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# Dear People, Just ran into some fresh difficulties during my

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Intern
Joined: 01 May 2009
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Dear People, Just ran into some fresh difficulties during my [#permalink]

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18 Jul 2009, 21:09
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Dear People,

Just ran into some fresh difficulties during my revision on DS...

The question is as below:

Is x^2 equal to xy?
(1) x^2 – y^2 = (x + 5)(y - 5)
(2) x = y

I feel that Statement 1 is quite deceiving, since only one part of it answers the question, while the other part seems irrelevant.

Please provide some explanations & workings if possible. THank you very much.

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SVP
Joined: 05 Jul 2006
Posts: 1742

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Re: What Happens if Only Half the Statement is Sufficient? [#permalink]

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19 Jul 2009, 10:30
[quote="cialit0506"]Dear People,

Just ran into some fresh difficulties during my revision on DS...

The question is as below:

Is x^2 equal to xy?
(1) x^2 – y^2 = (x + 5)(y - 5)
(2) x = y

x^2 can = xy only if /x/=/y/ or x = 0

(x-y)(x+y) = (x+5)(y-5)

if we assume that (x-y) = (x+5) thus y = -5 and if we assumed that(x+y) = (y-5) = then x=-5 either ways /y/=/x/
x = +or-ve 5 and so is y ie // is the same .............suff

from b.....obvious suff

Last edited by yezz on 19 Jul 2009, 14:51, edited 1 time in total.

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Senior Manager
Joined: 04 Jun 2008
Posts: 289

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Re: What Happens if Only Half the Statement is Sufficient? [#permalink]

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19 Jul 2009, 12:19
I am unable to see how stmt 1 is sufficient. Can someone please explain?

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Intern
Joined: 01 May 2009
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Re: What Happens if Only Half the Statement is Sufficient? [#permalink]

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23 Jul 2009, 08:21
Yeap, got it. Thanks a million

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Manager
Joined: 15 Apr 2008
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Location: Moscow
Re: What Happens if Only Half the Statement is Sufficient? [#permalink]

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24 Jul 2009, 03:01
yezz wrote:
(x-y)(x+y) = (x+5)(y-5)

if we assume that (x-y) = (x+5) thus y = -5 and if we assumed that(x+y) = (y-5) = then x=-5 either ways /y/=/x/
x = +or-ve 5 and so is y ie // is the same .............suff

If a*b=c*d, it's not right to assume that a is equal either to c or d. a is a factor or a multiple of either c or d.
In this problem if x=5, than $$25-y^2=10*y-50$$
$$y^2+10*y-75=0$$
which gives us 2 solutions: y1=5 and y2=-15
And as we are not given that x and y are integers, we can plug in any value of x and solve for y.
Hence, insuff. Nevertheless, working out a solution when x=y is necessary to prove that statement 1 is insuff. If there were no solution when x=y at all, then Stat.1 would be sufficient and the answer would be "no".

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Re: What Happens if Only Half the Statement is Sufficient?   [#permalink] 24 Jul 2009, 03:01
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