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# If a^2 – ab = 2b^2, which of the following could be b/a ?

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Math Expert
Joined: 02 Sep 2009
Posts: 64249
If a^2 – ab = 2b^2, which of the following could be b/a ?  [#permalink]

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20 Feb 2020, 04:20
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Difficulty:

55% (hard)

Question Stats:

63% (02:05) correct 37% (02:31) wrong based on 63 sessions

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If a^2 – ab = 2b^2, which of the following could be b/a ?

I. 1/2
II. 2
III. −1

(A) I only
(B) II only
(C) I and II
(D) I and III
(E) II and III

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Joined: 14 Dec 2019
Posts: 665
Location: Poland
GMAT 1: 570 Q41 V27
WE: Engineering (Consumer Electronics)
Re: If a^2 – ab = 2b^2, which of the following could be b/a ?  [#permalink]

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20 Feb 2020, 04:37
Bunuel wrote:
If a^2 – ab = 2b^2, which of the following could be b/a ?

I. 1/2
II. 2
III. −1

(A) I only
(B) II only
(C) I and II
(D) I and III
(E) II and III

Are You Up For the Challenge: 700 Level Questions

Divide by b^2 in the original equation a^2 – ab = 2b^2 we get $$(\frac{a}{b})^{2} - \frac{a}{b} = 2$$

Then substituting values for each case :-
i) $$\frac{b}{a} = \frac{1}{2}$$ => $$\frac{a}{b} = 2$$
$$(\frac{a}{b})^{2} - \frac{a}{b} = 2^{2} - 2 = 2$$ - Valid

ii) $$\frac{b}{a} = 2$$ => $$\frac{a}{b} = \frac{1}{2}$$
$$(\frac{a}{b})^{2} - \frac{a}{b} = (\frac{1}{2})^{2} - \frac{1}{2} = \frac{-1}{2}$$ - Not Valid

iii) $$\frac{ b}{a} = -1$$ => $$\frac{a}{b} = -1$$
$$(\frac{a}{b})^{2} - \frac{a}{b} = -1^{2} - (-1) = 2$$ - Valid

Hence i) and iii) must be true -> Answer D
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Joined: 12 Dec 2015
Posts: 496
Re: If a^2 – ab = 2b^2, which of the following could be b/a ?  [#permalink]

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20 Feb 2020, 05:27
If a^2 – ab = 2b^2, which of the following could be b/a ?

I. 1/2
II. 2
III. −1

(A) I only
(B) II only
(C) I and II
(D) I and III --> correct
(E) II and III

Solution:
$$a^2 – ab = 2b^2$$
=> $$1 – (ab/a^2) = (2b^2/a^2)$$, # divide both side by a^2
=> $$1 – x = 2x^2$$, # say, x= b/a
=> $$2x^2 +x -1 = 0$$
=> $$2x^2 +2x -x -1 = 0$$
=> (x+1)(2x-1)=0
=> (x+1)(x-1/2)=0
=> x =-1 or 1/2
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Joined: 24 Nov 2016
Posts: 1567
Location: United States
Re: If a^2 – ab = 2b^2, which of the following could be b/a ?  [#permalink]

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02 Apr 2020, 09:30
Bunuel wrote:
If a^2 – ab = 2b^2, which of the following could be b/a ?

I. 1/2
II. 2
III. −1

(A) I only
(B) II only
(C) I and II
(D) I and III
(E) II and III

a^2 – ab = 2b^2
a^2 – ab-2b^2=0
a^2-ab-2b^2=0
(a-2b)(a+b)=0
a=2b or a=-b
b/2b=1/2
b/-b=-1

Ans (D)
Re: If a^2 – ab = 2b^2, which of the following could be b/a ?   [#permalink] 02 Apr 2020, 09:30