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Re: Is 5^k less than 1,000? [#permalink]
26 Dec 2012, 03:42

1

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Expert's post

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.

Re: Is 5^k less than 1,000? [#permalink]
21 Nov 2013, 10:05

1

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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]
23 May 2014, 13:08

3

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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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