Question

When x is divided by 9, the reminder is 4. What will be the reminder if 2x + 3 is divided by 9?

A. 2
B. 4
C. 7
D. Cannot be determined by given information

Answer 1

possible values of x
13, 22, 31, 40, 49, 58, 67, ..... , each leaving a remainder of 3 when divided
by 9

possible values of 2x+3
29, 47, 65, 83, 101, 119, 137, ...

remainder when these are divided by 9:
2, 2, 2, 2, 2, ....

mmmmhhhh?

proof

the value of x we want takes the form 9k + 4
e.g. ( 31 = 9*3 + 4 , where k = 3 )

so the value of our x's after the transformation look like 2(9k+4) + 3
= 18k + 11
= 18k + 9 + 2
= 9(2k + 1 ) + 2 , the first part is multiplied by 9, so it is a multiple of 9
and the expression is 2 more than a multiple of 9
so when divided by 9 we are left with a remainder of 2

btw, it is a "remainder" , not a "reminder"