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# If the operation @ is defined for all a and b by the equatio

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If the operation @ is defined for all a and b by the equatio [#permalink]  18 Sep 2003, 06:58
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Question Stats:

74% (01:49) correct 26% (01:12) wrong based on 89 sessions
If the operation @ is defined for all a and b by the equation a@b =(a^2*b)/3, then 2@(3@-1) =

A. 4
B. 2
C. -4/3
D. -2
E. -4
[Reveal] Spoiler: OA

Last edited by Bunuel on 11 Aug 2014, 23:58, edited 1 time in total.
Renamed the topic, edited the question, added the OA and moved to PS forum.
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Re: If the operation @ is defined for all a and b by the equatio [#permalink]  21 Sep 2003, 10:37
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Formula: a@b=((a^2)*b)/3
Question: 2@(3@-1)= ?

work within the parenthesis first so solve (3@-1) first

(3@-1)= ((3^2)*-1)/3 = (9*-1)/3= -9/3=-3
now take -3 plug back into equation and solve the rest

2@(-3)=((2^2)*-3)/3 = (4*-3)/3= -12/3= -4

so -4 is the answer....this question is merely testing order of operations

remember PEMDAS
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Re: If the operation @ is defined for all a and b by the equatio [#permalink]  05 Aug 2014, 04:18
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Re: If the operation @ is defined for all a and b by the equatio [#permalink]  12 Aug 2014, 00:03
Expert's post
pete300 wrote:
If the operation @ is defined for all a and b by the equation a@b =(a^2*b)/3, then 2@(3@-1) =

A. 4
B. 2
C. -4/3
D. -2
E. -4

Check other Operations/functions defining algebraic/arithmetic expressions probelms in our Special Questions Directory.
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Kudos [?]: 1069 [0], given: 193

Re: If the operation @ is defined for all a and b by the equatio [#permalink]  12 Aug 2014, 00:09
pete300 wrote:
If the operation @ is defined for all a and b by the equation a@b =(a^2*b)/3, then 2@(3@-1) =

A. 4
B. 2
C. -4/3
D. -2
E. -4

Hi Bunuel,

Kindly write this equation in mathematical format. It's impossible to understand otherwise

Thanks
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Math Expert
Joined: 02 Sep 2009
Posts: 29172
Followers: 4735

Kudos [?]: 50006 [0], given: 7518

Re: If the operation @ is defined for all a and b by the equatio [#permalink]  12 Aug 2014, 01:29
Expert's post
PareshGmat wrote:
pete300 wrote:
If the operation @ is defined for all a and b by the equation a@b =(a^2*b)/3, then 2@(3@-1) =

A. 4
B. 2
C. -4/3
D. -2
E. -4

Hi Bunuel,

Kindly write this equation in mathematical format. It's impossible to understand otherwise

Thanks

There is nothing wrong with the format.
_________________
SVP
Status: The Best Or Nothing
Joined: 27 Dec 2012
Posts: 1859
Location: India
Concentration: General Management, Technology
WE: Information Technology (Computer Software)
Followers: 26

Kudos [?]: 1069 [0], given: 193

Re: If the operation @ is defined for all a and b by the equatio [#permalink]  12 Aug 2014, 02:05
Bunuel wrote:
PareshGmat wrote:
pete300 wrote:
If the operation @ is defined for all a and b by the equation a@b =(a^2*b)/3, then 2@(3@-1) =

A. 4
B. 2
C. -4/3
D. -2
E. -4

Hi Bunuel,

Kindly write this equation in mathematical format. It's impossible to understand otherwise

Thanks

There is nothing wrong with the format.

a@b =(a^2*b)/3

Is it $$\frac{a^{2b}}{3}$$ or

$$\frac{ba^2}{3}$$ ??
_________________

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Math Expert
Joined: 02 Sep 2009
Posts: 29172
Followers: 4735

Kudos [?]: 50006 [0], given: 7518

Re: If the operation @ is defined for all a and b by the equatio [#permalink]  12 Aug 2014, 02:12
Expert's post
PareshGmat wrote:
Bunuel wrote:
PareshGmat wrote:
If the operation @ is defined for all a and b by the equation a@b =(a^2*b)/3, then 2@(3@-1) =

A. 4
B. 2
C. -4/3
D. -2
E. -4

Hi Bunuel,

Kindly write this equation in mathematical format. It's impossible to understand otherwise

Thanks

There is nothing wrong with the format.

a@b =(a^2*b)/3

Is it $$\frac{a^{2b}}{3}$$ or

$$\frac{ba^2}{3}$$ ??

If it were $$\frac{a^{2b}}{3}$$, then it would be written as (a^(2*b))/3.
_________________
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Status: The Best Or Nothing
Joined: 27 Dec 2012
Posts: 1859
Location: India
Concentration: General Management, Technology
WE: Information Technology (Computer Software)
Followers: 26

Kudos [?]: 1069 [0], given: 193

Re: If the operation @ is defined for all a and b by the equatio [#permalink]  12 Aug 2014, 02:27
a@b $$= \frac{ba^2}{3}$$

2@(3@-1)

Solving the bracket first

3@-1$$= \frac{-1*3^2}{3} = -3$$

2@-3$$= \frac{-3*2^2}{3} = -4$$

Answer = E
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Re: If the operation @ is defined for all a and b by the equatio   [#permalink] 12 Aug 2014, 02:27
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# If the operation @ is defined for all a and b by the equatio

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