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# x and y are two positive integers. D is the greatest common divisor of

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Math Expert
Joined: 02 Sep 2009
Posts: 52902
x and y are two positive integers. D is the greatest common divisor of  [#permalink]

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14 Sep 2016, 04:59
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Difficulty:

25% (medium)

Question Stats:

78% (01:25) correct 22% (01:29) wrong based on 108 sessions

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x and y are two positive integers. D is the greatest common divisor of x and y. Is D > 20?

(1) x is a multiple of 4

(2) y is a multiple of 20

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Posts: 592
Re: x and y are two positive integers. D is the greatest common divisor of  [#permalink]

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14 Sep 2016, 06:14
1
Bunuel wrote:
x and y are two positive integers. D is the greatest common divisor of x and y. Is D > 20?

(1) x is a multiple of 4

(2) y is a multiple of 20

Stat 1: Given x is a multiple of 4 and x can be 20,24,28...etc...but we don't have information about y...Insufficient.

Stat 2: Y can be 20,40,80...but we don't have information about x...Insufficient.

Stat 1+2 : Now we can take x as 24 and y as 40 then GCD is 8. now if x is 8 and y is 20 then we GCD is 4...we can get different GCDs based on numbers we assume...no unique result..Insufficient.

IMO option E.
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Re: x and y are two positive integers. D is the greatest common divisor of  [#permalink]

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28 Nov 2017, 22:36
Statement 1 gives NO information about y, and statement 2 gives NO information about x. So alone they are insufficient. Lets combine the two statements.

x is a multiple of 4, so x=4m, where m is a positive integer.
y is a multiple of 20, so y=20n, where n is a positive integer.

Now, if m&n have no common factor, in that case GCD of x&y will be 4 (because then thats the only common number out of 4m and 20n).
But its possible that m&n have a common factor which is equal to 6 or more, in that case GCD of x&y will be greater than 20. Eg, if m=6, n=12, then GCD of x&y would be 4*6=24 (since 4 is common out of 4&20, while 6 is common out of 6&12).
So we cant say whether D is less than or equal to or greater than 20. so Insufficient.

(Another way to look at it is this: x is a multiple of 4, y is a multiple of 20. Every multiple of 20 is also going to be a multiple of 4. Its possible that x is 4 and y=20, in which case GCD is 4, but its also possible that x and y are both 80, in which case GCD is 80. Many possibilities here. So we cant say)

Re: x and y are two positive integers. D is the greatest common divisor of   [#permalink] 28 Nov 2017, 22:36
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