GMAT Prep - Exponents and Factoring

This topic has expert replies
Master | Next Rank: 500 Posts
Posts: 158
Joined: Mon Nov 02, 2009 5:49 pm
Thanked: 2 times
Followed by:3 members

GMAT Prep - Exponents and Factoring

by tonebeeze » Fri May 20, 2011 12:44 pm
What is the best way not to get tripped up or slowed down by these problems?

{(1000)^2 - (999)^2} / {(101)^2 - (99)^2} =

a. 10
b. 20
c. 40
d. 80
e. 100

OA = 10
Our collective understanding of the GMAT grows through research, contribution, and teamwork. If you found a problem or comment challenging, helpful, or encouraging, please consider hitting the THANKS button!

GMAT/MBA Expert

User avatar
GMAT Instructor
Posts: 2621
Joined: Mon Jun 02, 2008 3:17 am
Location: Montreal
Thanked: 1090 times
Followed by:355 members
GMAT Score:780

by Ian Stewart » Fri May 20, 2011 12:57 pm
If you found this question time-consuming, you'll certainly benefit from learning to recognize the difference of squares whenever it shows up - it will almost definitely appear on your real GMAT. If you ever have anything in the a^2 - b^2 pattern, you can factor it as (a+b)(a-b). So in the question above,

(1001^2 - 999^2)/(101^2 - 99^2) = [(1001+999)(1001-99))]/[(101+99)(101-99)] = (2000*2)/(200*2) = 10
For online GMAT math tutoring, or to buy my higher-level Quant books and problem sets, contact me at ianstewartgmat at gmail.com

ianstewartgmat.com