Find all School-related info fast with the new School-Specific MBA Forum

 It is currently 09 Oct 2015, 21:38

### 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

# Events & Promotions

###### Events & Promotions in June
Open Detailed Calendar

# Least possible value of n

Author Message
TAGS:
Manager
Joined: 17 Aug 2009
Posts: 237
Followers: 4

Kudos [?]: 145 [0], given: 25

Least possible value of n [#permalink]  11 Jan 2010, 04:24
00:00

Difficulty:

(N/A)

Question Stats:

75% (02:12) correct 25% (02:57) wrong based on 7 sessions
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
Joined: 20 Aug 2009
Posts: 312
Location: Tbilisi, Georgia
Schools: Stanford (in), Tuck (WL), Wharton (ding), Cornell (in)
Followers: 14

Kudos [?]: 110 [2] , given: 69

Re: Least possible value of n [#permalink]  11 Jan 2010, 05:22
2
KUDOS
$$4,000,000 = 2^2*1,000,000 = 2^2*10^6=2^2*2^6*5^6 = 2^8*5^6$$

$$5^n>2^8*5^6$$

$$5^{n-6}>256$$

$$625=5^4>256$$

$$n-6=4$$

$$n=10$$
Manager
Joined: 27 Apr 2008
Posts: 190
Followers: 1

Kudos [?]: 48 [0], given: 1

Re: Least possible value of n [#permalink]  11 Jan 2010, 06:28
You can solve it with the same way you find LCM.

5 | 4,000,000
5 | 800,000
5 | 160,000
5 | 32,000
5 | 6,400
5 | 1,280
5| 256
5 | 56
5 | 11
2

We have 9 5's and 1x2. For $$5^n$$ to be bigger than 4,000,000, we therefore need n=10.
Intern
Joined: 17 Nov 2009
Posts: 37
Schools: University of Toronto, Mcgill, Queens
Followers: 0

Kudos [?]: 59 [0], given: 9

Re: Least possible value of n [#permalink]  14 Feb 2010, 09:51
shalva wrote:
$$4,000,000 = 2^2*1,000,000 = 2^2*10^6=2^2*2^6*5^6 = 2^8*5^6$$

$$5^n>2^8*5^6$$

$$5^{n-6}>256$$

$$625=5^4>256$$

$$n-6=4$$

$$n=10$$

nice approach. What is OA?
_________________

--Action is the foundational key to all success.

Current Student
Status: Nothing comes easy: neither do I want.
Joined: 12 Oct 2009
Posts: 2798
Location: Malaysia
Concentration: Technology, Entrepreneurship
Schools: ISB '15 (M)
GMAT 1: 670 Q49 V31
GMAT 2: 710 Q50 V35
Followers: 202

Kudos [?]: 1248 [0], given: 235

Re: Least possible value of n [#permalink]  14 Feb 2010, 11:15
IMO D -10

$$5^n > 5^6 * 4 * 2^6$$
$$5^n > 5^6 * 2^8$$
$$5^n > 5^6 * 256$$
$$5^n > 5^6 * 5^3 * \frac{256}{125}$$
$$5^n > 5^9* \frac{256}{125}$$ since $$\frac{256}{125}< 5$$

n = 10
_________________

Fight for your dreams :For all those who fear from Verbal- lets give it a fight

Money Saved is the Money Earned

Jo Bole So Nihaal , Sat Shri Akaal

GMAT Club Premium Membership - big benefits and savings

Gmat test review :
670-to-710-a-long-journey-without-destination-still-happy-141642.html

Re: Least possible value of n   [#permalink] 14 Feb 2010, 11:15
Similar topics Replies Last post
Similar
Topics:
23 If y is an integer, then the least possible value of |23-5| 14 01 Oct 2012, 03:58
4 If y is an integer, then the least possible value of |23–5| 2 06 May 2012, 08:41
2 Least Possible Value 6 26 Jun 2011, 04:07
1 least possible value? 1 06 Jan 2011, 18:26
2 what is the least possible value of k? 12 16 Jan 2010, 04:30
Display posts from previous: Sort by