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

 It is currently 15 Dec 2019, 05:52 ### 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

#### Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.  # For how many (not necessarily positive) integer values of n is the val

Author Message
TAGS:

### Hide Tags

Senior Manager  P
Status: Manager
Joined: 02 Nov 2018
Posts: 280
For how many (not necessarily positive) integer values of n is the val  [#permalink]

### Show Tags

1 00:00

Difficulty:   45% (medium)

Question Stats: 55% (02:17) correct 45% (02:40) wrong based on 11 sessions

### HideShow timer Statistics

For how many (not necessarily positive) integer values of n is the value of $$4000.(\frac{2}{5})^n$$an integer?

(A) 3

(B) 4

(C) 6

(D) 8

(E) 9
Veritas Prep GMAT Instructor V
Joined: 16 Oct 2010
Posts: 9876
Location: Pune, India
Re: For how many (not necessarily positive) integer values of n is the val  [#permalink]

### Show Tags

2
For how many (not necessarily positive) integer values of n is the value of $$4000.(\frac{2}{5})^n$$an integer?

(A) 3

(B) 4

(C) 6

(D) 8

(E) 9

4000 = 2^5 * 5^3

So the denominator of the fraction $$(\frac{2}{5})^n$$ could be 1 or 5^1 or 5^2 or 5^3 or 2^1 or 2^2 or 2^3 or 2^4 or 2^5 for the expression to be an integer.

Hence n could be 0 (2/5 = 1/1)
n could be 1 [(2/5)^n = (2/5)]
n could be 2 [(2/5)^n = (2/5)^2]
n could be 3 [(2/5)^n = (2/5)^3]
n could be -1 [(2/5)^n = (2/5)^-1 = (5/2)^1]
and similarly, n could be -2, -3, -4 and -5

In all, we get 9 values of n.

_________________
Karishma
Veritas Prep GMAT Instructor Re: For how many (not necessarily positive) integer values of n is the val   [#permalink] 18 Mar 2019, 06:19
Display posts from previous: Sort by

# For how many (not necessarily positive) integer values of n is the val  