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Math Revolution GMAT Instructor V
Joined: 16 Aug 2015
Posts: 7758
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]

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Difficulty:   65% (hard)

Question Stats: 61% (02:34) correct 39% (02:38) wrong based on 66 sessions

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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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VP  D
Joined: 09 Mar 2016
Posts: 1255
If a≠b, and a^2/(a-b)=b, which of the following could be a?  [#permalink]

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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  P
Joined: 31 Jul 2017
Posts: 514
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]

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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.
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Math Revolution GMAT Instructor V
Joined: 16 Aug 2015
Posts: 7758
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]

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=>

$$\frac{a^2}{(a-b)}=b$$
$$⇔ a^2=b(a-b)$$
$$⇔ a^2=ab – b^2$$
$$⇔ a^2 - ab + b^2 = 0$$
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
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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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_________________ 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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