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Is it Ok to take the roots first?For example, in question 1

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Joined: 21 Aug 2010
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Is it Ok to take the roots first?For example, in question 1 [#permalink]

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28 Aug 2010, 13:49
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Is it Ok to take the roots first?For example, in question 1 the roots for statement 1 are 0 and 5. For statement II, 0 and -5

Data sufficiency
1) Is X=5?

(I) $$x^2$$ – 5x = 0
(II)$$2x^2$$ + 10x= 0

2) Is x = y?

(I) |x-2|= 5
(II) $$y^2$$ – 4y – 21=0
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Joined: 02 Sep 2009
Posts: 39701

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28 Aug 2010, 14:16
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briandoldan wrote:
Is it Ok to take the roots first?For example, in question 1 the roots for statement 1 are 0 and 5. For statement II, 0 and -5

Data sufficiency
1) Is X=5?

(I) $$x^2$$ – 5x = 0
(II)$$2x^2$$ + 10x= 0

2) Is x = y?

(I) |x-2|= 5
(II) $$y^2$$ – 4y – 21=0

I'm not sure that I understand your question... But as for the problems:

Is x=5?

(1) $$x^2-5x=0$$ --> $$x=0$$ OR $$x=5$$. Not sufficient, to answer whether $$x=5$$.

(2) $$2x^2+10x=0$$ --> $$x=0$$ OR $$x=-5$$. Here we know that $$x\neq{5}$$, hence sufficient.

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 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.

Hope it helps.
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Joined: 21 Aug 2010
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28 Aug 2010, 14:23
Bunuel wrote:
briandoldan wrote:
Is it Ok to take the roots first?For example, in question 1 the roots for statement 1 are 0 and 5. For statement II, 0 and -5

Data sufficiency
1) Is X=5?

(I) $$x^2$$ – 5x = 0
(II)$$2x^2$$ + 10x= 0

2) Is x = y?

(I) |x-2|= 5
(II) $$y^2$$ – 4y – 21=0

I'm not sure that I understand your question... But as for the problems:

Is x=5?

(1) $$x^2-5x=0$$ --> $$x=0$$ OR $$x=5$$. Not sufficient, to answer whether $$x=5$$.

(2) $$2x^2+10x=0$$ --> $$x=0$$ OR $$x=-5$$. Here we know that $$x\neq{5}$$, hence sufficient.

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 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.

Hope it helps.

Thanks a lot Bunuel. It helped a lot. =)

Regards
VP
Joined: 17 Feb 2010
Posts: 1491

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29 Aug 2010, 20:56
Bunuel, For the 1st question, I did not understand the highlighted part. How do we know that x is not equal to -5?

(2)$$2x^2 + 10x = 0$$ --> $$x = 0 or x = -5.$$ [highlight]Here we know that x # 5[/highlight], hence sufficient
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Status: Nothing comes easy: neither do I want.
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Concentration: Technology, Entrepreneurship
Schools: ISB '15 (M)
GMAT 1: 670 Q49 V31
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29 Aug 2010, 21:02
seekmba wrote:
Bunuel, For the 1st question, I did not understand the highlighted part. How do we know that x is not equal to -5?

(2)$$2x^2 + 10x = 0$$ --> $$x = 0 or x = -5.$$ [highlight]Here we know that x # 5[/highlight], hence sufficient

the question is : Is x = 5

(2)$$2x^2 + 10x = 0$$ --> $$x = 0 or x = -5.$$

=> x is not equal to 5. Hence it is sufficient to answer the question.
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Joined: 17 Feb 2010
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29 Aug 2010, 21:05
I got so lost in the options that completely forgot abt the original question. thats silly... thanks a bunch.
Re: DS Inequalities I   [#permalink] 29 Aug 2010, 21:05
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