Is the integer z divisible by 6? : GMAT Data Sufficiency (DS)
Check GMAT Club App Tracker for the Latest School Decision Releases http://gmatclub.com/AppTrack

It is currently 07 Dec 2016, 07:03
GMAT Club Tests

Chicago-Booth

is Releasing R1 Admission Decisions | Keep Watch on App Tracker | Join Chat Room2 for Live Updates


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

Events & Promotions

Events & Promotions in June
Open Detailed Calendar

Is the integer z divisible by 6?

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

Hide Tags

Director
Director
avatar
Status: Finally Done. Admitted in Kellogg for 2015 intake
Joined: 25 Jun 2011
Posts: 537
Location: United Kingdom
Concentration: International Business, Strategy
GMAT 1: 730 Q49 V45
GPA: 2.9
WE: Information Technology (Consulting)
Followers: 74

Kudos [?]: 2863 [0], given: 217

Is the integer z divisible by 6? [#permalink]

Show Tags

New post 25 Jun 2011, 11:22
5
This post was
BOOKMARKED
00:00
A
B
C
D
E

Difficulty:

  45% (medium)

Question Stats:

57% (01:43) correct 43% (00:52) wrong based on 189 sessions

HideShow timer Statistics

Is the integer z divisible by 6?

(1) The greatest common factor of z and 12 is 3.
(2) The greatest common factor of z and 15 is 3.

[Reveal] Spoiler:
Can someone please help and let me know how to approach this question?

My approach is:

Considering statement 1: Prime factors of 12 are: 2,2 & 3. As the GCF of z and 12 is 3, z should be a multiple of 3. Now if its a multiple of 3 it could be 3, 6, 12, 18..... which will be give Yes and No answers to the question and therefore insufficient. But in the book it says it sufficient. Where I am going wrong?

Considering statement 2: Prime factors of 15 are 3 and 5. ...Again I struggle to complete. Can someone please help?
[Reveal] Spoiler: OA

_________________

Best Regards,
E.

MGMAT 1 --> 530
MGMAT 2--> 640
MGMAT 3 ---> 610
GMAT ==> 730

Senior Manager
Senior Manager
avatar
Joined: 24 Mar 2011
Posts: 457
Location: Texas
Followers: 5

Kudos [?]: 154 [0], given: 20

Re: Is the integer z divisible by 6? [#permalink]

Show Tags

New post 25 Jun 2011, 11:28
1
This post was
BOOKMARKED
Is the integer Z divisible by 6?

1. The GCF of z and 12 is 3.
2. The GCF of z and 15 is 15.

st-1 is tricky - if the GCF is given as 3, then value of z cannot be 6,12 or any other multiple of 2, because the GCF then would not be 3.
So value of Z could be 3, 9, 15, 21 - in all cases the GCF of z and 12 is 3. So Z as per st1 is not divisible by 6.

st 2 - obviously can have values of Z as 15, 30, 45 etc. So Z divisible by 6 may be true or may not be true.

so st-1 is sufficient. A
Director
Director
avatar
Status: Finally Done. Admitted in Kellogg for 2015 intake
Joined: 25 Jun 2011
Posts: 537
Location: United Kingdom
Concentration: International Business, Strategy
GMAT 1: 730 Q49 V45
GPA: 2.9
WE: Information Technology (Consulting)
Followers: 74

Kudos [?]: 2863 [0], given: 217

Re: Is the integer z divisible by 6? [#permalink]

Show Tags

New post 25 Jun 2011, 11:48
My sincere apologies. I got it now. GCD will be the multiplication of common factors. So it will be 6 for 12 & 12.

Thanks for all your help.
_________________

Best Regards,
E.

MGMAT 1 --> 530
MGMAT 2--> 640
MGMAT 3 ---> 610
GMAT ==> 730

Math Forum Moderator
avatar
Joined: 20 Dec 2010
Posts: 2021
Followers: 162

Kudos [?]: 1669 [0], given: 376

Re: Is the integer z divisible by 6? [#permalink]

Show Tags

New post 25 Jun 2011, 11:49
enigma123 wrote:
My sincere apologies. I got it now. GCD will be the multiplication of common factors. So it will be 6 for 12 & 12.

