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If f(x) and g(x) are two functions, what is the value of g(2)?

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If f(x) and g(x) are two functions, what is the value of g(2)?  [#permalink]

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New post 10 Jul 2017, 03:37
00:00
A
B
C
D
E

Difficulty:

  55% (hard)

Question Stats:

61% (01:52) correct 39% (01:42) wrong based on 174 sessions

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If f(x) and g(x) are two functions, what is the value of g(2)?  [#permalink]

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New post 09 Aug 2017, 03:35
4
1
Bunuel wrote:
If f(x) and g(x) are two functions, what is the value of g(2)?

(1) f(x − 1) = 2x + 4
(2) f(g(x)) = 4x


Statement 1: \(f(x-1) = 2x+4\), or
\(f(x-1) = 2(x-1)+6\)
therefore \(f(x) = 2x+6\). but this equation doe not give any value of \(g(x)\). hence not sufficient

Statement 2: \(f(g(x)) = 4x\). this does not give any value of function \(f(x)\). hence not sufficient

Combining 1 & 2 we get
\(f(x) = 2x+6\), or \(f(g(x)) = 2g(x) + 6\)
\(2g(x)+6 = 4x\), or \(g(x) = 2x-3\)
therefore \(g(2) = 2*2-3 = 1\)

Option C
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Re: If f(x) and g(x) are two functions, what is the value of g(2)?  [#permalink]

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New post 10 Jul 2017, 04:21
stat1: clearly not suff,,no link to g(x)

stat2: we cannot deduce g(x) from the equation...not suff

combined is sufficient..
use stat1 to get the value of f(x) and then use stat2 to get the value of g(x)

IMO C
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Re: If f(x) and g(x) are two functions, what is the value of g(2)?  [#permalink]

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New post 10 Jul 2017, 18:02
I would go with E

may be I am wrong, but, I don't know the equation for g(x) either from stmt 1 or stmt 2.
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Re: If f(x) and g(x) are two functions, what is the value of g(2)?  [#permalink]

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New post 09 Aug 2017, 03:08
mohshu wrote:
stat1: clearly not suff,,no link to g(x)

stat2: we cannot deduce g(x) from the equation...not suff

combined is sufficient..
use stat1 to get the value of f(x) and then use stat2 to get the value of g(x)

IMO C


Can you please explain how to get g(x) ?
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Re: If f(x) and g(x) are two functions, what is the value of g(2)?  [#permalink]

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New post 19 Dec 2017, 10:06
Bunuel wrote:
If f(x) and g(x) are two functions, what is the value of g(2)?

(1) f(x − 1) = 2x + 4
(2) f(g(x)) = 4x


Given
=> f(x) & g(x) are 2 function. f(2)= ?

Statement 1 f(x-1)=2x+4
=> put x=x+1
=> f(x+1-1)=2(x+1)+4
=> f(x)=2x+6 -------------(1)
Since there is no relation between f(x) & g(x) we cannot find g(2)
Therefore NOT sufficient

Statement 2 f(g(x))=4x
=> f(g(2))=4*2=8
=> f(g(2))=8 -------------(2)
BUT g(2) cannot be found. Therefore NOT sufficient

BOTH Statement 1 & 2
=> f(x)=2x+6 from (1)
=> substituting x=g(2) we have
=> f(g(2))=2g(2)+6
=> But f(g(2))=8 from (2)
=> 8=2g(2)+6
=> 2=2g(2)
=>g(2)=1
Therefore SUFFICIENT

Hence 'C'

Thanks
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Re: If f(x) and g(x) are two functions, what is the value of g(2)?  [#permalink]

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New post 19 Dec 2017, 20:55
If f(x) and g(x) are two functions, what is the value of g(2)?

(1) f(x − 1) = 2x + 4
(2) f(g(x)) = 4x

Statement (1) - f(x − 1) = 2x + 4

Does not give us any information of g(x)

Not sufficient.

Negate A and D

Statement (2) f(g(x)) = 4x

Does not give any Information of f(x)

Not sufficient.

Negate B

Both Together

We now have equations through which we can find f(x) and g(x) and solve the equation ahead.

Negate E

Answer C

Equations are solved by the other members in the post.
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Re: If f(x) and g(x) are two functions, what is the value of g(2)?  [#permalink]

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New post 21 Dec 2017, 10:10
Bunuel wrote:
If f(x) and g(x) are two functions, what is the value of g(2)?

(1) f(x − 1) = 2x + 4
(2) f(g(x)) = 4x


Forget conventional ways of solving math questions. For DS problems, the VA (Variable Approach) method is the quickest and easiest way to find the answer without actually solving the problem. Remember that equal numbers of variables and independent equations ensure a solution.

Since we have 2 variables (\(f(x)\) and \(g(x)\)) and 0 equations, we should consider both conditions 1) & 2) together first.

\(f(g(2)) = 4 \cdot 2 = 8\) from the condition 2)
From \(f(x-1) = 2x+4\), we have \(f(x) = 2(x+1)+4 = 2x + 6\) and \(f(g(2)) = 2 \cdot g(2) + 6 = 8\)
Thus \(2 \cdot g(2) = 2\) and \(g(2) = 1\).

Therefore, C is the answer.

Normally, in problems which require 2 or more additional equations, such as those in which the original conditions include 2 variables, or 3 variables and 1 equation, or 4 variables and 2 equations, each of conditions 1) and 2) provide an additional equation. In these problems, the two key possibilities are that C is the answer (with probability 70%), and E is the answer (with probability 25%). Thus, there is only a 5% chance that A, B or D is the answer. This occurs in common mistake types 3 and 4. Since C (both conditions together are sufficient) is the most likely answer, we save time by first checking whether conditions 1) and 2) are sufficient, when taken together. Obviously, there may be cases in which the answer is A, B, D or E, but if conditions 1) and 2) are NOT sufficient when taken together, the answer must be E.
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Re: If f(x) and g(x) are two functions, what is the value of g(2)? &nbs [#permalink] 21 Dec 2017, 10:10
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