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When the number  is divided by , what is the remainder?We have positive integers $a,$ $b,$ and $c$ such that $a > b > c.$ When $a,$ $b,$ and $c$ are divided by $19$, the remainders are $4,$ $2,$ and $18,$ respectively. When the number $2a + b - c$ is divided by $19$, what is the remainder?

 

Thank you so so so much in advance!

 Dec 21, 2020
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A mod 19 = 4
B mod 19 = 2
C mod 19 = 18, solve for A, B, C

 

A =19m + 4,  B=19m + 2,   C =19m  +  18, where m=0, 1, 2, 3.......etc.

Since A > B > C, then:


A=19*2 + 4 = 42
B =19*2 + 2 = 40
C =19*1 + 18= 37

 

[2A + B - C] =[2*42 + 40 - 37]==87 mod 19==11

 Dec 21, 2020

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