[phpBB Debug] PHP Notice: in file /includes/check_new_recommended_questions.php on line 37: Undefined array key "last_recommended_questions_epoch"
[phpBB Debug] PHP Notice: in file /includes/check_new_recommended_questions.php on line 41: Undefined array key "last_recommended_questions_epoch"
If x is a positive integer greater than 1, what is the value of x? : Data Sufficiency (DS)
 Last visit was: 20 Jul 2024, 03:50 It is currently 20 Jul 2024, 03:50
Toolkit
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.

# If x is a positive integer greater than 1, what is the value of x?

SORT BY:
Tags:
Show Tags
Hide Tags
Math Expert
Joined: 02 Sep 2009
Posts: 94428
Own Kudos [?]: 642463 [134]
Given Kudos: 86606
GMAT Club Legend
Joined: 12 Sep 2015
Posts: 6804
Own Kudos [?]: 30839 [55]
Given Kudos: 799
Current Student
Joined: 18 Oct 2014
Posts: 679
Own Kudos [?]: 1787 [16]
Given Kudos: 69
Location: United States
GMAT 1: 660 Q49 V31
GPA: 3.98
General Discussion
Retired Moderator
Joined: 26 Nov 2012
Posts: 473
Own Kudos [?]: 497 [0]
Given Kudos: 46
If x is a positive integer greater than 1, what is the value of x? [#permalink]
Bunuel wrote:
If x is a positive integer greater than 1, what is the value of x?

(1) 2x is a common factor of 18 and 24
(2) x is a factor of 6

This is how tried..

1. 2X is a common factor of 18 and 24. Take LCM of 18 and 24 i.e. 72 is the number. Then 2X = 72 => X = 36...Sufficient.

2 x is a factor of 6 - factors of 6 are 1,2,3 and 6 and here we get different X values.. Insufficient..

IMO correct option is A.

OA please...will correct if I missed anything...
Intern
Joined: 06 Jul 2015
Posts: 19
Own Kudos [?]: 11 [1]
Given Kudos: 9
Re: If x is a positive integer greater than 1, what is the value of x? [#permalink]
1
Kudos
If x is a positive integer greater than 1, what is the value of x?

(1) 2x is a common factor of 18 and 24
(2) x is a factor of 6

Statement 1 : GCD of 18 and 24 IS 72 . So x is 36..! Hold on , the next common factor is 2x72=144 so X is 72.
This is insufficient.

Statement 2: 6 has many factors which are positive such as 6,12,36 ..etc

Statement 1& Statement 2 : 36 and 72 are factors of 6 .

So we can determine the value of X using the statement 1 and statement 2
Manager
Joined: 07 May 2015
Posts: 159
Own Kudos [?]: 73 [0]
Given Kudos: 21
Location: India
GMAT 1: 660 Q48 V31
GPA: 3
Re: If x is a positive integer greater than 1, what is the value of x? [#permalink]
common factors of 18 and 24 are 2, 3, 6
ST1: 2x is factor of 18 and 24 .
we know x >1
thus only one value satisfies this x = 3
sufficient

St 2:
x is factor of 6
factors of 6 greater than 1 = 2, 3
insufficient

Ans :A
Retired Moderator
Joined: 19 Mar 2014
Posts: 815
Own Kudos [?]: 981 [0]
Given Kudos: 199
Location: India
Concentration: Finance, Entrepreneurship
GPA: 3.5
Re: If x is a positive integer greater than 1, what is the value of x? [#permalink]
If x is a positive integer greater than 1, what is the value of x?

x>1

(1) 2x is a common factor of 18 and 24

As 2x is a common fator of 18 & 24, lets fiigure out what can take the value of 2x

18 = 1*2*3*3
24 = 1*2*2*2*3

Common factors are: 1*2*3 = = 2*3 - Here 3 replaces x from the equation 2x, so get the value of x = 3 which is > 1

Hence =====> (1) is SUFFICIENT

(2) x is a factor of 6

x is a factor of 6

Which means x can be any of these numbers: 1, 2, 3

As you an clearly see that we can have twp possibilities, =1 and >1 we really cannot answer the question is x > 1.

