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# Is a positive integer x odd?

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Math Expert
Joined: 02 Sep 2009
Posts: 64222
Is a positive integer x odd?  [#permalink]

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14 May 2018, 00:58
1
5
00:00

Difficulty:

45% (medium)

Question Stats:

60% (01:53) correct 40% (01:44) wrong based on 144 sessions

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GMAT CLUB'S FRESH QUESTION

Is a positive integer x odd?

(1) The greatest common factor of the smallest positive factor of x and the largest positive factor of x is odd
(1) The least common multiple of the smallest positive factor of x and the largest positive factor of x is even

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e-GMAT Representative
Joined: 04 Jan 2015
Posts: 3367
Re: Is a positive integer x odd?  [#permalink]

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14 May 2018, 01:56
1

Solution

Given:
• x is a positive integer

To find:
• Is the value of x odd?

Approach and Working:
As x is a positive integer,
• The smallest positive factor of x = 1
• The largest positive factor of x = x

Analysing Statement 1
• As per the information provided in Statement 1, the GCF of the smallest positive factor of x and the largest positive factor of x is odd
o Or, GCF (1, x) = odd
• We know, the GCF of 1 and any other positive number will always be equal to 1 only, which is an odd number
o Hence, we cannot say anything about the nature of the number x
Hence, Statement 1 is not sufficient to answer

Analysing Statement 2
• As per the information provided in Statement 2, the LCM of the smallest positive factor of x and the largest positive factor of x is even
o Or, LCM (1, x) = even
• We know, the LCM of 1 and any other positive number will always be equal to that number only – given that it is an even number
o Hence, we can say that the number x is an even number
Hence, Statement 2 is sufficient to answer

Hence, the correct answer is option B.

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Math Expert
Joined: 02 Sep 2009
Posts: 64222
Re: Is a positive integer x odd?  [#permalink]

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24 Dec 2018, 01:31
Bunuel wrote:

GMAT CLUB'S FRESH QUESTION

Is a positive integer x odd?

(1) The greatest common factor of the smallest positive factor of x and the largest positive factor of x is odd
(1) The least common multiple of the smallest positive factor of x and the largest positive factor of x is even

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Manager
Joined: 24 Dec 2018
Posts: 107
Concentration: Entrepreneurship, Finance
Re: Is a positive integer x odd?  [#permalink]

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02 Jan 2019, 03:45
Interesting question because it tests the basics of the topic LCM & HCF.

Two concepts that are tested are: 1) Smallest positive factor of a positive integer will always be 1 and 2) largest positive factor of a positive integer will always be the number itself

Statement 1: Given that GCF of 1 and x is odd, does not tell us anything about the number x. This is because whether x is odd or even, GCF between the number and 1 will always be 1 (i.e. odd). Hence, this statement is insufficient

Statement 2: Given that LCM of 1 and x is even shows that x is definitely even. This is because LCM between a number and 1 is essentially x*1=x. Since this LCM is even, it proves that x is even.
Hence, this statement is insufficient

Re: Is a positive integer x odd?   [#permalink] 02 Jan 2019, 03:45