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• ### $450 Tuition Credit & Official CAT Packs FREE November 15, 2018 November 15, 2018 10:00 PM MST 11:00 PM MST EMPOWERgmat is giving away the complete Official GMAT Exam Pack collection worth$100 with the 3 Month Pack ($299) • ### Free GMAT Strategy Webinar November 17, 2018 November 17, 2018 07:00 AM PST 09:00 AM PST Nov. 17, 7 AM PST. Aiming to score 760+? Attend this FREE session to learn how to Define your GMAT Strategy, Create your Study Plan and Master the Core Skills to excel on the GMAT. # The greatest common factor of two positive integers is X. The least co  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics Author Message TAGS: ### Hide Tags Math Expert Joined: 02 Sep 2009 Posts: 50585 The greatest common factor of two positive integers is X. The least co [#permalink] ### Show Tags 10 Jan 2016, 08:04 00:00 Difficulty: 5% (low) Question Stats: 92% (01:10) correct 8% (01:38) wrong based on 122 sessions ### HideShow timer Statistics 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 _________________ Current Student Joined: 02 Jun 2015 Posts: 63 Location: United States Concentration: Strategy, Human Resources WE: Engineering (Manufacturing) Re: The greatest common factor of two positive integers is X. The least co [#permalink] ### Show Tags 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 EMPOWERgmat Instructor Status: GMAT Assassin/Co-Founder Affiliations: EMPOWERgmat Joined: 19 Dec 2014 Posts: 12853 Location: United States (CA) GMAT 1: 800 Q51 V49 GRE 1: Q170 V170 Re: The greatest common factor of two positive integers is X. The least co [#permalink] ### Show Tags 13 Jan 2016, 23:02 1 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 Final Answer: GMAT assassins aren't born, they're made, Rich _________________ 760+: Learn What GMAT Assassins Do to Score at the Highest Levels Contact Rich at: Rich.C@empowergmat.com # Rich Cohen Co-Founder & GMAT Assassin Special Offer: Save$75 + GMAT Club Tests Free
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Re: The greatest common factor of two positive integers is X. The least co  [#permalink]

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23 Mar 2018, 06:31
1
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

Cheers,
Brent
_________________

Brent Hanneson – GMATPrepNow.com

Manager
Joined: 28 Jan 2018
Posts: 54
Location: Netherlands
Concentration: Finance
GMAT 1: 710 Q50 V36
GPA: 3
Re: The greatest common factor of two positive integers is X. The least co  [#permalink]

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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)
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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