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# If two of four expressions x + y, x + 5y, x - y and 5x - y

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Manager
Joined: 11 Jan 2008
Posts: 54
If two of four expressions x + y, x + 5y, x - y and 5x - y  [#permalink]

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04 Jan 2009, 21:59
If two of four expressions x + y, x + 5y, x - y and 5x - y are chosen at random, what is the probability that their product will be of the form of x^2 - (by)^2, where b is an integer.

just a quick question on this one,

in this do we need to figure out which 2 expressions to choose? or is it sure any 2 of them will have the asked form.

so, in that case we need to pick 2 exp.
for first one prob is 2/4 and for 2nd it is 1/3.

its easier here since we know the 2 expressions that would give the asked form...but what if it is not so easy to figure that out.

I hope i am not confusing much....

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VP
Joined: 17 Jun 2008
Posts: 1474

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04 Jan 2009, 22:28
We certainly need to figure out the product which two of the expressions will be of the form a^2 - (by)^2.

For example, if I change the expressions in the original equation to x+y, x-y, x+5y, x-5y, the desired probability will be different.

Hope I am clear.
Intern
Joined: 03 Jan 2009
Posts: 10

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07 Jan 2009, 10:44
There are 4C2 ways in which 2 expressions can be chosen at random from 4.
Out of that exactly one combination (x+y)*(x-y) gives the desired result.

So, the probability of getting this one specific combonation = 1/4C2 = 1/6

HTH

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Re: probability expressions &nbs [#permalink] 07 Jan 2009, 10:44
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# If two of four expressions x + y, x + 5y, x - y and 5x - y

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