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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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29 Jan 2017, 07:31
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81% (00:49) correct 19% (01:05) wrong based on 95 sessions

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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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29 Jan 2017, 09:31
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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

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

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

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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

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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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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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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