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, 23:56

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 p, q and r are positive integers and 2p + 3q = r , do r and 6 have

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

Hide Tags

Find Similar Topics 
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 56272
If p, q and r are positive integers and 2p + 3q = r , do r and 6 have  [#permalink]

Show Tags

New post 24 Sep 2018, 06:09
00:00
A
B
C
D
E

Difficulty:

  45% (medium)

Question Stats:

66% (01:35) correct 34% (01:50) wrong based on 42 sessions

HideShow timer Statistics


Math Expert
User avatar
V
Joined: 02 Aug 2009
Posts: 7764
Re: If p, q and r are positive integers and 2p + 3q = r , do r and 6 have  [#permalink]

Show Tags

New post 24 Sep 2018, 08:06
1
If p, q and r are positive integers and 2p + 3q = r, do r and 6 have a common factor greater than 1?

(1) p is a multiple of 3.
Let p = 3x
\(2p+3q=r...........2*3x+3q=r.........3(2x+q)=r\)
So r is a multiple of 3 and 6 is also multiple of 3, so Ans is YES
Sufficient

(2) q is a multiple of 3.
Let q=3y...
\(2p+3q=r...........2p+3*3y=r\)
Let p be a multiple of 3 then r is a multiple of 3 OR if y=2, r is a multiple of 2 and 6 is also multiple of 2 and 3
In each of the cases above, ans is YES
But say p=2 and y=3 r = 2*2+3*3*3=31, so 31 and 6 do not have common factors other than 1
Insufficient

A
_________________
GMAT Club Bot
Re: If p, q and r are positive integers and 2p + 3q = r , do r and 6 have   [#permalink] 24 Sep 2018, 08:06
Display posts from previous: Sort by

If p, q and r are positive integers and 2p + 3q = r , do r and 6 have

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





cron

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