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Re: what is the value of y? [#permalink]
16 Dec 2012, 07:06

2

This post received KUDOS

Expert's post

mridulparashar1 wrote:

JJ2014 wrote:

What is the value of y?

(1) x^2 - y^2 = 5 (2) x and y are each positive integers

Hi,

From 1, we get (x-y)(x+y)=5 i.e (x-y)=1,5 or (x+y)= 5,1...solving we get 2 values of y (one positive and one negative)

From 2 alone we get nothing

combining 1 & 2 we get X and Y as postive and we get one solution

The red part is not correct. From x^2 - y^2 = 5 we cannot say that x-y=1 and x+y=5 (or vise-versa) because for (1) we don't know whether x and y are integers. So, for example it's possible that x-y=10 and x+y=1/2. Even if we knew that x and y are integers, still from (x+y)(x-y)=5 it follows that x+y=5 and x-y=1 (or vise versa) OR x+y=-5 and x-y=-1 (or vise versa).

What is the value of y?

(1) x^2 - y^2 = 5. Infinitely many solutions exist for x and y. Not sufficient.

(2) x and y are each positive integers. Not sufficient.

(1)+(2) Since \(x\) and \(y\) are positive integers then \(x+y=integer>0\) and \(x-y=integer\) AND \(x+y>x-y\). Thus from \(x^2 - y^2 =(x+y)(x-y)= 5\) we'd have that \(x+y=5\) and \(x-y=1\), from which it follows that \(y=2\). Sufficient.

What is the value of y?? [#permalink]
28 Feb 2013, 21:07

1

This post received KUDOS

(1)\(x^{2}\)-\(y^{2}\)=5 (2) x and y are each positive integers. _________________

I've failed over and over and over again in my life and that is why I succeed--Michael Jordan Kudos drives a person to better himself every single time. So Pls give it generously Wont give up till i hit a 700+

Re: What is the value of y?? [#permalink]
28 Feb 2013, 22:28

NonYankee wrote:

Did you want an explanation?

nope just posted the question! If you think its too easy please tag this question as sub 600 _________________

I've failed over and over and over again in my life and that is why I succeed--Michael Jordan Kudos drives a person to better himself every single time. So Pls give it generously Wont give up till i hit a 700+

Re: What is the value of y?? [#permalink]
28 Feb 2013, 22:36

1

This post received KUDOS

NonYankee wrote:

rajathpanta wrote:

NonYankee wrote:

Did you want an explanation?

nope just posted the question! If you think its too easy please tag this question as sub 600

Ok. Thanks for contributing this problem! As for the difficulty, I have no gauge for the level of questions.

we mere mortals talk in terms of difficulty level For you, its a different ball game! you should ask is this a sub-800 question?? LOL _________________

I've failed over and over and over again in my life and that is why I succeed--Michael Jordan Kudos drives a person to better himself every single time. So Pls give it generously Wont give up till i hit a 700+

Re: What is the value of y? [#permalink]
04 Mar 2013, 03:50

Expert's post

shreerajp99 wrote:

Hi Bunuel,

It sounds stupid but can u tell me about this step:

X+y=5 and X-y=1. I always used to think that it will mean x+y=5 or x-y=5.

When we consider the two statements together we have that both \(x\) and \(y\) are positive integers, thus \(x+y=integer>0\) and \(x-y=integer\) AND \(x+y>x-y\).

Next, we also have that \(x^2 - y^2 =(x+y)(x-y)= 5\), so we have that the product of two multiple, x+y and x-y is equal to 5, a prime number. Since \(x+y=integer>0\) and \(x-y=integer\), then x+y must be 5 AND x-y must be 1: 5*1=5.

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