If x is a positive integer, is x^2 + 6x +10 odd?

Question

(1) x^2 + 4x + 5 is odd
(2) x^2 + 3x + 4 is even

Kudos for a correct  solution .

ManojReddy · Answer

If x is a positive integer, is x^2 + 6x +10 odd?

In the expression x^2 + 6x + 10, 6x + 10 is always even. So we need to check whether x^2 is either even or odd to decide if the expression x^2 + 6x +10 is odd.
We have 2 conditions:
 1) If x^2 is even then x^2 + 6x +10 is even
 2) If x^2 is odd then x^2 + 6x +10 is odd

(1) x^2 + 4x + 5 is odd

In the above expression 4x + 5 is always odd. Since the expression x^2 + 4x + 5 is odd, x^2 has to be even.
As x^2 is even, x is also even.
Referring to the above 2 conditions we can say x^2 + 6x +10 is  even.

Sufficient

(2) x^2 + 3x + 4 is even

For the above expression to be even then x^2 + 3x has to be even.
If x is odd then x^2 + 3x is even 
If x is even then x^2 + 3x is even

So the expression x^2 + 6x +10 can be either odd or even.

Insufficient

Ans:A

KS15 · Answer

Statement 1: x^2 + 4x + 5 is odd: 4x is even, 5 is odd, therefore, x^2 is even and x is even. 
Now, x^2+6x+10 is even. Sufficient

Statement 2: x^2 + 3x + 4 is even: 4 is even, 3x+x^2 can be ODD or 3x+x^2 can be EVEN. Insufficient

Answer A

GMATinsight · Answer

Question : Is x^2 + 6x +10 odd?

Since x is a Positive Integer therefore 6x+10 will always be even

so for x^2 + 6x +10 to be odd, x^2 MUST be odd i.e. the question is asking whether x is an odd integer or not

QUESTION REDEFINED: is x an odd Integer?

Statement 1: x^2 + 4x + 5 is odd

Since 4x is even therefore we infer that, x^2 + 5 is odd
But Since EVEN + ODD = ODD
therefore, x^2 must be even for x^2+5 to be odd
i.e. x is certainly ODD
Hence,   SUFFICIENT

Statement 2: x^2 + 3x + 4 is even

EVE + EVE = EVEN
Since, 4 is even, therefore x^2 + 3x MUST be even as well
but, ODD + ODD = EVEN
also, EVEN + EVEN = EVEN
therefore x may be odd or even
Hence,   NOT SUFFICIENT

Answer: Option  A

chetan2u · Answer

the Q basically asks us "is x odd?"(as all terms except x^2 are even)..
1) stat 1 tells us that x^2 + 4x + 5 is odd... here x^2 has to be even... suff
2) stat 2 tells us that x^2 + 3x + 4 is even... here x can take even or odd value to satisfy the eq... insuff
ans A

Bunuel · Answer

MANHATTAN GMAT OFFICIAL SOLUTION:

The question can first be simplified by noting that, if x is even, x^2 + 6x + 10 will be even, and if x is odd, x^2 + 6x+ 10 will be odd.

Thus, you can simplify this question: “Is x odd or even?” (A couple of shortcuts to save time in reaching that conclusion: the exponent on the first term can be ignored, since an even squared is still even and an odd squared is still odd. 6x will be even no matter what, since 6 is even, and obviously 10 is even no matter what. So, an even plus two evens is even, and an odd plus two evens is odd.)

(1) SUFFICIENT: You can plug in numbers or simply use number theory. If x is even, you get even + even + odd = odd, and if x is odd, you get odd + even + odd = even. Thus, since x^2 + 4x + 5 is odd, x is even.

(2) INSUFFICIENT: x^2 + 3x + 4 is actually even regardless of what integer is plugged in for x. If x is even, you get even + even + even = even, and if x is odd, you get odd + odd + even = even. Thus, x could be odd or even. Plugging in numbers will yield the same conclusion - x could be any integer.

Note that you should not factor any of the expressions above. If you wasted time factoring, remember: factoring is meaningless if you don’t have an equation set equal to zero! This problem was about number theory (or number testing), not factoring.

The correct answer is (A).

Nunuboy1994 · Answer

The question is merely "is X odd?"

Statement 1

This basically tells us the expression must be

odd + odd + odd =odd

suff

Statement 2

An odd OR even could satisfy this condition such as 1 or 2

insuff

A

bumpbot · Answer

Automated notice from GMAT Club BumpBot: 

A member just gave Kudos to this thread, showing it’s still useful. I’ve bumped it to the top so more people can benefit. Feel free to add your own questions or solutions.

 This post was generated automatically.

If x is a positive integer, is x^2 + 6x +10 odd?

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

GMAT Data Sufficiency (DS) Questions

If x is a positive integer, is x^2 + 6x +10 odd?

Prep Toolkit

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