Question : Directions: Which two signs and two numbers should be interchanged in the following equation to make it correct? 14 × 8 + 64 ÷ 32 – 2 = 88
Option 1: 8 and 32; × and +
Option 2: 14 and 2; × and +
Option 3: 8 and 2; – and ÷
Option 4: 32 and 64; + and ÷
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Correct Answer: 8 and 2; – and ÷
Solution : Given: 14 × 8 + 64 ÷ 32 – 2 = 88
Let's check each option – First Option: 8 and 32; × and + On interchanging the mathematical signs and numbers, we get – 14 + 32 × 64 ÷ 8 – 2 = 88 On solving the L.H.S. of the equation – = 14 + 32 × 64 ÷ 8 – 2 = 14 + 32 × 8 – 2 = 14 + 256 – 2 = 268 ≠ 88 Second Option: 14 and 2; × and + On interchanging the mathematical signs and numbers, we get – 2 + 8 × 64 ÷ 32 – 14 = 88 On solving the L.H.S. of the equation – = 2 + 8 × 64 ÷ 32 – 14 = 2 + 8 × 2 – 14 = 2 + 16 – 14 = 4 ≠ 88 Third Option: 8 and 2; – and ÷ On interchanging the mathematical signs and numbers, we get – 14 × 2 + 64 – 32 ÷ 8 = 88 On solving the L.H.S. of the equation – = 14 × 2 + 64 – 32 ÷ 8 = 14 × 2 + 64 – 4 = 28 + 64 – 4 = 88 Fourth Option: 32 and 64; + and ÷ On interchanging the mathematical signs and numbers, we get – 14 × 8 ÷ 32 + 64 – 2 = 88 On solving the L.H.S. of the equation – = 14 × 8 ÷ 32 + 64 – 2 = 14 × 0.25 + 64 – 2 = 3.5 + 64 – 2 = 65.5 ≠ 88
So, only the third option satisfies the equation. Hence, the third option is correct.
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