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# Math Kangaroo (Benjamin) 2020 Problem 26 | Divisibility Rule Try this beautiful Problem based on Divisibility Rule from Math Kangaroo (Benjamin) 2020.

## Math Kangaroo (Benjamin), 2020 | Problem No 26

We say that a three-digit number is balanced if the middle digit is the arithmetic mean of the other two digits. How many balanced numbers are divisible by 18 ?

• 2
• 3
• 6
• 9
• 18

### Key Concepts

Arithmetic

Divisibility Rule

Arithmetic Mean

## Suggested Book | Source | Answer

Algebra by Gelfand

Math Kangaroo (Benjamin), 2020

6

## Try with Hints

Let the number be By the given condition of arithmetic mean we get, .

Now from here can I conclude are of the same parity?

Given that the number is divisible by  Given number must be divisible by both and .

Apply divisibility rule of to guess the values of .

Here the values of are . the values of are .

Now guess the values of ?

And then find the possible pair of ?

The possible values of are , , , , , .

So, how many possible numbers are there?

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Try this beautiful Problem based on Divisibility Rule from Math Kangaroo (Benjamin) 2020.

## Math Kangaroo (Benjamin), 2020 | Problem No 26

We say that a three-digit number is balanced if the middle digit is the arithmetic mean of the other two digits. How many balanced numbers are divisible by 18 ?

• 2
• 3
• 6
• 9
• 18

### Key Concepts

Arithmetic

Divisibility Rule

Arithmetic Mean

## Suggested Book | Source | Answer

Algebra by Gelfand

Math Kangaroo (Benjamin), 2020

6

## Try with Hints

Let the number be By the given condition of arithmetic mean we get, .

Now from here can I conclude are of the same parity?

Given that the number is divisible by  Given number must be divisible by both and .

Apply divisibility rule of to guess the values of .

Here the values of are . the values of are .

Now guess the values of ?

And then find the possible pair of ?

The possible values of are , , , , , .

So, how many possible numbers are there?

## Subscribe to Cheenta at Youtube

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