Thanks for all your help.


For 12 & 12; GCD is 12.
_________________

~fluke

GMAT Club Premium Membership - big benefits and savings

Director
Director
avatar
Status: Finally Done. Admitted in Kellogg for 2015 intake
Joined: 25 Jun 2011
Posts: 537
Location: United Kingdom
Concentration: International Business, Strategy
GMAT 1: 730 Q49 V45
GPA: 2.9
WE: Information Technology (Consulting)
Followers: 74

Kudos [?]: 2863 [0], given: 217

Re: Is the integer z divisible by 6? [#permalink]

Show Tags

New post 25 Jun 2011, 11:53
Ok - for GCD of 12 & 12

12 - 2,2,3
12- 2,2,3

So the common factors are 2 & 3. How come 12? Any guidance on GCD will be much appreciated. I say this with BIG please. :P
_________________

Best Regards,
E.

MGMAT 1 --> 530
MGMAT 2--> 640
MGMAT 3 ---> 610
GMAT ==> 730

Senior Manager
Senior Manager
avatar
Joined: 24 Mar 2011
Posts: 457
Location: Texas
Followers: 5

Kudos [?]: 154 [0], given: 20

Re: Is the integer z divisible by 6? [#permalink]

Show Tags

New post 25 Jun 2011, 12:04
enigma123 wrote:
Ok - for GCD of 12 & 12

12 - 2,2,3
12- 2,2,3

So the common factors are 2 & 3. How come 12? Any guidance on GCD will be much appreciated. I say this with BIG please. :P


its NOT UNIQUE common factors but ALL COMMON FACTORS. So, in above common factos are 2, 2 and 3, hence 12.
Director
Director
avatar
Status: Finally Done. Admitted in Kellogg for 2015 intake
Joined: 25 Jun 2011
Posts: 537
Location: United Kingdom
Concentration: International Business, Strategy
GMAT 1: 730 Q49 V45
GPA: 2.9
WE: Information Technology (Consulting)
Followers: 74

Kudos [?]: 2863 [0], given: 217

Re: Is the integer z divisible by 6? [#permalink]

Show Tags

New post 25 Jun 2011, 12:10
Agree and many thanks. On a separate note: If the LCM of a & 12 is 36 what could be the possible values of a?

How to approach such questions? I can only think upto

1. The value cannot be more than 36.
2. The factors of 36 are 2,2,3,3
3. The factors of 12 are 2,2,3.

I struggle when I see a variable like a,x or n. Can you please let me know how can I improve my thought process? And again how to approach this problem?
_________________

Best Regards,
E.

MGMAT 1 --> 530
MGMAT 2--> 640
MGMAT 3 ---> 610
GMAT ==> 730

Math Forum Moderator
avatar
Joined: 20 Dec 2010
Posts: 2021
Followers: 162

Kudos [?]: 1669 [0], given: 376

Re: Is the integer z divisible by 6? [#permalink]

Show Tags

New post 25 Jun 2011, 12:22
enigma123 wrote:
Agree and many thanks. On a separate note: If the LCM of a & 12 is 36 what could be the possible values of a?

How to approach such questions? I can only think upto

1. The value cannot be more than 36.
2. The factors of 36 are 2,2,3,3
3. The factors of 12 are 2,2,3.

I struggle when I see a variable like a,x or n. Can you please let me know how can I improve my thought process? And again how to approach this problem?


I recommend you go through MGMAT number properties guide. It really provides a clear picture about how to find HCF and LCM.
_________________

~fluke

GMAT Club Premium Membership - big benefits and savings

Director
Director
avatar
Status: Finally Done. Admitted in Kellogg for 2015 intake
Joined: 25 Jun 2011
Posts: 537
Location: United Kingdom
Concentration: International Business, Strategy
GMAT 1: 730 Q49 V45
GPA: 2.9
WE: Information Technology (Consulting)
Followers: 74

Kudos [?]: 2863 [0], given: 217

Re: Is the integer z divisible by 6? [#permalink]

Show Tags

New post 25 Jun 2011, 12:29
This question is from MGMAT Number Properties guide buddy and it says

The LCM of 12 and a contains two 2's. Since the LCM contains each prime factor to the power it appears the MOST, we know that a cannot contain more than two 2's.

