If P is an odd integer and (P^2 + Q * R) is an even integer,

BREAKING: Target Test Prep releases Brand New 2026 On Demand GMAT prep course

Redeem

This topic has expert replies

Post new topic Post Reply

Previous Topic Next Topic

BTGmoderatorDC: Moderator; Posts: 7187; Joined: Thu Sep 07, 2017 4:43 pm; Followed by:23 members

If P is an odd integer and (P^2 + Q * R) is an even integer,

by BTGmoderatorDC » Tue Oct 09, 2018 5:47 pm

Timer

00:00

Your Answer

Global Stats

If P is an odd integer and (P^2 + Q * R) is an even integer, then which of the following must be true?

A. either Q or R is an odd integer
B. either Q or R is an even integer
C. both Q and R are odd integer
D. both Q and R are even integers
E. nothing can be concluded

OA E

Source: Magoosh

Quote

Source: Beat The GMAT — Problem Solving | Tue Oct 09, 2018 5:47 pm

GMAT/MBA Expert

[email protected]: Elite Legendary Member; Posts: 10392; Joined: Sun Jun 23, 2013 6:38 pm; Location: Palo Alto, CA; Thanked: 2867 times; Followed by:511 members; GMAT Score:800

by [email protected] » Tue Oct 09, 2018 7:10 pm

Hi All,

We're told that If P is an ODD integer and (P^2 + Q * R) is an EVEN integer. We're asked which of the following MUST be true. This question can be solved with a mix of Number Properties and TESTing VALUES.

To start, since P is ODD, we know that P^2 will also be ODD (since ODD^2 = ODD).
For (ODD + Q * R) to be EVEN, we know that (Q * R) must also be ODD. However we do NOT know whether Q and R are integers or not...

IF Q=1 and R=1, then all 3 variables are ODD.
IF Q=2 ad R = 1/2, then the 3 variables include one ODD, one EVEN and one non-integer.

Thus, none of the first 4 answers is always going to be true.

Final Answer: E

GMAT assassins aren't born, they're made,
Rich

Contact Rich at [email protected]

Quote

GMAT/MBA Expert

Scott@TargetTestPrep: GMAT Instructor; Posts: 8086; Joined: Sat Apr 25, 2015 10:56 am; Location: Los Angeles, CA; Thanked: 43 times; Followed by:29 members

by Scott@TargetTestPrep » Fri Oct 19, 2018 2:26 pm

BTGmoderatorDC wrote:If P is an odd integer and (P^2 + Q * R) is an even integer, then which of the following must be true?

A. either Q or R is an odd integer
B. either Q or R is an even integer
C. both Q and R are odd integer
D. both Q and R are even integers
E. nothing can be concluded

Since P is odd, P^2 is also odd.In order for P^2 + Q * R to be even, Q * R must be odd, since odd + odd = even. If we knew that both Q and R were integers, then necessarily both Q and R would have to be odd. However, Q could be 2 and R could be 1/2, in which case the product Q * R = 2 x 1/2 = 1 is still an odd integer. Therefore, we cannot conclude anything about the parity of Q and R. Thus, the answer is E.

Answer: E

Scott Woodbury-Stewart
Founder and CEO
[email protected]