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# If the operation @ is defined by x@y=(xy)^1/2 for all

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If the operation @ is defined by x@y=(xy)^1/2 for all [#permalink]  17 Dec 2012, 06:43
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If the operation @ is defined by $$x@y=\sqrt{xy}$$ for all positive numbers x and y, then (5@45)@60 =

(A) 30
(B) 60
(C) 90
(D) $$30\sqrt{15}$$
(E) $$60\sqrt{15}$$
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Re: If the operation @ is defined by x@y=(xy)^1/2 for all [#permalink]  17 Dec 2012, 06:46
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If the operation @ is defined by $$x@y=\sqrt{xy}$$ for all positive numbers x and y, then (5@45)@60 =

(A) 30
(B) 60
(C) 90
(D) $$30\sqrt{15}$$
(E) $$60\sqrt{15}$$

$$(5@45)@60 =(\sqrt{5*45})@60=(\sqrt{225})@60=15@60=\sqrt{15*60}=30$$.

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Re: If the operation @ is defined by x@y=(xy)^1/2 for all [#permalink]  17 Dec 2012, 06:50
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I'm writing the answer but Bunuel is too fast to reply, a machine
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Status: 1,750 Q's attempted and counting
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Joined: 09 Jul 2013
Posts: 514
Location: United States (FL)
Schools: UFL (A)
GMAT 1: 600 Q45 V29
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GMAT 3: 570 Q42 V28
GMAT 4: 610 Q44 V30
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WE: Accounting (Accounting)
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Re: If the operation @ is defined by x@y=(xy)^1/2 for all [#permalink]  24 Oct 2013, 19:11
I tried to keep the numbers as manageable as possible and use numbers that I knew the perfect squares of.

$$(5@45)@60$$= $$\sqrt{5*(5*9)}$$ $$=5*3=15$$

$$15@60=$$ $$\sqrt{(3*5)*(3*4*5)}$$ $$= 3*5*2= 30$$
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Re: If the operation @ is defined by x@y=(xy)^1/2 for all [#permalink]  01 Nov 2014, 04:13
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).

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Re: If the operation @ is defined by x@y=(xy)^1/2 for all   [#permalink] 01 Nov 2014, 04:13
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