Author 
Message 
TAGS:

Hide Tags

Director
Joined: 07 Aug 2011
Posts: 552
Concentration: International Business, Technology

x and y are positive integers such that x < y. If
[#permalink]
Show Tags
Updated on: 16 Feb 2015, 03:59
Question Stats:
62% (02:31) correct 38% (02:07) wrong based on 191 sessions
HideShow timer Statistics
x and y are positive integers such that x < y. If \(x\sqrt{y} = 6\sqrt{6}\), then xy could equal A. 36 B. 48 C. 54 D. 96 E. 108
Official Answer and Stats are available only to registered users. Register/ Login.
_________________
Thanks, Lucky
_______________________________________________________ Kindly press the to appreciate my post !!
Originally posted by Lucky2783 on 15 Feb 2015, 23:24.
Last edited by Bunuel on 16 Feb 2015, 03:59, edited 1 time in total.
Renamed the topic and edited the question.



Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
Posts: 8298
Location: Pune, India

Re: x and y are positive integers such that x < y. If
[#permalink]
Show Tags
15 Feb 2015, 23:42
Lucky2783 wrote: x and y are positive integers such that x < y. If x sqrt(y) = 6 sqrt(6) , then xy could equal
36 48 54 96 108 First instinct, when you see \(x*\sqrt{y} = 6*\sqrt{6}\), you say that x = 6, y = 6 will satisfy this. But note that x < y. So y should be 6*Perfect square so that when you square root it, you are left with \(\sqrt{6}\). Try y = 6*4. Then x will be 3 so that you get 3*2 = 6 outside the square root. x*y = 3*24 = 72 (not in the options) Try y = 6*9. Then x will be 2 so that you get 2*3 = 6 outside the square root. x*y = 2*54 = 108 Answer (E)
_________________
Karishma Veritas Prep GMAT Instructor
Learn more about how Veritas Prep can help you achieve a great GMAT score by checking out their GMAT Prep Options >
GMAT selfstudy has never been more personalized or more fun. Try ORION Free!



EMPOWERgmat Instructor
Status: GMAT Assassin/CoFounder
Affiliations: EMPOWERgmat
Joined: 19 Dec 2014
Posts: 12459
Location: United States (CA)

Re: x and y are positive integers such that x < y. If
[#permalink]
Show Tags
16 Feb 2015, 19:38
HI Lucky2783, This question is a mix of Exponent rules and Number Properties. We're told that X and Y are POSITIVE INTEGERS and that X < Y. We're also told that X(sqrt Y) = 6(sqrt 6). In most cases, we're asked to "simplify" a radical... For example: (sqrt 50) = 5(sqrt 2) Here, we have to go "in reverse" and put the 6 "back in" to the radical... 6(sqrt 6) = (sqrt 216) The question asks for a possible value of XY... We have (X)(X)(Y) = 216 as a reference Since the answers are ALL integers, we're looking for one, that when multiplied by another positive integer, gives us 216... Notice how 108 is exactly HALF of 216....? IF... (X)(Y) = 108 and X=2, then (X)(X)(Y) = 216. 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
CoFounder & GMAT Assassin
Special Offer: Save $75 + GMAT Club Tests Free
Official GMAT Exam Packs + 70 Pt. Improvement Guarantee www.empowergmat.com/
***********************Select EMPOWERgmat Courses now include ALL 6 Official GMAC CATs!***********************



Intern
Joined: 15 Feb 2015
Posts: 13

Re: x and y are positive integers such that x < y. If
[#permalink]
Show Tags
16 Feb 2015, 19:50
X and Y are positive integer, which eliminates all negative situation.
x\sqrt{y} = 6\sqrt{6} > \sqrt{x*x*y} = \sqrt{6*6*6} 6*6*6 = 3*2*3*2*3*2 since x<y > x= 2, xy = 3*2*3*2*3 = 108



Math Expert
Joined: 02 Aug 2009
Posts: 6810

Re: x and y are positive integers such that x < y. If
[#permalink]
Show Tags
16 Feb 2015, 20:02
Lucky2783 wrote: x and y are positive integers such that x < y. If \(x\sqrt{y} = 6\sqrt{6}\), then xy could equal
A. 36 B. 48 C. 54 D. 96 E. 108 hi, since it is given \(x\sqrt{y} = 6\sqrt{6}\)... It is clear that \(\sqrt{y} = t\sqrt{6}\)... and t can be 2 or 3 or 6 as 6=2*3.. 1)let t=3 so x will be 2.. \(\sqrt{y} = 3\sqrt{6}\)... so y=\((3\sqrt{6})^2\) y=54 and xy=108.. ans E.. although we already have our ans, the two other possible values can be.. 2) the other possible value is t=2 and x=3 xy=3*\((2\sqrt{6})^2\)=3*24=72.. not a choice 3) the other possible value is t=6 and x=1 xy=1*\((6\sqrt{6})^2\)=1*216=216.. not a choice
_________________
1) Absolute modulus : http://gmatclub.com/forum/absolutemodulusabetterunderstanding210849.html#p1622372 2)Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html 3) effects of arithmetic operations : https://gmatclub.com/forum/effectsofarithmeticoperationsonfractions269413.html
GMAT online Tutor



