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

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Senior Manager
Joined: 17 Mar 2014
Posts: 310
If a^2 – ab = 2b^2, which of the following could be b/a  [#permalink]

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31 Jul 2017, 13:09
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55% (hard)

Question Stats:

61% (01:46) correct 39% (01:46) wrong based on 82 sessions

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Could you help me with following question.

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
Senior Manager
Joined: 24 Apr 2016
Posts: 333
Re: If a^2 – ab = 2b^2, which of the following could be b/a  [#permalink]

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31 Jul 2017, 21:59
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$$a^2 – ab = 2b^2$$ can be written as $$a^2 – 2b^2 - ab = 0$$ --- Equation 1

Divide Equation 1 by $$a^2$$, this results in ==> 1 - 2 $$(\frac{b}{a})^2$$ - $$\frac{b}{a}$$ = 0 -- Equation 2

Replace $$\frac{b}{a}$$ by x in Equation 2, this results in ==> 1 - 2 $$x^2$$ - x = 0 ==> 2 $$x^2$$ + x - 1 = 0 ==> (2x-1)(x+1) = 0

Therefore, x = -1 or$$\frac{1}{2}$$

$$\frac{b}{a}$$ = -1 or $$\frac{1}{2}$$

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Posts: 6277
Re: If a^2 – ab = 2b^2, which of the following could be b/a  [#permalink]

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31 Jul 2017, 22:00
ammuseeru wrote:
Could you help me with following question.

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

HI..
If you are seeing an equation in terms of variables and value asked in terms of fraction, try dividing the equation by the variable in denominator..

here divide equation $$a^2$$ – $$ab$$ = $$2b^2$$ by $$a^2..$$..
so $$\frac{a^2-ab}{a^2}=\frac{2b^2}{a^2}.......... 1-\frac{b}{a}=2*\frac{b}{a}^2$$..
here you can do two things ..
(A) substitute the given values ..
$$1-\frac{b}{a}=2*\frac{b}{a}^2$$..
1) 1/2..
$$1-\frac{1}{2}=2*\frac{1}{2}^2........1-1/2=1/2$$...YES
2) 2..
$$1-2=2*2^2$$.....No
3) -1
$$1-(-1)=2*(-1)^2....1+1=2$$.....YES

so I and III
D

(B) solve ..
$$1-\frac{b}{a}=2*\frac{b}{a}^2$$..
let b/a = x..
so $$1-x=2x^2.....2x^2+x-1=0....(2x-1)(x+1)=0$$..
so x=1/2 or x=-1

D
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Senior Manager
Joined: 17 Mar 2014
Posts: 310
Re: If a^2 – ab = 2b^2, which of the following could be b/a  [#permalink]

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01 Aug 2017, 09:51
quantumliner wrote:
$$a^2 – ab = 2b^2$$ can be written as $$a^2 – 2b^2 - ab = 0$$ --- Equation 1

Divide Equation 1 by $$a^2$$, this results in ==> 1 - 2 $$(\frac{b}{a})^2$$ - $$\frac{b}{a}$$ = 0 -- Equation 2

Replace $$\frac{b}{a}$$ by x in Equation 2, this results in ==> 1 - 2 $$x^2$$ - x = 0 ==> 2 $$x^2$$ + x - 1 = 0 ==> (2x-1)(x+1) = 0

Therefore, x = -1 or$$\frac{1}{2}$$

$$\frac{b}{a}$$ = -1 or $$\frac{1}{2}$$

How did you factorize into 2 $$x^2$$ + x - 1 = 0 ==> (2x-1)(x+1) = 0
Senior Manager
Joined: 24 Apr 2016
Posts: 333
Re: If a^2 – ab = 2b^2, which of the following could be b/a  [#permalink]

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02 Aug 2017, 10:24
ammuseeru wrote:
quantumliner wrote:
$$a^2 – ab = 2b^2$$ can be written as $$a^2 – 2b^2 - ab = 0$$ --- Equation 1

Divide Equation 1 by $$a^2$$, this results in ==> 1 - 2 $$(\frac{b}{a})^2$$ - $$\frac{b}{a}$$ = 0 -- Equation 2

Replace $$\frac{b}{a}$$ by x in Equation 2, this results in ==> 1 - 2 $$x^2$$ - x = 0 ==> 2 $$x^2$$ + x - 1 = 0 ==> (2x-1)(x+1) = 0

Therefore, x = -1 or$$\frac{1}{2}$$

$$\frac{b}{a}$$ = -1 or $$\frac{1}{2}$$

How did you factorize into 2 $$x^2$$ + x - 1 = 0 ==> (2x-1)(x+1) = 0

2$$x^2$$ + x - 1 = 0 can be written as 2$$x^2$$ - x + 2x - 1 = 0 ==> x(2x-1) +1(2x-1) ==> (2x-1)(x+1)

Hope this helps
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Re: If a^2 – ab = 2b^2, which of the following could be b/a  [#permalink]

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17 Jul 2018, 12:07
$$a^2$$-ab-2$$b^2$$=0
(a-2b)(a+b)=0
a-2b=0 OR a+b=0
a=2b OR a=-b
$$b/a$$= 1/2 OR $$a/b$$=-1

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Re: If a^2 – ab = 2b^2, which of the following could be b/a &nbs [#permalink] 17 Jul 2018, 12:07
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