If -13 < 7x + 1 < 29 and 19 < 2 - b < 23, what is the maximum possible integer value of x + y?  Pick:  A) -23  B) -18  C) -13  D) -14  E) -12
Really nice question and plays with a classic GMAT trap. We arrive at the final equation that a + b &lt; -13. So the maximum integer values of a + b should be LESSER THAN -13 and that can only be -14.   -13 &lt; 7a + 1 &lt; 29   Subtracting 1 from the equation   -14 &lt; 7a &lt; 28   Dividing by 7   -2 &lt; a &lt; 4 ........... (1)   19 &lt; 2 - b &lt; 23   Multiplying by -1   -23 &lt; b - 2 &lt; -19   Adding 2 to the equation   -21 &lt; b &lt; -17 ........... (2)   Adding 1 and 2   -23 &lt; a + b &lt; -13   Answer is -14
<result>D</result>
If -13 < 7x + 1 < 29 and 19 < 2 - b < 23, what is the maximum possible integer value of x + y?