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

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 integers
D. both Q and R are even integers
E. nothing can be concluded

[spoiler]OA=E[/spoiler].

I need help here. I've got confused. Help, please. <i class="em em-pray"></i>

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by GMATGuruNY » Mon Jun 25, 2018 2:39 am

Gmat_mission 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 integers
D. both Q and R are even integers
E. nothing can be concluded

Let P=1.

Case 1: (PÂ² + QR) = 2
Plugging P=1 into the equation above, we get:
1Â² + QR = 2
QR = 1.

If Q=1 and R=1, then B and D are not true.
Eliminate B and D.
If Q=2 and R=1/2, then A and C is not true.
Eliminate A and C.

The correct answer is E.

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by Scott@TargetTestPrep » Tue Jun 26, 2018 5:16 pm

Gmat_mission 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 integers
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

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