Last visit was: 19 Jul 2025, 14:40 It is currently 19 Jul 2025, 14:40
Home
GMAT
Messages
Tests
Schools
Events
Rewards
Chat
My Profile
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.
Go to My Error Log Learn more
Close
Request Expert Reply
Confirm Cancel
Back to Forum
Create Topic
User avatar
Bunuel
User avatar
Math Expert
Joined: 02 Sep 2009
Last visit: 19 July 2025
Posts: 102,625
Own Kudos:
742,783
 [10]
Given Kudos: 98,235
Products:
GMAT Club Tests Forum Quiz
Expert
Expert reply
Active GMAT Club Expert! Tag them with @ followed by their username for a faster response.
Posts: 102,625
Kudos: 742,783
 [10]
If p and q are integers and 20p + 3q is odd, which of the following 20 Nov 2017, 11:11
1
Kudos
Add Kudos
9
Bookmarks
Bookmark this Post
00:00
Start Timer
Pause Timer
Resume Timer
Show Answer
Hide
Show
History
D
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!

Difficulty:

25% (medium)

Question Stats:

75% (01:53) correct 25% (01:55) wrong based on 352 sessions

History

Date
Time
Result
Not Attempted Yet
If p and q are integers and 20p + 3q is odd, which of the following must be odd?

(A) p – q

(B) p + 2q

(C) 3p + q

(D) 2p + q^2

(E) 3p + 3q
ShowHide Answer
Official Answer
D
User avatar
rulingbear
User avatar
Joined: 03 May 2017
Last visit: 03 Oct 2018
Posts: 58
Own Kudos:
56
 [3]
Given Kudos: 15
Posts: 58
Kudos: 56
 [3]
If p and q are integers and 20p + 3q is odd, which of the following Updated on: 20 Nov 2017, 12:00
Originally posted by rulingbear on 20 Nov 2017, 11:29.
Last edited by rulingbear on 20 Nov 2017, 12:00, edited 1 time in total.
1
Kudos
Add Kudos
2
Bookmarks
Bookmark this Post
Bunuel
If p and q are integers and 20p + 3q is odd, which of the following must be odd?

(A) p – q

(B) p + 2q

(C) 3p + q

(D) 2p + q^2

(E) 3p + 3q

\(p\) could be odd/even and \(q\) will always be odd as both variables are integers.

The answer could be narrowed down to D as \(2p\) is always even regardless and \(q^2\) is odd. \(Odd + Even = Odd\).

Hence, D.
User avatar
pushpitkc
User avatar
Joined: 26 Feb 2016
Last visit: 19 Feb 2025
Posts: 2,819
Own Kudos:
5,874
 [1]
Given Kudos: 47
Location: India
GPA: 3.12
Posts: 2,819
Kudos: 5,874
 [1]
If p and q are integers and 20p + 3q is odd, which of the following 20 Nov 2017, 11:54
Kudos
Add Kudos
1
Bookmarks
Bookmark this Post
Given data: p,q are integers and 20p + 3q is odd.

Whatever the value of p(odd/even), 20p will be even.
Since the resultant sum is odd, q must be odd.

Substituting values

1. p = q = 1 Option A,C and E are even. Both B and D are odd.
2. p=2, q=1 Option B is even. Only Option D remains

Therefore, Option D(\(2p + q^2\)) must be the only expression which is ODD for all possibilities of p,q
User avatar
JeffTargetTestPrep
User avatar
Target Test Prep Representative
Joined: 04 Mar 2011
Last visit: 05 Jan 2024
Posts: 2,996
Own Kudos:
7,952
 [1]
Given Kudos: 1,646
Status:Head GMAT Instructor
Affiliations: Target Test Prep
Expert
Expert reply
Posts: 2,996
Kudos: 7,952
 [1]
If p and q are integers and 20p + 3q is odd, which of the following 22 Nov 2017, 13:14
1
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Bunuel
If p and q are integers and 20p + 3q is odd, which of the following must be odd?

(A) p – q

(B) p + 2q

(C) 3p + q

(D) 2p + q^2

(E) 3p + 3q

There are three rules that are useful for this problem:

even x any integer = even

even + odd = odd

odd x odd = odd

We see that 20p must be even, so we have:

even + 3q = odd

We see that 3q must be odd, so q must be odd.

Therefore we see that answer D must be odd, because 2p is even and q^2 = odd x odd = odd.

Answer: D
User avatar
Paras96
User avatar
Joined: 11 Sep 2022
Last visit: 30 Dec 2023
Posts: 488
Own Kudos:
281
Given Kudos: 2
Location: India
Paras: Bhawsar
GMAT 1: 590 Q47 V24
GMAT 2: 580 Q49 V21
GMAT 3: 700 Q49 V35
GPA: 3.2
WE:Project Management (Other)
GMAT 3: 700 Q49 V35
Posts: 488
Kudos: 281
If p and q are integers and 20p + 3q is odd, which of the following 10 Aug 2023, 04:37
Kudos
Add Kudos
Bookmarks
Bookmark this Post
If p and q are integers and 20p + 3q is odd, which of the following must be odd?

According to the question, we can infer that q = odd and nothing can be said about p i.e. p can be odd or even

Going by the options

(A) p – q = even/odd - odd = even/odd. Incorrect

(B) p + 2q = even/odd + even = even/odd. Incorrect

(C) 3p + q = even/odd + odd = even/odd. Incorrect

(D) 2p + q^2 = even + odd = odd. correct hence answer

(E) 3p + 3q = even/odd + odd = even/odd. Incorrect
User avatar
bumpbot
User avatar
Non-Human User
Joined: 09 Sep 2013
Last visit: 04 Jan 2021
Posts: 37,450
Own Kudos:
1,013
Posts: 37,450
Kudos: 1,013
If p and q are integers and 20p + 3q is odd, which of the following 18 Jun 2025, 19:44
Kudos
Add Kudos
Bookmarks
Bookmark this Post
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.
Moderators:
Bunuel
Math Expert
102625 posts
Krunaal
PS Forum Moderator
698 posts