Hence, =====> (2) is NOT-SUFFICIENT

Manager
Joined: 12 Dec 2016
Posts: 57
Own Kudos [?]: 126 [1]
Given Kudos: 67
Re: If x is a positive integer greater than 1, what is the value of x? [#permalink]
1
Kudos
Attachment:
File comment: Solution

DS Solution.JPG [ 1.57 MiB | Viewed 55139 times ]
A. see attached.
Intern
Joined: 29 Dec 2018
Posts: 2
Own Kudos [?]: 0 [0]
Given Kudos: 3
Location: United States (NY)
Concentration: Social Entrepreneurship, Sustainability
GPA: 3.45
WE:Underwriter (Venture Capital)
Re: If x is a positive integer greater than 1, what is the value of x? [#permalink]
I'm confused - why can't x = 1.5 in this case? If 3 and 6 are both factors of 18 and 24 in statement 1. And X > 1.

Then can't 2x = 3 (x=1.5) and 2x = 6 (x=3) work?
Intern
Joined: 01 Dec 2018
Posts: 3
Own Kudos [?]: 6 [0]
Given Kudos: 524
Location: United States (IL)
Concentration: Strategy, Finance
GPA: 3
WE:Supply Chain Management (Transportation)
Re: If x is a positive integer greater than 1, what is the value of x? [#permalink]
elonmusk

The prompt states that X is an (positive) integer.
LBS Moderator
Joined: 30 Oct 2019
Posts: 830
Own Kudos [?]: 789 [1]
Given Kudos: 1576
If x is a positive integer greater than 1, what is the value of x? [#permalink]
1
Kudos
(1)18, 24 has positive factors 1,2,3,6
Now 2x cannot be 1 and 3 because x is an integer
Also 2x cannot be 2, because x>1
Therefore, 2x must be 6, x=3
Sufficient

(2) Positive factors of 6 are 1,2,3 and 6
It cannot be 1 because x>1
but x can be either 2 or 3 or 6.
Not sufficient

Director
Joined: 14 Jul 2010
Status:No dream is too large, no dreamer is too small
Posts: 959
Own Kudos [?]: 5017 [0]
Given Kudos: 690
Concentration: Accounting
Re: If x is a positive integer greater than 1, what is the value of x? [#permalink]
Top Contributor
Bunuel wrote:
If x is a positive integer greater than 1, what is the value of x?

(1) 2x is a common factor of 18 and 24
(2) x is a factor of 6

X is greater than or equal to 2

1) The common factors of 18 and 24 are: 2, and 3
The option says 2x is factor of 18 and 24
only 3 satisfies the condition. So x = 3
Option 1 is sufficient.

2) This gives 2, 3, and 6; several options. Insufficient.

Ans. A.
Director
Joined: 09 Jan 2020
Posts: 953
Own Kudos [?]: 234 [0]
Given Kudos: 432
Location: United States
Re: If x is a positive integer greater than 1, what is the value of x? [#permalink]
Bunuel wrote:
If x is a positive integer greater than 1, what is the value of x?

(1) 2x is a common factor of 18 and 24
(2) x is a factor of 6

Bunuel,

Statement 1 says 2x is a common factor of 18 and 24.

Can we then say that x is a common factor of 9 and 12?

9 and 12 share 3 as a common factor; x must be 3.
Target Test Prep Representative
Joined: 14 Oct 2015
Status:Founder & CEO
Affiliations: Target Test Prep
Posts: 19175
Own Kudos [?]: 22679 [0]
Given Kudos: 286
Location: United States (CA)
Re: If x is a positive integer greater than 1, what is the value of x? [#permalink]
Bunuel wrote:
If x is a positive integer greater than 1, what is the value of x?

(1) 2x is a common factor of 18 and 24
(2) x is a factor of 6

Solution:

Question Stem Analysis:

We need to determine the value of x given that x is a positive integer greater than 1.

Statement One Alone:

The common factors of 18 and 24 are 1, 2, 3, 6. Setting 2x equal to 1, 2, 3 and 6, we have x equal to 0.5, 1, 1.5 and 3, respectively. Since we are given that x is a positive integer greater than 1, we see that the only possible value for x is 3. Statement one alone is sufficient.

