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Which two numbers should be interchanged to make the given equation correct? 21├Ч4+(84├╖7)├Ч2тИТ15├Ч5+42=105 (Note: Interchange should be done of entire number and not individual digits of a given number.)
4 and 2
84 and 42
4 and 5
7 and 21
84 and 42
Test options by replacing numbers one by one, focusing first on division terms to ensure clean integer division.
Test options by replacing numbers one by one, focusing first on division terms to ensure clean integer division.
Analyze the Equation
The given equation is 21 * 4 + (84 / 7) * 2 - 15 * 5 + 42 = 105. We need to find which pair of numbers when interchanged makes LHS equal to RHS.
Test Option B (84 and 42)
Replacing 84 with 42 and 42 with 84 gives: 21 * 4 + (42 / 7) * 2 - 15 * 5 + 84 = 105.
Evaluate Step-by-Step using BODMAS
Bracket: (42 / 7) = 6. Multiplications: 21 * 4 = 84, 6 * 2 = 12, 15 * 5 = 75. Expression becomes: 84 + 12 - 75 + 84 = 96 - 75 + 84 = 21 + 84 = 105.
A: Interchanging 4 and 2 results in an incorrect value. C: Interchanging 4 and 5 does not yield 105. D: Interchanging 7 and 21 does not yield 105.
B is correct because interchanging 84 and 42 satisfies the equation, making the left-hand side equal to 105.
Always inspect division terms first during number interchange problems to ensure the division remains exact or results in clean integers.
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