What will come in place of the question mark (?) in the following equation, if…
2025
What will come in place of the question mark (?) in the following equation, if ‘+’ and ‘−’ are interchanged and ‘×’ and ‘÷’ are interchanged?
1048 ÷ 2 + 4016 × 8 − 145 = ?
- A.
1536
- B.
1842
- C.
1643
- D.
1739
Attempted by 5 students.
Show answer & explanation
Correct answer: D
Concept
When two arithmetic symbols in an expression are interchanged, replace every occurrence of each symbol with the other one throughout the expression, then evaluate the new expression using the standard order of operations: multiplication and division are carried out first (left to right), followed by addition and subtraction (left to right).
Application
The interchange '+' with '−' and '×' with '÷' turns 1048 ÷ 2 + 4016 × 8 − 145 into 1048 × 2 − 4016 ÷ 8 + 145.
Multiply 1048 by 2: 1048 × 2 = 2096.
Divide 4016 by 8: 4016 ÷ 8 = 502.
Subtract the division result from the multiplication result: 2096 − 502 = 1594.
Add 145 to the result: 1594 + 145 = 1739.
Cross-check
Regrouping the same rewritten expression as 1048 × 2 − (4016 ÷ 8 − 145) gives 2096 − (502 − 145) = 2096 − 357 = 1739, confirming the value obtained above.