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WAEC Mathematics 2019 Paper

Question : 8

Total: 50

If 23

_y

_{\;\text{two}\;}

, find the value of y

Solution:

Concept:

The value of a numeral in any base is found by multiplying each digit by the base raised to its place value.

Explanation:

Expand

23_y

using base

y

23_y = 2 \times y^1 + 3 \times y^0

= 2y + 3

Expand

1111_{\mathrm{two}}

using base

2

1111_{\mathrm{two}} = 1 \times 2^3 + 1 \times 2^2 + 1 \times 2^1 + 1 \times 2^0

= 8 + 4 + 2 + 1

= 15

Equate the two expansions:

2y + 3 = 15

2y = 15 - 3

2y = 12

y = \frac{12}{2}

y = 6

Answer:

y = 6

Therefore, the correct option is C.

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