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# If a > 0 and |a| ≠ |b|, is 2/(a+b) + 2/(a-b) = 1 ?

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Intern
Joined: 23 Oct 2019
Posts: 7
If a > 0 and |a| ≠ |b|, is 2/(a+b) + 2/(a-b) = 1 ?  [#permalink]

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Updated on: 24 Jan 2020, 23:58
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Difficulty:

35% (medium)

Question Stats:

63% (01:30) correct 37% (01:49) wrong based on 41 sessions

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If $$a > 0$$ and $$|a| ≠ |b|$$, is $$\frac{2}{a+b }+ \frac{2}{a-b} = 1$$ ?

(1) $$b = 0$$

(2) $$a^2 − b^2 = 4a$$

Originally posted by ajgoupil on 24 Jan 2020, 09:24.
Last edited by Bunuel on 24 Jan 2020, 23:58, edited 1 time in total.
Renamed the topic and edited the question.
SVP
Joined: 20 Jul 2017
Posts: 1509
Location: India
Concentration: Entrepreneurship, Marketing
WE: Education (Education)
Re: If a > 0 and |a| ≠ |b|, is 2/(a+b) + 2/(a-b) = 1 ?  [#permalink]

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24 Jan 2020, 11:30
ajgoupil wrote:
If a > 0 and |a| ≠ |b|, is 2/a+b + 2/a-b = 1 ?

(1) b = 0
(2) a2 − b2 = 4a

Is $$\frac{ 2}{a+b } + \frac{ 2}{a-b } = 1$$?
—> $$2(a - b) + 2(a + b) = (a + b)(a - b)$$ ?
—> $$2a - 2b + 2a + 2b = a^2 - b^2$$?
—> $$a^2 - b^2 = 4a$$?

(1) $$b = 0$$
—> Not relavant —> Insufficient

(2) $$a^2 - b^2 = 4a$$
—> Yes —> Sufficient

Option B

Hope it helps.

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Manager
Joined: 30 Jul 2019
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If a > 0 and |a| ≠ |b|, is 2/(a+b) + 2/(a-b) = 1 ?  [#permalink]

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25 Jan 2020, 07:55
$$\frac{2}{a+b} + \frac{2}{a-b} = \frac{2(a+b) + 2(a-b) }{ (a+b)*(a-b)} = \frac{4a}{ a^2 - b^2}$$
statement (1) b=0 not enough to conclusion.
statement (2) $$a^2 - b^2 = 4a => 4a/4a = 1$$
Choice B.
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Re: If a > 0 and |a| ≠ |b|, is 2/(a+b) + 2/(a-b) = 1 ?  [#permalink]

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26 Jan 2020, 00:56
ajgoupil wrote:
If $$a > 0$$ and $$|a| ≠ |b|$$, is $$\frac{2}{a+b }+ \frac{2}{a-b} = 1$$ ?

(1) $$b = 0$$

(2) $$a^2 − b^2 = 4a$$

Given:
1. $$a > 0$$ and
2. $$|a| ≠ |b|$$,

Is $$\frac{2}{a+b }+ \frac{2}{a-b} = 1$$ ?
or Is 4a/(a^2 - b^2) = 1
or Is 4a = a^2 -b^2

(1) $$b = 0$$
$$\frac{2}{a+b }+ \frac{2}{a-b}$$
= $$\frac{2}{a} + \frac{2}{a} = \frac{4}{a }$$
4/a is NOT NECESSARILY = 1
NOT SUFFICIENT

(2) $$a^2 − b^2 = 4a$$
Is $$\frac{2}{a+b }+ \frac{2}{a-b} = 1$$ ?
or Is 4a/(a^2 - b^2) = 1
or Is 4a = a^2 -b^2
SUFFICIENT

IMO B
Re: If a > 0 and |a| ≠ |b|, is 2/(a+b) + 2/(a-b) = 1 ?   [#permalink] 26 Jan 2020, 00:56
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