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What is the greatest common factor of the positive integers x and y? 1

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What is the greatest common factor of the positive integers x and y? 1 [#permalink]

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New post 11 Apr 2016, 04:04
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Question Stats:

73% (00:41) correct 27% (00:44) wrong based on 119 sessions

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What is the greatest common factor of the positive integers x and y? 1 [#permalink]

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New post 11 Apr 2016, 20:44
St1: x = y^20
If y = 3 and x = 3^20 then GCD(3^20, 3) = 3; LCM(3^20, 3) = 3^20
If y = 2 and x = 2^20 then GCD(2^20, 2) = 2; LCM(2^20, 2) = 2^20
Thus GCD(x, y) = GCD(y^20, y) = y
Not Sufficient.

St2: y = 3; Clearly insufficient as we do not know the value of x. If x = 2 then GCD = 1 but if x = 3^2 then GCD(x, y) = 3

Combining St1 and St2, we have that GCD(x, y) = y = 3

Answer: C

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Re: What is the greatest common factor of the positive integers x and y? 1 [#permalink]

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New post 11 Apr 2016, 23:40
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GCD(y, y^20) = y
St. 1 insufficient

y = (243)^(1/5) = 3
But doesn't give any info of x
St. 2 insufficient

Both statements when combined tell us GCD = 3

hence C.

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Re: What is the greatest common factor of the positive integers x and y? 1 [#permalink]

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New post 13 Apr 2016, 02:31
GCD (x,y) = ?

1) x = y^20

y.y.y.y.y.y.y.y.y.y.y.y.y.y.y.y.y.y.y.y
y
--------------------
GCD (x,y)= y
Insufficient

2) y = 243^1/5 x = ?
Insufficient

1)2) GCD (x,y)= y
y = 243^1/5
y = 3
GCD (x,y) = 3
SUFFICIENT
answer : C
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Re: What is the greatest common factor of the positive integers x and y? 1 [#permalink]

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New post 15 Apr 2016, 05:25
Combining the two statements we can say that the GCD is 3
Hence C
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Re: What is the greatest common factor of the positive integers x and y? 1 [#permalink]

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New post 18 Apr 2016, 04:06
Bunuel wrote:
What is the greatest common factor of the positive integers x and y?

(1) x = y^20
(2) \(y=\sqrt[5]{243}\)


C...good question to build GCD concepts
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Re: What is the greatest common factor of the positive integers x and y? 1 [#permalink]

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New post 18 Apr 2016, 07:22
I do not think any calculation is needed here. We can save a lot of time by avoiding un-necessary calculations

1) x = y^ 20 = y*y*.......*y
we do not know the value of x or y and hence statement 1 is insufficient

2) y = (243) ^ 1/5 = some definite value (someone above has mentioned that (243)^1/3 = 3 but I do not think we need to do this calculation)
So, statement 2 gives us the value of y but not of x and hence it is insufficient

Now, combine 1 & 2,
putting the definite value of y in 1st equation, we can find a definite value of x.

At the end we can calculate a GCD of 2 definite values but there is no need to do actual calculations.
Both 1 and 2 together are sufficient and hence C is the answer

This is a data sufficiency question and not a problem solving one. Try to save your time by avoiding un-necessary calculations

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Re: What is the greatest common factor of the positive integers x and y? 1 [#permalink]

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Re: What is the greatest common factor of the positive integers x and y? 1   [#permalink] 12 Sep 2017, 07:24
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