Problem Solving

Max@Math Revolution wrote:[GMAT math practice question]

If x is the sum of all odd numbers between 1001 and 2000, inclusive and y is the sum of all even numbers between 1001 and 2000, inclusive, what is the value of x - y?

A. -1000
B. -500
C. 0
D. 500
E. 1000

We se that x = 1001 + 1003 + 1005 + ... + 1999 and y = 1002 + 1004 + 1006 + ... + 2000. Thus,

x - y = (1001 + 1003 + 1005 + ... + 1999) - (1002 + 1004 + 1006 + ... + 2000)

x - y = (1001 - 1002) + (1003 - 1004) + (1005 - 1006) + ... + (1999 - 2000)

x - y = (-1) + (-1) + (-1) + ... + (-1)

We see that x - y is the sum of some quantity of -1's. We need to determine the number of -1's we are adding. Notice that there are 500 odd numbers from 1001 to 1999, inclusive. Likewise, there are 500 even numbers from 1002 to 2000, inclusive. When we pair a number from the 'x' sum and a number from the 'y' sum, we have 500 pairs. Thus, we are adding 500 -1's. Therefore,

x - y = 500(-1)

x - y = -500

Answer: B