Question

Consider the equation: (7526)8−(Y)8=(4364)8(7526)_8 - (Y)_8 = (4364)_8, where (X)N(X)_N stands for XX to the base NN. Find YY.

Choose one option
Official answer and solution
Official answer
C
From
Official GATE 2014 answer key

Solution

Isolate Y and perform base-8 (octal) subtraction column by column with borrows.

Given the octal equation:

(7526)8−(Y)8=(4364)8  ⟹  (Y)8=(7526)8−(4364)8.(7526)_8 - (Y)_8 = (4364)_8 \implies (Y)_8 = (7526)_8 - (4364)_8.

Perform subtraction column by column from right to left (base 8):

  1. Position 0 (units):

    6−4=2.6 - 4 = 2.
  2. Position 1 (eights):
    2<62 < 6, so borrow 11 from the next position (worth 88 in base 8).

    (2+8)−6=10−6=4.(2 + 8) - 6 = 10 - 6 = 4.
  3. Position 2 (sixty-fours):
    55 becomes 44 after lending the borrow.

    4−3=1.4 - 3 = 1.
  4. Position 3 (five-hundred-twelves):

    7−4=3.7 - 4 = 3.

Combining the digits gives:

(Y)8=(3142)8.(Y)_8 = (3142)_8.

This matches option C.

Final answer

C

Common trap

Borrowing 10 instead of 8 when subtracting in base 8.

The answer is the one in the official GATE answer key. The solution is this site's own explanation.

Source

Paper
GATE 2014 Computer Science and Information Technology (CS) Session 3
Question
10 of 65, printed as GA Q.10
Section
General Aptitude

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