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OG C DS 131 Is 5^k less than 1000? a. 5^(k+1) >3000 b.

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OG C DS 131 Is 5^k less than 1000? a. 5^(k+1) >3000 b. [#permalink]  23 Jun 2008, 00:20
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OG C DS 131
Is 5^k less than 1000?
a. 5^(k+1) >3000
b. 5^(k-1)=5^k - 500
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Re: OG C DS 131 [#permalink]  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]  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]  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]  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]  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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Re: OG C DS 131 Is 5^k less than 1000? a. 5^(k+1) >3000 b. [#permalink]  23 Nov 2011, 11:52
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]  23 Nov 2011, 11:55
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.
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Re: OG C DS 131 Is 5^k less than 1000? a. 5^(k+1) >3000 b. [#permalink]  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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Re: OG C DS 131 Is 5^k less than 1000? a. 5^(k+1) >3000 b. [#permalink]  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]  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] 23 Nov 2011, 14:20
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