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Is a > 10?

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Is a > 10?

(1) 1/a + 1/b = 1/c
(2) 1/a < 1/10
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New post 10 Nov 2010, 06:55
(2) 1/a < 1/10 --> a>10 or a<0. Not sufficient.
BUNUEL PLEASE EXPLAIN ME HOW a<0
thanks in advance
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anilnandyala wrote:
(2) 1/a < 1/10 --> a>10 or a<0. Not sufficient.
BUNUEL PLEASE EXPLAIN ME HOW a<0
thanks in advance


\(\frac{1}{10}>\frac{1}{a}\) --> \(\frac{1}{10}-\frac{1}{a}>0\) --> \(\frac{a-10}{10a}>0\):

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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Re: is a>10? [#permalink]

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New post 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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