GMAT Question of the Day - Daily to your Mailbox; hard ones only

It is currently 19 Oct 2019, 05:24

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, y, and z are positive integers, what is the greatest prime facto

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

Hide Tags

Find Similar Topics 
Senior Manager
Senior Manager
User avatar
Joined: 12 Aug 2015
Posts: 280
Concentration: General Management, Operations
GMAT 1: 640 Q40 V37
GMAT 2: 650 Q43 V36
GMAT 3: 600 Q47 V27
GPA: 3.3
WE: Management Consulting (Consulting)
If x, y, and z are positive integers, what is the greatest prime facto  [#permalink]

Show Tags

New post 30 Jan 2016, 12:08
6
25
00:00
A
B
C
D
E

Difficulty:

  75% (hard)

Question Stats:

49% (01:37) correct 51% (01:35) wrong based on 265 sessions

HideShow timer Statistics

If x, y, and z are positive integers, what is the greatest prime factor of the product xyz?

(1) The greatest common factor of x, y, and z is 7.

(2) The lowest common multiple of x, y, and z is 84

_________________
KUDO me plenty
Most Helpful Expert Reply
GMAT Club Legend
GMAT Club Legend
User avatar
V
Joined: 12 Sep 2015
Posts: 4009
Location: Canada
Re: If x, y, and z are positive integers, what is the greatest prime facto  [#permalink]

Show Tags

New post 30 Jan 2016, 12:13
12
7
Quote:
If x, y, and z are positive integers, what is the greatest prime factor of the product xyz?

(1) The greatest common factor of x, y, and z is 7.
(2) The lowest common multiple of x, y, and z is 84.


Target question: What is the greatest prime factor of the product xyz?
Let's first clarify what the target question is asking.
It's essentially saying that, if we find the prime factorization of xyz, we want to determine the biggest prime number in this factorization.
Example: 120 = (2)(2)(2)(3)(5). Here, the biggest prime factor is 5

Statement 1: The greatest common factor of x, y, and z is 7
There are several conflicting sets of values that meet this condition. Here are two:
Case a: x = 7, y = 7 and z = 7, in which case xyz = (7)(7)(7), which means the greatest prime factor of the product xyz is 7
Case b: x = 7, y = 7 and z = 77, in which case xyz = (7)(7)(77) = (7)(7)(7)(11), which means the greatest prime factor of the product xyz is 11
Since we cannot answer the target question with certainty, statement 1 is NOT SUFFICIENT

Statement 2: The lowest common multiple (LCM) of x, y, and z is 84.
This tells us that 84 is a multiple x, 84 is a multiple y, and 84 is a multiple z
Notice that 84 = (2)(2)(3)(7)
If 84 is the LOWEST common multiple (LCM), none of the numbers (x, y or z) can have a number bigger than 7 in their prime factorization.
Also, at least one of the numbers (x, y or z) must have a 7 in its prime factorization (otherwise the LCM would not have a 7 in its prime factorization).
All of this tells us that the prime factorization of xyz includes at least one 7 AND it does not include any primes greater than 7.
So, we can be certain that the greatest prime factor of the product xyz is 7

Answer = B

Cheers,
Brent
_________________
Test confidently with gmatprepnow.com
Image
General Discussion
Veritas Prep GMAT Instructor
User avatar
V
Joined: 16 Oct 2010
Posts: 9706
Location: Pune, India
Re: If x, y, and z are positive integers, what is the greatest prime facto  [#permalink]

Show Tags

New post 16 Mar 2016, 06:26
1
shasadou wrote:
If x, y, and z are positive integers, what is the greatest prime factor of the product xyz?

(1) The greatest common factor of x, y, and z is 7.

(2) The lowest common multiple of x, y, and z is 84


Prime factors of xyz are prime numbers which are factors of at least one of x, y and z.
By multiplying x, y and z, you will not get a new prime factor because a prime number cannot be obtained by multiplying two positive integers (other than 1 and itself).

So "what is the greatest prime factor of the product xyz" basically asks you for the greatest prime factor out of all prime factors of x, y and z.

