least value

Expert replies

Previous Topic Next Topic

[email protected]: Master | Next Rank: 500 Posts; Posts: 117; Joined: Mon Oct 27, 2008 5:08 pm; Thanked: 1 times

by [email protected] » Sat Feb 14, 2009 7:17 pm

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

7
8
9
10
11

D

Like this post

Source: Beat The GMAT — Problem Solving | Sat Feb 14, 2009 7:17 pm

cramya: Legendary Member; Posts: 2467; Joined: Thu Aug 28, 2008 6:14 pmFollowed by: 11 members; Thanked: 331 times

by cramya » Sat Feb 14, 2009 7:30 pm

5^n > 4 000000

5^n > 4 * 10^6

> 4 * 2^6 * 5^6
> 4^4 * 5^6

n must be alteast 10 since 5^4 > 4^4

Therefore 5^10 > 4^4 * 5^6
5^4 * 5^6 > 4^4 * 5^6

Like this post

dmateer25: Community Manager; Posts: 1049; Joined: Sun Apr 06, 2008 5:15 pmFollowed by: 27 members; Location: Pittsburgh, PA; Thanked: 113 times; GMAT Score:710

by dmateer25 » Sat Feb 14, 2009 8:24 pm

4000000 = 2^8 * 5^6

2^8 = 256

so we need 5 to a power that will make the value greater than 256.

5^3 = 125 so that isn't big enough. But 5^4 definitely is.

Therefore, 5^4 * 5^6 (which is 5^10) > 4000000

Like this post

Post new topic Post Reply

• Page 1 of 1

GMAT Course Reviews

560 reviews

1168 reviews

431 reviews

359 reviews

147 reviews

5/5

5 Star (560 Reviews)

"Target Test Prep is the closest to the official version of the GMAT exam, about 99% accuracy in terms of the quality and quantity of information. The course has excellently created singular sets of focused lessons and tests for every possible topic that one could come across in the official GMAT exam."

"The TTP course maximizes the efficiency of the time you spend studying. It will take time and effort but I could almost guarantee that if you complete the course exactly as it is laid out you will get an amazing score. They also have a very responsive team willing to help with any questions you might have."

"TTP has two things that I think no other test prep company offers: A teaching approach that reinforces understanding and an attitude that will give you the mental preparedness needed to succeed on the test. TTP gives you a deep understanding of the concept you need to know while teaching you how to think."

Write a Review