LCM of 12 and a contain two 3's. But 12 only contains one 3. The 3^2 factor in the LCM must have come from prime factorization of a. Thus we know that a contains exactly two 3's.

Since a must contain exactly two 3's nd can contain no 2's, one 2 or two 2's a could be

3*3=9
3*3*2=18
3*3*2**2=36.

Thus 9,18 and 36 are three values.

I am struggling to understand the concept.
_________________

Best Regards,
E.

MGMAT 1 --> 530
MGMAT 2--> 640
MGMAT 3 ---> 610
GMAT ==> 730

2 KUDOS received
Math Forum Moderator
avatar
Joined: 20 Dec 2010
Posts: 2021
Followers: 162

Kudos [?]: 1669 [2] , given: 376

Re: Is the integer z divisible by 6? [#permalink]

Show Tags

New post 25 Jun 2011, 12:37
2
This post received
KUDOS
enigma123 wrote:
Ok - for GCD of 12 & 12

12 - 2,2,3
12- 2,2,3

So the common factors are 2 & 3. How come 12? Any guidance on GCD will be much appreciated. I say this with BIG please. :P



12= 2^2*3
24= 2^3*3

GCF(12, 24)= Product of minimum power of all common prime factors.

Locate the common prime factors; 2 and 3;
Let's check the minimum power of 2;
In 12: 2 has a power of 2.
In 24; 2 has a power of 3.
Here; 2<3
Thus; GCF will have 2^2(The minimum of the two powers)

Now;
In 12; 3 has a power of 1.
In 24; 3 has a power of 1.
Thus, minimum power of 3 is 1;
GCF will have 3^1

GCF=2^2*3^1=12

So; what's the GCF of 630 and 240.

630=3^2*5*2*7
240=2^4*5*3

Locate common prime factors; 2, 3 and 5.
Locate minimum powers of 2, 3 and 5 in both of these.

630 has 2 3's i.e. 3^2
240 has 1 3 i.e. 3^1
Thus, we consider: 3^1 for GCF

630 has 1 2 i.e. 2^1
240 has 4 2's i.e. 2^4
Thus, we consider 2^1 for GCF

630 has 1 5 i.e. 5^1
240 has 1 5 i.e. 5^1
Thus, we consider 5^1 for GCF

GCF(630,240)=3^1*2^1*5^1=30
************************************

So, if we are given that GCF of z and 12 is 3, what do we know about z.
12=2^2*3

We know that z has at least one "3" in its factor AND z has no factor of 2 because even if there is one factor of 2 present in z, the GCF becomes 2^1*3^1=6, invalidating the statement; you see the point
***********************************************
_________________

~fluke

GMAT Club Premium Membership - big benefits and savings

1 KUDOS received
Math Forum Moderator
avatar
Joined: 20 Dec 2010
Posts: 2021
Followers: 162

Kudos [?]: 1669 [1] , given: 376

Re: Is the integer z divisible by 6? [#permalink]

Show Tags

New post 25 Jun 2011, 12:46
1
This post received
KUDOS
enigma123 wrote:
This question is from MGMAT Number Properties guide buddy and it says

The LCM of 12 and a contains two 2's. Since the LCM contains each prime factor to the power it appears the MOST, we know that a cannot contain more than two 2's.

LCM of 12 and a contain two 3's. But 12 only contains one 3. The 3^2 factor in the LCM must have come from prime factorization of a. Thus we know that a contains exactly two 3's.

Since a must contain exactly two 3's nd can contain no 2's, one 2 or two 2's a could be

3*3=9
3*3*2=18
3*3*2**2=36.

