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Which two numbers should be interchanged to make the given equation correct? 3├Ч(9+7тИТ5)+(64├╖2)тИТ22+78тИТ8├Ч4=82 (Note: Interchange should be done of the entire number and not individual digits of a given number.)
3 and 4
2 and 4
64 and 78
7 and 5
64 and 78
Test options by substituting the numbers and checking divisibility and arithmetic order.
Test options by substituting the numbers and checking divisibility and arithmetic order.
Analyze the Given Equation
The original equation is 3 x (9 + 7 - 5) + (64 / 2) - 22 + 78 - 8 x 4 = 82.
Test Option C (64 and 78)
Replace 64 with 78 and 78 with 64. The equation becomes: 3 x (9 + 7 - 5) + (78 / 2) - 22 + 64 - 8 x 4.
Calculate Step-by-Step
Parentheses: (9 + 7 - 5) = 11, Division: (78 / 2) = 39, Multiplication: 3 x 11 = 33 and 8 x 4 = 32. Expression: 33 + 39 - 22 + 64 - 32 = 82.
Verify RHS
LHS = 82 which matches RHS = 82. Hence, Option C is correct.
A: 3 and 4 does not balance the equation. B: 2 and 4 results in an incorrect arithmetic value. D: 7 and 5 does not satisfy the target value.
64 and 78 is correct because replacing 64 with 78 and 78 with 64 balances the equation to 82 = 82.
Always check division compatibility first when testing interchanging numbers to speed up calculations.
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