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# Is 10^m < 5,000?

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Joined: 27 Sep 2009
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07 Jun 2010, 16:04
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Is 10^m < 5,000?

(1) 10^(m+1) > 9,000
(2) 10^(m–1) = 10^m – 900
Math Expert
Joined: 02 Sep 2009
Posts: 50670

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08 Jun 2010, 04:45
2
6
shekar123 wrote:
Is 10^m < 5,000?

(1) 10^m+1 > 9,000

(2) 10^m – 1 = 10^m – 900

Could anyone help me in solving this.

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: $$900=10^m(1-\frac{1}{10})$$ --> $$10^m=1000<5000$$ ($$m=3$$).

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Manager
Joined: 20 Apr 2010
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07 Jun 2010, 20:06
1
I went it the following way :

1. 10^m+1 > 9,000
or 10^m * 10 > 9000
or 10^m > 900

Therefore 10 ^m can be > or < 5000 .
So not sufficient.

2. Not sufficient in anyway

Might be i am wrong somewhere... if its not E...
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Joined: 04 Apr 2010
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07 Jun 2010, 22:56
S1 tells us m>3, therefore 10^m must be at least 10^4, and the result must be 10,000 or greater. Suff
S2 gives an exact value for m. m can only be 3. Suff

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Schools: IU, UT Dallas, Univ of Georgia, Univ of Arkansas, Miami University
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08 Jun 2010, 03:47
TheGmatTutor wrote:
S1 tells us m>3, therefore 10^m must be at least 10^4, and the result must be 10,000 or greater. Suff
S2 gives an exact value for m. m can only be 3. Suff

S1 mentions that 10^(m+1) > 9000. Doesn't that mean m can be >=3. 10^4 is greater than 9000 and hence, m can be 3 also.
Why is it that m>3 and not m>=3? In that S1 will be insufficient. Please explain.
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08 Jun 2010, 06:21
Thanks Bunuel. Thats what I though too.
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08 Jun 2010, 19:55
1
Bunuel wrote:
shekar123 wrote:
Is 10^m < 5,000?

(1) 10^m+1 > 9,000

(2) 10^m – 1 = 10^m – 900

Could anyone help me in solving this.

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: $$900=10^m(1-\frac{1}{10})$$ --> $$10^m=1000<5000$$ ($$m=3$$).

Thanks Bunuel... I answered D as statement 2 was not clear...
2) 10^m – 1 = 10^m – 900 ; whether both m-1 and m-900 are exponents or 900 is just getting subracted..
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Joined: 02 Sep 2009
Posts: 50670
Re: Is 10^m < 5,000?  [#permalink]

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25 Jun 2013, 03:46
Bumping for review and further discussion*. Get a kudos point for an alternative solution!

*New project from GMAT Club!!! Check HERE

Theory on Exponents: math-number-theory-88376.html

All DS Exponents questions to practice: search.php?search_id=tag&tag_id=39
All PS Exponents questions to practice: search.php?search_id=tag&tag_id=60

Tough and tricky DS exponents and roots questions with detailed solutions: tough-and-tricky-exponents-and-roots-questions-125967.html
Tough and tricky PS exponents and roots questions with detailed solutions: tough-and-tricky-exponents-and-roots-questions-125956.html

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Joined: 25 Jun 2013
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GMAT 1: 710 Q49 V35
Re: Is 10^m < 5,000?  [#permalink]

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25 Jun 2013, 11:05
2
Is 10^m < 5,000?

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

(1) 10^(m+1) > 9000 => 10^m > 900
No conclusions can be further made.

(2) 10^(m–1) = 10^m – 900
=> 900 = 10^m - 10^(m-1) --- taking values with variables on one side
=> 900 = 10^(m-1) [10 - 1] --- simplifying the equation
=> 900 = 10^(m-1)*9
=> 100 = 10^(m-1)
=> m-1 = 2 => m=3
10^m = 10^3 = 1000 < 5000
We get a definite answer from statement (2)
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Concentration: General Management, Technology
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Re: Is 10^m < 5,000?  [#permalink]

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25 Jun 2013, 16:53
1
Bunuel wrote:
Bumping for review and further discussion*. Get a kudos point for an alternative solution!

