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Source: — Data Sufficiency |

by Rahul@gurome » Mon Dec 20, 2010 1:47 am
Rahul Lakhani
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by beat_gmat_09 » Mon Dec 20, 2010 4:22 am
Thanks for the link Rahul.
I feel the algebraic approach time consuming sometimes, it works for certain problems.
I was look for picking numbers (proper numbers) for this problem to evaluate the question.
I think it works faster for some problems.
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by Rahul@gurome » Mon Dec 20, 2010 5:35 am
beat_gmat_09 wrote:Thanks for the link Rahul.
I feel the algebraic approach time consuming sometimes, it works for certain problems.
I was look for picking numbers (proper numbers) for this problem to evaluate the question.
I think it works faster for some problems.
Yes algebraic approaches are time consuming sometimes. But picking numbers also has its own limitations. You must have a good idea about which number you should pick which is equivalent to having a good algebraic concept :).

For this particular question there is also another method which I feel the most easy and elegant method. But to apply this method you should have a clear concept on graphs of certain standard functions.

As I have mentioned earlier, to solve this question we must find the relations of x with √x and x³. Now if you plot these functions (namely f(x) = x, f(x) = √x and f(x) = x³), we can literally see the regions in which y lies.

Image

Referring to the above figure the analysis becomes pretty easier as you visually can see the whole picture.

According to statement 1, y must lie below the blue line. But we can see that for some region y is above the green line (meaning greater than x) and in some region lies below the green line (less than x). Same for statement 2.

Now consider both the statement together. y must lie below both the blue and red lines. We can clearly see this means y always lies below the green line i.e. less than x.
Rahul Lakhani
Quant Expert
Gurome, Inc.
https://www.GuroMe.com
On MBA sabbatical (at ISB) for 2011-12 - will stay active as time permits
1-800-566-4043 (USA)
+91-99201 32411 (India)
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by beat_gmat_09 » Mon Dec 20, 2010 7:19 am
Thanks for the effort Rahul, but i am not comfortable with plotting graphs :(
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