Question : Directions: Which two signs and two numbers interchange (not digits) that will make the equation correct?
7 – 5 × 2 + 8 ÷ 4 = 17
Option 1: – and ÷, 8 and 5
Option 2: × and ÷, 5 and 4
Option 3: + and –, 4 and 5
Option 4: + and –, 7 and 5
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Correct Answer: + and –, 7 and 5
Solution :
Given:
7 – 5 × 2 + 8 ÷ 4 = 17
Replace the given symbols and numbers in the options one by one with the original symbols and numbers in the given equation.
Let's check the given options –
First option:
– and ÷, 8 and 5
7 – 5 × 2 + 8 ÷ 4 = 17
⇒ 7 ÷ 8 × 2 + 5 – 4
⇒ 0.875 × 2 + 5 – 4
⇒ 1.75 + 5 – 4
⇒ 2.75 ≠ 17
Second option:
× and ÷, 5 and 4
7 – 5 × 2 + 8 ÷ 4 = 17
⇒ 7 – 4 ÷ 2 + 8 × 5
⇒ 7 – 2 + 8 × 5
⇒ 7 – 2 + 40
⇒ 45 ≠ 17
Third option:
+ and –, 4 and 5
7 – 5 × 2 + 8 ÷ 4 = 17
⇒ 7 + 4 × 2 – 8 ÷ 5
⇒ 7 + 4 × 2 – 1.6
⇒ 7 + 8 – 1.6
⇒ 13.4 ≠ 17
Fourth option:
+ and –, 7 and 5
7 – 5 × 2 + 8 ÷ 4 = 17
⇒ 5 + 7 × 2 – 8 ÷ 4
⇒ 5 + 7 × 2 – 2
⇒ 5 + 14 – 2
⇒ 19 – 2
⇒ 17
Here, the fourth option satisfies the equation. Hence the fourth option is correct.
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