Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized for You

we will pick new questions that match your level based on your Timer History

Track Your Progress

every week, we’ll send you an estimated GMAT score based on your performance

Practice Pays

we will pick new questions that match your level based on your Timer History

Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.

It appears that you are browsing the GMAT Club forum unregistered!

Signing up is free, quick, and confidential.
Join other 500,000 members and get the full benefits of GMAT Club

Registration gives you:

Tests

Take 11 tests and quizzes from GMAT Club and leading GMAT prep companies such as Manhattan GMAT,
Knewton, and others. All are free for GMAT Club members.

Applicant Stats

View detailed applicant stats such as GPA, GMAT score, work experience, location, application
status, and more

Books/Downloads

Download thousands of study notes,
question collections, GMAT Club’s
Grammar and Math books.
All are free!

Thank you for using the timer!
We noticed you are actually not timing your practice. Click the START button first next time you use the timer.
There are many benefits to timing your practice, including:

If m is a positive integer, then m^3 has how many digits? 1. m has 3 digits 2. m^2 has 5 digits

How would you do this quickly? Is there a rule that I am unaware of? I could do it, but I had to pick a few numbers. Thanks.

as we know,

the minimum value of a 3 digit integer is 100 = \(10^2\) the maximum value of a 3 digit integer is 999 = \(10^4 - 1\) the minimum value of a 5 digit integer is 10000 = \(10^4\) the maximum value of a 5 digit integer is 99999 = \(10^6 - 1\) . . hence, .

the minimum value of a \(n\) digit integer is \(10^(n-1)\) the maximum value of a \(n\) digit integer is \(10^(n+1) - 1\)

Back to original qtn:

If m is a positive integer, then \(m^3\) has how many digits? stmnt1: \(m\) has 3 digits ==> \(10^2 <= m < 10^4\) ==> \(10^6 <= m^3 < 10^12\) ==> \(m^3\) can have minimum of 7 (i.e 6+1) and max of 11 digits (i.e. 12-1) hence NOT suff.

stmnt2: m^2 has 5 digits ==> \(10^4 <= m^2 < 10^6\) ==> \(10^2 <= m < 10^3\) ==> \(10^6 <= m^3 < 10^9\) ==> \(m^3\) can have minimum of 7 (i.e 6+1) and max of 8 digits (i.e. 9-1) hence NOT suff.

stmnt1&2 together: We can conclude that \(m^3\) can have minimum of 6 and max of 8 digits(i.e. 12-1) ==> m can have 7 or 8 digits hence NOT suff.

Answer "E".

Regards, Murali. Kudos?

Last edited by muralimba on 22 Dec 2010, 06:14, edited 1 time in total.

If m is a positive integer, then m^3 has how many digits? 1. m has 3 digits 2. m^2 has 5 digits

How would you do this quickly? Is there a rule that I am unaware of? I could do it, but I had to pick a few numbers. Thanks.

1. m has 3 digits

When I look at such statements, I invariably think of the extremities. (as muralimba did above) Smallest m = 100 which implies m^3 = 10^6 giving 7 digits. Largest m = 999 but it is not easy to find its cube so I take a number close to it i.e. 1000 and find its cube which is 10^9 i.e. smallest 10 digit number. Hence 999^3 will have 9 digits. Since we can have 7, 8 or 9 digits, this statement is not sufficient.

2. m^2 has 5 digits Now try to forget what you read above. Just focus on this statement. Smallest m^2 = 10000 which implies m = 100 Largest m^2 is less than 99999 which gives m as something above 300 but less than 400. Now, if m is 100, m^3 = 10^6 giving 7 digits. If m is 300, m^3 = 27000000 giving 8 digits. Since we have 7 or 8 digits for m, this statement is not sufficient.

Now combining both, remember one important point - If one statement is already included in the other, and the more informative statement is not sufficient alone, both statements will definitely not be sufficient together.

e.g. statement 1 tells us that m has 3 digits. Statement 2 tells us that m is between 100 and 300 something, so statement 2 tells us that m has 3 digits (what statement 1 told us) and something extra (that its value lies between 100 and 300 something). Statement 2 is more informative and is not sufficient alone. Since statement 1 doesn't add any new information to statement 2, no way will they both together be sufficient. Hence answer (E).
_________________

If m is a positive integer, then m^3 has how many digits? 1. m has 3 digits 2. m^2 has 5 digits

How would you do this quickly? Is there a rule that I am unaware of? I could do it, but I had to pick a few numbers. Thanks.

If m is a positive integer, then m^3 has how many digits?

Pick some easy numbers.

(1) m has 3 digits --> if \(m=100=10^2\) then \(m^3=10^6\) so it will have 7 digits but if \(m=300=3*10^2\) then \(m^3=27*10^6\) so it will have 8 digits. Not sufficient.

(2) m^2 has 5 digits --> the same values of \(m\) (100 and 300) satisfy this statement too (because if \(m=10^2\) then \(m^2=10^4\) and has 5 digits and if \(m=3*10^2\) then \(m^2=9*10^4\) also has 5 digits), so \(m^3\) may still have 7 or 8 digits. Not sufficient.

