Question : Directions: Which two numbers and two signs should be interchanged in the following equation to make it correct?
18 – 6 + 11 × 5 + 18 = 113
Option 1: 6 and 5, + and ×
Option 2: 18 and 5, + and ×
Option 3: 6 and 5, – and ×
Option 4: 18 and 5, – and ×
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Correct Answer: 6 and 5, – and ×
Solution :
Given:
18 – 6 + 11 × 5 + 18 = 113
Replace the symbols and numbers given in the equation with the assigned symbols and numbers in the options one by one –
First option:
6 and 5, + and ×
⇒ 18 – 5 × 11 + 6 × 18 = 113
Solving the L.H.S of the equation –
= 18 – 5 × 11 + 6 × 18
= 18 – 55 + 108
= 71 ≠ 113
Second option:
18 and 5, + and ×
⇒ 5 – 6 × 11 + 18 × 5 = 113
Solving the L.H.S of the equation –
= 5 – 6 × 11 + 18 × 5
= 5 – 66 + 90
= 95 – 66
= 29 ≠ 113
Third option:
6 and 5, – and ×
⇒ 18 × 5 + 11 – 6 + 18 = 113
Solving the L.H.S of the equation –
= 18 × 5 + 11 – 6 + 18
= 90 + 11 – 6 + 18
= 119 – 6
= 113
Fourth option:
18 and 5, – and ×
⇒ 5 × 6 + 11 – 18 + 5 = 113
Solving the L.H.S of the equation –
= 5 × 6 + 11 – 18 + 5
= 30 + 11 – 18 + 5
= 46 – 18
= 28 ≠ 113
So, only the third option satisfies the equation. Hence, the third option is correct.
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