Last visit was: 18 May 2024, 00:58 It is currently 18 May 2024, 00:58
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.

# Is the integer z divisible by 15?

SORT BY:
Tags:
Show Tags
Hide Tags
Math Expert
Joined: 02 Sep 2009
Posts: 93334
Own Kudos [?]: 624598 [6]
Given Kudos: 81898
Intern
Joined: 07 Nov 2020
Posts: 10
Own Kudos [?]: 12 [0]
Given Kudos: 44
Location: Belgium
GMAT 1: 710 Q48 V38
Current Student
Joined: 14 Mar 2018
Posts: 318
Own Kudos [?]: 441 [0]
Given Kudos: 43
Manager
Joined: 12 Dec 2010
Posts: 79
Own Kudos [?]: 81 [2]
Given Kudos: 640
Re: Is the integer z divisible by 15? [#permalink]
2
Kudos
Is integer z divisible by 15?

Statement 1: The greatest common factor of z and 10 is 5. This means there is atleast one 5 in z but no info about a 3. We can't say whether z is divisible by 15. INSUFFICIENT

Statement 2: The greatest common factor of z and 15 is 5.

This means there is atleast one 5 in z but no 3. If z also had a 3 then the GCF would be 5*3 which is 15.

So we can conclude z is not divisible by 15. SUFFICIENT.

Ans:B

Posted from my mobile device
VP
Joined: 11 Aug 2020
Posts: 1258
Own Kudos [?]: 203 [2]
Given Kudos: 332
Re: Is the integer z divisible by 15? [#permalink]
2
Kudos
I think the answer is B.

Statement 1
x = 10, z = 15 YES
x = 10, z = 25 NO

Statement 2
x = 15, z = 5 NO
x = 15, z = 20 NO
The only way for z/15 to be divisible by 15 is if it is some multiple of 15 (e.g. 15, 30, 45, 60). But, if it's a multiple of 15 then that multiple would violate the condition in statement 2.
e.g. x = 15, z = 30 <--GCF(15,30) = 15 NOT 5
Manager
Joined: 27 May 2015
Posts: 60
Own Kudos [?]: 61 [0]
Given Kudos: 28
Re: Is the integer z divisible by 15? [#permalink]
Is the integer z divisible by 15?

(1) The greatest common factor of z and 10 is 5.
(2) The greatest common factor of z and 15 is 5.

1) The greatest common factor of z and 10 is 5.

a) z can be 5
b) z can be 15 itself
Insufficient

(2) The greatest common factor of z and 15 is 5.

for integer z to be divisible by 15, z and 15 gcd should be 15 itself

z is not divisible by 15. Sufficient

IMO (B)
Retired Moderator
Joined: 31 May 2017
Posts: 749
Own Kudos [?]: 672 [2]
Given Kudos: 53
Concentration: Technology, Strategy
Re: Is the integer z divisible by 15? [#permalink]
1
Kudos
1
Bookmarks
Is the integer z divisible by 15?

(1) The greatest common factor of z and 10 is 5.
Z can be 15, which is divisble by 15
Z can be 25 ,which is not divisble by 15

We get 2 different answers. Option A - Not Sufficient.

(2) The greatest common factor of z and 15 is 5.
We know that Z has to be less than 15, to have 5 as GCF. Because if z is equal to greater than 15 , then GCF of Z and 15 will be minimum 15.

So Z is not divisble by 15.

Option B alone is sufficient.

Ans: B
Director
Joined: 14 Jul 2010
Status:No dream is too large, no dreamer is too small
Posts: 969
Own Kudos [?]: 4954 [1]
Given Kudos: 690
Concentration: Accounting
Re: Is the integer z divisible by 15? [#permalink]
1
Kudos
Top Contributor
Bunuel wrote:
Is the integer z divisible by 15?

(1) The greatest common factor of z and 10 is 5.
(2) The greatest common factor of z and 15 is 5.

(1) If z=10 then $$NO$$, if $$z=15$$ then $$YES$$. Insufficient.

(2) Again z=10
The GCF of 10 and 15 is 5;
$$z<15$$ to have GCF 5. So, z is not divisible by 15

Sufficient.

