GMAT Practice Question: If x>y and y>z, which of the following represents the greatest number?

Step 1

We first note the given inequalities.

x>y y>z

Step 2

We apply \textbf{\text{"Chain Rule for Inequalities"}} to combine them.

x>z

Step 3

We subtract y from both sides of x>y to find the sign of x-y.

x-y>0

Step 4

We subtract z from both sides of x>z to find the sign of x-z.

x-z>0

Step 5

We express x-z as the sum of the positive differences x-y and y-z.

x-z=(x-y)+(y-z)

Step 6

Since both x-y and y-z are positive, their sum x-z is the greatest among the listed expressions.