BTGModeratorVI wrote: ↑Tue May 12, 2020 2:18 pm
The integers x and y are both positive, the remainder when x is divided by 12 is 7, and the remainder when y is divided by 12 is 3. Each of the following is a possible value of 2x+y EXCEPT
A. 125
B. 101
C. 77
D. 51
E. 41
Answer:
D
Source: Kaplan
One approach is to
test values
IMPORTANT: When it comes to remainders, we have a nice rule that says:
If N divided by D, leaves remainder R, then the possible values of N are R, R+D, R+2D, R+3D,. . . etc.
For example, if k divided by 5 leaves a remainder of 1, then the possible values of k are: 1, 1+5, 1+(2)(5), 1+(3)(5), 1+(4)(5), . . . etc.
Okay, onto the question....
The remainder when x is divided by 12 is 7
Possible values of x = 7, 19, 31, 43, 55, ...
So, possible values of
2x are: 14, 38, 62, 86, 110, ...
The remainder when y is divided by 12 is 3
Possible values of
y are: 3, 15, 28, 40, 52, ...
Each of the following is a possible value of 2x + y EXCEPT
A) 125 This equals
110 +
15. ELIMINATE A
B) 101 This equals
86 +
15. ELIMINATE B
C) 77 This equals
62 +
15. ELIMINATE C
D) 51
E) 41 This equals
38 +
3. ELIMINATE E
Answer: D
Cheers,
Brent
