GMAT Question of the Day - Daily to your Mailbox; hard ones only

It is currently 19 Oct 2019, 07:56

Close

GMAT Club Daily Prep

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.

Close

Request Expert Reply

Confirm Cancel

If n is an integer and 5^n > 4,000,000, what is the least

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:

Hide Tags

Find Similar Topics 
Manager
Manager
User avatar
Status: Back to (GMAT) Times Square!!!
Joined: 15 Aug 2011
Posts: 117
Location: United States (IL)
GMAT 1: 650 Q49 V30
WE: Information Technology (Computer Software)
Reviews Badge
If n is an integer and 5^n > 4,000,000, what is the least  [#permalink]

Show Tags

New post 19 Feb 2012, 19:02
2
21
00:00
A
B
C
D
E

Difficulty:

  65% (hard)

Question Stats:

59% (01:55) correct 41% (01:50) wrong based on 759 sessions

HideShow timer Statistics

If n is an integer and 5^n > 4,000,000, what is the least possible value of n?

(A) 7
(B) 8
(C) 9
(D) 10
(E) 11

_________________
Working towards a goal...
V.
Most Helpful Community Reply
Manager
Manager
User avatar
Status: Employed
Joined: 17 Nov 2011
Posts: 78
Location: Pakistan
Concentration: International Business, Marketing
GMAT 1: 720 Q49 V40
GPA: 3.2
WE: Business Development (Internet and New Media)
Re: If n is an integer and 5^n > 4,000,000, what is the least  [#permalink]

Show Tags

New post 21 Feb 2012, 14:05
8
6
Answer should be D. Here is how I solved it.

Original Statement: \(5^n>4,000,000\)
so \(5^n>4*10^6\)
so \(5^n>4*2^6*5^6\)

dividing by 5^6 on both sides leads to:

so \(5^{n-6}>2^8\)
so \(5^{n-6}>256\)

Now we know that \(5^3=125\)

so it has to be that the number is \(5^4\), the least number that is greater than \(256\)
so \(n-6=4\)
so \(n=10\)

Hence D.
_________________
"Nowadays, people know the price of everything, and the value of nothing." Oscar Wilde
General Discussion
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 58446
Re: If n is an integer and...  [#permalink]

Show Tags

New post 19 Feb 2012, 21:42
2
2
vix wrote:
If n is an integer and 5^n > 4,000,000, what is the least possible value of n?

(A) 7
(B) 8
(C) 9
(D) 10
(E) 11


Make prime factorization of \(4,000,000=2^2*1,000,000=2^2*(10^6)=2^8*5^6=256*5^6\).

So, we have: \(5^n>256*5^6\) --> \(5^4=625>256\) (5^3=125<256), so \(5^n\) must be at least equal to \(5^4*5^6=5^{10}\) to be more than \(256*5^6\).

Hence, the least possible value of n is 10.

Answer: D.

Hope it's clear.
_________________
Intern
Intern
avatar
Joined: 29 Aug 2012
Posts: 8
If n is an integer and 5^n > 4,000,000, what is the least possib  [#permalink]

Show Tags

New post 29 Sep 2012, 23:18
Hi everyone,
This is an old thread, however I do have a question. Are we supposed to know value such as 2^9 off the top of our head?
Thanks for your help
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 58446
Re: If n is an integer and 5^n > 4,000,000, what is the least po  [#permalink]

Show Tags

New post 01 Oct 2012, 06:42
Target Test Prep Representative
User avatar
D
Status: Founder & CEO
Affiliations: Target Test Prep
Joined: 14 Oct 2015
Posts: 8109
Location: United States (CA)
Re: If n is an integer and 5^n > 4,000,000, what is the least  [#permalink]

Show Tags

New post 16 Jul 2017, 17:24
vix wrote:
If n is an integer and 5^n > 4,000,000, what is the least possible value of n?

(A) 7
(B) 8
(C) 9
(D) 10
(E) 11


Let’s break 4,000,000 into primes:

4,000,000 = 4 x 10^6 = 4 x 2^6 x 5^6 = 256 x 5^6.

So, we have:

5^n > 256 x 5^6

We see that n will definitely have to be greater than 6. We have to figure out what power of 5 is going to get us to a number greater than 256. We see that 5^3 = 125 isn’t big enough, but 5^4 = 625 fulfills our requirement of being greater than 256. Thus, n will be (6 + 4) = 10, because it is true that 5^10 > 256 x 5^6.

Answer: D
_________________

Scott Woodbury-Stewart

Founder and CEO

Scott@TargetTestPrep.com
TTP - Target Test Prep Logo
122 Reviews

5-star rated online GMAT quant
self study course

See why Target Test Prep is the top rated GMAT quant course on GMAT Club. Read Our Reviews

If you find one of my posts helpful, please take a moment to click on the "Kudos" button.

Non-Human User
User avatar
Joined: 09 Sep 2013
Posts: 13277
Re: If n is an integer, and 5^n > 4,000,000. What is the least possible  [#permalink]

Show Tags

New post 30 Sep 2019, 23:41
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.
_________________
GMAT Club Bot
Re: If n is an integer, and 5^n > 4,000,000. What is the least possible   [#permalink] 30 Sep 2019, 23:41
Display posts from previous: Sort by

If n is an integer and 5^n > 4,000,000, what is the least

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  





Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne