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Math Expert V
Joined: 02 Sep 2009
Posts: 58429
If f(a + b) = f(a) + f(b), what is the value of f(5)?  [#permalink]

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Difficulty:   95% (hard)

Question Stats: 28% (01:57) correct 72% (01:52) wrong based on 85 sessions

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If f(a + b) = f(a) + f(b), what is the value of f(5)?

(1) f(2) = 4
(2) f(2a) = 2f(a)

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Director  S
Joined: 21 Mar 2016
Posts: 508
If f(a + b) = f(a) + f(b), what is the value of f(5)?  [#permalink]

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1
Bunuel wrote:
If f(a + b) = f(a) + f(b), what is the value of f(5)?

(1) f(2) = 4
(2) f(2a) = 2f(a)

stat1: cannot deduce the value of f(5) from this.,,,not suff

stat2: Implies f(2a) = f(a) + f(a)
f(5) = f(2.5) + f(2.5),,,not suff

both combined... f(1) = 2
f(2) = 4
f(3) = f(1) + f(2)
hence f(5) = f(2) + f(3) can be deduced,,,

ans C

Originally posted by mohshu on 10 Jul 2017, 05:46.
Last edited by mohshu on 10 Jul 2017, 06:12, edited 1 time in total.
Intern  B
Joined: 01 May 2017
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Re: If f(a + b) = f(a) + f(b), what is the value of f(5)?  [#permalink]

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f(2)=4
f(1+1)=4=f(1)+f(1)=2f(1).
Therefore f(1)=2.

Now, f(5)=f(2)+f(3).
f(3)=f(2)+f(1)=4+2=6

Substituting, f(5)=f(2)+f(3)=4+6=10.

Thus statement 1 is sufficient. Option A would be the answer.

Statement 2 just repeats the question.

Hopefully this helps.

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Director  S
Joined: 21 Mar 2016
Posts: 508
Re: If f(a + b) = f(a) + f(b), what is the value of f(5)?  [#permalink]

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shreyashree wrote:
f(2)=4
f(1+1)=4=f(1)+f(1)=2f(1).
Therefore f(1)=2.

Now, f(5)=f(2)+f(3).
f(3)=f(2)+f(1)=4+2=6

Substituting, f(5)=f(2)+f(3)=4+6=10.

Thus statement 1 is sufficient. Option A would be the answer.

Statement 2 just repeats the question.

Hopefully this helps.

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what if f(2) = f(0+2) = f(0) + f(2)???
Non-Human User Joined: 09 Sep 2013
Posts: 13215
Re: If f(a + b) = f(a) + f(b), what is the value of f(5)?  [#permalink]

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_________________ Re: If f(a + b) = f(a) + f(b), what is the value of f(5)?   [#permalink] 25 Sep 2018, 22:42
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