It is currently 10 Dec 2017, 20:55

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

Positive integer x has n factors; 3x has 3 factors; Which of the follo

  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: 42529

Kudos [?]: 135171 [0], given: 12664

Positive integer x has n factors; 3x has 3 factors; Which of the follo [#permalink]

Show Tags

New post 09 Mar 2016, 12:40
Expert's post
8
This post was
BOOKMARKED
00:00
A
B
C
D
E

Difficulty:

  65% (hard)

Question Stats:

59% (01:12) correct 41% (01:13) wrong based on 162 sessions

HideShow timer Statistics

Positive integer x has n factors; 3x has 3 factors; Which of the following values can n take?

I. 1
II. 2
III. 3

A. I only
B. II only
C. I or II
D. II or III
E. I or III
[Reveal] Spoiler: OA

_________________

New to the Math Forum?
Please read this: Ultimate GMAT Quantitative Megathread | All You Need for Quant | PLEASE READ AND FOLLOW: 12 Rules for Posting!!!

Resources:
GMAT Math Book | Triangles | Polygons | Coordinate Geometry | Factorials | Circles | Number Theory | Remainders; 8. Overlapping Sets | PDF of Math Book; 10. Remainders | GMAT Prep Software Analysis | SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) | Tricky questions from previous years.

Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


What are GMAT Club Tests?
Extra-hard Quant Tests with Brilliant Analytics

Kudos [?]: 135171 [0], given: 12664

Current Student
User avatar
Joined: 18 Oct 2014
Posts: 903

Kudos [?]: 453 [0], given: 69

Location: United States
GMAT 1: 660 Q49 V31
GPA: 3.98
GMAT ToolKit User
Re: Positive integer x has n factors; 3x has 3 factors; Which of the follo [#permalink]

Show Tags

New post 09 Mar 2016, 21:06
I would choose 'B'

Given statement is that 3x has three factors which means 3x is a perfect square of 3. hence x=3

3 has 2 factors, making n=2
_________________

I welcome critical analysis of my post!! That will help me reach 700+

Kudos [?]: 453 [0], given: 69

Intern
Intern
avatar
Joined: 03 Mar 2016
Posts: 15

Kudos [?]: 20 [0], given: 5

Location: India
Schools: ISB '19
Re: Positive integer x has n factors; 3x has 3 factors; Which of the follo [#permalink]

Show Tags

New post 09 Mar 2016, 22:18
1
This post was
BOOKMARKED
Squares have odd number of factors.The square which is a multiple of 3 is 9.
3 has factors 1,3 .
Therefore 2 factors
Answer B

Kudos [?]: 20 [0], given: 5

Manager
Manager
avatar
B
Status: Persevere
Joined: 09 Jan 2016
Posts: 123

Kudos [?]: 260 [0], given: 94

Location: Hong Kong
GMAT 1: 750 Q50 V41
GPA: 3.52
Reviews Badge
Re: Positive integer x has n factors; 3x has 3 factors; Which of the follo [#permalink]

Show Tags

New post 09 Mar 2016, 23:19
2
This post was
BOOKMARKED
Bunuel wrote:
Positive integer x has n factors; 3x has 3 factors; Which of the following values can n take?

I. 1
II. 2
III. 3

A. I only
B. II only
C. I or II
D. II or III
E. I or III


Given: (i) \(x\) is an integer; (ii) \(x > 0\); and (iii) \(3x\) has 3 factors
Rule: Only perfect squares have odd number of factors. Only perfect squares of prime numbers have exactly 3 factors.
Therefore, \(x\) must be equal to 3 for \(3x\) to be a perfect square of a prime number. So, \(x\) has exactly 2 factors.
Correct answer is B.

Kudos [?]: 260 [0], given: 94

Retired Moderator
avatar
P
Joined: 12 Aug 2015
Posts: 2209

Kudos [?]: 898 [0], given: 607

GRE 1: 323 Q169 V154
GMAT ToolKit User Premium Member
Re: Positive integer x has n factors; 3x has 3 factors; Which of the follo [#permalink]

Show Tags

New post 14 Mar 2016, 05:33
Excellent Question..
her the only value of x possible is 3
so x=3
hence the number of factors of 3= 1,3 => two
hence B is correct
_________________

Give me a hell yeah ...!!!!!

Kudos [?]: 898 [0], given: 607

Expert Post
Target Test Prep Representative
User avatar
S
Status: Head GMAT Instructor
Affiliations: Target Test Prep
Joined: 04 Mar 2011
Posts: 1771

Kudos [?]: 971 [0], given: 5

Re: Positive integer x has n factors; 3x has 3 factors; Which of the follo [#permalink]

Show Tags

New post 26 Sep 2017, 16:37
Bunuel wrote:
Positive integer x has n factors; 3x has 3 factors; Which of the following values can n take?

I. 1
II. 2
III. 3

A. I only
B. II only
C. I or II
D. II or III
E. I or III


Notice that 3x must be a perfect square since only perfect squares have an odd number of factors. Furthermore, 3x must be the square of a prime number since only squares of prime numbers have 3 factors. That is, if p is a prime, then p^2 has 3 factors, namely, 1, p, and p^2.

Since 3x is the square of a prime number, we see that x must be 3 so that 3x = 9. Since x = 3 and 3 has 2 factors, then n must be 2.

Alternate Solution:

Let’s go over Roman numerals I and III:

Roman Numeral I: x has only 1 factor

The only positive integer with 1 factor is 1 itself; but 3(1) = 3 does not have 3 factors. This is impossible.

Roman Numeral III: x has 3 factors

If x is a number with 3 factors, then 3x will have more than 3 factors. For instance, x = 9 has 3 factors and 3x = 27 has 4 factors. x = 4 has 3 factors and 3x = 12 has 6 factors. This is impossible as well.

The only remaining possibility is n = 2.

Answer: B
_________________

Jeffery Miller
Head of GMAT Instruction

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

Kudos [?]: 971 [0], given: 5

Re: Positive integer x has n factors; 3x has 3 factors; Which of the follo   [#permalink] 26 Sep 2017, 16:37
Display posts from previous: Sort by

Positive integer x has n factors; 3x has 3 factors; Which of the follo

  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®.