Question 1022880
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The five digit number a986b is divisible by 72. What is the value of a+b ?
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72 = 9*8.

The sum of digits S = a + 9 + 8 + 6 + b must be multiple of 9 and the number 86b must be multiple of 8.

See the divisibility by 9 rule in the lesson <A HREF=http://www.algebra.com/algebra/homework/divisibility/lessons/Divisibility-by-9-rule.lesson>Divisibility by 9 rule</A> in this site.

The divisibility by 8 rule says that the number 86b is multiple of 8.

From this condition ("86b must be multiple of 8") we have with necessity that b = 4. There is no other possibility.

Now, S = 23 + (a + b) = 23 + 4 + a = 27 + a.

a >= 1 and <= 9.

Since S is multiple of 9, there is only one possibility for a:

a = 9.

<U>Answer</U>. a = 9, b= 4 and a + b = 9 + 4 = 13.
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