A and B=?

Number Theory Level pending

How many possible ordered pairs ( A , B A, B ) of digits are there for which the decimal number

7 A 8 B \large 7\ A\ 8 \ B is divisible by 45?

3 0 2 4 1

Hana Wehbi by Hana Wehbi , 51, USA

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1 solution

Hana Wehbi
Mar 7, 2017

The ordered pair is ( 3 , 0 ) (3,0) and ( 7 , 5 ) (7,5) . The number is divisible by 5 5 and 9 9 , so B B must be 0 0 or 5 5 , and the sum of the digits must be divisible by 9 9 .

2 Helpful 0 Interesting 0 Brilliant 0 Confused

It's ( 7 , 5 ) (7,5)

Freddie Hand - 4 years, 3 months ago

@Freddie Hand , Thanks, I fixed it.

Hana Wehbi - 4 years, 3 months ago

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