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Is a positive integer x odd?

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Is a positive integer x odd?  [#permalink]

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New post 14 May 2018, 00:58
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  45% (medium)

Question Stats:

62% (15:00) correct 38% (01:25) wrong based on 102 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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Re: Is a positive integer x odd?  [#permalink]

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New post 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.

Answer: B
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Re: Is a positive integer x odd?  [#permalink]

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New post 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


Par of GMAT CLUB'S New Year's Quantitative Challenge Set


_________________

New to the Math Forum?
Please read this: Ultimate GMAT Quantitative Megathread | All You Need for Quant | PLEASE READ AND FOLLOW: 12 Rules for Posting!!!

Resources:
GMAT Math Book | Triangles | Polygons | Coordinate Geometry | Factorials | Circles | Number Theory | Remainders; 8. Overlapping Sets | PDF of Math Book; 10. Remainders | GMAT Prep Software Analysis | SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) | Tricky questions from previous years.

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 a positive integer x odd?  [#permalink]

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New post 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

Hence, answer is B
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Re: Is a positive integer x odd? &nbs [#permalink] 02 Jan 2019, 03:45
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