Is the integer p even? (1) The integer p^2 + 1 is odd. (2) The integer

Question

Is the integer p even?

(1) The integer p^2 + 1 is odd.
(2) The integer p + 2 is even.

(DS01104)

Mo2men · Answer

(1) The integer p^2 + 1 is odd.

This means even + odd = odd...........P is even

Sufficient

(2) The integer p + 2 is even.

This means even + even = even...........P is even

Sufficient

Answer: D

KSBGC · Answer

Statement 1:

p^2 + 1 = odd

P has to be even in this case. odd + odd = even but even + odd = odd.

Sufficient.

Statement 2:

p + 2 = even

Sufficient.

Odd + 2 = odd

even + 2 = even .

The best answer is D.

sudarshan22 · Answer

(1) The integer p^2 + 1 is odd.
For p^2 + 1 to be odd, p^2 must be even, and an square of even integer is always even
  Sufficient

(2) The integer p + 2 is even.
For p + 2 to be even, p must always be even, for 2 is anyway even
  Sufficient

Hence,   D  .

securegmat · Answer

(A) The integer p^2 + 1 is odd. Therefore, E+O = O Thus.P is Even Sufficient (B) The integer p + 2 is even. Therefore, E+E = E Thus.P is Even Sufficient IMO D

mashedpotatoooo · Answer

What about 0? Or is zero considered an even number? Many thanks!

db0108 · Answer

What if p was 9 or 11? Then 9^2 = 18 + 1 = ODD, but p is also odd? The same would happen with 11

Bunuel · Answer

9^2 = 81, not 18 and 81 + 1 is even not odd.

db0108 · Answer

Thank you, clearly I need more sleep!!

sujoykrdatta · Answer

Yes, 0 is considered even!

Even integer => Any integer divisible by 2; and 0 is divisible by 2 (any all other numbers except 0 itself - the quotient in each case is 0 itself !)

In fact: -2, -4, etc. are also even integers

Clearly, the answer is D:

From 1: p^2 + 1 = Odd => p^2 = Odd - 1 Odd - Odd = Even => p = Even - Sufficient 
From 2: p + 2 = Even => p = Even - 2 = Even - Even = Even - Sufficient

Answer D

Basshead · Answer

Is the integer p even?

(1) The integer p^2 + 1 is odd.

even + odd = odd

(2) The integer p + 2 is even.

even + even = even

Answer is D.

rxb266 · Answer

Is the integer p even?

(1) The integer p^2 + 1 is odd.

Even +odd = odd
This means p^2 is even.. hence, p is even (sufficient)

(2) The integer p + 2 is even.

Even+even = even
This means that p is even.. (sufficient)

Ans Choice D

demawtf · Answer

Is the integer p even?

(1) The integer p^2 + 1 is odd.
--> p^2=odd-1 = EVEN -->SUFFICIENT
(2) The integer p + 2 is even.
--> p=even-2 =EVEN --> SUFFICIENT

totaltestprepNick · Answer

D https://www.youtube.com/watch?v=6hlYlc9ipIU Nick Slavkovich, GMAT/GRE tutor with 20+ years of experience tutoring@totaltestprep.net

Is the integer p even? (1) The integer p^2 + 1 is odd. (2) The integer

Prep Toolkit

Top 5 GMAT Debrief Videos

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards