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

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If x is an integer, is x odd?

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