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# Is 5^k less than 1,000?

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Manager
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Is 5^k less than 1,000? [#permalink]

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23 Jun 2008, 00:20
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72% (01:23) correct 28% (01:43) wrong based on 173 sessions

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Is 5^k less than 1,000?

(1) 5^(k+1) > 3,000

(2) 5^(k-1) = 5^k - 500

OPEN DISCUSSION OF THIS QUESTION IS HERE: is-5-k-less-than-144719.html
[Reveal] Spoiler: OA

Last edited by Bunuel on 15 Feb 2014, 03:05, edited 2 times in total.
Renamed the topic, edited the question and added the OA.

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Manager
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Re: OG C DS 131 [#permalink]

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23 Jun 2008, 00:27
Is 5^k less than 1000?
a. 5^(k+1) >3000
b. 5^(k-1)=5^k - 500

St1: 5^k >600 ----insuffi

St2: 5^(k-1) x4 = 500 => k=4 ----suffic

hence B!

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Re: OG C DS 131 [#permalink]

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23 Jun 2008, 05:04
B for me as well.

from stat 1, you can simplify to 5^k > 600. insuff on its own

from stat 2, you can simplify down to 5^k = 1625 , which is sufficient to answer the q.

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Re: OG C DS 131 [#permalink]

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26 Jun 2008, 15:30
pmenon wrote:
B for me as well.

from stat 1, you can simplify to 5^k > 600. insuff on its own

from stat 2, you can simplify down to 5^k = 1625 , which is sufficient to answer the q.

pmenon or anybody else, for further clarification, can you explain how you got 5^k = 1625? Thanks

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Re: OG C DS 131 [#permalink]

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26 Jun 2008, 16:51
lucyqin wrote:
pmenon or anybody else, for further clarification, can you explain how you got 5^k = 1625? Thanks

I think that was a typo- it should say '625', not '1625'. We have:

5^(k-1)=5^k - 500
500 = 5^k - 5^(k-1)

The trick now is to recognize that you can factor out 5^(k-1) on the right:

500 = (5^(k-1))*(5 - 1)
500 = (5^(k-1))*4
125 = 5^(k-1)
5^3 = 5^(k-1)
3 = k-1
4 = k

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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Re: OG C DS 131 [#permalink]

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26 Jun 2008, 19:19
OG C DS 131
Is 5^k less than 1000?
a. 5^(k+1) >3000
b. 5^(k-1)=5^k - 500

B.

a. gives us 5^k >600
b. gives us k=4, which is suff to answer "No, 5^k is less than 1000"

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Manager
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Re: OG C DS 131 Is 5^k less than 1000? a. 5^(k+1) >3000 b. [#permalink]

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23 Nov 2011, 11:52
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St1: $$5^k >600$$ ----insufficient as we don't know if $$5^k <1000$$

St2: $$5^{k-1} = 5^K - 500$$
$$500 = 5^k (1- \frac{1}{5})$$
$$500 (\frac{5}{4})= 5^k$$ ----sufficient as we can determine if $$5^k <1000$$

hence B!

Last edited by icaniwill on 23 Nov 2011, 12:15, edited 1 time in total.

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

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23 Nov 2011, 11:55
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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.
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Re: OG C DS 131 Is 5^k less than 1000? a. 5^(k+1) >3000 b. [#permalink]

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23 Nov 2011, 12:12
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@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.

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Manager
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Re: OG C DS 131 Is 5^k less than 1000? a. 5^(k+1) >3000 b. [#permalink]

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23 Nov 2011, 12:17
Hmmm...Point taken icaniwill.
Kudos given.

I have to stop jumping to conclusions so soon!
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Re: OG C DS 131 Is 5^k less than 1000? a. 5^(k+1) >3000 b. [#permalink]

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23 Nov 2011, 14:20
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.
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Re: OG C DS 131 Is 5^k less than 1000? a. 5^(k+1) >3000 b. [#permalink]

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14 Feb 2014, 11:20
Hi,
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Re: OG C DS 131 Is 5^k less than 1000? a. 5^(k+1) >3000 b. [#permalink]

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15 Feb 2014, 03:06
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seabhi wrote:
Hi,

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.

OPEN DISCUSSION OF THIS QUESTION IS HERE: is-5-k-less-than-144719.html
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Re: OG C DS 131 Is 5^k less than 1000? a. 5^(k+1) >3000 b.   [#permalink] 15 Feb 2014, 03:06
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