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OG 2016 DS 41

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OG 2016 DS 41

by nsuen » Tue Apr 05, 2016 7:15 am
HI-

I could not understand the explanation of OG 2015 DS 41, in particular, i dont understand the part that said..greater than 10^n if 1 is greater than 10^2n, I tried to test case using mahattan prep method but couldnt get the right answer.

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Thanks for your help in advance.
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by DavidG@VeritasPrep » Tue Apr 05, 2016 8:44 am
nsuen wrote:HI-

I could not understand the explanation of OG 2015 DS 41, in particular, i dont understand the part that said..greater than 10^n if 1 is greater than 10^2n, I tried to test case using mahattan prep method but couldnt get the right answer.

Image

Thanks for your help in advance.
The question: If n is an integer is (.1)^n greater than (10)^n?

Let's rephrase. .1 = (10)^-1. So (.1)^n = [(10)^-1]^n = (10)^-n. Rephrased question Is (10)^-n > (10)^n?

S1: n > -10.
Case 1: n = -9. (10)^-n = (10)^9 and (10)^n = (10)^-9. (10)^9 is greater than (10)^-9 so the answer to Is (10)^-n > (10)^n? is YES.
Case 2: n = 9. (10)^-n = (10)^-9 and (10)^n = (10)^9. (10)^-9 is NOT greater than (10)^9 so the answer to Is (10)^-n > (10)^n? is NO.
Because we can get a YES and a NO, this statement is not sufficient.

S2: n< 10
We can reuse both cases that we used in statement 1, because 9 and -9 are both less than 10, so we already know we can get a YES and a NO. So this statement alone is not sufficient, and the statements together are not sufficient. Answer is E
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by [email protected] » Tue Apr 05, 2016 9:11 am
Hi nsuen,

This question can be solved by TESTing VALUES (the approach David used). To make the work as simple as possible, you could use the values 0 and -1 and quickly prove the insufficiency of both Facts.

(.1)^0 = 1
10^0 = 1
So the first is NOT greater than the second

(.1)^(-1) = 1/.1 = 10
10^(-1) = 1/10
So the first IS greater than the second

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by nsuen » Wed Apr 06, 2016 5:37 am
Dear David and Rich,

Thank you very much, I understand now.

Rich: how do you just know to use 0 and -1 will be the quickest way? Is it something I will gain better as practice or is there a strategy that makes you pick 0 and -1?
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by DavidG@VeritasPrep » Wed Apr 06, 2016 8:12 am
nsuen wrote:Dear David and Rich,

Thank you very much, I understand now.

Rich: how do you just know to use 0 and -1 will be the quickest way? Is it something I will gain better as practice or is there a strategy that makes you pick 0 and -1?
Generally speaking, you want to pick numbers that yield simple calculations. 0 is always easy. And if we see that one term is raised to a negative exponent, and the other is not, we'll want to pick a negative number too, as this will be likely to yield a different result. -1 is easiest.
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by [email protected] » Wed Apr 06, 2016 8:58 am
Hi nsuen,

GMAT question often provide 'clues' as to what would be the best/easiest numbers to TEST. In PS questions, sometimes the answer choices or the types of numbers used in the prompt provide a hint. In DS, you have to look at whatever 'restrictions' you have to work with, but generally - the numbers 0, 1 and -1 are remarkably easy to manipulate, so they often provide the best 'starting TEST.' Once you have that first TEST CASE result, you should look for VALUES that will prove an inconsistency (if one exists).

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