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JAMB Mathematics 2011 Paper

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Question : 1

Total: 46

If 2q3₅ = 77₈, find q

2
1
4
O

Solution:

Concept:

Convert both numbers from their given bases to base

10

, then solve for

q

.

Explanation:

Write

2q3_5

in expanded base

5

notation.

2q3_5 = 2 \times 5^2 + q \times 5^1 + 3 \times 5^0

= 2 \times 25 + 5q + 3 \times 1

= 50 + 5q + 3 = 53 + 5q

Write

77_8

in expanded base

8

notation.

77_8 = 7 \times 8^1 + 7 \times 8^0

= 7 \times 8 + 7 \times 1 = 56 + 7 = 63

Set the two expressions equal since

2q3_5 = 77_8

.

53 + 5q = 63

5q = 63 - 53

5q = 10

q = \frac{10}{5} = 2

Answer:

q = 2

, which is Option A.

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