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JAMB 2011 · UTME · Q2

If 2q35=7782q3_5 = 77_8, find qq.

Worked solution (try it first)
  1. Change the right side to base ten: 778=7×8+7=6377_8 = 7 \times 8 + 7 = 63.
  2. In base five, 2q35=50+5q+3=53+5q2q3_5 = 50 + 5q + 3 = 53 + 5q.
  3. Set 53+5q=6353 + 5q = 63: 5q=105q = 10, so q=2q = 2, option A.

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