Thus 9,18 and 36 are three values.

I am struggling to understand the concept.


For LCM you will have to consider all prime factors and maximum powers.

LCM(a, 12)=36

12=2^2*3
a=?
36=2^2*3^3
--------------

What does this tell about a?

LCM always has maximum power of the factor;
Thus if LCM is 36 and its factors are 2^2*3^2. It means that a only has a maximum of two distinct prime factors 2 and 3 and the maximum powers of those factors are 2 and 2 respectively.

Now, let's see what 12 tells us;
12=2^2*3
Means; a can have 2^0, 2^1 or 2^2 as its factor because the minimum criteria for 36 to have at least 2^2 has already been taken care by 12.
Thus, it really doesn't matter whether a contains 2^2 or not.
a may contain 2^0, 2^1 or 2^2. Note a can't contain 2^3 because in 36, maximum power of 2 is 2. Thus, any of the numbers can't have more than 2 2's.

Likewise; let's check for 3.
12 has 1 3.
But 36 has two 3's i.e. 3^2
Thus, a must contain 3^2; because 36 is LCM of a and 12. As 12 doesn't have 2 factors of 3. It's become necessary for a to have 2 3's. Thus, a has 3^2. Also, note that a can't contain more than 2 3's because 36 has maximum of 2 3's. Also, a can't contain any other prime factor as 36 has only two distinct factors; 3 and 2.

Now, how many values of a are possible;
2^0*3^2=9
2^1*3^2=18
2^2*3^2=36
****************************************
_________________

~fluke

GMAT Club Premium Membership - big benefits and savings

1 KUDOS received
Director
Director
avatar
Joined: 01 Feb 2011
Posts: 757
Followers: 14

Kudos [?]: 114 [1] , given: 42

Re: Is the integer z divisible by 6? [#permalink]

Show Tags

New post 25 Jun 2011, 17:57
1
This post received
KUDOS
1.Sufficient
GCF of z and 12 is 3. that tells us that Z doesn't have any 3 , but has a 2.

for a number to be divisible by 6 , it needs to have both 2 and 3 as factors. in the above as 3 is ruled out, we can clearly say that the number is not divisible by 6.

2. Not sufficient
GCF of z and 15 is 15 . That tells us that z has 3 and 5 as factors.

But we dont whether there is 2 in it or not. If z has 2 as a factor it is divisible by 6 or else not.

Answer is A.
Expert Post
Math Expert
User avatar
Joined: 02 Sep 2009
Posts: 35911
Followers: 6851

Kudos [?]: 90014 [0], given: 10402

Re: Is the integer z divisible by 6? [#permalink]

Show Tags

New post 23 Feb 2012, 14:25
Is the integer z divisible by 6?

Realistic GMAT question would mention that z is a positive integer.

(1) The greatest common factor of z and 12 is 3 --> if z were divisible by 6 (for example 6, 12, 18, ...) then the GCF of z and 12 (which is also divisible by 6) would have been more than 3 (6 or 12) and since the GCF is 3 then z is not divisible by 6. Sufficient.

(2) The greatest common factor of z and 15 is 3 --> if z=3 then the answer is NO but if z=6 then the answer is YES. Two different answers, not sufficient.

Answer: A.

Hope it's clear.
_________________

New to the Math Forum?
Please read this: 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

GMAT Club Legend
GMAT Club Legend
User avatar
Joined: 09 Sep 2013
Posts: 12885
Followers: 561

Kudos [?]: 158 [0], given: 0

Premium Member
Re: Is the integer z divisible by 6? [#permalink]

Show Tags

New post 19 Aug 2015, 12:56
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.
_________________

GMAT Books | GMAT Club Tests | Best Prices on GMAT Courses | GMAT Mobile App | Math Resources | Verbal Resources

Manager
Manager
User avatar
Joined: 16 Jul 2015
Posts: 58
GMAT 1: 580 Q37 V33
GMAT 2: 580 Q39 V31
GMAT 3: 660 Q44 V36
GMAT 4: 560 Q40 V28
GMAT 5: 580 Q37 V32
GMAT 6: 680 Q45 V37
GMAT 7: 690 Q47 V37
Followers: 0

