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

 It is currently 20 Mar 2019, 06:31

### 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

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

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

Author Message
TAGS:

### Hide Tags

Manager
Status: Back to (GMAT) Times Square!!!
Joined: 15 Aug 2011
Posts: 125
Location: United States (IL)
GMAT 1: 650 Q49 V30
WE: Information Technology (Computer Software)
If n is an integer and 5^n > 4,000,000, what is the least  [#permalink]

### Show Tags

19 Feb 2012, 19:02
2
17
00:00

Difficulty:

65% (hard)

Question Stats:

59% (01:56) correct 41% (01:52) wrong based on 685 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.

Manager
Status: Employed
Joined: 17 Nov 2011
Posts: 80
Location: Pakistan
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

21 Feb 2012, 14:05
7
3
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
Joined: 02 Sep 2009
Posts: 53734
Re: If n is an integer and...  [#permalink]

### Show Tags

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.

Hope it's clear.
_________________
Intern
Joined: 04 Aug 2012
Posts: 4
Re: If n is an integer and...  [#permalink]

### Show Tags

09 Aug 2012, 13:17
1
I may be wrong here but with the question written as 5^n <4000000,
and wanting the least possible value for n, it would just be the lowest answer choice (7) since it will easily be under 4000000
Intern
Joined: 16 Apr 2012
Posts: 8
Re: If n is an integer and...  [#permalink]

### Show Tags

09 Aug 2012, 13:40
sdrobbi wrote:
I may be wrong here but with the question written as 5^n <4000000,
and wanting the least possible value for n, it would just be the lowest answer choice (7) since it will easily be under 4000000

Really sorry, I made a mistake on the sign. Corrected, thx..
Math Expert
Joined: 02 Sep 2009
Posts: 53734
Re: If n is an integer and...  [#permalink]

### Show Tags

09 Aug 2012, 14:59
arthuro69 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

How would you guys answer quickly this question ?

Merging similar topics. Please refer to the solutions above.

_________________
Intern
Joined: 29 Aug 2012
Posts: 9
If n is an integer and 5^n > 4,000,000, what is the least possib  [#permalink]

### Show Tags

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?
Math Expert
Joined: 02 Sep 2009
Posts: 53734
Re: If n is an integer and 5^n > 4,000,000, what is the least po  [#permalink]

### Show Tags

01 Oct 2012, 06:42
mockney wrote:
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?

Yes, it's good to know the powers of 2 till 2^10=1024. Check here for a solution: if-n-is-an-integer-and-5-n-4-000-000-what-is-the-least-127815.html#p1046805

Hope it helps.
_________________
Manager
Joined: 15 Aug 2013
Posts: 53
Re: If n is an integer and 5^n > 4,000,000, what is the least  [#permalink]

### Show Tags

20 Nov 2013, 12:42
here is my approach -
5^n > 4000000.
=> (10/2)^n > 4000000 .. now 10^10 will have 1 followed by 10 zeros. Dividing by 2^10 = 1024, the expression will become 10^7/1.024.
its simple to see 10^9/512 means 1000000/5.12 < 4000000.

If you know the values of power of 2 (which I think is really helpful), you might do calculation this way in mind implicitly.
Intern
Joined: 19 Aug 2015
Posts: 9
If n is an integer and 5^n > 4,000,000, what is the least  [#permalink]

### Show Tags

03 Mar 2016, 22:03
My approach

5^2 = 25
5^3 = 125
5^4 = 625
5^5 = 3.X thousand
5^6 = 16-18K
5^7 = ~80k
5^8 = ~450K
5^9 = ~2 mil
5^10 = less than 40 mil, therefore the highest answer is 11. E
Current Student
Joined: 12 Aug 2015
Posts: 2616
Schools: Boston U '20 (M)
GRE 1: Q169 V154
Re: If n is an integer and 5^n > 4,000,000, what is the least  [#permalink]

### Show Tags

09 Mar 2016, 23:41
Excellent Question...!!
here we need to just write 256 as 5^3 *2 (approx)
so N>9 => 10 atleast
_________________
Intern
Joined: 08 Jun 2011
Posts: 18
Re: If n is an integer and 5^n > 4,000,000, what is the least  [#permalink]

### Show Tags

02 Jul 2017, 10:17
5^n > 4000000.
=> (10/2)^n > 4000000 .. now 10^10 will have 1 followed by 10 zeros. Dividing by 2^10 = 1024, the expression will become 10^7/1.024.
its simple to see 10^9/512 means 1000000/5.12 < 4000000.

SO , ans is 10. D
Manager
Status: Profile 1
Joined: 20 Sep 2015
Posts: 63
GMAT 1: 690 Q48 V37
GPA: 3.2
WE: Information Technology (Investment Banking)
Re: If n is an integer and 5^n > 4,000,000, what is the least  [#permalink]

### Show Tags

12 Jul 2017, 09:46
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

I thing we can convert the above question as

$$5^n > 4,000,000 ..... sqrt(5^n) > 2,000 .....5^n/2 > 2,000$$

now it is much easier to find the value of n/2 so it $$5^n/2$$ greater than 2000.

$$5^n/2 > 2,000 ... 5^5 > 2000$$ so n/2 = 5 and n = 10.
Target Test Prep Representative
Status: Founder & CEO
Affiliations: Target Test Prep
Joined: 14 Oct 2015
Posts: 5375
Location: United States (CA)
Re: If n is an integer and 5^n > 4,000,000, what is the least  [#permalink]

### Show Tags

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.

_________________

# Scott Woodbury-Stewart

Founder and CEO

Scott@TargetTestPrep.com
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

Non-Human User
Joined: 09 Sep 2013
Posts: 10152
Re: If n is an integer and 5^n > 4,000,000, what is the least  [#permalink]

### Show Tags

02 Jan 2019, 00:05
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 n is an integer and 5^n > 4,000,000, what is the least   [#permalink] 02 Jan 2019, 00:05
Display posts from previous: Sort by