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# Is x even? (1) x^5 is even. (2) 4x – 2 is even.

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Math Expert
Joined: 02 Sep 2009
Posts: 47879
Is x even? (1) x^5 is even. (2) 4x – 2 is even.  [#permalink]

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23 Jan 2017, 09:30
2
2
00:00

Difficulty:

65% (hard)

Question Stats:

12% (00:44) correct 88% (00:30) wrong based on 77 sessions

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Is x even?

(1) x^5 is even.
(2) 4x – 2 is even.

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Senior Manager
Joined: 06 Jul 2016
Posts: 415
Location: Singapore
Concentration: Strategy, Finance
Re: Is x even? (1) x^5 is even. (2) 4x – 2 is even.  [#permalink]

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23 Jan 2017, 10:04

As 2) will always be even regardless of the value of x so it's not sufficient IMO

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Director
Joined: 05 Mar 2015
Posts: 983
Is x even? (1) x^5 is even. (2) 4x – 2 is even.  [#permalink]

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24 Jan 2017, 11:26
2
Bunuel wrote:
Is x even?

(1) x^5 is even.
(2) 4x – 2 is even.

(1) if x= 2^1/5 then X^5= 2 thus x is not even
IF x=2 then x^5=32 thus X is even

Not suff

(2) if x=3 then 4x – 2 = 10 even thus x =odd
if x=2 then 4x – 2 = 6 even thus x=even
Not suff

combining both
we know x must be integer
thus from (1) x must be even(as odd^x = odd)

Ans C
Math Expert
Joined: 02 Aug 2009
Posts: 6501
Is x even? (1) x^5 is even. (2) 4x – 2 is even.  [#permalink]

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25 Jan 2018, 21:58
1
Bunuel wrote:
Is x even?

(1) x^5 is even.
(2) 4x – 2 is even.

With almost 100% going wrong in a sub-600 level question shows that we tend to overlook number properties at many times..
(1) $$x^5$$ is even.
If x is an integer, yes x is even..
But if x is not an integer
$$x=\sqrt[5]{2}$$.. $$x^5 is even but x is NOT Insuff$$

(2) $$4x – 2$$ is even
$$4x-2=2(2x-1)$$
so x could be any integer, 1,2, or even fraction 1.5,2.5...
insuff

combined..
statement II gives x as an integer and statement I says if x is integer, x is even..
sufficient

C
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1) Absolute modulus : http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
2)Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html
3) effects of arithmetic operations : https://gmatclub.com/forum/effects-of-arithmetic-operations-on-fractions-269413.html

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Joined: 06 Jan 2018
Posts: 7
Re: Is x even? (1) x^5 is even. (2) 4x – 2 is even.  [#permalink]

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25 Jan 2018, 23:06
1-Since x is not necessarily an integer, then it is easy to prove x could either be even (2^5 = 32, but (2^(1/5))^5 = 2, but x is not even
Not suff

2- 4x-2 is even. X could be even (2) or x could not be even (i.e. 0.5)
Not suff

1,2 combined will be satisfied since x would have to be an integer in this case... then C will be the answer

Great question!!!!!

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Re: Is x even? (1) x^5 is even. (2) 4x – 2 is even. &nbs [#permalink] 25 Jan 2018, 23:06
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