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

It is currently 08 Dec 2019, 15:05

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 and q are positive integers, is q odd?

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

Hide Tags

Find Similar Topics 
Intern
Intern
avatar
G
Joined: 21 May 2016
Posts: 27
GMAT ToolKit User
If p and q are positive integers, is q odd?  [#permalink]

Show Tags

New post 04 Oct 2018, 03:40
1
2
00:00
A
B
C
D
E

Difficulty:

  45% (medium)

Question Stats:

60% (01:44) correct 40% (02:09) wrong based on 53 sessions

HideShow timer Statistics

If p and q are positive integers, is q odd?

(1) 2p+3q=12

(2) 4p/5q is an odd integer
Director
Director
avatar
G
Joined: 19 Oct 2013
Posts: 511
Location: Kuwait
GPA: 3.2
WE: Engineering (Real Estate)
GMAT ToolKit User
If p and q are positive integers, is q odd?  [#permalink]

Show Tags

New post Updated on: 04 Oct 2018, 08:13
a70 wrote:
If p and q are positive integers, is q odd?

(1) 2p+3q=12

(2) 4p/5q is an odd integer


p and q > 0

1) \(2p+3q = 12\) this also comes down to \(p + \frac{3q}{2} = \frac{12}{2}\)

\(p + \frac{3q}{2} = 6\)

q must be a multiple of 2 to get an integer number. So it is not ODD

Sufficient

2) \(\frac{4p}{5q}\) = odd integer

\(\frac{4}{5} * \frac{p}{q}\) this means P must be an odd multiple of 5 and q must be a multiple of 4

(4/5) * (15/4) = 3 odd integer
(4/5) * (5/4) = 1 odd integer

Meaning q must be even. so it is sufficient to say q is NOT ODD

Sufficient

D is the answer choice

Originally posted by Salsanousi on 04 Oct 2018, 04:54.
Last edited by Salsanousi on 04 Oct 2018, 08:13, edited 1 time in total.
GMATH Teacher
User avatar
P
Status: GMATH founder
Joined: 12 Oct 2010
Posts: 935
If p and q are positive integers, is q odd?  [#permalink]

Show Tags

New post 04 Oct 2018, 06:10
a70 wrote:
If p and q are positive integers, is q odd?

(1) 2p+3q=12

(2) 4p/5q is an odd integer

\(p,q\,\, \ge 1\,\,{\rm{ints}}\,\,\,\left( * \right)\)

\(q\,\,\mathop = \limits^? \,\,{\rm{odd}}\)

\(\left( 1 \right)\,\,\,2p + 3q = 12\,\,\,\,\,\mathop \Rightarrow \limits^{\left( {**} \right)} \,\,\,\,\left\langle {{\rm{NO}}} \right\rangle\)
\(\left( {**} \right)\,\,q\,\,{\rm{odd}}\,\,\,\mathop \Rightarrow \limits^{\left( * \right)} \,\,\,\,\left( {12 = } \right)\,\,2p + 3q\,\,{\rm{odd}}\,\,{\rm{,}}\,\,\,{\rm{impossible}}\)

\(\left( 2 \right)\,\,\,{{4p} \over {5q}} = {\rm{odd}}\,\,\,\,\, \Rightarrow \,\,\,4p = 5q \cdot {\rm{odd}}\,\,\,\,\,\mathop \Rightarrow \limits^{\left( {***} \right)} \,\,\,\,\left\langle {{\rm{NO}}} \right\rangle\)
\(\left( {***} \right)\,\,\,q\,\,{\rm{odd}}\,\,\,\mathop \Rightarrow \limits^{\left( * \right)} \,\,\,\,\,\left( {4p = } \right)\,\,5q \cdot {\rm{odd}}\,\,{\rm{ = }}\,\,{\rm{odd}}\,\,{\rm{,}}\,\,\,{\rm{impossible}}\,\)


The correct answer is therefore (D).


This solution follows the notations and rationale taught in the GMATH method.

Regards,
Fabio.
_________________
Fabio Skilnik :: GMATH method creator (Math for the GMAT)
Our high-level "quant" preparation starts here: https://gmath.net
GMAT Club Bot
If p and q are positive integers, is q odd?   [#permalink] 04 Oct 2018, 06:10
Display posts from previous: Sort by

If p and q are positive integers, is q odd?

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





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