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# If the operation ˆˆ is deﬁned for all x and y by the equatio

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Joined: 01 Sep 2010
Posts: 3350
If the operation ˆˆ is deﬁned for all x and y by the equatio  [#permalink]

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21 Jun 2014, 07:19
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5% (low)

Question Stats:

84% (01:06) correct 16% (01:25) wrong based on 135 sessions

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If the operation ^ ^ is deﬁned for all x and y by the equation x ^ ^ y = $$\frac{x^2 y}{2}$$ , then (2 ^ ^ − 1) ^ ^ (−2 ^ ^1) =

(A) -4
(B) -2
(C) 2
(D) 4
(E) 8

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Math Expert
Joined: 02 Sep 2009
Posts: 52971
Re: If the operation ˆˆ is deﬁned for all x and y by the equatio  [#permalink]

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21 Jun 2014, 07:41
carcass wrote:
If the operation ^ ^ is deﬁned for all x and y by the equation x ^ ^ y = $$\frac{x^2 y}{2}$$, then (2 ^ ^ − 1) ^ ^ (−2 ^ ^1) =

(A) -4
(B) -2
(C) 2
(D) 4
(E) 8

(2 ^ ^ − 1) = $$\frac{2^2*(-1)}{2}=-2$$;

(−2 ^ ^1) = $$\frac{(-2)^2*1}{2}=2$$;

Thus, -2 ^ ^ 2 = $$\frac{(-2)^2*2}{2}=4$$.

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Posts: 52971
If the operation ˆˆ is deﬁned for all x and y by the equatio  [#permalink]

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21 Jun 2014, 09:59
1
Bunuel wrote:
carcass wrote:
If the operation ^ ^ is deﬁned for all x and y by the equation x ^ ^ y = $$\frac{x^2 y}{2}$$, then (2 ^ ^ − 1) ^ ^ (−2 ^ ^1) =

(A) -4
(B) -2
(C) 2
(D) 4
(E) 8

(2 ^ ^ − 1) = $$\frac{2^2*(-1)}{2}=-2$$;

(−2 ^ ^1) = $$\frac{(-2)^2*1}{2}=2$$;

Thus, -2 ^ ^ 2 = $$\frac{(-2)^2*2}{2}=4$$.

Just compiled questions about various functions in Special Questions Directory

Operations/functions defining algebraic/arithmetic expressions
Symbols Representing Arithmetic Operation
Rounding Functions
Various Functios

Hope it helps.
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Posts: 3350
Re: If the operation ˆˆ is deﬁned for all x and y by the equatio  [#permalink]

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21 Jun 2014, 10:20
I didn't know this topic. It is very useful to cover topics not so common.

As soon as I will have time, I will compile an archive with questions and explanations.

Thanks
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Joined: 26 Feb 2015
Posts: 114
Re: If the operation ˆˆ is deﬁned for all x and y by the equatio  [#permalink]

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05 Mar 2015, 02:52
Bunuel wrote:
Bunuel wrote:
carcass wrote:
If the operation ^ ^ is deﬁned for all x and y by the equation x ^ ^ y = $$\frac{x^2 y}{2}$$, then (2 ^ ^ − 1) ^ ^ (−2 ^ ^1) =

(A) -4
(B) -2
(C) 2
(D) 4
(E) 8

(2 ^ ^ − 1) = $$\frac{2^2*(-1)}{2}=-2$$;

(−2 ^ ^1) = $$\frac{(-2)^2*1}{2}=2$$;

Thus, -2 ^ ^ 2 = $$\frac{(-2)^2*2}{2}=4$$.

Various Functios

Hope it helps.

I thought you were supposed to take those two results you got minus each other, ie -2 - (2) = -4?

I mean, the two things you are solving for, arent those the actual equation?
Math Expert
Joined: 02 Sep 2009
Posts: 52971
If the operation ˆˆ is deﬁned for all x and y by the equatio  [#permalink]

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05 Mar 2015, 05:08
erikvm wrote:
Bunuel wrote:
Bunuel wrote:
If the operation ^ ^ is deﬁned for all x and y by the equation x ^ ^ y = $$\frac{x^2 y}{2}$$, then (2 ^ ^ − 1) ^ ^ (−2 ^ ^1) =

(A) -4
(B) -2
(C) 2
(D) 4
(E) 8

(2 ^ ^ − 1) = $$\frac{2^2*(-1)}{2}=-2$$;

(−2 ^ ^1) = $$\frac{(-2)^2*1}{2}=2$$;

Thus, -2 ^ ^ 2 = $$\frac{(-2)^2*2}{2}=4$$.

Various Functios

Hope it helps.

I thought you were supposed to take those two results you got minus each other, ie -2 - (2) = -4?

I mean, the two things you are solving for, arent those the actual equation?

There is function sign between them: (2 ^ ^ − 1) ^ ^ (−2 ^ ^1)

(2 ^ ^ − 1) = -2 and (−2 ^ ^1) = 2, hence (2 ^ ^ − 1) ^ ^ (−2 ^ ^1) = (-2) ^ ^ 2 = (-2)^2*2/2 = 4.

Hope it's clear.
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Posts: 9851
Re: If the operation ˆˆ is deﬁned for all x and y by the equatio  [#permalink]

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22 Oct 2018, 22:29
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 ˆˆ is deﬁned for all x and y by the equatio   [#permalink] 22 Oct 2018, 22:29
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