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What is the Greatest Common Factor of Three positive, nonzero numbers

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What is the Greatest Common Factor of Three positive, nonzero numbers  [#permalink]

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New post 09 Jan 2019, 07:19
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A
B
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D
E

Difficulty:

  55% (hard)

Question Stats:

47% (00:55) correct 53% (01:01) wrong based on 45 sessions

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What is the Greatest Common Factor of Three positive, nonzero numbers X, Y, Z?

A. X= 64, Y = 81

B. Y = 81, Z= 49

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Re: What is the Greatest Common Factor of Three positive, nonzero numbers  [#permalink]

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New post 09 Jan 2019, 07:56
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Top Contributor
fitzpratik wrote:
What is the Greatest Common Factor of Three positive, nonzero numbers X, Y, Z?

(1) X= 64, Y = 81

(3) Y = 81, Z= 49


Target question: What is the Greatest Common Factor of Three positive, nonzero numbers X, Y, Z?

Statement 1: X= 64, Y = 81
Since the greatest common factor (GCF) of 64 and 81 is 1, the GCF of X, Y, and Z cannot be greater than 1.
Since 1 is a factor of all positive integers, the answer to the target question is the GFC of X, Y and Z is 1
Since we can answer the target question with certainty, statement 1 is SUFFICIENT

Statement 2: Y = 81, Z= 49
We can apply the same logic we applied to statement 1.
Since the greatest common factor (GCF) of 81 and 49 is 1, the GCF of X, Y, and Z cannot be greater than 1.
So, the answer to the target question is the GFC of X, Y and Z is 1
Since we can answer the target question with certainty, statement 2 is SUFFICIENT

Answer: D

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Re: What is the Greatest Common Factor of Three positive, nonzero numbers  [#permalink]

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New post 09 Jan 2019, 11:08
fitzpratik wrote:
What is the Greatest Common Factor of Three positive, nonzero numbers X, Y, Z?

A. X= 64, Y = 81

B. Y = 81, Z= 49


Great problem! I actually got it wrong at first. A mistake is to think of this problem as a LCM problem (which many problems I have been working lately ask)

(1) Notice that X and Y have a GCF of 1. Since No other number will divide into both X and y, Z can equal 1,2,3,4,5,6,7,8......100 ANYTHING and the GCF will still be 1
Suff

(2) As with (1), notice that only the number 1 will divide into both 81 and 49, therefore it doesnt matte what X is here, the GCF will be 1
Suff

Answer is D
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Re: What is the Greatest Common Factor of Three positive, nonzero numbers   [#permalink] 09 Jan 2019, 11:08
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