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

Question

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

mohshu · Answer

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

shreyashree · Answer

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.

Posted from my mobile device

mohshu · Answer

what if f(2) = f(0+2) = f(0) + f(2)???

TestPrepUnlimited · Answer

Plug in b = a. Then we have  f(2a) = f(a) + f(a) = 2f(a) . Hence if we know f(a) we can double it to get f(2a).

Statement 1: 
Using the formula above we can get f(2) = 2*f(1) = 4. Then f(1) = 2. Thus f(5) = f(4) + f(1) = f(2) + f(2) + f(1) = 4 + 4 + 2 = 10. Sufficient.

Statement 2: 
We already know this but note the statement doesn't give any values so it's insufficient regardless.

Ans: A

TestPrepUnlimited · Answer

It's an old question but worth clarifying, the equation given would imply f(0) = 0.

GMATGuruNY · Answer

Since f(a + b) = f(a) + f(b), we get:
f(2) = f(1 + 1) = f(1) + f(1) = 2f(1)
f(3) = f(2 + 1) = f(2) + f(1) = 2f(1) + f(1) = 3f(1)
f(5) = f(2 + 3) = 2f(1) + 3f(1) = 5f(1)

Question stem, rephrased:
What is the value of f(1)?

Statement 1: f(2) = 4
Since f(2) = 2f(1), we get:
2f(1) = 4
f(1) = 2
SUFFICIENT.

Statement 2: f(2a) = 2f(a)
Since f(a + b) = f(a) + f(b), the information in the prompt implies the following:
f(2a) = f(a + a) = f(a) + f(a) = 2f(a)
ON ITS OWN, the prompt implies that f(2a) = 2f(a).
Since Statement 2 offers no information beyond that given in the prompt, INSUFFICIENT.

A

Dhwanii · Answer

I am still not clear why aren't we taking f(2) = f(0) + f(2),  TestPrepUnlimited  did mention eqn would imply f(0) = 0
I cannot comprehend it's meaning, if someone can elaborate

Dhwanii · Answer

I am still not clear why aren't we taking f(2) = f(0) + f(2),  TestPrepUnlimited  did mention eqn would imply f(0) = 0
I cannot comprehend it's meaning, if someone can elaborate

ElninoEffect · Answer

Dhwanii You are taking the condition which is of no help but which is good for reasoning.!

But You need to think this way that is it possible to find out the value of f(5) with the information given.? We are not trying to negate the statement |must be true condition rather We are trying to find a solution | may be true condition How to differentiate between the two conditions.? Here we are trying to see if the information given is sufficient to get our answer.? |we are not trying to see yes, no condition here. Now lets see the problem again.! We need f(5) Which can be done in f(3+2) or f(4+1) or f(5+0). |eq1 I) f(2) = 4 Now f(2) can be written as f(1+1) = 2f(1) =4 or f(2+0) = f(2)+f(0) =4 Now solution can be found with f(2)+f(0) as well but its a long shot. | will come to this later. taking the first option 2f(1) =4 f(1) =2 Now look at eq1 in f(4+1) we are having f(1) So all we need is the value of f(4) which can be written as f(2+2) = 2f(2) And we already know the value of f(2) So Sufficient. Now coming to your doubt let's do it that way also: f(0) is present in f(5+0) now f(5) can be written as f(4+1) or f(3+2) You seeing what's happening here again we have to do the process which we have just done above. You touch your ear with this side or that result will be same. Why go for extra step and time.! But its good for concept build up.

Hope that helps.

bumpbot · Answer

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

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