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JAMB Mathematics 2023 Paper

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Question : 26

Total: 80

Find the value of y if

402_y = 102_{\text{ten}}

4
2
5
3

Solution:

Concept:

A number written in base

y

is expanded using powers of

y

before solving for

y

.

Explanation:

Expand

402_y

in powers of

y

.

402_y = 4 \times y^2 + 0 \times y^1 + 2 \times y^0

Since

y^0 = 1

, this becomes:

4y^2 + 0 + 2(1) = 102

So,

4y^2 + 2 = 102

Subtract 2 from both sides:

4y^2 = 100

Divide both sides by 4:

y^2 = 25

Take the positive square root because a base must be positive:

y = \sqrt{25} = 5

Answer:

y = 5

Correct option: C. 5

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