Summer is Coming! Join the Game of Timers Competition to Win Epic Prizes. Registration is Open. Game starts Mon July 1st.

It is currently 17 Jul 2019, 02:23

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

If x is a positive integer

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

Hide Tags

Find Similar Topics 
e-GMAT Representative
User avatar
V
Joined: 04 Jan 2015
Posts: 2942
If x is a positive integer  [#permalink]

Show Tags

New post Updated on: 13 Aug 2018, 02:51
1
11
00:00
A
B
C
D
E

Difficulty:

  95% (hard)

Question Stats:

32% (02:10) correct 68% (02:11) wrong based on 147 sessions

HideShow timer Statistics


e-GMAT Question:



If \(x\) is a positive integer, is the GCD of \(x+3\) and \(x+5\) more than \(1\)?
1. \(3x\) is the common factor of \(12\) and \(6\).
2. \(2x^n\) has \(1\) prime factor.
    A) Statement (1) ALONE is sufficient, but statement (2) ALONE is not sufficient.
    B) Statement (2) ALONE is sufficient, but statement (1) ALONE is not sufficient.
    C) Both statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
    D) EACH statement ALONE is sufficient.
    E) Statement (1) and (2) TOGETHER are NOT sufficient.

This is

Question 7 of The e-GMAT Number Properties Marathon




Go to

Question 8 of the Marathon


_________________

Originally posted by EgmatQuantExpert on 28 Feb 2018, 03:08.
Last edited by EgmatQuantExpert on 13 Aug 2018, 02:51, edited 2 times in total.
Retired Moderator
User avatar
P
Joined: 07 Jan 2016
Posts: 1090
Location: India
GMAT 1: 710 Q49 V36
Reviews Badge
Re: If x is a positive integer  [#permalink]

Show Tags

New post 28 Feb 2018, 04:01
EgmatQuantExpert wrote:

Question:



If \(x\) is a positive integer, is the GCD of \(x+3\) and \(x+5\) more than \(1\)?
1. \(3x\) is the common factor of \(12\) and \(6\).
2. \(2x^n\) has \(1\) prime factor.
    A) Statement (1) ALONE is sufficient, but statement (2) ALONE is not sufficient.
    B) Statement (2) ALONE is sufficient, but statement (1) ALONE is not sufficient.
    C) Both statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
    D) EACH statement ALONE is sufficient.
    E) Statement (1) and (2) TOGETHER are NOT sufficient.


we need to find value of x and check if x+3 and x+5 are co-prime together

1) 3x is the common factor of 12 and 6

factors of 12= 1,2,3,4,6,12
factors of 6 = 1,2,3,6

common factor = 1,2,3,6

3x = 3 or 3x=6

x= 1 or x =2

if x=1

x+3 and x+5 are 4 and 6 hcf >1

but if x=2

x+3 and x+5 are 5 and 7 hcf not greater than insufficient


2) 2x^n has 1 prime factor

i.e x^n is a power of 2/x=1

if x=1

2x^n = 2

x=2 n=2

2x^n = 2^3

x=2

similar cases to A

insufficient


combining we get x as 1/2

(E) imo


If common factor = HCF then (A) imo
My understanding of common factor is neccesatrily not the greatest common factor

niks18, pushpitkc and amanvermagmat what do you guys think?
Senior PS Moderator
User avatar
V
Joined: 26 Feb 2016
Posts: 3360
Location: India
GPA: 3.12
Re: If x is a positive integer  [#permalink]

Show Tags

New post 28 Feb 2018, 06:14
Hey Hatakekakashi

A common factor is not necessarily the HCF.
HCF is the highest common factor and there can be other common factors for two numbers as well.
Consider the numbers 4 and 12. The HCF is 4, but 2 is also a common factor.

As per my understanding, the solution you have given is perfect and the OA must be E!
_________________
You've got what it takes, but it will take everything you've got
e-GMAT Representative
User avatar
V
Joined: 04 Jan 2015
Posts: 2942
Re: If x is a positive integer  [#permalink]

Show Tags

New post 28 Feb 2018, 12:19

Solution:



We need to find:
If the GCD of \(x+3\) and \(x+5\) is more than \(1\) or not.
Statement 1
“\(3x\) is the common factor of \(12\) and \(6\)”.
Factors of \(12= 1, 2, 3, 4, 6,12\)
Factors of \(6= 1,2,3,6\)
Common factor of \(12\) and \(6\) which are in the form \(3x\) are, \(3\) and \(6\).
When,
    \(3x=3\)
      \(x=1\)
    \(3x=6\)
      \(x=2\)
Thus, we do not have a single value of x.
Therefore, Statement 1 alone is NOT sufficient to answer the question.

Statement 2
“\(2x^n\) has \(1\) prime factor “
We know, \(x^n\) has the same number of prime factors as \(x\) has. Therefore,
\(2x\) also has \(1\) factor.
\(2x= 2*x\)
For \(2x\) to have only \(1\) prime factor, the value of \(x\) can be \(1\) or \(2\).
Thus, we do not have a single value of x.
Therefore, Statement 2 alone is NOT sufficient to answer the question.
We are getting the same value of \(x\) from both the statements. Thus, both statements combined will not give the answer.
Therefore, statement 1 and 2 TOGETHER are not sufficient.

Answer: Option E
_________________
Manager
Manager
avatar
B
Joined: 29 Sep 2016
Posts: 103
Re: If x is a positive integer  [#permalink]

Show Tags

New post 01 Jun 2019, 18:53
EgmatQuantExpert wrote:

e-GMAT Question:



If \(x\) is a positive integer, is the GCD of \(x+3\) and \(x+5\) more than \(1\)?
1. \(3x\) is the common factor of \(12\) and \(6\).
2. \(2x^n\) has \(1\) prime factor.
    A) Statement (1) ALONE is sufficient, but statement (2) ALONE is not sufficient.
    B) Statement (2) ALONE is sufficient, but statement (1) ALONE is not sufficient.
    C) Both statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
    D) EACH statement ALONE is sufficient.
    E) Statement (1) and (2) TOGETHER are NOT sufficient.

This is

Question 7 of The e-GMAT Number Properties Marathon




Go to

Question 8 of the Marathon



Pls correct statement 2 as
2. \(2x^n\) has only \(1\) prime factor.
GMAT Club Bot
Re: If x is a positive integer   [#permalink] 01 Jun 2019, 18:53
Display posts from previous: Sort by

If 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