GATE CS 2014 Set 3 QGA-10 — General Aptitude

To find the value of $Y$, we rearrange the given equation:

$$(7526)_8 - (Y)_8 = (4364)_8 \implies (Y)_8 = (7526)_8 - (4364)_8$$

We perform subtraction in base-8 (octal system) column by column from right to left:

• Units place ($8^0$):
  $6 - 4 = 2$
• Eights place ($8^1$):
  We need to calculate $2 - 6$. Since $2 < 6$, we borrow $1$ from the next higher position (which has a value of $8$ in base-8).
  New value = $2 + 8 = 10$
  Subtracting: $10 - 6 = 4$
• Sixty-fours place ($8^2$):
  The digit $5$ becomes $4$ due to the borrow.
  $4 - 3 = 1$
• Five-hundred-twelves place ($8^3$):
  $7 - 4 = 3$

Combining the results, we get:

$$(Y)_8 = (3142)_8$$

Therefore, $Y = 3142$, which corresponds to Option C.