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# The function f(x,y) is defined by the equation f(x,y)=x^3−5xy^2. If

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Math Expert
Joined: 02 Sep 2009
Posts: 55670
The function f(x,y) is defined by the equation f(x,y)=x^3−5xy^2. If  [#permalink]

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09 Nov 2016, 00:09
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15% (low)

Question Stats:

81% (02:27) correct 19% (02:46) wrong based on 148 sessions

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The function f(x,y) is defined by the equation f(x,y)=x^3−5xy^2. If f(10,m)=200, then what is the value of f(20,2m)?

A. 200
B. 400
C. 800
D. 1200
E. 1600

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Re: The function f(x,y) is defined by the equation f(x,y)=x^3−5xy^2. If  [#permalink]

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09 Nov 2016, 00:31
Bunuel wrote:
The function f(x,y) is defined by the equation f(x,y)=x^3−5xy^2. If f(10,m)=200, then what is the value of f(20,2m)?

A. 200
B. 400
C. 800
D. 1200
E. 1600

IMO E

f(10,m)= 200 =10^3 - 5(10)m*m==> 200= 1000 - 50*m*m
800 = 50*m*m ==> m= +4 or -4
f(20,2m)= 20^3 - 5(20)*(2*4)*(2*4) = 8000 - 100 (64) = 1600
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Re: The function f(x,y) is defined by the equation f(x,y)=x^3−5xy^2. If  [#permalink]

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09 Nov 2016, 05:09
Bunuel wrote:
The function f(x,y) is defined by the equation f(x,y)=x^3−5xy^2. If f(10,m)=200, then what is the value of f(20,2m)?

A. 200
B. 400
C. 800
D. 1200
E. 1600

f(x,y)=x^3−5xy^2.

f(10,m)=10^3−5*10*m^2 = 200

i.e. 1000−50*m^2 = 200
i.e. 800 = 50m^2
i.e. m^2 = 16
i.e. m = 4

f(20,2m) = 20^3−5*20*(2m)^2 = 8000 - 100*64 = 1600

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Re: The function f(x,y) is defined by the equation f(x,y)=x^3−5xy^2. If  [#permalink]

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13 Nov 2016, 17:31
I might offer a slightly faster way:

f(10,m)=10^3-5*10*m^2=200
f(20,2m)=20^3-5*20*4*m^2

Notice you only need to solve for 50m^2 from the first equation - 50m^2=10^3-200=800
Plug into the second equation: 20^3-(2*4)(50m^2)=8000-(8)(800)
Factor out 800: 800(10-8)=800*2=1600

The answer is E.
Math Expert
Joined: 02 Aug 2009
Posts: 7757
Re: The function f(x,y) is defined by the equation f(x,y)=x^3−5xy^2. If  [#permalink]

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13 Nov 2016, 19:42
1
1
Bunuel wrote:
The function f(x,y) is defined by the equation f(x,y)=x^3−5xy^2. If f(10,m)=200, then what is the value of f(20,2m)?

A. 200
B. 400
C. 800
D. 1200
E. 1600

Hi,
If you look at the relation between the x in two cases and y in two cases, you can easily solved this in 20seconds..
Both x and y in F(20,2m) and F(10,m) is that each is twice of previous..

Now look at the equation$$x^3-5xy^2$$ , it consists of power of 3 ...x^3 and x^1*y^2 & 1+2=3..
So new answer will be 2^3 times the previous one, so 2^3*200=8*200=1600
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Re: The function f(x,y) is defined by the equation f(x,y)=x^3−5xy^2. If  [#permalink]

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18 Jan 2019, 01:41
Do we know that 5xy^2 is 5x(y)^2 rather than (5xy)^2 due to BODMAS?
Math Expert
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Posts: 55670
Re: The function f(x,y) is defined by the equation f(x,y)=x^3−5xy^2. If  [#permalink]

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18 Jan 2019, 01:43
philipssonicare wrote:
Do we know that 5xy^2 is 5x(y)^2 rather than (5xy)^2 due to BODMAS?

5xy^2 is 5*x*y^2. If it were (5xy)^2, then it would have been written that way.
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Re: The function f(x,y) is defined by the equation f(x,y)=x^3−5xy^2. If   [#permalink] 18 Jan 2019, 01:43
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# The function f(x,y) is defined by the equation f(x,y)=x^3−5xy^2. If

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