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# What is the value of x?

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Intern
Joined: 23 Sep 2011
Posts: 17

Kudos [?]: 25 [1], given: 26

What is the value of x? [#permalink]

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30 Oct 2016, 03:07
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Question Stats:

66% (01:06) correct 34% (01:27) wrong based on 128 sessions

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What is the value of x?

1) The Greatest Common Factor of 90 and x is 30

2) The Least Common Multiple of 90 and x is 900
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Kudos [?]: 25 [1], given: 26

Intern
Joined: 18 Sep 2016
Posts: 49

Kudos [?]: 17 [1], given: 97

What is the value of x? [#permalink]

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30 Oct 2016, 04:35
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interceptor77 wrote:
What is the value of x?

1) The Greatest Common Factor of 90 and x is 30

2) The Least Common Multiple of 90 and x is 900

1) The Greatest Common Factor of 90 and x is 30
$$90= 2*3^2*5$$ 30= 2*3*5

The Greatest Common Factor is the product of all the common prime factors of x and 90 at the least power.
therefore, $$3^1$$ is a factor of x

but x can be infinite numbers INSUFFICIENT

2) The Least Common Multiple of 90 and x is 900

$$900=2^2*3^2*5^2$$

$$90= 2*3^2*5$$

The Least Common Multiple is is the product of all the prime factors of x and 90 at the giggest power

x must have 2^2 and 5^2 and can have a 3 or 3^2, but we do't know it, INSUFFICIENT

1+2)
1)$$3^1$$ is a factor of x
2)x must have 2^2 and 5^2 and can have a 3 or 3^2

$$x=2^2*3^1*5^2$$ SUFFICIENT

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Math Expert
Joined: 02 Sep 2009
Posts: 43348

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Re: What is the value of x? [#permalink]

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30 Oct 2016, 04:51
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damybox wrote:
interceptor77 wrote:
What is the value of x?

1) The Greatest Common Factor of 90 and x is 30

2) The Least Common Multiple of 90 and x is 900

1) The Greatest Common Factor of 90 and x is 30
$$90= 2*3^2*5$$ 30= 2*3*5

The Greatest Common Factor is the product of all the common prime factors of x and 90 at the least power.
therefore, $$3^1$$ is a factor of x

but x can be infinite numbers INSUFFICIENT

2) The Least Common Multiple of 90 and x is 900

$$900=2^2*3^2*5^2$$

$$90= 2*3^2*5$$

The Least Common Multiple is is the product of all the prime factors of x and 90 at the giggest power

x must have 2^2 and 5^2 and can have a 3 or 3^2, but we do't know it, INSUFFICIENT

1+2)
1)$$3^1$$ is a factor of x
2)x must have 2^2 and 5^2 and can have a 3 or 3^2

$$x=2^2*3^1*5^2$$ SUFFICIENT

When considering (1) and (2) together you can apply the most important property of LCM and GCD: for any positive integers $$a$$ and $$b$$, $$a*b=GCD(a,b)*LCM(a,b)$$. According to this 90x=30*900 --> x=300.
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Re: What is the value of x? [#permalink]

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28 Nov 2017, 03:50
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Re: What is the value of x?   [#permalink] 28 Nov 2017, 03:50
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