Is x an even? b0, x is an integer. 1. x^(a+b) is even 2.

Question

Is x an even? b>0, x is an integer.

1. x^(a+b) is even
2. a>b

BG · Answer

given X is integer, B>0
From A) since X^(a+b) is EVEN then X is Even or A) sufficient
So the ans is A IMHO..

ranga41 · Answer

Is zero an even number, I keep forgetting that? if so the answer is C otherwise the answer is A.

Dan · Answer

picked A, but OA is C!

qpoo · Answer

Dan

can you provide OE (original explaination) please ?

Dilshod · Answer

The answer must be C

1. x^(a+b) is even 
2. a>b

St.1
suppose, X is 1/2, a+b=-2, then x^(a+b)=4, which is even integer. So x could be a fraction as well as integer. insufficicient.

From St 2, all we got to know is that a+b is always positive. Insuffic.

Combining both stataments, we would get C, since x^(a+b), where a+b>0, cannot be even unless X is intger.

Dan · Answer

The stem already specifies that x is an integer.

OE: 

The character of the integer does not change if the integer is raised to any positive integer index. So, a+b must be positive.

Arsene_Wenger · Answer

Please explain in more details, Dan. I still do not understand.

christoph · Answer

C)...

1) consider: x=2 a=2 b=0 (YES) x=5 a=-2 b=2 (NO)

2) nothing about x

1)+2) a+b is not 0. sufficient

qpoo · Answer

Chris said:
 
C)...

1) consider: x=2 a=2 b=0 (YES) x=5 a=-2 b=2 (NO)

when x = 5 (a=-2, b=2) => x^(a+b) = 1 => not satisfying 1), being even


-------

Dan said:
 
The character of the integer does not change if the integer is raised to any positive integer index. So, a+b must be positive.
 

The odd/even character of the integer will not change, even if the integer is raised to a   negative   integer index. Can you find an example that is not working this way ?

christoph · Answer

chris says: i am an idiot. qpoo, you are right.

Dilshod · Answer

Sorry. I thought the question is asking whether x is integer

mandy · Answer

PLZ Dilshod Why do you suppose that X is is 1/2 since it is stated in the stem that x is an integer

Dilshod · Answer

I misread the question. I thought it was asking, whether x is integer

mandy · Answer

b>0, x is an integer. Is x an even? St1.X^(a+b) is even ST2. a>b Well i got it

St1.X^(a+b) is even for X^(a+b)to be even X Has to be even no matter the power for instance 2^3 =2*2*2 =8 3^4=3*3*3*3 The only way X^(a+b) is even where X not even will be if X^0 X^0=1 since we don't know the sign of a insufficient St2 a>b b>o tell us than a is positive but nothing about X insufficient together sufficient because we know that we don 't have X^0 since a and b positive and X^(a+b) is even so x has to be even :wink:

qpoo · Answer

Mandy said:

...
St1.X^(a+b) is even
for X^(a+b)to be even X Has to be even no matter the power
for instance 2^3 =2*2*2 =8
3^4=3*3*3*3
 The only way X^(a+b) is even where X not even
will be if X^0 
X^0=1
since we don't know the sign of a
insufficient
...

Is the part in bold correct ? --> X^0=1 is not even

Also, do we need to prove in what situation will X^(a+b) is even ?
- I thought that is a given condition.

Arsene_Wenger · Answer

I still believe the answer here is  A .


Consider stmt 1 again. Given that x is an integer, I cannot conceivale thing of anyhow that stmt 1 will hold, unless x is even. Thus stmt 1 is sufficient.

Dan · Answer

sorry Arsene, I haven't seen your earlier post. Yes I think it's A too, and OA may be wrong - just may be.

Is x an even? b>0, x is an integer. 1. x^(a+b) is even 2.

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