Easy Peasy

Number Theory Level 3

Consider the number above where x and y are digits not multiplication.

Find the difference between the greatest possible value of the number (divisible by 3 and 15) and the least possible value of the number (also divisible by 3 and 15).


The answer is 90.

William Isoroku by William Isoroku , 25, USA

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1 solution

William Isoroku
Aug 1, 2014

The smallest possible value is 201300, which is divisible by 3 and 15. The greatest possible value is 201390, which is also divisible by 3 and 15. So 201390-201300= 90.

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If it is divisible by 15, it has to be divisible by 3. Any reason why you wrote it in such a way?

Calvin Lin Staff - 6 years, 10 months ago

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Why can I not?

William Isoroku - 6 years, 10 months ago

Is there a rule for divisibility by 15? Or, is there a general rule for divisibility by x for numbers in base 10 similar to the rule for 3 and 9?

Braden Gammon - 6 years, 10 months ago

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