Question : Directions: Which of the following interchanges of signs would make the given equation correct?
162 ÷ 3 + 5 × 6 – 2 = 274
Option 1: + and –
Option 2: ÷ and ×
Option 3: – and ÷
Option 4: + and ×
Correct Answer: + and ×
Solution :
Given:
162 ÷ 3 + 5 × 6 – 2 = 274
Replace the given symbols in the options one by one with the original symbols in the given equation.
First option:
+ and –
= 162 ÷ 3 – 5 × 6 + 2
= 54 – 5 × 6 + 2
= 54 – 30 + 2
= 56 – 30
= 26 ≠ 274
Second option:
÷ and ×
= 162 × 3 + 5 ÷ 6 – 2
= 162 × 3 + 0.84 – 2
= 486 + 0.84 – 2
= 486.84 – 2
= 484.84 ≠ 274
Third option:
– and ÷
= 162 – 3 + 5 × 6 ÷ 2
= 162 – 3 + 5 × 3
= 162 – 3 + 15
= 177 – 3
= 174 ≠ 274
Fourth option:
+ and ×
= 162 ÷ 3 × 5 + 6 – 2
= 54 × 5 + 6 – 2
= 270 + 6 – 2
= 276 – 2
= 274
So, from the above, only the fourth option satisfies the given equation. Hence, the fourth option is correct.
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