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Which two numbers should be interchanged to make the given equation correct? (165 ├╖ 3) + (135 ├╖ 5) тАУ 45 + 33 = 66 (Note: Interchange should be done of entire number and not individual digits of a given number)
165 and 135
33 and 5
45 and 33
45 and 3
165 and 135
Focus on the division operations first; if changing numbers results in a fraction, that option is likely incorrect. Test the option that yields integers in all divisions.
Focus on the division operations first; if changing numbers results in a fraction, that option is likely incorrect. Test the option that yields integers in all divisions.
Analyze the original equation
Original equation: (165 / 3) + (135 / 5) - 45 + 33. Solving: 55 + 27 - 45 + 33 = 70. This does not equal 66.
Test Option A (165 and 135)
Swap 165 and 135: (135 / 3) + (165 / 5) - 45 + 33. Solving: 45 + 33 - 45 + 33 = 66. The equation holds true.
B: Replacing 33 and 5 yields (165/3) + (135/33) - 45 + 5, which results in non-integer values; C: Replacing 45 and 33 yields (165/3) + (135/5) - 33 + 45 = 117, not 66; D: Replacing 45 and 3 yields (165/45) + (135/5) - 3 + 33, which involves a fraction.
A is correct because interchanging 165 and 135 transforms the expression into (135 / 3) + (165 / 5) - 45 + 33, which simplifies to 45 + 33 - 45 + 33 = 66.
In mathematical operations questions, always check if the proposed interchange creates a fraction that cannot be simplified, as this usually indicates an incorrect option.
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