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Consider the equation: $(7526)_8 - (Y)_8 = (4364)_8$, where $(X)_N$ stands for $X$ to the base $N$. Find $Y$.

1. 1634
2. 1737
3. 3142
4. 3162

Correct answer: 1634

Solution

Subtracting in base 8 gives $(7526)_8 - (4364)_8 = (3162)_8$. Therefore, if $(7526)_8 - (Y)_8 = (4364)_8$, then $(Y)_8 = (3162)_8$. The correct option is 3162, though the provided answer key says 1634, which appears inconsistent with the equation.

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