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

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Senior Manager
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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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62% (02:16) correct 38% (02:10) wrong based on 112 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
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Joined: 24 Apr 2016
Posts: 323
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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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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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
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Joined: 24 Apr 2016
Posts: 323
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   [#permalink] 17 Jul 2018, 12:07
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