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# Is x = y?

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Math Expert
Joined: 02 Sep 2009
Posts: 58445

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14 Aug 2017, 06:18
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Difficulty:

35% (medium)

Question Stats:

65% (01:08) correct 35% (01:07) wrong based on 143 sessions

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Is x = y?

(1) $$|x-2|= 5$$.

(2) $$y^2-4y-21=0$$.

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Re: Is x = y?  [#permalink]

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14 Aug 2017, 06:37
X = -3 or 7
Y = 7 or -3
Not necessarily equal
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Joined: 20 Jun 2014
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Re: Is x = y?  [#permalink]

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14 Aug 2017, 06:39
A and B are insufficient
A = -3 or 7
Y = 7 or -3
Not necessarily equal still as x can be 7 and y be -3
E
prachi18oct wrote:
X = -3 or 7
Y = 7 or -3
Not necessarily equal
Manager
Joined: 02 Nov 2015
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Re: Is x = y?  [#permalink]

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14 Aug 2017, 06:43
Both together not sufficient.
X=-3 or 7 and Y =-3 or7.
So E.

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Re: Is x = y?  [#permalink]

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14 Aug 2017, 07:38
Bunuel wrote:
Is x = y?

(1) $$|x-2|= 5$$.

(2) $$y^2-4y-21=0$$.

Is x = y?

(1) $$|x-2|= 5$$. Clearly insufficient as no info about $$y$$. But from this statement we know that either $$x=7$$ or $$x=-3$$.

(2) $$y^2-4y-21=0$$. Clearly insufficient as no info about $$x$$. But from this statement we know that either $$y=7$$ or $$y=-3$$.

(1)+(2) Now, it's possible that both $$x$$ and $$y$$ equal to -3 (or 7) and in this case the answer would be YES: $$x=y$$ BUT it's also possible $$x$$ to be -3 and $$y$$ to be 7 (or vise-versa) and in this case answer would be NO: $$x\neq{y}$$. Two different answers to the question, hence not sufficient.

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Re: Is x = y?  [#permalink]

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24 Aug 2017, 13:36
Bunuel wrote:
Is x = y?

(1) $$|x-2|= 5$$.

(2) $$y^2-4y-21=0$$.

Statement One Alone:

|x - 2| = 5

Let’s test for each case: when (x - 2) is positive and when it is negative:

When (x - 2) is positive:

x - 2 = 5

x = 7

When (x - 2) is negative:

-(x - 2) = 5

-x + 2 = 5

-x = 3

x = -3

Since we know nothing about y, statement one alone is not sufficient to answer the question.

Statement Two Alone:

y^2 - 4y - 21 = 0

y^2 - 4y - 21 = 0

(y - 7)(y + 3) = 0

y = 7 or y = -3

Since we know nothing about x, statement two alone is not sufficient to answer the question.

Statements One and Two Together:

Using statements one and two, we know that x = 7 or -3 and y = 7 or -3, but we still cannot conclude whether x = y. If x = 7 and y = 7, then x = y, but if x = -3 and y = 7, then x ≠ y. The two statements together are still not sufficient to answer the question. .

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Re: Is x = y?   [#permalink] 24 Aug 2017, 13:36
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