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WAEC 2019 · Paper 1 · Q8

If 23y=1111two23_y = 1111_{\text{two}}, find the value of yy.

Worked solution (try it first)
  1. Change the right side to base ten: 1111two=8+4+2+1=151111_{\text{two}} = 8 + 4 + 2 + 1 = 15.
  2. In base yy, 23y=2y+323_y = 2y + 3, so 2y+3=152y + 3 = 15.
  3. Subtract 3 and divide by 2: y=6y = 6, option C.

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