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Is 10^m < 5,000?

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Joined: 18 Nov 2013
Posts: 62
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GMAT Date: 12-26-2014
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Re: Is 10^m < 5,000?  [#permalink]

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New post 10 Feb 2014, 04:33
Bunuel wrote:
coolredwine wrote:
Bunuel wrote:

...

In a Yes/No Data Sufficiency questions, statement is sufficient if the answer is “always yes” or “always no” while a statement is insufficient if the answer is "sometimes yes" and "sometimes no". The first statement is not sufficient because we can get both YES (for m=3) and NO (for m=4) answers to the question.


And am I correct in assuming that we can't consider both the statements together for this question?


Based on the questions you ask you don't understand what a data sufficiency question is about. After you get that the first statement is NOT sufficient and the second statement IS sufficient, you do NOT need to consider the statements together. You already have an answer, which is B: Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question asked.

My advice is to brush up fundamentals and only then attempt the questions.

The following posts might help.

All you need for quant: new-to-the-math-forum-please-read-this-first-140445.html

Best GMAT Quantitative Books: best-gmat-math-prep-books-reviews-recommendations-77291.html


Yup. Thanks for your patience though.
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Re: Is 10^m < 5,000?  [#permalink]

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New post 06 Nov 2015, 05:41
Is \(10^m<5000\)?

(1) \(10^{m+1}>9000\) --> \(10^m>900\). If \(10^m\) is in the range \(900<10^m<{5000}\) (for instance if \(m=3\)) then the answer to the question will be YES, but if \(10^m\geq{5000}\) (for instance if \(m=4\)) then the answer to the question will be NO. Not sufficient.

To elaborate more: \(10^m>900\) means \(m>log_{10}900\approx{2.95}\).

(2) \(10^{m-1}=10^m-900\) --> we can calculate \(m\), so we can answer to the question whether \(10^m<5000\). Sufficient.

To show how it can be done: \(900=10^m(1-\frac{1}{10})\) --> \(10^m=1000<5000\) (\(m=3\)).

Answer: B.[/quote]


Dear Bunuel,
I tried solving it this way :

10^m < 5,000
i.e 10^1 = 10
10^2 = 100
10^3 = 1,000
10^4 = 10,000

Therefore, I concluded 3<m<4.

Now, using the data points given :

(1) 10^m+1 > 9,000
assuming m=3, m+1 = 4.
Therefore, 10^4 = 10,000 > 9,000........SUFFICIENT.

(2) 10^m-1 = 10^m - 900
assuming m=3, m-1 = 2.
Therefore, 10^2 = 100 = 10^3 - 900.....SUFFICIENT.

Thus, answer becomes D.

Please let me know where I am going wrong.
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Re: Is 10^m < 5,000?  [#permalink]

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New post 09 Apr 2016, 07:14
shekar123 wrote:
Is 10^m < 5,000?

(1) 10^(m+1) > 9,000
(2) 10^(m–1) = 10^m – 900


stmt-1

10^m * 10 > 9000
10^m > 9 * 10^2

if m =3 then yes else no insuff.

stmt-2

10^m / 10 = 10^m - 900

10^m = 10^(m+1) - 9000

10^(m+1) - 10^m = 9000

10^m (10-1) = 9000

10^m * 9 = 9 * 10^3

m = 3, sufficient.
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Re: Is 10^m < 5,000?  [#permalink]

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New post 10 Sep 2018, 01:53
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Re: Is 10^m < 5,000?   [#permalink] 10 Sep 2018, 01:53

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