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# If x and y are positive integers, what is the value of xy?

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Manager
Joined: 13 Dec 2005
Posts: 64
Followers: 1

Kudos [?]: 5 [0], given: 0

If x and y are positive integers, what is the value of xy? [#permalink]  21 Dec 2005, 05:50
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If x and y are positive integers, what is the value of xy?

(1) The greatest common factor of x and y is 10.
(2) The least common multiple of x and y is 180.

A) Statement 1 sufficient...
B) Statement 2 sufficient...
C) Both statements together...
D) Each statement alone...
E) Neither statement ...

The book answer is C. Could someone please explain the steps you would need to take in order to figure out this answer?

Thanks,
Jim
Intern
Joined: 26 Sep 2005
Posts: 49
Followers: 1

Kudos [?]: 0 [0], given: 0

It says that the GCF = 10 and LCM = 180.
Now, GCF = 10 = 5 x 2
and LCM = 180 = 5 x 2 x 3 x 3 x 2
Now we have to find two numbers which do not have anything common besides factors of 5 and 2 (because GCF = 10).
So we are left with 3, 3 and 2.
We have to split this into such a combination that they do not have anything in common. Thus we split it, 3 x 3 and 2.
Hence, the numbers are: 5x2x2 = 20
and 5x2x3x3 = 90

Therefore, xy = 1800

P.S. High school math books will never be out of fashion....
Rule: To find the product of any two number, xy = GCF x LCM..... keep this rule in mind! :)
VP
Joined: 22 Aug 2005
Posts: 1120
Location: CA
Followers: 1

Kudos [?]: 49 [0], given: 0

Agree:
LCM(x,y) * HCF(x,y) = x*y

just remember it.
_________________

Whether you think you can or think you can't. You're right! - Henry Ford (1863 - 1947)

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