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

Author Message
TAGS:

### Hide Tags

Math Expert 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 00:00

Difficulty:   45% (medium)

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

### HideShow timer Statistics 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.
(2) q is a multiple of 3.

_________________
Math Expert 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

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
_________________ 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   