GMAT Question of the Day – Data Sufficiency – Absolute Value

If x is an integer is \( y < 2 \)? (1) \( \lvert x \rvert-x = y \) (2) \( x < \lvert x \rvert \) [spoiler]C.[/spoiler]

GMAT Question of the Day Solution

For GMAT absolute value questions think about the signs (+, -). What happens when the underlying variable is positive? What happens when it is negative? In statement (1) we can see that a positive value of x will yield a value of zero for y whereas a negative value for x will yield a value of -2x for y. This leaves us with many possible values and so statement (1) is insufficient. Statement (2) doesn’t tell us anything about y but tells us that x must be negative. Insufficient. Putting the statements together y must equal -2x and x must be negative. So the least possible value for y is 2 (when x is -1). This means that y cannot be less than 2. Sufficient.