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# If a≠b, and a^2/(a-b)=b, which of the following could be a?

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Math Revolution GMAT Instructor
Joined: 16 Aug 2015
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If a≠b, and a^2/(a-b)=b, which of the following could be a?  [#permalink]

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01 Feb 2018, 01:39
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[GMAT math practice question]

If $$a≠b$$, and $$\frac{a^2}{(a-b)}=b$$, which of the following could be $$a$$?

A. -1
B. 0
C. 1
D. 2
E. a does not exist

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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" VP Joined: 09 Mar 2016 Posts: 1223 If a≠b, and a^2/(a-b)=b, which of the following could be a? [#permalink] ### Show Tags 01 Feb 2018, 11:37 MathRevolution wrote: [GMAT math practice question] If $$a≠b$$, and $$\frac{a^2}{(a-b)}=b$$, which of the following could be $$a$$? A. -1 B. 0 C. 1 D. 2 E. a does not exist i think this question goes well with good wine how should i know what value is b? start plugging -1 ---> i get 1 =-b+b so how can understand if $$a≠b$$ cant understand the concept .. Director Joined: 31 Jul 2017 Posts: 503 Location: Malaysia Schools: INSEAD Jan '19 GMAT 1: 700 Q50 V33 GPA: 3.95 WE: Consulting (Energy and Utilities) Re: If a≠b, and a^2/(a-b)=b, which of the following could be a? [#permalink] ### Show Tags 01 Feb 2018, 23:10 2 MathRevolution wrote: [GMAT math practice question] If $$a≠b$$, and $$\frac{a^2}{(a-b)}=b$$, which of the following could be $$a$$? A. -1 B. 0 C. 1 D. 2 E. a does not exist We can write the equation as - $$b^2 - ab + a^2 = 0$$ $$b = a+- \sqrt{(-3a^2)}.$$.. So, there is no value of a for which b will be a non-imaginary number. Math Revolution GMAT Instructor Joined: 16 Aug 2015 Posts: 8456 GMAT 1: 760 Q51 V42 GPA: 3.82 If a≠b, and a^2/(a-b)=b, which of the following could be a? [#permalink] ### Show Tags 04 Feb 2018, 18:13 => $$\frac{a^2}{(a-b)}=b$$ $$⇔ a^2=b(a-b)$$ $$⇔ a^2=ab – b^2$$ $$⇔ a^2 - ab + b^2 = 0$$ Since $$a≠b$$, one of a and b is not zero. If $$a ≠ 0$$ or $$b ≠ 0$$, $$a^2 - ab + b^2$$ cannot be zero for the following reason: $$a^2 - ab + b^2 = a^2 – 2a(\frac{b}{2}) + b^2 = a2 – 2a(\frac{b}{2}) + \frac{b^2}{3} + (\frac{3}{4})b^2$$ $$= (a – \frac{b}{2})^2 + (\frac{3}{4})b^2 > 0$$ Thus, there is no pair of real numbers $$(a,b)$$ satisfying the equation $$a^2 - ab + b^2 = 0.$$ Therefore, $$a$$ cannot exist, and the answer is E. Answer: E _________________ 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: If a≠b, and a^2/(a-b)=b, which of the following could be a?  [#permalink]

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17 Apr 2019, 09:07
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Re: If a≠b, and a^2/(a-b)=b, which of the following could be a?   [#permalink] 17 Apr 2019, 09:07
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# If a≠b, and a^2/(a-b)=b, which of the following could be a?

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