Question : Directions: Which two signs must be interchanged to correct the following equation? 26 ÷ 24 + 6 × 27 – 105 = 29
Option 1: + and –
Option 2: ÷ and +
Option 3: + and ×
Option 4: ÷ and –
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Correct Answer: ÷ and +
Solution : Given: 26 ÷ 24 + 6 × 27 – 105 = 29
Replace the given symbols in the options one by one with the original symbols in the given equation. First options: + and – 26 ÷ 24 – 6 × 27 + 105 = 29 On solving the L.H.S. of the given equation – = 26 ÷ 24 – 6 × 27 + 105 = 1.08 – 6 × 27 + 105 = 1.08 – 162 + 105 = –55.92 ≠ 29 Second option: ÷ and + 26 + 24 ÷ 6 × 27 – 105 = 29 On solving the L.H.S. of the given equation – = 26 + 24 ÷ 6 × 27 – 105 = 26 + 4 × 27 – 105 = 26 + 108 – 105 = 29 Third option: + and × 26 ÷ 24 × 6 + 27 – 105 = 29 On solving the L.H.S. of the given equation – = 26 ÷ 24 × 6 + 27 – 105 = 1.08 × 6 + 27 – 105 = 6.48 + 27 – 105 = –71.52 ≠ 29 Fourth option: ÷ and – 26 – 24 + 6 × 27 ÷ 105 = 29 On solving the L.H.S. of the given equation – = 26 – 24 + 6 × 27 ÷ 105 = 26 – 24 + 6 × 0.257 = 26 – 24 + 1.542 = 3.542 ≠ 29
So, the second option satisfies the equation. Hence, the second option is correct.
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