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

 It is currently 14 Oct 2019, 07:16 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.  a = 5^15 - 625^3 and a/x is an integer, where x is a positive integer

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

Hide Tags

Intern  B
Joined: 20 Sep 2013
Posts: 1
Location: India
Concentration: Entrepreneurship, General Management
WE: General Management (Manufacturing)
Re: a = 5^15 - 625^3 and a/x is an integer, where x is a positive integer  [#permalink]

Show Tags

Bunuel wrote:
Bunuel wrote:
a = 5^15 - 625^3 and a/x is an integer, where x is a positive integer such that it does NOT have a factor p such that 1 < p < x, then how many different values for x are possible?

A. None
B. One
C. Two
D. Three
E. Four

Kudos for a correct solution.

OFFICIAL SOLUTION:

First of all, notice that x is a positive integer such that it does NOT have a factor p such that 1 < p < x simply means that x is a prime number.

Next, $$a = 5^{15} - 625^3=5^{15} - 5^{12}=5^{12}(5^3-1)=5^{12}*124=2^2*5^{12}*31$$.

Finally, for a/x to be an integer where x is a prime, x can take 3 values: 2, 5, or 31.

Hi Bunnel,

Can you please clarify if the value of x = 2, then according to 1 < p < x, what will be the value of p. I marked option C because x has to be a prime number and I assumed p = 2 as its given 1 < p < x and x has to be greater than p
Math Expert V
Joined: 02 Sep 2009
Posts: 58310
Re: a = 5^15 - 625^3 and a/x is an integer, where x is a positive integer  [#permalink]

Show Tags

sujay840 wrote:
Bunuel wrote:
Bunuel wrote:
a = 5^15 - 625^3 and a/x is an integer, where x is a positive integer such that it does NOT have a factor p such that 1 < p < x, then how many different values for x are possible?

A. None
B. One
C. Two
D. Three
E. Four

Kudos for a correct solution.

OFFICIAL SOLUTION:

First of all, notice that x is a positive integer such that it does NOT have a factor p such that 1 < p < x simply means that x is a prime number.

Next, $$a = 5^{15} - 625^3=5^{15} - 5^{12}=5^{12}(5^3-1)=5^{12}*124=2^2*5^{12}*31$$.

Finally, for a/x to be an integer where x is a prime, x can take 3 values: 2, 5, or 31.

Hi Bunnel,

Can you please clarify if the value of x = 2, then according to 1 < p < x, what will be the value of p. I marked option C because x has to be a prime number and I assumed p = 2 as its given 1 < p < x and x has to be greater than p

We are told that x is a positive integer such that it does NOT have a factor p such that 1 < p < x.

2 does not have a factor p such that 1 < p < 2.
_________________
Target Test Prep Representative D
Status: Founder & CEO
Affiliations: Target Test Prep
Joined: 14 Oct 2015
Posts: 8040
Location: United States (CA)
Re: a = 5^15 - 625^3 and a/x is an integer, where x is a positive integer  [#permalink]

Show Tags

Bunuel wrote:
a = 5^15 - 625^3 and a/x is an integer, where x is a positive integer greater than 1, such that it does NOT have a factor p such that 1 < p < x, then how many different values for x are possible?

A. None
B. One
C. Two
D. Three
E. Four

We can start by simplifying a:

5^15 - 625^3 = 5^15 - (5^4)^3 = 5^15 - 5^12 = 5^12(5^3 - 1) = 5^12(124) = 5^12(4)(31) = 5^12( 2^2)(31)

If a/x is an integer, then x is a factor of a. However, if x does not have a factor p such that 1 < p < x, then x must be prime number. For example, if x = 5, we see that x doesn’t have a factor between 1 and itself. Since a has three distinct prime factors, there are three distinct values for x: 2, 5 and 31.

_________________

Scott Woodbury-Stewart

Founder and CEO

Scott@TargetTestPrep.com

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 Joined: 09 Sep 2013
Posts: 13119
Re: a = 5^15 - 625^3 and a/x is an integer, where x is a positive integer  [#permalink]

Show Tags

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: a = 5^15 - 625^3 and a/x is an integer, where x is a positive integer   [#permalink] 01 Jul 2019, 08:27

Go to page   Previous    1   2   [ 24 posts ]

Display posts from previous: Sort by

a = 5^15 - 625^3 and a/x is an integer, where x is a positive integer

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

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