UKMT Special (Problem 1515)

The five-digit number a679ba679b is a multiple of 7272

What are the values of aa and bb?

[UKMT Hamilton Olympiad 20152015, H11]

Note by Yajat Shamji
8 months, 2 weeks ago

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You have until next Monday, 3:003:00pm!

Yajat Shamji - 8 months, 2 weeks ago

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Step 1) A number is divisible by 72, if and only if it is divisible by 8 and 9.

Step 2) According to divisibility rules, a679b is divisible by 8 if 79b is divisible by 8.

   Only b = 2 that satisfy.

Step 3) According to divisibility rules, a6792 is divisible by 8 if a + 6 + 7 + 9 + 2 is divisible by 9.

   a + 6 + 7 + 9 + 2 = a + 24 is divisible by 9.
   Only a = 3 that satisfy

The five-digit number is 36792.

Quest Keeper - 8 months, 2 weeks ago

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Correct solution and method!

Yajat Shamji - 8 months, 2 weeks ago

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