(1001^2 - 999^2)/(101^2 - 99^2) =

Question

\frac{1001^2-999^2}{101^2-99^2}=

A. 10
B. 20
C. 40
D. 80
E. 100

Bunuel · Answer

\frac{1001^2-999^2}{101^2-99^2}=

A. 10
B. 20
C. 40
D. 80
E. 100

\frac{1001^2-999^2}{101^2-99^2}=\frac{(1001-999)(1001+999)}{(101-99)(101+99)}=\frac{2*2000}{2*200}=10

Answer: A.

ScottTargetTestPrep · Answer

Both the numerator and the denominator are a difference of squares. Using the given information, we have:

(1001 - 999)(999 + 1001)/

(2)(2000)/  = 10

Answer: A

BrentGMATPrepNow · Answer

Key Property:  x^2 - y^2 = (x+y)(x-y)  (i.e., factoring a difference of squares)

\frac{1001^2-999^2}{101^2-99^2}=\frac{(1001+999)(1001-999)}{(101+999)(101-99)}

=\frac{(2000)(2)}{(200)(2)}

=\frac{4000}{400}

= 10

Answer: A

totaltestprepNick · Answer

A https://www.youtube.com/watch?v=qvI-ONcXih4 Nick Slavkovich, GMAT/GRE tutor with 20+ years of experience tutoring@totaltestprep.net

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