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Exponent Math

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Exponent Math

by cbenk121 » Wed Nov 11, 2009 6:52 pm
(1001^2 - 999^2) / (101^2 - 99^2) = ?

(A) 10
(B) 20
(C) 40
(D) 80
(E) 100

OA: A

My first reaction was "What the fuck??", but realized there's always a trick...can you figure it out?
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by jaroth04 » Wed Nov 11, 2009 7:16 pm
This seems to me to be an application of the difference of two squares:

(a * a - b * b) = (a + b)(a - b)

Substituting 1001 for a and 999 for b in the numerator gives us:

(1001 + 999) * (1001 - 999) = 2000 * 2 = 4000

We can make a similar substitution in the denominator and get:

(101 + 99) * (101 - 99) = 200 * 2 = 400

Simple division from there gives us 10.
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by cbenk121 » Thu Nov 12, 2009 11:32 am
jaroth04 wrote:This seems to me to be an application of the difference of two squares:

(a * a - b * b) = (a + b)(a - b)

Substituting 1001 for a and 999 for b in the numerator gives us:

(1001 + 999) * (1001 - 999) = 2000 * 2 = 4000

We can make a similar substitution in the denominator and get:

(101 + 99) * (101 - 99) = 200 * 2 = 400

Simple division from there gives us 10.
Yup right on. If you were writing it out, you could cancel out the "2"s and two zeroes, leaving 20/2 = 10, instead of calculating numerator and denominator (assuming you would write those out as well).
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