If x is an integer, is x odd?

Question

(1) x + 4 is an odd integer. 
(2) x/3 is NOT an even integer.

HardWorkBeatsAll · Answer

(A) - (1) IS SUFFICIENT, (2) IS NOT

(1) x+4 is odd. Therefore, x+2 is odd, and so is x+0 (i.e. x). Basically, adding a multiple of two to any integer keeps its odd/even'ness' the same.

(2) x/3 is not an even integer. So, it could be - a fraction OR an odd integer. Consider x = 7 . Then x/3 is a fraction. Similarly, x=8 gives x/3 as a fraction. However, x=15 gives an odd quotient. NOT SUFFICIENT.

DharLog · Answer

(1) x + even = odd ---> x - odd ---> sufficient
(2) x/3 can be either odd integer or a fraction
2.1. x/3=5 ---> x = 15 ---> yes
2.2. x/3 = 0,5 ---> x = 1,5 ---> no

The answer is A.

(2_new). x/3 is an integer, not even
If instead of (2) we had (2_new) then the answer would be D.

shashankism · Answer

x is an integer
Question : is x odd or not.

Statement 1 : x+4 is odd.. 
Also odd - even = odd
So, odd - 4 = odd = x
 SUFFICIENT

Statement 2: x/3 is not even .. So x/3 can be fraction or odd .
If x/3 is odd , definitely x will be odd. For e.g. x/3 = 3 -> x = 9
If x/3 is a fraction, x may be odd or even. For e.g. if x/3 = 2/3 a fraction -> x=2
Also if x/3 = 7/3 a fraction -> x = 7
 NOT SUFFICIENT

Answer A

abhishekdadarwal2009 · Answer

If x is an integer, is x odd?

(1) x + 4 is an odd integer. 
(2) x/3 is NOT an even integer.

1)odd + odd is always even,and even +even is always even but odd + even is always odd. so we know that 4 is even that means that x must be odd.
2) odd*even=even even*even=even so we dont know for sure.

OPtion A is correct Answer.

BrentGMATPrepNow · Answer

Target question :    Is x odd?

Some important rules: 
1. ODD + ODD = EVEN
2. ODD + EVEN = ODD
3. EVEN + EVEN = EVEN
  
   Statement 1 : x + 4 is an odd integer.   
Since 4 is EVEN, we have: x + EVEN = ODD
From  rule #2  above, we can see that  x must be odd 
Since we can answer the  target question  with certainty, statement 1 is SUFFICIENT

Statement 2 : x/3 is NOT an even integer. 
There are several values of x that satisfy statement 2. Here are two: 
 Case a : x = 3. Here, x/3 = 3/3 = 1, and 1 is NOT an even integer. In this case,  x IS odd 
 Case b : x = 4. Here, x/3 = 4/3 = 1.333333...., and 1.333333.... is NOT an even integer. In this case,  x is NOT odd 
Since we cannot answer the  target question  with certainty, statement 2 is NOT SUFFICIENT

Answer: A

Cheers,
Brent

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 an integer, is x 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 an integer, is x 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