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Do you remember the rules of divisibility from your junior mathematics class?

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**LEVEL: JUNIOR** **MATHEMATICS**

**TOPIC: RULES OF DIVISIBILITY**

## QUESTION

If 526y9 is exactly divisible by 11

Find the possible value of y

## WORKED EXAMPLE

If 406y8 is exactly divisible by 11

Find the possible value of y

## SOLUTION WORKED EXAMPLE

#### RULE OF DIVISIBITY OF 11: SUM OF ALTERNATIVE DIGITS MUST BE EQUAL.

Hence, we have:

4 + 6 + 8 = 0 + y

18 = y

OR

y = 18

But y must be a single digit:

The remainder when 18 is divided by 11 is 7

\frac{18}{11} = 1\frac{7}{11}

Therefore,

y = 7

## THE QUESTION WAS:

If 526y9 is exactly divisible by 11

Find the possible value of y

## SOLUTION

#### RULE OF DIVISIBITY OF 11: SUM OF ALTERNATIVE DIGITS MUST BE EQUAL.

Hence, we have:

5 + 6 + 9 = 2 + y

20 = y + 2

OR

y = 18

But y must be a single digit:

The remainder when 18 is divided by 11 is 7

\frac{18}{11} = 1\frac{7}{11}

Therefore,

y = 7

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