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edit: I should add, though, that because this is a DS question, we can stop long before we reach the answer.

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Nov 2011: After years of development, I am now making my advanced Quant books and high-level problem sets available for sale. Contact me at ianstewartgmat at gmail.com for details.

Re: OG C DS 131 Is 5^k less than 1000? a. 5^(k+1) >3000 b. [#permalink]
23 Nov 2011, 10:55

Simple Solution: 1) One variable. Inequality. Cannot determine the value of k -> Insufficiant 2) One Vasriable. One euality Equation. I can determine the value of k -> Sufficient

Hence B. I would not calculate anything. Time to solve - < 10 Secs.

Re: OG C DS 131 Is 5^k less than 1000? a. 5^(k+1) >3000 b. [#permalink]
23 Nov 2011, 11:12

1

This post received KUDOS

@iamgame I agree with your theory for statement 2 but I disagree for statement 1

Just because it is inequality and one variable you can't dismiss it. If after simplification you got the statement 1 as 5^k > 1200, it would have been sufficient.

We have to be careful in generalizing that rule. This is especially dangerous for high level inequality problems.

Re: OG C DS 131 Is 5^k less than 1000? a. 5^(k+1) >3000 b. [#permalink]
23 Nov 2011, 13:20

iamgame wrote:

Simple Solution: 1) One variable. Inequality. Cannot determine the value of k -> Insufficiant 2) One Vasriable. One euality Equation. I can determine the value of k -> Sufficient

Hence B. I would not calculate anything. Time to solve - < 10 Secs.

If you're approaching DS questions in that way, you won't get very many of them right, unfortunately. For example, if you saw this question:

Is 5^k < 125?

1) k < 3 2) 5^k = 5*5^(k-1)

then Statement 1 is sufficient, since if k is less than 3, then 5^k is less than 5^3 = 125. Statement 2 gives an equation, but it is not sufficient, since it is always true - it gives you no information at all about the value of k. So in this example, the statement with the inequality *is* sufficient, and the statement with the equation is *not* sufficient. There are countless similar examples that you can find among official questions.

_________________

Nov 2011: After years of development, I am now making my advanced Quant books and high-level problem sets available for sale. Contact me at ianstewartgmat at gmail.com for details.

Re: OG C DS 131 Is 5^k less than 1000? a. 5^(k+1) >3000 b. [#permalink]
15 Feb 2014, 02:06

Expert's post

seabhi wrote:

Hi, Please add OA. Thanks.

Done.

Is 5^k less than 1,000?

Is 5^k<1,000?

(1) 5^(k+1) > 3,000 --> 5^k>600 --> if k=4 then the answer is YES: since 600<(5^4=625)<1,000 but if k=10, for example, then the answer is NO. Not sufficient.

(2) 5^(k-1) = 5^k - 500 --> we can solve for k and get the single numerical value of it, hence this statement is sufficient. Just to illustrate: 5^k-5^{k-1}=500 --> factor out 5^{k-1}: 5^{k-1}(5-1)=500 --> 5^{k-1}=125 --> k-1=3 --> k=4. Sufficient.