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Which two numbers should be interchanged to make the given equation correct? 75├╖5+15├Ч4тИТ17├Ч3+(60├╖6)├Ч10=100 (Note: Interchange should be done of the entire number and not individual digits of a given number.)
5 and 3
3 and 6
17 and 15
3 and 4
5 and 3
Test option interchange on terms where division results cleanly without fractional remainders, or check the numbers that drastically alter the large product terms.
Test option interchange on terms where division results cleanly without fractional remainders, or check the numbers that drastically alter the large product terms.
Analyze the Original Equation
The given equation is 75 / 5 + 15 * 4 - 17 * 3 + (60 / 6) * 10 = 100. Evaluating it using standard BODMAS gives 15 + 60 - 51 + 100 = 124, which does not equal 100.
Test Option A (Interchange 5 and 3)
Replace every 5 with 3 and every 3 with 5. The equation becomes: 75 / 3 + 15 * 4 - 17 * 5 + (60 / 6) * 10 = 100.
Evaluate the Modified Equation
Calculate step-by-step: (75 / 3) = 25; (15 * 4) = 60; (17 * 5) = 85; (60 / 6) * 10 = 100. Combining terms: 25 + 60 - 85 + 100 = 85 - 85 + 100 = 100. This perfectly matches the RHS.
B: 3 and 6 yields an incorrect value. C: 17 and 15 does not balance the equation. D: 3 and 4 fails to yield 100.
A is correct because interchanging the numbers 5 and 3 satisfies the equation and equates the LHS to 100.
When testing interchange options, prioritize numbers involved in division terms to avoid fractional values that rarely appear in integer answer keys.
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