Positive integer

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Ashetty: Senior | Next Rank: 100 Posts; Posts: 49; Joined: Sun May 08, 2011 4:33 pm

Positive integer

by Ashetty » Sun Sep 18, 2011 5:41 pm

Which of following functions is f(a+b)=f(a)+(b) for all positive integer number a and b?
a)f(x)=x^2
B)f(x)=x+1
c)f(x)=âˆšx
d)f(x)=2/x
e)f(x)=-3x

Ans: E

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Source: Beat The GMAT — Problem Solving | Sun Sep 18, 2011 5:41 pm

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by Anurag@Gurome » Sun Sep 18, 2011 8:25 pm

Solution:
Check each option one by one.
Take a).
f(a+b) = (a+b)^2 = a^2 + 2ab + b^2 where as f(a) + f(b) = a^2 + b^2.
So,a) is ruled out.
Take b).
f(a+b) = a + b + 1 where as f(a) + f(b) = a + 1 + b + 1 = a + b + 2
Even b)is ruled out.
Take c).
f(a+b) = sqrt(a+b) where as f(a) + f(b) = sqrt(a) + sqrt(b)
c) is ruled out.
Take d).
f(a+b) = 2/(a+b) where as f(a) + f(b) = 2/a + 2/b
d) is eliminated.
Take e).
f(a+b) = -3(a+b) = -3a -3b = f(a) + f(b)

So, e) is the correct answer.

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