Question : Directions: Which two numbers should be interchanged, to make the given equation correct? 7 × 3 – 98 ÷ 14 + 5 = 31
Option 1: 5 and 3
Option 2: 7 and 98
Option 3: 31 and 7
Option 4: 3 and 14
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Correct Answer: 5 and 3
Solution : Given: 7 × 3 – 98 ÷ 14 + 5 = 31
Replace the given numbers in the options one by one with the original numbers in the given equation. First option: 5 and 3 7 × 3 – 98 ÷ 14 + 5 = 31 ⇒ 7 × 5 – 98 ÷ 14 + 3 = 31 ⇒ 7 × 5 – 7 + 3 = 31 ⇒ 35 – 7 + 3 = 31 ⇒ 31 = 31 Second option: 7 and 98 7 × 3 – 98 ÷ 14 + 5 = 31 ⇒ 98 × 3 – 7 ÷ 14 + 5 = 31 ⇒ 294 – 0.5 + 5 = 31 ⇒ 298.5 ≠ 31 Third option: 31 and 7 7 × 3 – 98 ÷ 14 + 5 = 31 ⇒ 31 × 3 – 98 ÷ 14 + 5 = 7 ⇒ 31 × 3 – 7 + 5 = 7 ⇒ 91 ≠ 7 Fourth option: 3 and 14 7 × 3 – 98 ÷ 14 + 5 = 31 ⇒ 7 × 14 – 98 ÷ 3 + 5 = 31 ⇒ 98 – 32.6 + 5 = 31 ⇒ 70.4 ≠ 31
So, only the first option satisfies the given equation. Hence, the first option i s correct.
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