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# Is a > 10?

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Intern
Joined: 05 Nov 2010
Posts: 32

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07 Nov 2010, 13:45
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Difficulty:

55% (hard)

Question Stats:

36% (01:46) correct 64% (00:33) wrong based on 25 sessions

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Is a > 10?

(1) 1/a + 1/b = 1/c
(2) 1/a < 1/10
[Reveal] Spoiler: OA
Math Expert
Joined: 02 Sep 2009
Posts: 39754

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07 Nov 2010, 14:08
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Expert's post
Creeper300 wrote:
is a>10?

1. 1/a +1/b=1/c
2. 1/a < 1/10

(1) 1/a +1/b=1/c. Clearly insufficient.
(2) 1/a < 1/10 --> a>10 or a<0. Not sufficient.

(1)+(2) Statement (1) is absolutely useless and (2) is not sufficient.

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Manager
Joined: 07 Feb 2010
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10 Nov 2010, 06:55
(2) 1/a < 1/10 --> a>10 or a<0. Not sufficient.
BUNUEL PLEASE EXPLAIN ME HOW a<0
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10 Nov 2010, 07:24
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Expert's post
anilnandyala wrote:
(2) 1/a < 1/10 --> a>10 or a<0. Not sufficient.
BUNUEL PLEASE EXPLAIN ME HOW a<0

$$\frac{1}{10}>\frac{1}{a}$$ --> $$\frac{1}{10}-\frac{1}{a}>0$$ --> $$\frac{a-10}{10a}>0$$:

Either both denominator and nominator are positive or both are negative:
$$a>0$$ and $$a-10>0$$, or $$a>10$$ --> $$a>10$$;
$$a<0$$ and $$a-10<0$$, or $$a<10$$ --> $$a<0$$;

So, inequality $$\frac{1}{10}>\frac{1}{a}$$ holds true for: $$a<0$$ and $$a>10$$ (even without the above solution you can spot that when a is negative then 1/a is negative, thus it's less than positive 1/10. Also when a>10, 1/10>1/a).

Hope it's clear.
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Intern
Joined: 28 Oct 2010
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11 Nov 2010, 08:37
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You can't cross multiply as a can be -ve or +ve. The inequality will change accordingly.
Re: is a>10?   [#permalink] 11 Nov 2010, 08:37
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