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WAEC Mathematics 2018 Paper

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Question : 4

Total: 50

Find the value of x for which

32_{\text{four}} = 22_x

three
five
six
seven

Solution:

Concept:

Convert both base numerals to base ten and then equate them.

Explanation:

Write

32_{\text{four}}

in base ten.

32_{\text{four}} = 3 \times 4^1 + 2 \times 4^0

= 3 \times 4 + 2 \times 1 = 12 + 2 = 14

Write

22_x

in base ten.

22_x = 2 \times x^1 + 2 \times x^0 = 2x + 2

Since

32_{\text{four}} = 22_x

, equate the values.

14 = 2x + 2

14 - 2 = 2x

12 = 2x

x = \frac{12}{2} = 6

Answer:

The value of

x

is

6

.

The correct option is C. six.

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