How Cheenta works to ensure student success?
Explore the Back-Story

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 abc.

By the given condition of arithmetic mean we get,

    \[\frac{a+c}{2}=b\]

.

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

Given that the number is divisible by 18

\Rightarrow Given number must be divisible by both 2 and 9.

Apply divisibility rule of 9 to guess the values of a, b, c.

Here the values of 3b are 9, 18, 27.

\Rightarrow the values of 2b are 6, 12, 18.

Now guess the values of a+c?

And then find the possible pair of (a, c)?

The possible values of (a, c) are (2,4), (4,2), (6,0), (4,8), (6,6), (8,4).

So, how many possible numbers are there?

Subscribe to Cheenta at Youtube


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 abc.

By the given condition of arithmetic mean we get,

    \[\frac{a+c}{2}=b\]

.

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

Given that the number is divisible by 18

\Rightarrow Given number must be divisible by both 2 and 9.

Apply divisibility rule of 9 to guess the values of a, b, c.

Here the values of 3b are 9, 18, 27.

\Rightarrow the values of 2b are 6, 12, 18.

Now guess the values of a+c?

And then find the possible pair of (a, c)?

The possible values of (a, c) are (2,4), (4,2), (6,0), (4,8), (6,6), (8,4).

So, how many possible numbers are there?

Subscribe to Cheenta at Youtube


Leave a Reply

This site uses Akismet to reduce spam. Learn how your comment data is processed.

Knowledge Partner

Cheenta is a knowledge partner of Aditya Birla Education Academy
Cheenta

Cheenta Academy

Aditya Birla Education Academy

Aditya Birla Education Academy

Cheenta. Passion for Mathematics

Advanced Mathematical Science. Taught by olympians, researchers and true masters of the subject.
JOIN TRIAL
support@cheenta.com
Menu
Trial
Whatsapp
magic-wandrockethighlight