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

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

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New post 08 Feb 2011, 10:53
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41% (02:14) correct 59% (01:55) wrong based on 76 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.
[Reveal] Spoiler: OA
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Re: variables and functions [#permalink]

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New post 08 Feb 2011, 13:44
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I don't have a generalized way of solving these types of questions; here's how I solved this one.

Given:
B(A+1) = B(A) * 3
C(A+1) = C(A) * 5

Q: What is the value for \(\frac{B(8)}{C(8)-B(8)}\)

1.
B(5) = 2*C(5)
B(6) = 3*2*C(5)
B(7) = 3*3*2*C(5)
B(8) = 3*3*3*2*C(5) = 54*C(5)

C(6) = 5*C(5)
C(7) = 5*5*C(5)
C(8) = 5*5*5*C(5) = 125*C(5)

\(\frac{B(8)}{C(8)-B(8)}\)
\(\frac{54*C(5)}{125*C(5) - 54C(5)}\)
\(\frac{54}{125-54}\) {as C(5) cancels out}

Sufficient.


2.

\(B(5) = C(5) + 15\)
\(B(8) = 27*(C(5) + 15) = 27*C(5) + 405\)
\(C(8) = 125*C(5)\)

\(\frac{B(8)}{C(8)-B(8)}\)
\(\frac{27*C(5) + 27*15}{125*C(5) - 27*C(5) - 405}\)

C(5) can't be canceled out and we don't know its value either.

Not sufficient.

Ans : "A"
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Manager
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Joined: 15 Aug 2010
Posts: 73
Location: Moscow, Russia
Schools: top schools
WE 1: Foreign Ministry - 6 years
WE 2: Law Firm - 3 years
Re: variables and functions [#permalink]

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New post 09 Feb 2011, 01:29
fluke wrote:
I don't have a generalized way of solving these types of questions; here's how I solved this one.

Given:
B(A+1) = B(A) * 3
C(A+1) = C(A) * 5


Thanks, Fluke. It was helpful to see your approach. :)
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Re: The variables B and C are functions of the value of A such [#permalink]

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New post 28 Dec 2014, 04:40
IF we try to solve what we get : Statm 1) A=5, B=2C, C So A =8 , B=3*3*3*2C, C=5*5*5C=125C so B/B-C we get a value so sufficient, but statement B if we follow for expression B/B-C we get the following 9(C+15)/16C-135 so we cant cancel C so not sufficient.
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Re: The variables B and C are functions of the value of A such [#permalink]

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New post 20 Dec 2017, 08:32
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Re: The variables B and C are functions of the value of A such   [#permalink] 20 Dec 2017, 08:32
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