fattty wrote:
When x is divided by 2, remainder is 1 and y is divided by 8, remainder is 2. Which of following
could be the value of 2x + y? (x and y are integers)
A) 10
B) 11
C) 12
D) 13
E) 14
When dealing with remainders and equations, it is often helpful to translate the words into formulas.
"When x is divided by 2, remainder is 1" --> This means that x is 1 more than a multiple of 2 --> \(x = 2a+1\), where \(a\) is an integer.
"y is divided by 8, remainder is 2" --> This means that y is 2 more than a multiple of 8 --> \(y = 8b+2\), where \(b\) is an integer.
Now if we plug those expressions into 2x + y we get:
\(2x + y = [2(2a+1)] + [8b+2]\)
\(= 4a+2 + 8b+2\)
\(= 4(a+2b+1)\)
So 2x + y = 4*(some integer), and is therefore a multiple of 4. The only answer choice that is a multiple of 4 is C) 12.
Answer: C
_________________
Dave de Koos
GMAT aficionado