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

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Manager
Joined: 15 Aug 2010
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Location: Moscow, Russia
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The variables B and C are functions of the value of A such  [#permalink]

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08 Feb 2011, 09:53
3
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Difficulty:

95% (hard)

Question Stats:

40% (02:33) correct 60% (02:34) wrong based on 81 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: variables and functions  [#permalink]

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08 Feb 2011, 12:44
3
2
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
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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09 Feb 2011, 00:29
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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28 Dec 2014, 03:40
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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20 Dec 2017, 07:32
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Re: The variables B and C are functions of the value of A such &nbs [#permalink] 20 Dec 2017, 07:32
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# The variables B and C are functions of the value of A such

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