Intern
Joined: 02 Jun 2022
Posts: 32
Own Kudos [?]: 9 [0]
Given Kudos: 24
Location: India
GPA: 3.33
WE:Analyst (Venture Capital)
Re: Is the integer z divisible by 15? [#permalink]
Bunuel wrote:
Is the integer z divisible by 15?

(1) The greatest common factor of z and 10 is 5.
(2) The greatest common factor of z and 15 is 5.

Project DS Butler Data Sufficiency (DS3)

Hi Bunuel , if the second statement was like -

"The greatest common factor of z and 15 is 3"

then the question's answer would have been E right?

Just a curious doubt to understand the question better. Thanks, Bunuel!
Math Expert
Joined: 02 Sep 2009
Posts: 93334
Own Kudos [?]: 624598 [0]
Given Kudos: 81898
Re: Is the integer z divisible by 15? [#permalink]
raghav1708 wrote:
Bunuel wrote:
Is the integer z divisible by 15?

(1) The greatest common factor of z and 10 is 5.
(2) The greatest common factor of z and 15 is 5.

Project DS Butler Data Sufficiency (DS3)

Hi Bunuel , if the second statement was like -

"The greatest common factor of z and 15 is 3"

then the question's answer would have been E right?

Just a curious doubt to understand the question better. Thanks, Bunuel!

No, (2) would still be sufficient.

The question asks: Is the integer z divisible by 15?

(2) sys that the greatest common factor of z and 15 is 5. Now, IF z were divisible by 15 (15, 30, 45, 60, ...), then the greatest common factor of z = 15k (for some integer k) and 15 would have been 15, not 5. Here z can be ..., -20, -10, -5, 5, 10, 20, 25, 35, ... So, z can be any multiple of 5, which is NOT a multiple of 3!

Similarly, IF (2) were the greatest common factor of z and 15 is 3 it would mean that z is NOT divisible by 5, so not divisible by 15 either. IF z were divisible by 15 (15, 30, 45, 60, ...), the the greatest common factor of z = 15k (for some integer k) and 15 would have been 15, not 3. Here z can be ..., -12, -9, -6, -3, 3, 6, 9, 12, 18, ... So, z can be any multiple of 3, which is NOT a multiple of 5!

Hope it's clear.
Intern
Joined: 02 Jun 2022
Posts: 32
Own Kudos [?]: 9 [0]
Given Kudos: 24
Location: India
GPA: 3.33
WE:Analyst (Venture Capital)
Is the integer z divisible by 15? [#permalink]
Bunuel wrote:
raghav1708 wrote:
Bunuel wrote:
Is the integer z divisible by 15?

(1) The greatest common factor of z and 10 is 5.
(2) The greatest common factor of z and 15 is 5.

Hi Bunuel , if the second statement was like -

"The greatest common factor of z and 15 is 3"

then the question's answer would have been E right?

Just a curious doubt to understand the question better. Thanks, Bunuel!

No, (2) would still be sufficient.

The question asks: Is the integer z divisible by 15?

(2) sys that the greatest common factor of z and 15 is 5. Now, IF z were divisible by 15 (15, 30, 45, 60, ...), then the greatest common factor of z = 15k (for some integer k) and 15 would have been 15, not 5. Here z can be ..., -20, -10, -5, 5, 10, 20, 25, 35, ... So, z can be any multiple of 5, which is NOT a multiple of 3!

Similarly, IF (2) were the greatest common factor of z and 15 is 3 it would mean that z is NOT divisible by 5, so not divisible by 15 either. IF z were divisible by 15 (15, 30, 45, 60, ...), the the greatest common factor of z = 15k (for some integer k) and 15 would have been 15, not 3. Here z can be ..., -12, -9, -6, -3, 3, 6, 9, 12, 18, ... So, z can be any multiple of 3, which is NOT a multiple of 5!

Hope it's clear.

Thank you Bunuel, my doubt is clear. Grateful for your detailed explanations! Always! Thanks­
Non-Human User
Joined: 09 Sep 2013
Posts: 33055
Own Kudos [?]: 828 [0]
Given Kudos: 0
Re: Is the integer z divisible by 15? [#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: Is the integer z divisible by 15? [#permalink]
Moderator:
Math Expert
93334 posts