(1)+(2) The same example worked for both statements so even taken together statements are not sufficient.

If m is a positive integer, then m^3 has how many digits? 1. m has 3 digits 2. m^2 has 5 digits

How would you do this quickly? Is there a rule that I am unaware of? I could do it, but I had to pick a few numbers. Thanks.

as we know,

the minimum value of a 3 digit integer is 100 = \(10^2\) the maximum value of a 3 digit integer is 999 = \(10^4 - 1\) the minimum value of a 5 digit integer is 10000 = \(10^4\) the maximum value of a 5 digit integer is 99999 = \(10^6 - 1\) . . hence, .

the minimum value of a \(n\) digit integer is \(10^n\) the maximum value of a \(n\) digit integer is \(10^(n+1) - 1\)

Back to original qtn:

If m is a positive integer, then \(m^3\) has how many digits? stmnt1: \(m\) has 3 digits ==> \(10^2 <= m < 10^4\) ==> \(10^6 <= m^3 < 10^12\) ==> \(m^3\) can have minimum of 6 and max of 11 digits (i.e. 12-1) hence NOT suff.

stmnt2: m^2 has 5 digits ==> \(10^4 <= m^2 < 10^6\) ==> \(10^2 <= m < 10^3\) ==> \(10^6 <= m^3 < 10^9\) ==> \(m^3\) can have minimum of 6 and max of 8 digits (i.e. 9-1) hence NOT suff.

stmnt1&2 together: We can conclude that \(m^3\) can have minimum of 6 and max of 8 digits(i.e. 12-1) ==> m can have 6,7, or 8 digits hence NOT suff.

Answer "E".

Regards, Murali. Kudos?

m^3 can have only 7 or 8 digits, not 6. If m=100=10^2 then m^3=10^6 and it has 6 trailing zeros but 7 digits.
_________________

Re: If m is a positive integer, then m^3 has how many digits? 1. [#permalink]

Show Tags

11 Oct 2013, 23:07

Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________

If m is a positive integer, then m^3 has how many digits? 1. m has 3 digits 2. m^2 has 5 digits

How would you do this quickly? Is there a rule that I am unaware of? I could do it, but I had to pick a few numbers. Thanks.

as we know,

the minimum value of a 3 digit integer is 100 = \(10^2\) the maximum value of a 3 digit integer is 999 = \(10^4 - 1\) the minimum value of a 5 digit integer is 10000 = \(10^4\) the maximum value of a 5 digit integer is 99999 = \(10^6 - 1\) . . hence, .

the minimum value of a \(n\) digit integer is \(10^(n-1)\) the maximum value of a \(n\) digit integer is \(10^(n+1) - 1\)

Back to original qtn:

If m is a positive integer, then \(m^3\) has how many digits? stmnt1: \(m\) has 3 digits ==> \(10^2 <= m < 10^4\) ==> \(10^6 <= m^3 < 10^12\) ==> \(m^3\) can have minimum of 7 (i.e 6+1) and max of 11 digits (i.e. 12-1) hence NOT suff.

stmnt2: m^2 has 5 digits ==> \(10^4 <= m^2 < 10^6\) ==> \(10^2 <= m < 10^3\) ==> \(10^6 <= m^3 < 10^9\) ==> \(m^3\) can have minimum of 7 (i.e 6+1) and max of 8 digits (i.e. 9-1) hence NOT suff.

stmnt1&2 together: We can conclude that \(m^3\) can have minimum of 6 and max of 8 digits(i.e. 12-1) ==> m can have 7 or 8 digits hence NOT suff.

Answer "E".

Regards, Murali. Kudos?

Murali, While you approach is conceptually solid, it is marred by silly errors. For instance, here "==> \(10^2 <= m < 10^4\)" it should be 10^2 <= m < 10^3 and hence m^3 can have no. of digits from 5-9. Another one was already pointed by Bunuel. Thanks for sharing nonetheless.
_________________

Please contact me for super inexpensive quality private tutoring

My journey V46 and 750 -> http://gmatclub.com/forum/my-journey-to-46-on-verbal-750overall-171722.html#p1367876

Re: If m is a positive integer, then m^3 has how many digits? [#permalink]

Show Tags

16 May 2015, 00:59

Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________

Re: If m is a positive integer, then m^3 has how many digits? [#permalink]

Show Tags

19 May 2016, 09:53

Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________

Campus visits play a crucial role in the MBA application process. It’s one thing to be passionate about one school but another to actually visit the campus, talk...

Its been long time coming. I have always been passionate about poetry. It’s my way of expressing my feelings and emotions. And i feel a person can convey...

Marty Cagan is founding partner of the Silicon Valley Product Group, a consulting firm that helps companies with their product strategy. Prior to that he held product roles at...

Written by Scottish historian Niall Ferguson , the book is subtitled “A Financial History of the World”. There is also a long documentary of the same name that the...