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DS: Inequality, 700-800 Ranking

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Re: DS: Inequality, 700-800 Ranking [#permalink]

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New post 29 Aug 2008, 08:41
x2suresh wrote:
lexis wrote:
Image
\(Green: x^3>y

Blue: sqrt{x}>y


Pink: x>y\)



NICE FIGURE.. :cool Good job.



Is this figure saying the answer is E ??!! :shock:

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Re: DS: Inequality, 700-800 Ranking [#permalink]

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New post 29 Aug 2008, 08:52
bhushangiri wrote:
x2suresh wrote:
lexis wrote:
Image
\(Green: x^3>y

Blue: sqrt{x}>y


Pink: x>y\)



NICE FIGURE.. :cool Good job.



Is this figure saying the answer is E ??!! :shock:


Its saying C... anything below x=y line is x>y..
IN this figure dark dots represent ... combined area.. which is always below x=y line i.e x>y
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Re: DS: Inequality, 700-800 Ranking [#permalink]

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New post 29 Aug 2008, 08:54
I have a question. When we have the condition sqrt(x) > y... why are we not considering the red shaded region alone? This regions satisfies both +ve and -ve aspects of the sqrt.
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Re: DS: Inequality, 700-800 Ranking [#permalink]

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New post 29 Aug 2008, 09:24
lexis wrote:
Image


1: sqrt(x) > y.

if x is 0.36 and y = 0.3, sqrtx > y and x > y.
if x is 0.25 and y = 0.3, sqrtx > y but x < y.
so nsf.... but we know here x is +ve

2. x^3 > y

if x is 6 and y = 5 x^3 > y and x > y.
if x is 2 and y = 5, x^3 > y but x < y.

so nsf.... but we do not know whether x and y are +ve ( or -ve).

togather form 1 and 2:
first, it is clear that x is +ve.
second, to hold both statements (sqrt (x) > y and x^3 > y) true, x has to be > y.

So C for me..
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Re: DS: Inequality, 700-800 Ranking [#permalink]

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New post 29 Aug 2008, 11:09
I'm pretty sure on the real GMAT the question would specify that x was positive in the stem. In any case, presenting essentially the same reasoning as Kevin,

\(\text{If } x > 1 \text{, then } \sqrt{x} < x < x^3 \text{ so if } y \text{ is less than both } \sqrt{x} \text{ and } x^3 \text{, } y \text{ must be less than } x \\
\text{If } 0 < x < 1 \text{, then } x^3 < x < \sqrt{x} \text{ so if } y \text{ is less than both } \sqrt{x} \text{ and } x^3 \text{, } y \text{ must be less than } x \\
\text{If } x = 1 \text{ or } 0 \text{, then } x^3 = x = \sqrt{x} \text{ so if } y \text{ is less than both } \sqrt{x} \text{ and } x^3 \text{, } y \text{ must be less than } x \\\)

So C. Note that while every positive number has two square roots, \(\sqrt{x}\) has only one value: the non-negative square root of x.
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Re: DS: Inequality, 700-800 Ranking [#permalink]

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New post 29 Aug 2008, 23:10
bhushangiri wrote:
I have a question. When we have the condition sqrt(x) > y... why are we not considering the red shaded region alone? This regions satisfies both +ve and -ve aspects of the sqrt.


\(sqrt{x} >0\) with all x>=0 So, if y<0 ==> \(sqrt{x} >y\) with all x>0.



It is different from case \(x >y^2\)
In the case, the shaded zone is "inner" the parabol!

Image



Hope it helps!

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Re: DS: Inequality, 700-800 Ranking   [#permalink] 29 Aug 2008, 23:10

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