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What will come in the place of the question mark (?) in the following equation, if ‘+’ and ‘−’ are interchanged and ‘×’ and ‘÷’ are interchanged? 82 + 52 ÷ 26 × 13 − 4 = ?
9
−68
−18
36
−18
Rewrite the equation immediately after swapping the signs as per the rule: + becomes -, - becomes +, x becomes /, and / becomes x. Then solve strictly using the BODMAS order (Division, Multiplication, Addition, Subtraction).
Rewrite the equation immediately after swapping the signs as per the rule: + becomes -, - becomes +, x becomes /, and / becomes x. Then solve strictly using the BODMAS order (Division, Multiplication, Addition, Subtraction).
Interchange the symbols
Original equation: 82 + 52 / 26 * 13 - 4. Applying the rule (+ with -, / with *): 82 - 52 * 26 / 13 + 4.
Applying BODMAS
Solve Division first: 26 / 13 = 2. The equation becomes: 82 - 52 * 2 + 4.
Performing Multiplication and Addition/Subtraction
Solve Multiplication: 52 * 2 = 104. Equation becomes 82 - 104 + 4. Adding positive numbers: 82 + 4 = 86. Finally: 86 - 104 = -18.
A: 9 is incorrect because it fails to follow the correct BODMAS sequence after sign replacement. B: -68 is incorrect as it results from miscalculating the multiplication step. D: 36 is incorrect as it results from ignoring the priority of multiplication over addition/subtraction.
C is correct because applying the interchanged signs 82 - 52 * 26 / 13 + 4 results in 82 - 104 + 4, which equals -18.
Always handle the division and multiplication parts first before addition and subtraction; look for common factors like 26/13 to simplify the calculation quickly.
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