(1) The greatest common factor of x, y, and z is 7.
7 is the greatest COMMON factor. So all x, y and z have 7. But one or two of them could have a higher prime factor too such as 11 or 13 etc. We don't know the greatest prime factor out of all prime factors of these integers. Not sufficient.

(2) The lowest common multiple of x, y, and z is 84
84 = 2*2*3*7
These prime factors include all prime factors which are present in each of x, y and z. The greatest among them is 7. So 7 is the greatest prime factor out of all prime factors of these integers. Sufficient.

Answer (B)
_________________
Karishma
Veritas Prep GMAT Instructor

Learn more about how Veritas Prep can help you achieve a great GMAT score by checking out their GMAT Prep Options >
Current Student
User avatar
D
Joined: 12 Aug 2015
Posts: 2567
Schools: Boston U '20 (M)
GRE 1: Q169 V154
GMAT ToolKit User
Re: If x, y, and z are positive integers, what is the greatest prime facto  [#permalink]

Show Tags

New post 13 Jan 2017, 01:03
Excellent Question.
Testing our knowledge about GCD-LCM and Prime factorisation.

Given data -> x,y,z are positive integers.
We are asked about the Greatest prime factor of x*y*z

Statement 1->
GCD(x,y,z)=7
Lets use test cases->
Case 1=>
7
7
7
GCD=> 7
And Greatest prime =7
Case 2=>
7
7
7*13
GCD=>7
Greatest prime factor is 7*13

Actually this statement tells us that the greatest prime factor must be greater than or equal to 7.
Hence not sufficient.

Statement 2->
LCM(x,y,z)=84=2^2*3*7
Now if x,y,z had any prime factor other than 2,3,7 => It must have been present in the LCM.
In LCM => We pick the greatest power of each Prime factor.
Hence the greatest prime in the Product must be 7.
Hence sufficient.
Hence B.

_________________
Manager
Manager
User avatar
G
Joined: 15 Dec 2015
Posts: 114
GMAT 1: 680 Q49 V34
GPA: 4
WE: Information Technology (Computer Software)
If x, y, and z are positive integers, what is the greatest prime facto  [#permalink]

Show Tags

New post 05 Aug 2017, 23:41
Bunuel: Can you please provide similar questions to practice.
CEO
CEO
User avatar
D
Status: GMATINSIGHT Tutor
Joined: 08 Jul 2010
Posts: 2978
Location: India
GMAT: INSIGHT
Schools: Darden '21
WE: Education (Education)
Reviews Badge
Re: If x, y, and z are positive integers, what is the greatest prime facto  [#permalink]

Show Tags

New post 20 Apr 2018, 02:25
shasadou wrote:
If x, y, and z are positive integers, what is the greatest prime factor of the product xyz?

(1) The greatest common factor of x, y, and z is 7.

(2) The lowest common multiple of x, y, and z is 84



Please find explanation as mentioned in attachment

Answer: option B
Attachments

File comment: www.GMATinsight.com
Screen Shot 2018-04-20 at 2.53.51 PM.png
Screen Shot 2018-04-20 at 2.53.51 PM.png [ 483.94 KiB | Viewed 5448 times ]


_________________
Prosper!!!
GMATinsight
Bhoopendra Singh and Dr.Sushma Jha
e-mail: info@GMATinsight.com I Call us : +91-9999687183 / 9891333772
Online One-on-One Skype based classes and Classroom Coaching in South and West Delhi
http://www.GMATinsight.com/testimonials.html

ACCESS FREE GMAT TESTS HERE:22 ONLINE FREE (FULL LENGTH) GMAT CAT (PRACTICE TESTS) LINK COLLECTION
Non-Human User
User avatar
Joined: 09 Sep 2013
Posts: 13271
Re: If x, y, and z are positive integers, what is the greatest prime facto  [#permalink]

Show Tags

New post 07 Jun 2019, 09:21
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 Club Bot
Re: If x, y, and z are positive integers, what is the greatest prime facto   [#permalink] 07 Jun 2019, 09:21
Display posts from previous: Sort by

If x, y, and z are positive integers, what is the greatest prime facto

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  





Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne