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 ×
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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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