Another tougher GMAT question?

Question

This question goes:

What is 1001 (squared) minus 999 (squared) /(divided by) 101 (squared) minus 99 (squared)?

How do you do this problem in under 2 minutes?

Answer 1

Doesn't anyone remember factoring differences of squares?
a^2 - b^2 = (a+b)(a-b)
so 1001^2 - 999^2 = (1001+999)(1001-999) = (2000)(2) = 4000
Also
101^2 - 99^2 = (101+99)(101-99) = (200)(2) = 400

So 4000/400 = 10
The answer is 10.

Answer 2

use the formula a^2-b^2= (a+b)(a-b)
1001^2-999^2 = (1001+999)(1001-999) = 2000* 2
similarly
101^2-99^2 = (101+99)*2 = 200*2
so ratio = 10

Answer 3

(1001²-999²)/(101²-99²) or

( (a+2)² -a² )/( (b+2)² - b² ) with a=999 and b=99

(x+y)²=x²+2xy+y²

so
( (a+2)² -a² )/( (b+2)² - b² )
is
( (a²+(2*2)a + 2²)-a² )/( (b²+(2*2)b + 2²)-b² )
is
( (a² + 4a + 4 - a² )/( (b² + 4b + 4 - b² )
is
(4a + 4)/(4b + 4)
is
4(a+1)/4(b+1)
is (a+1)/(b+1)

now we substitute
(999+1)/(99+1)
1000/100
10 is the answer


this method takes a quick analysis and easy math
if the analysis is correct, then less room for error in the answer

good luck

Answer 4

(1001^2 - 999^2) / (101^2 - 99^2) =
(1001+999)*(1001-999) / ((101+99)*(101-99) =
2000*2 / (200*2) =
10

Answer 5

1001-999 (square result) / 101-99 (square result) =1

Answer 6

1
If it was writtien like this (1001^2-999^2)/(101^2-99^2)
They are all the same power, so reduce to the power of one.
then just do the subtraction and devision
(1001-999)/(101-99)
2/2=1
But if it is written differently then I don't know.

Answer 7

(1001+999)(1001-999)/(101+99)(101-99)=
2000x2/200x2=10
it comes from the identity
(a+b)(a-b)=a^2-b^2
good luck with gmat

Answer 8

i would square 1001 and square 999

then, subtract the answer of the 999 (998001) from 1001 (1002001) which is 4000

then, square 101 (10201) and 99 (9801) and subtract them which is 400

then, divide your two answers 4000 divided by 400 and your answer is 10

Answer 9

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Answer 10

Answer is 10...basically ignore the squared in the first part...and just do the simple math