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Is x odd?

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Is x odd? [#permalink] New post 15 Jul 2012, 03:30
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C
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13% (01:19) correct 88% (00:39) wrong based on 24 sessions
Is x odd?

(1) 2x - 1 is odd
(2) x^3 is odd
[Reveal] Spoiler: OA

Last edited by Bunuel on 15 Jul 2012, 03:41, edited 1 time in total.
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Re: Is x odd? [#permalink] New post 15 Jul 2012, 03:51
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Is x odd?

(1) 2x - 1 is odd --> 2x-1=odd --> 2x=even --> x=\frac{even}{2} --> x is an integer. Now, x=\frac{even}{2} could be even (consider x=\frac{even}{2}=\frac{4}{2}=2=even) as well as odd (consider x=\frac{even}{2}=\frac{2}{2}=1=odd). Not sufficient.


(2) x^3 is odd. If x=integer then in order x^3=odd to hold true, it must be odd (answer YES), but x could also be some irrational number, for example x=\sqrt[3]{5} (answer NO). Not sufficient.

(1)+(2) Since from (1) x=integer then from (2) we have that x=odd. Sufficient.

Answer: C.

Hope it's clear.
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Re: Is x odd? [#permalink] New post 16 Jul 2012, 10:18
@Bunuel:

I don't understand your approach for the first argument:

2x-1=odd

If the result muss be odd, so x must be even. It will be even if x is 2 or greater than 2. If x is odd the result won't be odd. If I say x = 1 so the result will be Zero. But Zero is neither even nor odd. So the satetement is sufficient ?
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Re: Is x odd? [#permalink] New post 16 Jul 2012, 12:06
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Alexmsi wrote:
@Bunuel:

I don't understand your approach for the first argument:

2x-1=odd

If the result muss be odd, so x must be even. It will be even if x is 2 or greater than 2. If x is odd the result won't be odd. If I say x = 1 so the result will be Zero. But Zero is neither even nor odd. So the satetement is sufficient ?


Several things:

1. 2x-1=odd --> 2x=odd+1=odd+odd=even --> so 2x=even --> x=\frac{even}{2}=integer. Hence 2x-1=odd just means that x is an integer (it can be even as well as odd).

2. If x=1the result wont be zero, it'l be 1, so odd: 2*1-1=2-1=1=odd.

3. Zero is an even integer. Zero is nether positive nor negative, but zero is definitely an even number.

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 (in fact zero is divisible by every integer except zero itself).

Or in another way: an even number is an integer of the form n=2k, where k is an integer. So for k=0 --> n=2*0=0.

Hope it's clear.
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COLLECTION OF QUESTIONS:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS ; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


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Re: Is x odd?   [#permalink] 16 Jul 2012, 12:06
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