Question

Consider the equation (43)_x = (y3)₈ where x and y are unknown. The number of possible solution is
1. 4
2. 6
3. 5
4. 7

Answer 1

Correct Answer - Option 3 : 5

Concept:

(ABCD)a = D* a0 + C* a1 + B* a2 + A* a3

Calculation:

Given: (43)x = (y3)8 

⇒ 3 * x⁰ + 4 * x¹ = 3 * 80 + y * 8¹

⇒ 3 + 4x = 3 + 8y

⇒ 4x = 8y

∴ x = 2y

Now, y < 8 and x > 4 (because the number represented in base x is 43 or redix is always greater ) 

The following are possible solutions
y = 3, 4, 5, 6, 7 (y < 8)
x = 6, 8, 10, 12, 14

Hence number of possible solution is five.