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#### Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.  # a, b and c are positive numbers. If a2b - c=2b3a + c=ab , what is the

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Math Revolution GMAT Instructor V
Joined: 16 Aug 2015
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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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Difficulty:   65% (hard)

Question Stats: 64% (03:13) correct 36% (02:54) wrong based on 28 sessions

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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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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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(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
Math Revolution GMAT Instructor V
Joined: 16 Aug 2015
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GMAT 1: 760 Q51 V42
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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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2
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 $$\frac{a}{2b - c}=\frac{2b}{3a} + c=\frac{a}{b}=\frac{a + 2b + a}{2b - c + 3a + c + b}= \frac{2a + 2b}{3a + 3b}= \frac{2(a + b)}{3(a + b)}=\frac{2}{3}.$$

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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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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 $$\frac{a}{2b - c}=\frac{2b}{3a} + c=\frac{a}{b}=\frac{a + 2b + a}{2b - c + 3a + c + b}= \frac{2a + 2b}{3a + 3b}= \frac{2(a + b)}{3(a + b)}=\frac{2}{3}.$$

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

Posted from my mobile device 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   