Can someone help me with this problem?

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Can someone help me with this problem?

by tonker » Tue Jan 16, 2007 3:57 pm
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,
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by beatthegmat » Tue Jan 16, 2007 4:19 pm
What is the source of this question?
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Re: Can someone help me with this problem?

by tonker » Tue Jan 16, 2007 4:22 pm
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.

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by rajs.kumar » Tue Jan 16, 2007 5:11 pm
check this approach a ^ 2 - b ^ 2 = (a + b) (a - b)

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solution

by axefx » Wed Jan 17, 2007 11:07 am
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

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by Stacey Koprince » Wed Jan 17, 2007 7:08 pm
Alternatively, using Raj's suggestion (this is the shortcut):
1001^2 - 999^2 / 101^2 - 99^2

(1001 + 999)(1001 - 999) / (101 + 99)(101-99)
(2000)(2)
(200)(2)
cross off 2's, cross off two zero's each from top and bottom
20/2
10
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by BTGmoderatorRO » Fri Sep 01, 2017 6:03 pm
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

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tonker wrote:
Tue Jan 16, 2007 3:57 pm
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
We can see that both the numerator and denominator are differences of two squares. Therefore, the numerator can be factored and simplified as:

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

Similarly, the denominator can be factored and simplified as:

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

Therefore, the quotient is 4000/400 = 10.

Answer: A

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