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

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Math Revolution GMAT Instructor
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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27 May 2020, 03:20
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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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"Only $79 for 1 month Online Course" "Free Resources-30 day online access & Diagnostic Test" "Unlimited Access to over 120 free video lessons - try it yourself" Senior Manager Joined: 24 Oct 2015 Posts: 487 Location: India Schools: Sloan '22, ISB, IIM GMAT 1: 650 Q48 V31 GPA: 4 Re: a, b and c are positive numbers. If a2b - c=2b3a + c=ab , what is the [#permalink] Show Tags 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 Intern Joined: 07 Mar 2020 Posts: 1 Re: a, b and c are positive numbers. If a2b - c=2b3a + c=ab , what is the [#permalink] Show Tags 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 Math Revolution GMAT Instructor Joined: 16 Aug 2015 Posts: 9144 GMAT 1: 760 Q51 V42 GPA: 3.82 Re: a, b and c are positive numbers. If a2b - c=2b3a + c=ab , what is the [#permalink] Show Tags 29 May 2020, 00:12 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 $$\frac{a}{2b - c}=\frac{2b}{3a} + c=\frac{a}{b}=\frac{a + 2b + a}{2b - c + 3a + c + b}= \frac{2a + 2b}{3a + 3b}= \frac{2(a + b)}{3(a + b)}=\frac{2}{3}.$$ Therefore, C is the answer. Answer: C _________________ MathRevolution: Finish GMAT Quant Section with 10 minutes to spare The one-and-only World’s First Variable Approach for DS and IVY Approach for PS with ease, speed and accuracy. "Only$79 for 1 month Online Course"
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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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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 $$\frac{a}{2b - c}=\frac{2b}{3a} + c=\frac{a}{b}=\frac{a + 2b + a}{2b - c + 3a + c + b}= \frac{2a + 2b}{3a + 3b}= \frac{2(a + b)}{3(a + b)}=\frac{2}{3}.$$

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