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

 It is currently 13 Dec 2019, 14:56 ### 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 non-negative integers and p^q + r is an even number

Author Message
TAGS:

### Hide Tags

Math Expert V
Joined: 02 Sep 2009
Posts: 59721
If p, q, and r are non-negative integers and p^q + r is an even number  [#permalink]

### Show Tags 00:00

Difficulty:   95% (hard)

Question Stats: 19% (01:36) correct 81% (01:43) wrong based on 37 sessions

### HideShow timer Statistics

If p, q, and r are non-negative integers and $$p^q + r$$ is an even number which of the following must also be even?

A. p + q + r

B. pqr

C. p + r

D. q + r

E. None of these

_________________
Math Expert V
Joined: 02 Aug 2009
Posts: 8310
Re: If p, q, and r are non-negative integers and p^q + r is an even number  [#permalink]

### Show Tags

Bunuel wrote:
If p, q, and r are non-negative integers and $$p^q + r$$ is an even number which of the following must also be even?

A. p + q + r

B. pqr

C. p + r

D. q + r

E. None of these

This is a must question and we have power in the term so we can play around with it and can have various combinations possible so in all likelihood it should be E

p^q+r is even, so if q=0, p could be anything odd or even and r would be odd.
So p+r and p+q+r are out.....2+1 or 2+0+1
All three could be odd, so 3^1+5...
So pqr is out 3*1*5
Finally q could be even and p and r odd.
So 3^2+3, but 2+3 is odd. Hence q+r is odd.

E
_________________
Target Test Prep Representative V
Status: Founder & CEO
Affiliations: Target Test Prep
Joined: 14 Oct 2015
Posts: 8699
Location: United States (CA)
Re: If p, q, and r are non-negative integers and p^q + r is an even number  [#permalink]

### Show Tags

Bunuel wrote:
If p, q, and r are non-negative integers and $$p^q + r$$ is an even number which of the following must also be even?

A. p + q + r

B. pqr

C. p + r

D. q + r

E. None of these

Let’s test some numbers. If p = q = r = 1, then 1^1 + 1 = 2, which is even. On the other hand, neither p + q + r = 3, nor pqr = 1 is even; thus, we eliminate A and B.

If p = 2, q = 0 and r = 1, then 2^0 + 1 = 2, which is even. On the other hand, neither p + r = 3, nor q + r = 1 is even. Thus, we eliminate C and D as well. E is the only remaining answer choice.

_________________

# Scott Woodbury-Stewart

Founder and CEO

Scott@TargetTestPrep.com

See why Target Test Prep is the top rated GMAT quant course on GMAT Club. Read Our Reviews

If you find one of my posts helpful, please take a moment to click on the "Kudos" button. Re: If p, q, and r are non-negative integers and p^q + r is an even number   [#permalink] 24 Nov 2019, 19:19
Display posts from previous: Sort by

# If p, q, and r are non-negative integers and p^q + r is an even number  