GMAT Question of the Day – Data Sufficiency – Absolute Value
If x > y > z, is |x+y| = |x-z|?
(1) Zero is equidistant from y and z
(2) y is greater than 0
GMAT Question of the Day Solution
Many GMAT tutoring students hate absolute value. They find it very confusing. Let’s think of absolute value as a measure of distance. So that whether a number is negative or positive it still represents the same distance which must be positive. In the question we are being asked whether the distance from x to -y is the same as the distance from x to z. Why x to -y? Because x+y is the same as x – (-y). We are also given a hierarchy which may be important once we go to the statements.
Statement 1 tells us that y and z must have the same absolute value. So they must either be the same number or be the same number with opposite signs. Given the hierarchy x > y > z we know that y and z cannot be the same number. So therefore |x+y| must equal |x-z| because y = -z. You can put the values on a number line to demonstrate this. You might be thinking – what about x? Well it doesn’t matter where x is as long as we know where y and z are relative to each other. Sufficient.
Statement 2 on it’s own reveals little about the positions of x, y, and z so we cannot answer the question. Insufficient.