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The greatest common factor of two positive integers is X. The least co

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The greatest common factor of two positive integers is X. The least co  [#permalink]

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New post 10 Jan 2016, 08:04
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The greatest common factor of two positive integers is X. The least common multiple of these two integers is Y. If one of the integers is Z, what is the other?

A. XY⁄Z
B. XZ + YZ
C. X⁄Z + Y
D. X + Y⁄Z
E. X + Z⁄Y

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Re: The greatest common factor of two positive integers is X. The least co  [#permalink]

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New post 10 Jan 2016, 08:35
Bunuel wrote:
The greatest common factor of two positive integers is X. The least common multiple of these two integers is Y. If one of the integers is Z, what is the other?

A. XY⁄Z
B. XZ + YZ
C. X⁄Z + Y
D. X + Y⁄Z
E. X + Z⁄Y



Say other integer is W

Formula
GCF(W&Z)*LCM(W&Z) = W*Z

X*Y = W*Z
So W= XY/Z

Answer A
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Re: The greatest common factor of two positive integers is X. The least co  [#permalink]

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New post 13 Jan 2016, 23:02
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Hi All,

This question can be solved by TESTing VALUES. You just have to pay careful attention to what each variable represents (and the VALUE that you choose for each).

We're told that the greatest common factor of two positive integers is X and the least common multiple of these two integers is Y. We're then told that one of the integers is Z and we are asked to find the OTHER integer.

IF....
the two integers are 2 and 3,
then the GCF = 1 and LCM = 6
So...
X = 1
Y = 6
Z = 2

We're looking for an answer that equals 3.

A. XY⁄Z = 6/2 = 3 This is a MATCH
B. XZ + YZ = (1)(2) + (6)(2) = 10 NOT a match
C. X⁄Z + Y = 1/2 + 6 = 6.5 NOT a match
D. X + Y⁄Z = 1 + 6/2 = 4 NOT a match
E. X + Z⁄Y = 1 + 2/6 = 1 1/3 NOT a match

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Re: The greatest common factor of two positive integers is X. The least co  [#permalink]

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New post 23 Mar 2018, 06:31
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Top Contributor
Bunuel wrote:
The greatest common factor of two positive integers is X. The least common multiple of these two integers is Y. If one of the integers is Z, what is the other?

A. XY⁄Z
B. XZ + YZ
C. X⁄Z + Y
D. X + Y⁄Z
E. X + Z⁄Y


--------ASIDE----------------------
There's a nice rule that says:
(greatest common divisor of A and B)(least common multiple of A and B) = AB
Example: A = 10 and B = 15
Greatest common divisor of 10 and 15 = 5
Least common multiple of 10 and 15 = 30
Notice that these values satisfy the above rule, since (5)(30) = (10)(15)
--------BACK TO THE QUESTION! ----------------------

One of the two integers is Z
Let the other integer be Q.
So, our goal is to determine the value of Q

GIVEN:
The greatest common factor (divisor) of Z and Q is X.
The least common multiple of Z and Q is Y.

Take the formula: (greatest common divisor of A and B)(least common multiple of A and B) = AB
And plug in the given info to get: (X)(Y) = ZQ
In other words: XY = ZQ

Divide both sides by Z to get: XY/Z = Q

Answer: A

Cheers,
Brent
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Re: The greatest common factor of two positive integers is X. The least co  [#permalink]

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New post 23 Mar 2018, 09:26
Bunuel wrote:
The greatest common factor of two positive integers is X. The least common multiple of these two integers is Y. If one of the integers is Z, what is the other?

A. XY⁄Z
B. XZ + YZ
C. X⁄Z + Y
D. X + Y⁄Z
E. X + Z⁄Y


Key point to remember: The greatest common factor * least common multiple of integer A and B will equal A*B (only applicable to 2 integer)

Denote the other integer as k, we got \(X*Y = Z*k => k = \frac{(X*Y)}{Z}\) (A)
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Re: The greatest common factor of two positive integers is X. The least co &nbs [#permalink] 23 Mar 2018, 09:26
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