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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