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Which is greater, cf or fg?

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Joined: 02 Sep 2009
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Which is greater, cf or fg? [#permalink]

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New post 24 Jan 2016, 06:16
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A
B
C
D
E

Difficulty:

  55% (hard)

Question Stats:

51% (01:11) correct 49% (01:37) wrong based on 39 sessions

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Kudos [?]: 132619 [0], given: 12326

Expert Post
Math Revolution GMAT Instructor
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Joined: 16 Aug 2015
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Re: Which is greater, cf or fg? [#permalink]

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New post 25 Jan 2016, 18:08
Forget conventional ways of solving math questions. In DS, Variable approach is the easiest and quickest way to find the answer without actually solving the problem. Remember equal number of variables and independent equations ensures a solution.

Which is greater, cf or fg?

(1) c > g
(2) f^2= cg


When you modify the original condition and the question, they become cf>fg?, f(c-g)>0?. There are 3 variables(c,f,g), which should match with the number of equations. So you need 3 equations. For 1) 1 equation, for 2) 1 equation, which is likely to make E the answer. When 1) & 2), in c-g>0, f can be both negative and positive, which is not sufficient.
Therefore, the answer is E.


 For cases where we need 3 more equations, such as original conditions with “3 variables”, or “4 variables and 1 equation”, or “5 variables and 2 equations”, we have 1 equation each in both 1) and 2). Therefore, there is 80% chance that E is the answer (especially about 90% of 2 by 2 questions where there are more than 3 variables), while C has 15% chance. These two are the majority. In case of common mistake type 3,4, the answer may be from A, B or D but there is only 5% chance. Since E is most likely to be the answer using 1) and 2) separately according to DS definition (It saves us time). Obviously there may be cases where the answer is A, B, C or D.
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Re: Which is greater, cf or fg? [#permalink]

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New post 07 Sep 2017, 01:15
Which is greater, cf or fg?

(1) c > g
we have to find relation between cf and fg
if f=+ve assume 1
cf>fg => c>g => given true
if f=-ve assume -1
cf>fg => -c> -g => c<g False
Not sufficient

(2) f^2= cg
This only tell us that cg=+ve
=> either c and g both +ve or c and g both -ve
so by this we cannot conclude anything for cf>fg
Not sufficient

1+2
c>g and either c and g both +ve or c and g both -ve
but here we dont knw value of f .. if f is +ve or -ve and that will change equation of cf>fg.

Not sufficient

Answer: E

Kudos [?]: 79 [0], given: 65

Re: Which is greater, cf or fg?   [#permalink] 07 Sep 2017, 01:15
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Which is greater, cf or fg?

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