Question : Directions: Which of the following interchanges in two mathematical operators and two numbers will balance the equation given below? 84 + 5 × 4 ÷ 32 – 7 = 75 NOTE: Operations should be performed on numbers, not on digits.
Option 1: + and ×, 84 and 32
Option 2: – and ÷, 4 and 7
Option 3: ÷ and +, 5 and 7
Option 4: + and –, 5 and 4
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Correct Answer: ÷ and +, 5 and 7
Solution : Given: 84 + 5 × 4 ÷ 32 – 7 = 75
Let's check the options – First option: + and ×, 84 and 32 = 32 × 5 + 4 ÷ 84 – 7 = 32 × 5 + 0.0476 – 7 = 160 + 0.0476 – 7 = 153.0476 ≠ 75 Second option: – and ÷, 4 and 7 = 84 + 5 × 7 – 32 ÷ 4 = 84 + 5 × 7 – 8 = 84 + 35 – 8 = 111 ≠ 75 Third option: ÷ and +, 5 and 7 = 84 ÷ 7 × 4 + 32 – 5 = 84 ÷ 7 × 4 + 32 – 5 = 12 × 4 + 32 – 5 = 48 + 32 – 5 = 75 = R.H.S. Fourth option: + and –, 5 and 4 = 84 – 4 × 5 ÷ 32 + 7 = 84 – 4 × 5 ÷ 32 + 7 = 84 – 4 × 0.15625 + 7 = 84 – 0.625 + 7 = 90.375 ≠ 75
So, only the third option satisfies the equation. Hence, the third option is correct.
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