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a, b and c are positive numbers. If a2b - c=2b3a + c=ab , what is the

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a, b and c are positive numbers. If a2b - c=2b3a + c=ab , what is the  [#permalink]

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New post 27 May 2020, 03:20
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C
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[GMAT math practice question]

\(a, b\) and \(c\) are positive numbers. If \(\frac{a}{2b - c}=\frac{2b}{3a + c}=\frac{a}{b}\) , what is the value of \(\frac{a}{b}\)?

A. \(\frac{1}{3}\)

B. \(\frac{1}{2} \)

C. \(\frac{2}{3}\)

D. \(\frac{3}{4} \)

E. \(\frac{4}{5}\)

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Re: a, b and c are positive numbers. If a2b - c=2b3a + c=ab , what is the  [#permalink]

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New post 27 May 2020, 09:33
MathRevolution wrote:

\(a, b\) and \(c\) are positive numbers. If \(\frac{a}{2b - c}=\frac{2b}{3a + c}=\frac{a}{b}\) , what is the value of \(\frac{a}{b}\)?

A. \(\frac{1}{3}\)

B. \(\frac{1}{2} \)

C. \(\frac{2}{3}\)

D. \(\frac{3}{4} \)

E. \(\frac{4}{5}\)


\(\frac{a}{2b - c}=\frac{2b}{3a + c}\)
\(3a^2 + ac=4b^2-2bc\) --- 1

\(\frac{a}{2b - c}=\frac{a}{b}\)
\(ab= 2ab - ac\)
\(ab= ac\); b = c, substitute value of c in equation 1

\(3a^2 + ab=4b^2-2b^2\)
\(3a^2 + ab -2b^2=0\), divide this equation by b^2
\(\frac{3a^2}{b^2} + \frac{a}{b} -2=0\), let a/b = x
\(3x^2 + x -2=0\)
\(x =\frac{-1±\sqrt{25}}{6}\)
x can not be negative, x = 4/6 = 2/3 = a/b
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Re: a, b and c are positive numbers. If a2b - c=2b3a + c=ab , what is the  [#permalink]

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New post 28 May 2020, 10:06
(1) a/(2b-c)
(2) 2b/(3a+c)
(3) a/b
(1)&(3)>> 2b-c=b >> b=c (4)
(2)&(3)& (4)>> 2b/(3a+b) = a/b>> 2b/(3a+b+2b)=a/(a+b) >> 2b/[3(a+b)]=a/(a+b) >>a/b= 2/3
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Re: a, b and c are positive numbers. If a2b - c=2b3a + c=ab , what is the  [#permalink]

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New post 29 May 2020, 00:12
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1
=>

Remember that \(\frac{a}{b}=\frac{c}{d}=\frac{e}{f}=\frac{a + c + e}{b + d + f}.\)

When we add numerators and denominators, we have \(\frac{a}{2b - c}=\frac{2b}{3a} + c=\frac{a}{b}=\frac{a + 2b + a}{2b - c + 3a + c + b}= \frac{2a + 2b}{3a + 3b}= \frac{2(a + b)}{3(a + b)}=\frac{2}{3}.\)

Therefore, C is the answer.
Answer: C
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Re: a, b and c are positive numbers. If a2b - c=2b3a + c=ab , what is the  [#permalink]

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New post 29 May 2020, 00:14
MathRevolution wrote:
=>

Remember that \(\frac{a}{b}=\frac{c}{d}=\frac{e}{f}=\frac{a + c + e}{b + d + f}.\)

When we add numerators and denominators, we have \(\frac{a}{2b - c}=\frac{2b}{3a} + c=\frac{a}{b}=\frac{a + 2b + a}{2b - c + 3a + c + b}= \frac{2a + 2b}{3a + 3b}= \frac{2(a + b)}{3(a + b)}=\frac{2}{3}.\)

Therefore, C is the answer.
Answer: C


It's easier to solve like that. Thank you.

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Re: a, b and c are positive numbers. If a2b - c=2b3a + c=ab , what is the   [#permalink] 29 May 2020, 00:14

a, b and c are positive numbers. If a2b - c=2b3a + c=ab , what is the

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