It is currently 19 Nov 2017, 13:21

Close

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
Your Progress

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.

Close

Request Expert Reply

Confirm Cancel

Events & Promotions

Events & Promotions in June
Open Detailed Calendar

For how many positive integer x is 130/x an integer?

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

Hide Tags

Expert Post
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 42259

Kudos [?]: 132707 [0], given: 12335

For how many positive integer x is 130/x an integer? [#permalink]

Show Tags

New post 12 Oct 2017, 23:55
00:00
A
B
C
D
E

Difficulty:

  45% (medium)

Question Stats:

52% (00:25) correct 48% (00:28) wrong based on 32 sessions

HideShow timer Statistics

Kudos [?]: 132707 [0], given: 12335

Director
Director
avatar
P
Joined: 22 May 2016
Posts: 981

Kudos [?]: 340 [0], given: 592

For how many positive integer x is 130/x an integer? [#permalink]

Show Tags

New post 13 Oct 2017, 05:28
Bunuel wrote:
For how many positive integer x is 130/x an integer?

(A) 8
(B) 7
(C) 6
(D) 5
(E) 3

This question is a version of "find the number of factors." An integer divided by any of its factors equals an integer.

To find the number of factors of 130 (factors 1 and 130 included)**

1) Do the prime factorization of 130: \(2^1*5^1*13^1\)

2) Take the exponents of each prime factor. Add 1 to each.

Exponents are 1, 1, 1
Add 1 to each, thus: 2, 2, 2

3) Multiply those numbers

2 * 2 * 2 = 8
There are 8 factors of 130*

Answer A

*Factors of 130 are
1, 2, 5, 10, 13, 26, 65, 130
130 divided by any of them yields an integer

**The theory, from Bunuel , SEE THIS POST, scroll down to NUMBER OF FACTORS is, verbatim

Finding the Number of Factors of an Integer

First make prime factorization of an integer \(n=a^p*b^q*c^r\), where \(a\), \(b\), and \(c\) are prime factors of \(n\) and \(p\), \(q\), and \(r\) are their powers.

The number of factors of \(n\) will be expressed by the formula \((p+1)(q+1)(r+1)\). NOTE: this will include 1 and n itself.

Example: Finding the number of all factors of 450: \(450=2^1*3^2*5^2\)

Total number of factors of 450 including 1 and 450 itself is \((1+1)*(2+1)*(2+1)=2*3*3=18\) factors.

Kudos [?]: 340 [0], given: 592

Expert Post
Top Contributor
SVP
SVP
User avatar
G
Joined: 12 Sep 2015
Posts: 1842

Kudos [?]: 2602 [0], given: 362

Location: Canada
Re: For how many positive integer x is 130/x an integer? [#permalink]

Show Tags

New post 13 Oct 2017, 07:03
Expert's post
Top Contributor
Bunuel wrote:
For how many positive integer x is 130/x an integer?

(A) 8
(B) 7
(C) 6
(D) 5
(E) 3


This question is asking us "How many positive divisors does 130 have?"

We can solve this using genxer123's technique or we can just list the divisors IN PAIRS and then count them. We get:
1 and 130
2 and 65
5 and 26
10 and 13

TOTAL = 8 divisors

Answer:
[Reveal] Spoiler:
A


Cheers,
Brent
_________________

Brent Hanneson – Founder of gmatprepnow.com

Image

Kudos [?]: 2602 [0], given: 362

Expert Post
Target Test Prep Representative
User avatar
S
Status: Head GMAT Instructor
Affiliations: Target Test Prep
Joined: 04 Mar 2011
Posts: 1684

Kudos [?]: 902 [0], given: 5

Re: For how many positive integer x is 130/x an integer? [#permalink]

Show Tags

New post 16 Oct 2017, 17:08
Bunuel wrote:
For how many positive integer x is 130/x an integer?

(A) 8
(B) 7
(C) 6
(D) 5
(E) 3


If x is a positive integer and 130/x is an integer, then x must be a factor of 130. Thus, we need to determine the number of factors of 130. To determine the number of factors, we break down 130 into its prime factorization, add 1 to the exponent of each unique prime, and then multiply. Thus:

130 = 10 x 13 = 2^1 x 5^1 x 13^1

Thus, 130 has (1 + 1)(1 + 1)(1 + 1) = 2 x 2 x 2 = 8 total factors.

Answer: A
_________________

Jeffery Miller
Head of GMAT Instruction

GMAT Quant Self-Study Course
500+ lessons 3000+ practice problems 800+ HD solutions

Kudos [?]: 902 [0], given: 5

Re: For how many positive integer x is 130/x an integer?   [#permalink] 16 Oct 2017, 17:08
Display posts from previous: Sort by

For how many positive integer x is 130/x an integer?

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


GMAT Club MBA Forum Home| About| Terms and Conditions| GMAT Club Rules| Contact| Sitemap

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

Kindly note that the GMAT® test is a registered trademark of the Graduate Management Admission Council®, and this site has neither been reviewed nor endorsed by GMAC®.