tonker wrote:1001^2 - 999^2 / 101^2 - 99^2 ?

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

Answer is a. Can someone please explain it.

Thanks,
Vito

This is from the GMAT Prep.

check this approach a ^ 2 - b ^ 2 = (a + b) (a - b)

Based on (a + b)^2 = a^2 + b^2 + 2*a*b
and (a - b)^2 = a^2 + b^2 - 2*a*b:

(1001^2 - 999^2) / (101^2 - 99^2)
= (1000 + 1)^2 - (1000 - 1)^2 / (100 + 1)^2 - (100 - 1)^2
= (1000^2 + 1^2 + 2*1*1000) - (1000^2 + 1^2 - 2*1*1000) / (100^2 + 1^2 + 2*1*100) - (100^2 + 1^2 - 2*1*100)
= 4000/400
= 10

In solving this question, let us first recall the algebraic equation
a^2 - b^2 = (a-b)(a+b)
(1001^2 - 999^2) / (101^2 - 99^2)
solving the numerator first,
1001^2 - 999^2 = (1001-999)(1001+999)
=(2)(2000)
=4000
let solve the denominator
101^2 - 99^2 = (101-99)(101+99)
=2*200
=400
Solving mathematically using the division method,
numerator/denominator= 4000/400
=10

we got 10 as the answer which is option A