*New project from GMAT Club!!! Check HERE

Theory on Exponents: math-number-theory-88376.html

All DS Exponents questions to practice: search.php?search_id=tag&tag_id=39
All PS Exponents questions to practice: search.php?search_id=tag&tag_id=60

Tough and tricky DS exponents and roots questions with detailed solutions: tough-and-tricky-exponents-and-roots-questions-125967.html
Tough and tricky PS exponents and roots questions with detailed solutions: tough-and-tricky-exponents-and-roots-questions-125956.html

Question: Is 10^m < 5,000?

Its a YES or NO question, getting either a YES or NO will be sufficient.

(1) 10^m+1 > 9,000
10^m >900 =>Clearly insufficient

(2) 10^m – 1 = 10^m – 900
No need to calculate, we are getting a value on 10^m directly.
No matter what it is we can come up with a definite NO or a definite YES
=>Sufficient

Ans: B
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Joined: 06 Sep 2013
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15 Oct 2013, 07:45
Bunuel wrote:
shekar123 wrote:
Is 10^m < 5,000?

(1) 10^m+1 > 9,000

(2) 10^m – 1 = 10^m – 900

Could anyone help me in solving this.

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: $$900=10^m(1-\frac{1}{10})$$ --> $$10^m=1000<5000$$ ($$m=3$$).

Hi Bunuel, this one was indeed tough. If we had been told that m is an integer then in that case it would have been (D) right?
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Joined: 06 Aug 2011
Posts: 340

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06 Feb 2014, 11:21
jlgdr wrote:
Bunuel wrote:
shekar123 wrote:
Is 10^m < 5,000?

(1) 10^m+1 > 9,000

(2) 10^m – 1 = 10^m – 900

Could anyone help me in solving this.

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: $$900=10^m(1-\frac{1}{10})$$ --> $$10^m=1000<5000$$ ($$m=3$$).

Hi Bunuel, this one was indeed tough. If we had been told that m is an integer then in that case it would have been (D) right?

I dont think so..

In statement 1..both interger values have been given still that statement is insufficient..

10^m> 900?

m>3 so m can be 4 or 5..or any value ! if its 3? ans we will be yes..10^m<5000 bt if its more than ans wud b no..
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Re: Is 10^m < 5,000?  [#permalink]

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06 Feb 2014, 22:32
A very silly question. Since Statement 1 says 10^m>900, we can say m>=3, isn't it? So why can't we combine Statement 1 and 2 to say m = 3?
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Joined: 02 Sep 2009
Posts: 50670
Re: Is 10^m < 5,000?  [#permalink]

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07 Feb 2014, 04:24
coolredwine wrote:
A very silly question. Since Statement 1 says 10^m>900, we can say m>=3, isn't it? So why can't we combine Statement 1 and 2 to say m = 3?

Not sure I can follow you.

$$10^m>900$$ means $$m>log_{10}900\approx{2.95}$$ not $$\geq{3}$$. Also, how can you combine info from (1) and (2) to solve the first statement?
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Re: Is 10^m < 5,000?  [#permalink]

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08 Feb 2014, 18:31
Bunuel wrote:
coolredwine wrote:
A very silly question. Since Statement 1 says 10^m>900, we can say m>=3, isn't it? So why can't we combine Statement 1 and 2 to say m = 3?

Not sure I can follow you.

$$10^m>900$$ means $$m>log_{10}900\approx{2.95}$$ not $$\geq{3}$$. Also, how can you combine info from (1) and (2) to solve the first statement?

Hi Bunuel,

If $$10^m>900$$ -> $$m>log_{10}900\approx{2.95}$$, then shouldn't that follow m>3 ? Then we can say 10^m>900, isn't it?

Then combining Statements 1 and 2, we would have C as the right option?
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Posts: 50670
Re: Is 10^m < 5,000?  [#permalink]

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09 Feb 2014, 00:23
coolredwine wrote:
Bunuel wrote:
coolredwine wrote:
A very silly question. Since Statement 1 says 10^m>900, we can say m>=3, isn't it? So why can't we combine Statement 1 and 2 to say m = 3?

