Find my A and B

Number Theory Level 2

If the 7-digit integer 3 A 54 B 10 ‾ \overline{3A54B10} is divisible by 330, which of the options are the possible values of A A and B B ?

A = 2 , B = 3 A=2,B=3 A = 1 , B = 4 A=1,B=4 A = 4 , B = 1 A=4, B=1 A = 3 , B = 2 A=3, B=2

Y'dnar Omalat by Y'dnar Omalat , 34, Philippines

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2 solutions

The number is divisible by 330 , means it must be divisible by 11 .

So from the options , the values of A A and B B which make the number divisible by 11 11 are 4 4 and 1 1 respectively . Other values do not make the number divisible by 11 . And hence , A = 4 , B = 1 \boxed{A=4 , B=1} .

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Denton Young
Jun 24, 2017

Divisibility by 11: add and subtract the digits alternately, you have to end up with 0. Doing this on the give number yields (B+3) - A =0, or A = B + 3.

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