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Is 5^k less than 1,000?

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Is 5^k less than 1,000? [#permalink] New post 26 Dec 2012, 03:41
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Is 5^k less than 1,000?

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

(2) 5^(k-1) = 5^k - 500
[Reveal] Spoiler: OA
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Re: Is 5^k less than 1,000? [#permalink] New post 26 Dec 2012, 03:42
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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.

Answer: B.

Hope it's clear.
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Re: Is 5^k less than 1,000? [#permalink] New post 06 Apr 2013, 22:12
Walkabout wrote:
Is 5^k less than 1,000?

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

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




I would to ask why is this wrong
(1) 5^(k+1) > 3000

5^(k+1) > 5^5
Hence, k+1= 5 , k =4

If so, 5^4 is less than 1000. The answer should b sufficient for (1).
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Re: Is 5^k less than 1,000? [#permalink] New post 07 Apr 2013, 08:40
From 1: (5^k)*5 > 3000
(5^k) > 600
Hence, insufficient.

From 2: Solving the equation k = 4

Hence, B
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Re: Is 5^k less than 1,000? [#permalink] New post 07 Apr 2013, 22:03
Expert's post
LMKong wrote:
Walkabout wrote:
Is 5^k less than 1,000?

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

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




I would to ask why is this wrong
(1) 5^(k+1) > 3000

5^(k+1) > 5^5
Hence, k+1= 5 , k =4

If so, 5^4 is less than 1000. The answer should b sufficient for (1).


First of all 5^5=3,125>3,000, thus 5^(k+1) > 3000 does NOT necessarily mean that 5^(k+1) > 5^5.

Next, even if we had 5^(k+1) > 5^5 it still does not mean that k+1=5. It means that k+1>5 --> k>4.

Hope it's clear.
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Re: Is 5^k less than 1,000? [#permalink] New post 21 Nov 2013, 08:15
Bunuel,
How did you factor out this
5^k-5^{k-1}=500 --> factor out 5^{k-1}: 5^{k-1}(5-1)=500

is that possible?
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Re: Is 5^k less than 1,000? [#permalink] New post 21 Nov 2013, 10:05
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Statement(1) : 5^(k+1) > 3000
The above inequality can be reduced to 5^k > 600. From this, we clearly know few possible values for k i.e., 4,5,6,..
Substituting these values in the inequality given in the question gives away both yes and no answers.
k = 4, 5^(4-1) < 1000
k = 5, 5^(5-1) < 1000
k = 6, 5^(6-1) > 1000
Hence statement(1) is not sufficient.

Statement(2): 5^(k-1) = 5^k - 500
Reducing the above inequality, 4/5 * 5^k = 500
So 5^k = 625 = 5^4. Clearly k = 4 and the original inequality is satisfied: 5^4 < 1000.
Hence statement(2) is sufficient.

Answer: B
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Is 5^k less than 1,000? [#permalink] New post 23 May 2014, 13:08
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The biggest take-away here should be that we don't need to solve the St-2. The moment you start solving St2, you have fallen for GMAT's classic time waster trap. See below.

Statement1: As 5^(k+1) > 3,000 --> k>4 and hence insufficient
Statement2: We dont need to solve the equation. Since this is an EQUATION (and not an inequality) with one variable, we will get the exact value of k and we will be able to answer the question one way or the other. SUFFICIENT.
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Is 5^k less than 1,000?   [#permalink] 23 May 2014, 13:08
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