Not sure I can follow you.

$$10^m>900$$ means $$m>log_{10}900\approx{2.95}$$ not $$\geq{3}$$. Also, how can you combine info from (1) and (2) to solve the first statement?

Hi Bunuel,

If $$10^m>900$$ -> $$m>log_{10}900\approx{2.95}$$, then shouldn't that follow m>3 ? Then we can say 10^m>900, isn't it?

Then combining Statements 1 and 2, we would have C as the right option?

I guess you are not familiar with data sufficiency questions.

The data sufficiency problem consists of a question and two statements, labeled (1) and (2), in which certain data are given. You have to decide whether the data given in the statements are sufficient for answering the question. Using the data given in the statements, plus your knowledge of mathematics and everyday facts (such as the number of days in July or the meaning of the word counterclockwise), you must indicate whether—

A. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question asked.
B. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question asked.
C. BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficient to answer the question asked.
E. Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data specific to the problem are needed.

Now, for the original question we have that Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question asked, which means that the answer is B.

Hope it's clear.
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Re: Is 10^m < 5,000?  [#permalink]

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10 Feb 2014, 02:39
Bunuel wrote:
coolredwine wrote:
Bunuel wrote:
Not sure I can follow you.

$$10^m>900$$ means $$m>log_{10}900\approx{2.95}$$ not $$\geq{3}$$. Also, how can you combine info from (1) and (2) to solve the first statement?

Hi Bunuel,

If $$10^m>900$$ -> $$m>log_{10}900\approx{2.95}$$, then shouldn't that follow m>3 ? Then we can say 10^m>900, isn't it?

Then combining Statements 1 and 2, we would have C as the right option?

I guess you are not familiar with data sufficiency questions.

The data sufficiency problem consists of a question and two statements, labeled (1) and (2), in which certain data are given. You have to decide whether the data given in the statements are sufficient for answering the question. Using the data given in the statements, plus your knowledge of mathematics and everyday facts (such as the number of days in July or the meaning of the word counterclockwise), you must indicate whether—

A. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question asked.
B. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question asked.
C. BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficient to answer the question asked.
E. Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data specific to the problem are needed.

Now, for the original question we have that Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question asked, which means that the answer is B.

Hope it's clear.

I understand the DS Questions. What I was confirming was that if we take St 1 and St 2 together, then also we are getting the answer, right? (m=3). Then how have we eliminated Statement 1 as not sufficient?
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Joined: 02 Sep 2009
Posts: 50670
Re: Is 10^m < 5,000?  [#permalink]

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10 Feb 2014, 02:48
coolredwine wrote:
Bunuel wrote:
coolredwine wrote:
Hi Bunuel,

If $$10^m>900$$ -> $$m>log_{10}900\approx{2.95}$$, then shouldn't that follow m>3 ? Then we can say 10^m>900, isn't it?

Then combining Statements 1 and 2, we would have C as the right option?

I guess you are not familiar with data sufficiency questions.

The data sufficiency problem consists of a question and two statements, labeled (1) and (2), in which certain data are given. You have to decide whether the data given in the statements are sufficient for answering the question. Using the data given in the statements, plus your knowledge of mathematics and everyday facts (such as the number of days in July or the meaning of the word counterclockwise), you must indicate whether—

A. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question asked.
B. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question asked.
C. BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficient to answer the question asked.
E. Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data specific to the problem are needed.

Now, for the original question we have that Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question asked, which means that the answer is B.

Hope it's clear.

I understand the DS Questions. What I was confirming was that if we take St 1 and St 2 together, then also we are getting the answer, right? (m=3). Then how have we eliminated Statement 1 as not sufficient?

...

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.
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Re: Is 10^m < 5,000?  [#permalink]

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10 Feb 2014, 02:57
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?
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Joined: 02 Sep 2009
Posts: 50670
Re: Is 10^m < 5,000?  [#permalink]

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10 Feb 2014, 03:06
1
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.

Best GMAT Quantitative Books: best-gmat-math-prep-books-reviews-recommendations-77291.html
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Re: Is 10^m < 5,000? &nbs [#permalink] 10 Feb 2014, 03:06

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