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# The numbers x and y are positive integers such that

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Senior Manager
Joined: 14 Feb 2018
Posts: 389
The numbers x and y are positive integers such that  [#permalink]

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15 Mar 2018, 05:12
The numbers x and y are positive integers such that x < y. If 6√6 = x√y, then XY could equal which of the following ?

A. 36
B. 48
C. 54
D. 96
E. 108

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Senior PS Moderator
Status: It always seems impossible until it's done.
Joined: 16 Sep 2016
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GMAT 1: 740 Q50 V40
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Re: The numbers x and y are positive integers such that  [#permalink]

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15 Mar 2018, 05:36
SonalSinha803 wrote:
The numbers x and y are positive integers such that x < y. If 6√6 = x√y, then XY could equal which of the following ?

A. 36
B. 48
C. 54
D. 96
E. 108

Sent from my Lenovo K53a48 using GMAT Club Forum mobile app

IMO E

$$6\sqrt{6}$$ can be expressed as $$2*3\sqrt{6}$$

Since x < y, we need to move one of the prime factors of 6 into the radical sign.

Hence two possibilities =

$$6\sqrt{6} = 2\sqrt{54}$$ ( where 3 become 9 inside the sq root sign and 9 times 6 is 54.

similarly,
$$6\sqrt{6} = 3\sqrt{24}$$

Only the first gives a possible answer among the choices and hence X = 2 and Y = 54.

XY = 108.

Option E.

Please give kudos if you liked the explanation...
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Intern
Joined: 13 Mar 2018
Posts: 8
Re: The numbers x and y are positive integers such that  [#permalink]

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15 Mar 2018, 06:02
I agree that it is this

IMO E

66√66 can be expressed as 2∗36√2∗36

Since x < y, we need to move one of the prime factors of 6 into the radical sign.

Hence two possibilities =

66√=254−−√66=254 ( where 3 become 9 inside the sq root sign and 9 times 6 is 54.

similarly,
66√=324−−√66=324

Only the first gives a possible answer among the choices and hence X = 2 and Y = 54.

XY = 108.

Option E.
Senior PS Moderator
Status: It always seems impossible until it's done.
Joined: 16 Sep 2016
Posts: 751
GMAT 1: 740 Q50 V40
GMAT 2: 770 Q51 V42
Re: The numbers x and y are positive integers such that  [#permalink]

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15 Mar 2018, 06:11
Ayesha421 wrote:
I agree that it is this

IMO E

66√66 can be expressed as 2∗36√2∗36

Since x < y, we need to move one of the prime factors of 6 into the radical sign.

Hence two possibilities =

66√=254−−√66=254 ( where 3 become 9 inside the sq root sign and 9 times 6 is 54.

similarly,
66√=324−−√66=324

Only the first gives a possible answer among the choices and hence X = 2 and Y = 54.

XY = 108.

Option E.

Hello Ayesha421,

Also it seems that you have pasted exactly identical answer as from my post above. Kindly refrain from doing this if possible.

abhimahna anything you want to add here?

Thanks,
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Regards,

“Do. Or do not. There is no try.” - Yoda (The Empire Strikes Back)
Senior Manager
Joined: 14 Feb 2018
Posts: 389
Re: The numbers x and y are positive integers such that  [#permalink]

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15 Mar 2018, 06:32
SonalSinha803 wrote:
The numbers x and y are positive integers such that x < y. If 6√6 = x√y, then XY could equal which of the following ?

A. 36
B. 48
C. 54
D. 96
E. 108

Sent from my Lenovo K53a48 using GMAT Club Forum mobile app

IMO E

$$6\sqrt{6}$$ can be expressed as $$2*3\sqrt{6}$$

Since x < y, we need to move one of the prime factors of 6 into the radical sign.

Hence two possibilities =

$$6\sqrt{6} = 2\sqrt{54}$$ ( where 3 become 9 inside the sq root sign and 9 times 6 is 54.

similarly,
$$6\sqrt{6} = 3\sqrt{24}$$

Only the first gives a possible answer among the choices and hence X = 2 and Y = 54.

XY = 108.

Option E.

Please give kudos if you liked the explanation...

Hello,

Thanks, your method is more simpler than mine.

Kudos !!

Sent from my Lenovo K53a48 using GMAT Club Forum mobile app
Senior PS Moderator
Status: It always seems impossible until it's done.
Joined: 16 Sep 2016
Posts: 751
GMAT 1: 740 Q50 V40
GMAT 2: 770 Q51 V42
Re: The numbers x and y are positive integers such that  [#permalink]

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15 Mar 2018, 06:52
[quote="SonalSinha803]
Hello,

Thanks, your method is more simpler than mine.

Kudos !!

Sent from my Lenovo K53a48 using GMAT Club Forum mobile app[/quote]

SonalSinha803,

However the correct way to give Kudos would be to press the red button which says "Kudos" on the post you want to award it to... rather than another post with it in written form.

Best,
_________________
Regards,

“Do. Or do not. There is no try.” - Yoda (The Empire Strikes Back)
Math Expert
Joined: 02 Sep 2009
Posts: 55683
Re: The numbers x and y are positive integers such that  [#permalink]

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15 Mar 2018, 07:54
SonalSinha803 wrote:
The numbers x and y are positive integers such that x < y. If 6√6 = x√y, then XY could equal which of the following ?

A. 36
B. 48
C. 54
D. 96
E. 108

Sent from my Lenovo K53a48 using GMAT Club Forum mobile app

Discussed here: x-and-y-are-positive-integers-such-that-x-y-if-193254.html

--== Message from the GMAT Club Team ==--

THERE IS LIKELY A BETTER DISCUSSION OF THIS EXACT QUESTION.
This discussion does not meet community quality standards. It has been retired.

If you would like to discuss this question please re-post it in the respective forum. Thank you!

To review the GMAT Club's Forums Posting Guidelines, please follow these links: Quantitative | Verbal Please note - we may remove posts that do not follow our posting guidelines. Thank you.

_________________
Re: The numbers x and y are positive integers such that   [#permalink] 15 Mar 2018, 07:54
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