Kudos [?]: 0 [0], given: 16

Re: Is the integer z divisible by 6? [#permalink]

Show Tags

New post 17 Jun 2016, 08:54
I am not clear with this question.First statement tells us that GCF of z & 12 is 3,which indicates that z is atleast 3 or in other words is a multiple of 3.
IF z is a multiple of 3,then it may or may not be divisible by 6.For e.g 3,9,27 is not divisible by 6 but 18 and 6 are divisible by 6.So how can we say that Statement 1 is sufficient???
Expert Post
Math Expert
User avatar
Joined: 02 Sep 2009
Posts: 35911
Followers: 6851

Kudos [?]: 90014 [0], given: 10402

Re: Is the integer z divisible by 6? [#permalink]

Show Tags

New post 17 Jun 2016, 09:18
bhamini1 wrote:
I am not clear with this question.First statement tells us that GCF of z & 12 is 3,which indicates that z is atleast 3 or in other words is a multiple of 3.
IF z is a multiple of 3,then it may or may not be divisible by 6.For e.g 3,9,27 is not divisible by 6 but 18 and 6 are divisible by 6.So how can we say that Statement 1 is sufficient???


This is explained in the post just above yours: if z were divisible by 6 (for example 6, 12, 18, ...) then the GCF of z and 12 (which is also divisible by 6) would have been more than 3 (6 or 12) and since the GCF is 3 then z is not divisible by 6. Sufficient.
_________________

New to the Math Forum?
Please read this: 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

Manager
Manager
User avatar
Joined: 16 Jul 2015
Posts: 58
GMAT 1: 580 Q37 V33
GMAT 2: 580 Q39 V31
GMAT 3: 660 Q44 V36
GMAT 4: 560 Q40 V28
GMAT 5: 580 Q37 V32
GMAT 6: 680 Q45 V37
GMAT 7: 690 Q47 V37
Followers: 0

Kudos [?]: 0 [0], given: 16

Re: Is the integer z divisible by 6? [#permalink]

Show Tags

New post 17 Jun 2016, 10:11
Bunuel,I had read your post but I am not clear as to how we can rule out that Z can be a multiple of 3 that may or may not be divisible by 6.Does GCF define the divisibility of z when we dont know which factors z has other than 3
Expert Post
Math Expert
User avatar
Joined: 02 Sep 2009
Posts: 35911
Followers: 6851

Kudos [?]: 90014 [0], given: 10402

Re: Is the integer z divisible by 6? [#permalink]

Show Tags

New post 17 Jun 2016, 10:28
bhamini1 wrote:
Bunuel,I had read your post but I am not clear as to how we can rule out that Z can be a multiple of 3 that may or may not be divisible by 6.Does GCF define the divisibility of z when we dont know which factors z has other than 3


Again, z cannot be divisible by 6, because if it were divisible by 6 then the greatest common factor of z and 12 would have been 6 (or 12) not 3. For example if z=6 then GCF of z=6 and 12 is 6 not 3.
_________________

New to the Math Forum?
Please read this: 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

Re: Is the integer z divisible by 6?   [#permalink] 17 Jun 2016, 10:28
    Similar topics Author Replies Last post
Similar
Topics:
3 Is the integer z divisible by 3? stonecold 4 28 Oct 2016, 05:39
3 Is the integer z divisible by 11? stonecold 2 28 Oct 2016, 05:36
5 Experts publish their posts in the topic Is the integer z divisible by 6? stonecold 3 21 Aug 2016, 06:33
2 Experts publish their posts in the topic Is the integer z divisible by 6? restore 9 08 Aug 2011, 06:56
4 This is what I have: Is the integer z divisible by 6? 1) The Lstadt 6 31 Jul 2011, 13:31
Display posts from previous: Sort by

Is the integer z divisible by 6?

  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 and phpBB SEO

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®.