Question : Directions: Which two numbers must be interchanged to correct the following equation?
27 − 8 × 4 − 3 ÷ 2 = 1
Option 1: 2 and 8
Option 2: 2 and 3
Option 3: 3 and 4
Option 4: 8 and 4
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Correct Answer: 3 and 4
Solution :
Given:
27 − 8 × 4 − 3 ÷ 2 = 1
Let's check the options –
First options:
2 and 8
27 − 2 × 4 − 3 ÷ 8 = 1
On solving the L.H.S. of the given equation –
= 27 − 2 × 4 − 3 ÷ 8
= 27 − 2 × 4 − 0.375
= 27 − 8 − 0.375
= 18.625 ≠ 1
Second option:
2 and 3
27 − 8 × 4 − 2 ÷ 3 = 1
On solving the L.H.S. of the given equation –
= 27 − 8 × 4 − 2 ÷ 3
= 27 − 8 × 4 − 0.67
= 27 − 32 − 0.67
= –5.67 ≠ 1
Third option:
3 and 4
27 − 8 × 3 − 4 ÷ 2 = 1
On solving the L.H.S. of the given equation –
= 27 − 8 × 3 − 4 ÷ 2
= 27 − 8 × 3 − 2
= 27 − 24 − 2
= 1
Fourth option:
8 and 4
27 − 4 × 8 − 3 ÷ 2 = 1
On solving the L.H.S. of the given equation –
= 27 − 4 × 8 − 3 ÷ 2
= 27 − 4 × 8 − 1.5
= 27 − 32 − 1.5
= –6.5 ≠ 1
So, the third option satisfies the equation. Hence, the third option is correct.
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