Math Expert
Joined: 02 Aug 2009
Posts: 6810

x and y are positive integers such that x < y. If
[#permalink]
Show Tags
16 Feb 2015, 20:08
EMPOWERgmatRichC wrote: HI Lucky2783, This question is a mix of Exponent rules and Number Properties. We're told that X and Y are POSITIVE INTEGERS and that X < Y. We're also told that X(sqrt Y) = 6(sqrt 6). In most cases, we're asked to "simplify" a radical... For example: (sqrt 50) = 5(sqrt 2) Here, we have to go "in reverse" and put the 6 "back in" to the radical... 6(sqrt 6) = (sqrt 216) The question asks for a possible value of XY... We have (X)(X)(Y) = 216 as a reference Since the answers are ALL integers, we're looking for one, that when multiplied by another positive integer, gives us 216... Notice how 108 is exactly HALF of 216....?IF... (X)(Y) = 108 and X=2, then (X)(X)(Y) = 216. Final Answer: GMAT assassins aren't born, they're made, Rich hi, the ans is correct but there are other values in choices which when multiplied by integer would give you 216.. A. 36.... 36*6=216 C. 54....54*4=216 E. 108...108*2=216... so it is important to see which of these satisfies the equation x<y to get the correct answer...
_________________
1) Absolute modulus : http://gmatclub.com/forum/absolutemodulusabetterunderstanding210849.html#p1622372 2)Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html 3) effects of arithmetic operations : https://gmatclub.com/forum/effectsofarithmeticoperationsonfractions269413.html
GMAT online Tutor



EMPOWERgmat Instructor
Status: GMAT Assassin/CoFounder
Affiliations: EMPOWERgmat
Joined: 19 Dec 2014
Posts: 12459
Location: United States (CA)

Re: x and y are positive integers such that x < y. If
[#permalink]
Show Tags
16 Feb 2015, 20:19
Hi chetan2u, As noted in my explanation, X and Y are both INTEGERS and X < Y; we need an answer that is in the format (X)(X)(Y) = 216 Of the 3 values that you listed, 2 of them do NOT fit that pattern. 36(6) = 216, but you would end up with (6)(6)(6) which is NOT a match (since X is NOT less than Y). 54(4) = 216, but you would end up with either (4)(4)(13.5) or (root54)(root54)(4), NEITHER of which is a match (since they both include NONinteger values). 108(2) = 216, which gives us (2)(2)(54), which IS the correct 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
CoFounder & GMAT Assassin
Special Offer: Save $75 + GMAT Club Tests Free
Official GMAT Exam Packs + 70 Pt. Improvement Guarantee www.empowergmat.com/
***********************Select EMPOWERgmat Courses now include ALL 6 Official GMAC CATs!***********************



Board of Directors
Joined: 17 Jul 2014
Posts: 2682
Location: United States (IL)
Concentration: Finance, Economics
GPA: 3.92
WE: General Management (Transportation)

x and y are positive integers such that x < y. If
[#permalink]
Show Tags
14 Dec 2015, 19:57
x is smaller than y
\(x*sqrt(y) = 6*sqrt(6) sqrt[(x^2)*y] = sqrt(36*6) sqrt[(x^2)*y] = sqrt(216)\)
ok, let's find prime factorization of 216 ok, 216 = 2 * 108 108 = 2 * 54 stop right here! we have two 2's, and 54. since x^2 * y = 216, it might be the case that x=2 and y = 54. 2*54 = 108, and it is in the answer choices. since it is a "could be" question, there is no need to check further.



NonHuman User
Joined: 09 Sep 2013
Posts: 8194

Re: x and y are positive integers such that x < y. If
[#permalink]
Show Tags
20 Jan 2018, 12:06
Hello from the GMAT Club BumpBot! Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up  doing my job. I think you may find it valuable (esp those replies with Kudos). Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________
GMAT Books  GMAT Club Tests  Best Prices on GMAT Courses  GMAT Mobile App  Math Resources  Verbal Resources




Re: x and y are positive integers such that x < y. If &nbs
[#permalink]
20 Jan 2018, 12:06






