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Impossible numbers

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Impossible numbers

by dvalenz » Sat Mar 23, 2013 5:11 pm
Hi I found this question and found it super hard. It was very time consuming and in the end I didn't e ven get close to the answer.
The question is the following:

1001^2-999^2 divided by 101^2-99^2

Is there a short cut?

Thank you
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by Brent@GMATPrepNow » Sat Mar 23, 2013 5:18 pm
dvalenz wrote:Hi I found this question and found it super hard. It was very time consuming and in the end I didn't e ven get close to the answer.
The question is the following:

1001^2-999^2 divided by 101^2-99^2

Is there a short cut?

Thank you
These kinds of questions are algebra questions in disguise (even though there are no variables).

We know that x^2 - y^2 = (x+y)(x-y)
Similarly, 1001^2 - 999^2 = (1001 + 999)(1001 - 999)

So...[1001^2 - 999^2]/[101^2 - 99^2] = (1001 + 999)(1001 - 999)/(101 + 99)(101 - 99)
= (2000)(2)/(200)(2)
= 4000/400
= 10

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by GMATGuruNY » Sat Mar 23, 2013 5:21 pm
dvalenz wrote:Hi I found this question and found it super hard. It was very time consuming and in the end I didn't e ven get close to the answer.
The question is the following:

1001^2-999^2 divided by 101^2-99^2

Is there a short cut?

Thank you
x² - y² = (x+y)(x-y).
Thus:

(1001²-999²) / (101²-99²)

= (1001+999)(1001-999) / (101+99)(101-99)

= (2000)(2) / (200)(2)

= 10.
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by rintoo22 » Sun Mar 24, 2013 7:40 am
As mentioned by experts above.

x^2 - y^2 = (x-y)(x+y) should do the trick.
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