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by karthikpandian19 » Tue Dec 20, 2011 11:35 pm
Find the value of this :

(100-100)/(100-100)

a. 0
b. 10
c. 100
d. -10
e. 2

"i know this is simple, but somewhere while browsing i found a different answer and also found a proper explanation, which is given below. After trying, check the answer below. And let me know what is right answer should be...."

[spoiler]=(100-100)/(100-100)
= (10^2 - 10^2)/(10(10-10))
= ((10-10)(10+10))/(10(10-10))...........using a^2 - b^2 formula
=now cancel out the common (10-10)
= (10+10)/10
= 20/10
= 2
??????i am really amazed??? [/spoiler]

Can you explain?
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by shankar.ashwin » Tue Dec 20, 2011 11:42 pm
You just can't cancel '0' on the numerator and denominator and equate the other 2 terms.

For eg; a * 0 = b * 0

But 'a' need not be equal to 'b'.

99*0 = 1*0

99=1 ? makes sense?
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by karthikpandian19 » Wed Dec 21, 2011 12:42 am
Ashwin,

So you mean to say that this solution should end up with the value "2" ???
shankar.ashwin wrote:You just can't cancel '0' on the numerator and denominator and equate the other 2 terms.

For eg; a * 0 = b * 0

But 'a' need not be equal to 'b'.

99*0 = 1*0

99=1 ? makes sense?
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by shankar.ashwin » Wed Dec 21, 2011 12:47 am
karthikpandian19 wrote:Ashwin,

So you mean to say that this solution should end up with the value "2" ???
No. (100-100)/(100-100) = 0/0 which is undefined. It cannot be any of the answer choices mentioned.
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by karthikpandian19 » Wed Dec 21, 2011 12:55 am
Ashwin,

I understood that 0/0 is indeterminate.

But what is your thought on the explanation given in the algebraic form to prove it is 2 ?
shankar.ashwin wrote:
karthikpandian19 wrote:Ashwin,

So you mean to say that this solution should end up with the value "2" ???
No. (100-100)/(100-100) = 0/0 which is undefined. It cannot be any of the answer choices mentioned.
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by shankar.ashwin » Wed Dec 21, 2011 1:09 am
karthikpandian19 wrote:Ashwin,

I understood that 0/0 is indeterminate.

But what is your thought on the explanation given in the algebraic form to prove it is 2 ?
Its faulty math. There are a few common algebraic solutions which lead to misleading answers sometimes.

Wiki has an article https://en.wikipedia.org/wiki/Invalid_proof

For the problem in question, read the division by 0 in that page. Hope it helps.

If that question was from a GMAT material, I believe the question is wrong and the proof is as absurd as 1=2 :)
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by GMATGuruNY » Wed Dec 21, 2011 5:51 am
karthikpandian19 wrote:Find the value of this :

(100-100)/(100-100)

a. 0
b. 10
c. 100
d. -10
e. 2
The given expression is UNDEFINED, so there is no correct answer here.
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