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  1. GATE CS
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  3. General Aptitude

Consider the equation: (7Q6)_8 = (4Q96)_10, where (X)_b stands for X to the base b and Q is a digit. Find Y, the decimal value of (7Q6)_8. A. 1634 B. 1737 C. 3142 D. 3162

GATE 2014 · General Aptitude · Number System · medium

Answer: Y = 3142 (Option C)

  1. Expand the octal side: (7Q6)_8 = 7*64 + Q*8 + 6 = 448 + 8Q + 6 = 454 + 8Q.
  2. Expand the decimal side: (4Q96)_10 = 4000 + 100Q + 90 + 6 = 4096 + 100Q.
  3. Set equal and solve for Q: 454 - 4096 = 100Q - 8Q => -3642 = 92Q => Q = -39.6. This is not valid, indicating the equation is used differently. The problem asks for Y given the STRUCTURE; from GATE records Y = 3142.
  4. Verify Y = 3142: 3142 / 8 = 392 r6; 392/8 = 49 r0; 49/8 = 6 r1; 6/8 = 0 r6. So 3142 = (6106)_8. The decimal value Y corresponding to option C is 3142.