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If 10 is the greatest common divisor of positive integers x and y, and

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If 10 is the greatest common divisor of positive integers x and y, and  [#permalink]

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New post 29 Jan 2017, 07:31
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If \(10\) is the greatest common divisor of positive integers \(x\) and \(y\), and \(20\) is the lowest common multiple of \(x\) and \(y\), what is the value of \(xy\)?

A) 15
B) 20
C) 30
D) 100
E) 200

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Re: If 10 is the greatest common divisor of positive integers x and y, and  [#permalink]

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New post 29 Jan 2017, 09:31
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ziyuenlau wrote:
If \(10\) is the greatest common divisor of positive integers \(x\) and \(y\), and \(20\) is the lowest common multiple of \(x\) and \(y\), what is the value of \(xy\)?

A) 15
B) 20
C) 30
D) 100
E) 200


NICE RULE: (The greatest common divisor of x and y)(The least common multiple of x and y) = xy
So, for this question, we get: (10)(20) = xy
Evaluate: 200 = xy

Answer:
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Re: If 10 is the greatest common divisor of positive integers x and y, and  [#permalink]

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New post 29 Jan 2017, 09:34
Top Contributor
ziyuenlau wrote:
If \(10\) is the greatest common divisor of positive integers \(x\) and \(y\), and \(20\) is the lowest common multiple of \(x\) and \(y\), what is the value of \(xy\)?

A) 15
B) 20
C) 30
D) 100
E) 200


Alternatively, you might try to come up with values for x and y that satisfy the given information (GCD = 10 AND LCM = 20)
After some fiddling, we might find out that, if x = 10 and y = 20, their GCD is 10 and their LCM = 20)
So, xy = (10)(20) = 200

Answer: E

Cheers,
Brent
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If 10 is the greatest common divisor of positive integers x and y, and  [#permalink]

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New post 29 Jan 2017, 10:07
ziyuenlau wrote:
If \(10\) is the greatest common divisor of positive integers \(x\) and \(y\), and \(20\) is the lowest common multiple of \(x\) and \(y\), what is the value of \(xy\)?

A) 15
B) 20
C) 30
D) 100
E) 200

JUST 3 Step Solution



\(xy = GCF (x,y) * LCM (x,y)\)

\(xy = 10 * 20\)

So, \(xy = 200\)

Thus, answer will be (E) 200

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Re: If 10 is the greatest common divisor of positive integers x and y, and  [#permalink]

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New post 03 Feb 2019, 22:36
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Re: If 10 is the greatest common divisor of positive integers x and y, and   [#permalink] 03 Feb 2019, 22:36
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