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Is x^2 equal to xy?

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Is x^2 equal to xy? [#permalink] New post 15 Dec 2009, 22:28
00:00
A
B
C
D
E

Difficulty:

  25% (low)

Question Stats:

71% (02:26) correct 28% (01:19) wrong based on 85 sessions
Is x^2 equal to xy?

(1) x^2 – y^2 = (x + 5)(y - 5)
(2) x = y
[Reveal] Spoiler: OA
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Re: ALGEBRA [#permalink] New post 16 Dec 2009, 05:39
Expert's post
dobinnoli wrote:
Is x^2 equal to xy?
(1) x^2 – y^2 = (x + 5)(y - 5)
(2) x = y
ANSWER IS D?


Question: is x^2=xy? --> x(x-y)=0 --> Equation holds true if x=0 or/and x=y.

So, basically question asks: Is x=0 or/and x=y true?

Obviously statement (2) is sufficient, as it gives directly that x=y.

(1) x^2-y^2 = (x + 5)(y - 5) --> (x+y)(x-y)=(x + 5)(y-5)

If y=5 --> (x+5)(x-5)=(x+5)(5-5) --> (x+5)(x-5)=0 --> Either x=5=y and in this case answer to the question is YES OR x=-5, hence x is not equal to y (nor to zero) and in this case answer to the question is NO. So two different answers.

Not sufficient.

Answer: B.
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Re: Algebra DS [#permalink] New post 02 Aug 2010, 07:08
Statement 1:
(x,y)=(5,5) --> x²=xy
(x,y)=(-5,5) --> x²<>xy
not sufficient

Statement 2:
x=y --> xx=xy or x²=xy
sufficient

B
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Re: Algebra DS [#permalink] New post 02 Aug 2010, 19:23
I agree with bogos.

Stmt1:
x^2 - y^2 = (x+5)(x-5)
x^2 - y^2 = x^2 - 25
0 = y^2 - 25
y = +5, -5

plugin a possible value of y into the equation x^2 - y^2 = x^2 - 25
you can see when that y can be -5 and x can 5. But plugging in the same value into x^2 = xy would yield 25 = -25.
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Re: ALGEBRA [#permalink] New post 03 Oct 2010, 23:21
X=5 =>> y=+/-5
But if you substitute back in eqn only y=5 is valid

Please post OA
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Is X^2 equal to xy? [#permalink] New post 26 Sep 2013, 07:00
Is X^2 equal to xy?

1) X^2 - Y^2 = ( x+5) ( y-5)
2) x=y


[Reveal] Spoiler:
Fairly easy question but I was wondering how do manipulate statement 1 am I missing something cos it seems insufficient on surface without any calculations?

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Re: Is X^2 equal to xy? [#permalink] New post 26 Sep 2013, 07:37
Expert's post
fozzzy wrote:
Is X^2 equal to xy?

1) X^2 - Y^2 = ( x+5) ( y-5)
2) x=y


[Reveal] Spoiler:
Fairly easy question but I was wondering how do manipulate statement 1 am I missing something cos it seems insufficient on surface without any calculations?


Merging similar topics.
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COLLECTION OF QUESTIONS:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS ; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


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Re: Is x^2 equal to xy? [#permalink] New post 02 Feb 2014, 16:06
dobinnoli wrote:
Is x^2 equal to xy?

(1) x^2 – y^2 = (x + 5)(y - 5)
(2) x = y


Is x(x-y)=0

So is x=0 or x=y?

Statement 1

Obviously x is not equal to y otherwise LHS and RHS should be zero

Is x = 0

Is -y^2 = -25, could be but we don't know

Statement 2

x=y, yes. This is correct and sufficient

B
Re: Is x^2 equal to xy?   [#permalink] 02 Feb 2014, 16:06
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