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Is a > 10?

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Is a > 10? [#permalink] New post 07 Nov 2010, 12:45
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Is a > 10?

(1) 1/a + 1/b = 1/c
(2) 1/a < 1/10
[Reveal] Spoiler: OA
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Re: is a>10? [#permalink] New post 07 Nov 2010, 13:08
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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.

Answer: E.
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Re: is a>10? [#permalink] New post 10 Nov 2010, 05:55
(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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Re: is a>10? [#permalink] New post 10 Nov 2010, 06:24
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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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DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS ; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


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Re: is a>10? [#permalink] New post 11 Nov 2010, 07:37
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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, 07:37
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