MHB What Is (x+y) Mod 11 If A=52x1y3 Equals 4 Mod 11?

[Albert1]

$A=52x1y3$ is a 6 digits number
if $A$ mod 11=4
find $(x+y)$ mod 11=?

 

[mente oscura]

$A=52x1y3$ is a 6 digits number
if $A$ mod 11=4
find $(x+y)$ mod 11=?

Hello.

Spoiler

If \ A \equiv{4 } \mod(11)

and

520103 \equiv{1 } \mod(11)

then

520183 \equiv{4 } \mod (11), \ for \ 80 \equiv{ 3} \mod(11)

Since:

1000 \equiv{10 } \mod(11)

and

10 \equiv{10 } \mod(11)

To increase it x in 1000 units is equivalent to diminish and in 10 units.

Therefore:

(x+y)=8

Regards.

 

[kaliprasad]

$A=52x1y3$ is a 6 digits number
if $A$ mod 11=4
find $(x+y)$ mod 11=?

Spoiler

A mod 11 =-(5+x+y) + (2+1+3) mod 11 = 4

so (x+y-1) mod 11 = - 4

(x+y) mod 11 = -3 or 8 to make it positive