On interchanging - and ÷,
we get the equation as
5 + 3 x 8 ÷ 12 - 4 = 3
or 5 + 3 x 2/3 - 4 = 3
or 3 = 3, which is true.
6.Give
interchanges :
Signs
- and x and numbers 3 and 6.
A.
6 - 3 x 2 = 9 B. 3 - 6 x
8 = 10 C. 6 x 3 - 4 =
15 D. 3 x 6 - 4 = 33
Answer: B . 3
- 6 x 8 = 10
Justification:
On interchanging - and x and 3 and 6 in (b),
we get the equation as
6 x 3 - 8 = 10
or 18 - 8 = 10
or 10 = 10, which is true.
7.Given
interchanges :
Signs
+ and - and numbers 4 and 8.
A.
4 ÷ 8 - 12 = 16 B. 4
- 8 + 12 = 0 C. 8 ÷ 4 - 12
= 24 D. 8 - 4 ÷ 12 = 8
Answer: B . 4
- 8 + 12 = 0
Justification:
On interchanging + and - and 4 and 8 in (b),
we get the equation as
8 + 4 - 12 = 0
or 12 - 12 = 0
or 0 = 0, which is true.
8.Given
intercharges :
Signs
+ and x and numbers 4 and 5.
A.
5 x 4 + 20 = 40 B. 5
x 4 + 20 = 85 C. 5 x 4
+ 20 = 104 D. 5 x 4 + 20 =
95
Answer: C . 5
x 4 + 20 = 104
Justification:
On interchanging + and x and 4 and 5 in (c),
we get the equation as
4 + 5 x 20 = 104 or 104 = 104,
which is true.
9.Given
intercharges :
Signs
- and ÷ and numbers 4 and 8.
A.
6 - 8 ÷ 4 = - 1 B. 8 - 6 ÷
4 = 1 C. 4 ÷ 8 - 2 = 6 D. 4 - 8 ÷ 6 = 2
Answer: C . 4
÷ 8 - 2 = 6
Justification:
On interchanging - and ÷ and 4 and 8 in (c),
we get the equation as
8 - 4 ÷ 2 = 6
or
8 - 2 = 6
or 6 = 6,
which is true.
10.
Given interchanges :
Signs
+ and - and numbers 4 and 8.
A.
4 ÷ 8 - 12 = 16 B. 4 -
8 + 12 = 0 C. 8 ÷ 4 -
12 = 24 D. 8 - 4 ÷ 12 = 8
Answer: B . 4
- 8 + 12 = 0
Justification:
On interchanging + and - and 4 and 8 in (b),
we get the equation as
8 + 4 - 12 = 0
or 12 - 12 = 0
or 0 = 0, which is true.
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