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If x and y are positive integers, what is the greatest common factor

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If x and y are positive integers, what is the greatest common factor  [#permalink]

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New post 17 May 2018, 04:52
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  85% (hard)

Question Stats:

45% (01:57) correct 55% (01:48) wrong based on 126 sessions

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Re: If x and y are positive integers, what is the greatest common factor  [#permalink]

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New post 17 May 2018, 06:08
1
Bunuel wrote:
If x and y are positive integers, what is the greatest common factor of 11x and 22y?

(1) x is an odd integer.
(2) y = x + 22


The HCF of 11x and 22y is 11*(HCF(x, 2y))
The question is basically about finding a unique value for HCF(x, 2y)

Statement 1: x is an odd integer.
There are infinite possibilities.
Approach: Counter Example
Example : x = 5 and y = 10. HCF(x, 2y) is HCF(5, 20) = 5
Counter example: x = 3 and y = 15. HCF(x, 2y) is HCF (3, 30) =3

No conclusive answer. Statement 1 alone is NOT sufficient.

Statement 2: y = x + 22
HCF (x, 2y) = HCF (x, 2x + 44)
Approach: Counter Example
Example: x = 11; HCF (x, 2x + 44) is HCF (11, 22 + 44) = 11
Counter example: x = 5; HCF (x, 2x + 44) is HCF (5, 10 + 44) = 1

No conclusive answer. Statement 2 alone is NOT sufficient.

Combining the two statements: x is odd and y = x + 22
The example and counter example used in statement 2 satisfy both these conditions.

Despite combining the information in the two statements, we will have multiple answers for the HCF (x, 2y) and therefore, for HCF(11x, 22y)
Choice E is the answer
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Re: If x and y are positive integers, what is the greatest common factor  [#permalink]

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New post 24 Dec 2018, 01:28
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Re: If x and y are positive integers, what is the greatest common factor  [#permalink]

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New post 24 Dec 2018, 03:08
Bunuel wrote:
If x and y are positive integers, what is the greatest common factor of 11x and 22y?

(1) x is an odd integer.
(2) y = x + 22



from 1:
x can be 1,3,5... no relation of y given in sufficient

#2: y=x+22

value of x not given in sufficient

from 1& 2
x=1
y=23

so 11*1 and 22*23 = 11*2*23 ; GCF is 11
at x=3, y=25

HCF (x, 2x + 44) is HCF (11, 22 + 44) = 11
x = 5; HCF (x, 2x + 44) is HCF (5, 10 + 44) = 1

IMOE
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Re: If x and y are positive integers, what is the greatest common factor  [#permalink]

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New post 25 Dec 2018, 22:48
1
Bunuel wrote:
If x and y are positive integers, what is the greatest common factor of 11x and 22y?

(1) x is an odd integer.
(2) y = x + 22


Statement 1) x is an odd integer. Doesn't tell anything about y. y could be odd or even or a multiple of x, in which GCF changes. Insufficient.

Statement 2) y=x+22. For x=11, 11x and 22y will have GCF 121, for x =3, 11x and 22y will have GCF=11, for x= even, gcf=22. Different values. Insufficient.

(1)+(2)
As for x=3 and x=11, there are two different values as stated in statement 2. Insufficient.

Option E is correct.
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Re: If x and y are positive integers, what is the greatest common factor  [#permalink]

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New post 02 Jan 2019, 03:37
Bunuel wrote:
If x and y are positive integers, what is the greatest common factor of 11x and 22y?

(1) x is an odd integer.
(2) y = x + 22


Hi Bunuel and other experts,

Is there an algebraic or logical approach to solve this question?

I have gone through the solutions other users have posted by picking numbers to come to a solution. I tried doing the same when combining Statements 1 and 2. However, picked x=3 and x=5 to check this. Of course after going through the answers I realised how x=11 and multiples of 11 proves that the two statements together are insufficient to come up with a unique answer, however I can't come up with general lessons from this question.

Can you please help me with the same.

Thanks!
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Re: If x and y are positive integers, what is the greatest common factor &nbs [#permalink] 02 Jan 2019, 03:37
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