Question : Directions: Which of the following interchanges of signs would make the given equation correct?
1000 – 448 + 14 ÷ 15 × 2 = 998
Option 1: + and ÷
Option 2: × and ÷
Option 3: – and +
Option 4: ÷ and –
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Correct Answer: + and ÷
Solution :
Given:
1000 – 448 + 14 ÷ 15 × 2 = 998
Let's check the options –
First option:
+ and ÷
The equation becomes ⇒ 1000 – 448 ÷ 14 + 15 × 2 = 998
Solving the L.H.S. of the equation –
= 1000 – 448 ÷ 14 + 15 × 2
= 1000 – 32 + 30
= 998
Second option:
× and ÷
The equation becomes ⇒ 1000 – 448 + 14 × 15 ÷ 2 = 998
Solving the L.H.S. of the equation –
= 1000 – 448 + 14 × 15 ÷ 2
= 1000 – 448 + 14 × 7.5
= 1000 – 448 + 105
= 657 ≠ 998
Third option:
– and +
The equation becomes ⇒ 1000 + 448 – 14 ÷ 15 × 2 = 998
Solving the L.H.S. of the equation –
= 1000 + 448 – 14 ÷ 15 × 2
= 1000 + 448 – 0.93 × 2
= 1000 + 448 – 1.87
= 1446.13 ≠ 998
Fourth option:
÷ and –
The equation becomes ⇒ 1000 ÷ 448 + 14 – 15 × 2 = 998
Solving the L.H.S. of the equation –
= 1000 ÷ 448 + 14 – 15 × 2
= 2.23 + 14 – 30
= –13.77 ≠ 998
So, only the first option satisfies the equation. Hence, the first option is correct.
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