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WAEC Mathematics 2020 Paper

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Question : 5

Total: 48

If 101

_{\text{two}}

_{\text{five}}

. Find the value of y

8
7
6
5

Solution:

Concept:

Convert all base numerals to base ten before equating and solving for

y

.

Explanation:

Convert

101_{\mathrm{two}}

to base ten:

101_{\mathrm{two}} = 1 \times 2^{2} + 0 \times 2^{1} + 1 \times 2^{0} = 4 + 0 + 1 = 5

.

Convert

12_y

to base ten:

12_y = 1 \times y^{1} + 2 \times y^{0} = y + 2

.

The right-hand base-five value is

23_{\mathrm{five}}

, which in base ten is:

23_{\mathrm{five}} = 2 \times 5^{1} + 3 \times 5^{0} = 10 + 3 = 13

.

So the equation becomes:

5 + (y + 2) = 13

.

y + 7 = 13

.

y = 13 - 7 = 6

.

Answer:

y = 6

, i.e. option C.

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