Question : Directions: Which of the following interchanges in two mathematical operations will balance the equation given below?
14 – 96 × 24 + 16 ÷ 4 = 74
Option 1: – and ÷
Option 2: + and –
Option 3: ÷ and ×
Option 4: + and ×
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Correct Answer: ÷ and ×
Solution :
Given:
14 – 96 × 24 + 16 ÷ 4 = 74
Replace the signs given in the equation with the assigned signs in the options one by one –
First option:
– and ÷
= 14 ÷ 96 × 24 + 16 – 4
= 0.146 × 24 + 16 – 4
= 3.5 + 16 – 4
= 19.5 – 4
= 15.5 ≠ 74
Second option:
+ and –
= 14 + 96 × 24 – 16 ÷ 4
= 14 + 96 × 24 – 4
= 14 + 2304 – 4
= 2318 – 4
= 2314 ≠ 74
Third option:
÷ and ×
= 14 – 96 ÷ 24 + 16 × 4
= 14 – 4 + 16 × 4
= 14 – 4 + 64
= 78 – 4
= 74
Fourth option:
+ and ×
= 14 – 96 + 24 × 16 ÷ 4
= 14 – 96 + 24 × 4
= 14 – 96 + 96
= 14 ≠ 74
So, only the third option satisfies the R.H.S. of the given equation. Hence, the third option is correct.
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