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# The variables B and C are functions of the value of A such that with

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Math Expert
Joined: 02 Sep 2009
Posts: 60727
The variables B and C are functions of the value of A such that with  [#permalink]

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25 Nov 2019, 02:36
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75% (hard)

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33% (03:07) correct 67% (02:28) wrong based on 21 sessions

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The variables B and C are functions of the value of A such that with every increase of 1 in the value of A, the value of B increases by a factor of 3 and the value of C increases by a factor of 5. If B and C are positive for all positive A, what is the value of B/(C-B) when A = 8?

(1) When A = 5, B = 2C.
(2) When A = 6, B = C + 15.

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Re: The variables B and C are functions of the value of A such that with  [#permalink]

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25 Nov 2019, 06:44
The variables B and C are functions of the value of A

dont get this.
Math Expert
Joined: 02 Aug 2009
Posts: 8327
Re: The variables B and C are functions of the value of A such that with  [#permalink]

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25 Nov 2019, 09:40
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Bunuel wrote:
The variables B and C are functions of the value of A such that with every increase of 1 in the value of A, the value of B increases by a factor of 3 and the value of C increases by a factor of 5. If B and C are positive for all positive A, what is the value of B/(C-B) when A = 8?

(1) When A = 5, B = 2C.
(2) When A = 6, B = C + 15.

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Hi..

So if A increases by 1, say A+1, the value of B increases by a factor of 3, that is it becomes 3B and the value of C increases by a factor of 5, that is 5C..

(1) When A = 5, B = 2C.
A=6..$$C_6=5C$$ and $$B_6=3*(2C_6)=3*(2*5C)=30C$$
A=7..$$C_7=5C_6=5*5C=25C$$ and $$B_7=3*(2C_7)=3*(2*25C)=150C$$
A=8..$$C_8=5C_7=5*25C=125C$$ and $$B_8=3*(2C_8)=3*(2*125C)=750C$$
Hence $$\frac{B_8}{(C_8-B_8)}=\frac{750C}{125C-750C}=\frac{750C}{-625C}=\frac{-6}{5}$$
Suff

(2) When A = 6, B = C + 15.
Now , here you have a term 15 which is free of variable so the answer will be in terms of variables, and NOT sufficient..
A=7..$$C_7=5C$$ and $$B_7=3*(C_7+15)=3*(5C+15)=15(C+3)$$
A=8..$$C_8=5C_7=25C$$ and $$B_8=3*(C_8+15)=3*(25C+15)=15(5C+3)$$
Hence $$\frac{B_8}{(C_8-B_8)}=\frac{15(5C+3)}{25C-15(5C+3)}$$
Insuff

A
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Re: The variables B and C are functions of the value of A such that with   [#permalink] 25 Nov 2019, 09:40
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