Statement Two Alone:

The factors of 6 are 1, 2, 3 and 6. Since x is a positive integer greater than 1, x could be 2, 3, or 6. Since we have more than one possible value for x, statement two alone is not sufficient.

GMAT Club Legend
Joined: 08 Jul 2010
Status:GMAT/GRE Tutor l Admission Consultant l On-Demand Course creator
Posts: 6020
Own Kudos [?]: 13810 [1]
Given Kudos: 125
Location: India
GMAT: QUANT+DI EXPERT
Schools: IIM (A) ISB '24
GMAT 1: 750 Q51 V41
WE:Education (Education)
Re: If x is a positive integer greater than 1, what is the value of x? [#permalink]
1
Bookmarks
Bunuel wrote:
If x is a positive integer greater than 1, what is the value of x?

(1) 2x is a common factor of 18 and 24
(2) x is a factor of 6

'

Wanna make solving the Official Questions interesting???

Click here and solve 1000+ Official Questions with Video solutions as Timed Sectional Tests
and Dedicated Data Sufficiency (DS) Course

Video solution by GMATinsight

Get TOPICWISE: Concept Videos | Practice Qns 100+ | Official Qns 50+ | 100% Video solution CLICK HERE.
Two MUST join YouTube channels : GMATinsight (1000+ FREE Videos) and GMATclub
Senior Manager
Joined: 25 Aug 2020
Posts: 250
Own Kudos [?]: 142 [0]
Given Kudos: 216
Re: If x is a positive integer greater than 1, what is the value of x? [#permalink]
Bunuel wrote:
If x is a positive integer greater than 1, what is the value of x?

(1) 2x is a common factor of 18 and 24
(2) x is a factor of 6

Bunuel,

Statement 1 says 2x is a common factor of 18 and 24.

Can we then say that x is a common factor of 9 and 12?

9 and 12 share 3 as a common factor; x must be 3.

good logic your approach works if you take into consideration that x is greater then 1.
Otherwise, there is an additional factor "1" for 9 and 12.
Senior Manager
Joined: 20 Dec 2020
Posts: 286
Own Kudos [?]: 30 [0]
Given Kudos: 497
Location: India
Re: If x is a positive integer greater than 1, what is the value of x? [#permalink]
avigutman

I was able to solve it by identifying factors of 18 and 24 ( 1, 2, 3, 6) and then 2x equal to 1, 2, 3 and 6.
So x could be 0.5, 1, 1.5 and 3, respectively. Given x>1, so x=3

Is there any way to solve it through reasoning?
Tutor
Joined: 17 Jul 2019
Posts: 1304
Own Kudos [?]: 1745 [1]
Given Kudos: 66
GMAT 1: 780 Q51 V45
GMAT 2: 780 Q50 V47
GMAT 3: 770 Q50 V45
Re: If x is a positive integer greater than 1, what is the value of x? [#permalink]
1
Kudos
Sneha2021 wrote:
avigutman

I was able to solve it by identifying factors of 18 and 24 ( 1, 2, 3, 6) and then 2x equal to 1, 2, 3 and 6.
So x could be 0.5, 1, 1.5 and 3, respectively. Given x>1, so x=3

Is there any way to solve it through reasoning?

Certainly, Sneha2021. Reduce statement (1) by a factor of 2 (since the question is about x, not 2x):
If 2x is a common factor of 18 and 24, then x is a common factor of 9 and 12. The only common factor of 9 and 12 (other than 1) is 3.
Tutor
Joined: 17 Jul 2019
Posts: 1304
Own Kudos [?]: 1745 [1]
Given Kudos: 66
GMAT 1: 780 Q51 V45
GMAT 2: 780 Q50 V47
GMAT 3: 770 Q50 V45
Re: If x is a positive integer greater than 1, what is the value of x? [#permalink]
1
Kudos
Video solution from Quant Reasoning:
Subscribe for more: https://www.youtube.com/QuantReasoning? ... irmation=1
Non-Human User
Joined: 09 Sep 2013
Posts: 34038
Own Kudos [?]: 853 [0]
Given Kudos: 0
Re: If x is a positive integer greater than 1, what is the value of x? [#permalink]
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: If x is a positive integer greater than 1, what is the value of x? [#permalink]
Moderator:
Math Expert
94427 posts