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Question 96

Computer Awareness Number representations Easy

Consider the equation (43)<sub>x</sub> = (y3)<sub>8 </sub>where x and y are unknown. The number of possible solution is

(A) 4

(B) 6

(C) 5

(D) 7

✓ Correct Answer: Option C Verified Solution

📘 Step-by-Step Solution & Detailed Explanation:

\((43)_x = 4x + 3\) and \((y3)_8 = 8y + 3\).

\(4x + 3 = 8y + 3 \Rightarrow x = 2y\).

Conditions:

Digit 4 in base x means \(x \ge 5\).
y is a digit in base 8, so \(0 \le y \le 7\).

\(x = 2y \ge 5\) gives \(y \ge 3\). So y = 3, 4, 5, 6, 7 (with x = 6, 8, 10, 12, 14).

Number of solutions = 5.

Answer: (C) 5

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