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If x is an integer and a is an even integer, is x even?

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If x is an integer and a is an even integer, is x even?  [#permalink]

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New post 26 Sep 2016, 03:40
2
9
00:00
A
B
C
D
E

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  95% (hard)

Question Stats:

24% (01:47) correct 76% (01:31) wrong based on 244 sessions

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If x is an integer and a is an even integer, is x even?  [#permalink]

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New post Updated on: 26 Sep 2016, 07:00
1
Bunuel wrote:
If x is an integer and a is an even integer, is x even?

(1) x^a is odd.

(2) a*x=12


When a is even integer we can take from 0,2,4,...etc.

Given x is an integer then x can be -3,-2,-1,0,1,2,3,...

Stat 1: When x^a is odd => 3^0 = odd or 2^0 = 1 = odd.

3^1 = 3 or 3^2 = odd...if 2^2 = even ...

then x can be even or odd...Insufficient.

Stat 2: a*x = 12..

we can take 4*3 = 12 or 3*4 = 12...Insufficient...we can still take many combinations...

Both : From stat 2 we can take x as odd or even...

but from stat 1 we have to get x^a = odd..

if x^a is odd...then x has to be odd.. when a = 0 or 2,4,etc...

IMO option C.

Originally posted by msk0657 on 26 Sep 2016, 06:03.
Last edited by msk0657 on 26 Sep 2016, 07:00, edited 1 time in total.
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Re: If x is an integer and a is an even integer, is x even?  [#permalink]

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New post 26 Sep 2016, 06:12
I did not understand it. I thought the answer would be A. a is an even integer. So x is always odd from st1. And st2, X is either 1,3 or 2. So not sufficient


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Re: If x is an integer and a is an even integer, is x even?  [#permalink]

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New post 29 Sep 2016, 13:52
ProfX : a can also be 0
so x^a will always be odd in this case, hence x can be even or odd ...

Second statement tells that a is not zero ... but either 4 or 12 ...
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Re: If x is an integer and a is an even integer, is x even?  [#permalink]

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New post 01 Oct 2016, 06:33
Its C

x can be both odd or even unless we know power of x because if a =0, x^a will be 1 and we can not determine the value of x

statement 2 states that a is not equal to zero.

COmbining 2 statements wee get C
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Re: If x is an integer and a is an even integer, is x even?  [#permalink]

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New post 02 Oct 2016, 12:52
Bunuel wrote:
If x is an integer and a is an even integer, is x even?

(1) x^a is odd.

(2) a*x=12



a is an even integer , hence a = 2,4,6,8...

(1) If x^a = odd , where a is even , then x = odd (suff)

odd ^ even = odd
even ^ even = even

(2)

Since a is even, when a=2, x = 6 (even)
but when a=4, x =3 (odd) (Therefore not suff)

12 = 1X12 or 2X6 or 3X4 or 4X3 or 6X2
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If x is an integer and a is an even integer, is x even?  [#permalink]

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New post 21 Nov 2016, 00:39
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This is a great Question.
WE need to check if x is even/odd
Statement 1
Again => Fundamental Principle used here is that => "Exponent does not effect the Even/Odd nature of any integer"
But here is a catch => Anything raised to zero is one
So if a is zero, x can be even or odd
hence not sufficient
Lets look at statement 2
Let (x,y) be
12,1
2,6
Using the above test cases we can say that a≠0 and x can be even/odd
Hence not sufficient
Combining the two statements
We can say that a≠0 so As x is an integer => x^a is odd => x must be odd
hence sufficient
Hence C

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Re: If x is an integer and a is an even integer, is x even?  [#permalink]

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New post 23 Nov 2016, 13:46
in my opinion statement one is sufficent as statement one is saying that x^a is odd so x should be odd and this statement gives that x is not even.
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Re: If x is an integer and a is an even integer, is x even?  [#permalink]

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New post 24 Nov 2016, 00:40
bilalshahid2003 wrote:
If x is an integer and a is an even integer, is x even?

(1) x^a is odd.

(2) a*x=12

in my opinion statement one is sufficent as statement one is saying that x^a is odd so x should be odd and this statement gives that x is not even.


Your doubt is already addressed above.

(1) says that x^a is odd, so we are given that \((integer)^{(even)} = odd\)

1^2 = 1 = odd --> x = 1 = odd
2^0 = 1 = odd --> x = 2 = even

Two different answers. Thuds, (1) is not sufficient.
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Re: If x is an integer and a is an even integer, is x even?  [#permalink]

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New post 01 Jan 2017, 09:00
Just to extend the concept here =>
If a was odd => Statement 1 would have been sufficient
If x^a was even => Statement 1 would have been sufficient

Although its true that Positive exponents do not affect the even/odd nature of any integer=> The exception to tis statement is when the exponent is 0.

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Re: If x is an integer and a is an even integer, is x even?  [#permalink]

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New post 01 Jan 2017, 22:37
deepthit wrote:
Its C

x can be both odd or even unless we know power of x because if a =0, x^a will be 1 and we can not determine the value of x

statement 2 states that a is not equal to zero.

COmbining 2 statements wee get C



Is 0 an even integer?
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Re: If x is an integer and a is an even integer, is x even?  [#permalink]

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New post 02 Jan 2017, 04:39
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1
ashokjha1986 wrote:
deepthit wrote:
Its C

x can be both odd or even unless we know power of x because if a =0, x^a will be 1 and we can not determine the value of x

statement 2 states that a is not equal to zero.

COmbining 2 statements wee get C



Is 0 an even integer?


ZERO:

1. 0 is an integer.

2. 0 is an even integer. An even number is an integer that is "evenly divisible" by 2, i.e., divisible by 2 without a remainder and as zero is evenly divisible by 2 then it must be even.

3. 0 is neither positive nor negative integer (the only one of this kind).

4. 0 is divisible by EVERY integer except 0 itself.

Check more here: number-properties-tips-and-hints-174996.html
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Re: If x is an integer and a is an even integer, is x even?  [#permalink]

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Re: If x is an integer and a is an even integer, is x even?   [#permalink] 14 Sep 2018, 22:53
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