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Math Revolution GMAT Instructor V
Joined: 16 Aug 2015
Posts: 7999
GMAT 1: 760 Q51 V42 GPA: 3.82
f(x) has the properties, f(x+y) = x + f(y) and f(0) = 5. What is the v  [#permalink]

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Difficulty:   15% (low)

Question Stats: 82% (01:21) correct 18% (01:27) wrong based on 41 sessions

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[GMAT math practice question]

$$f(x)$$ has the properties, $$f(x+y) = x + f(y)$$ and $$f(0) = 5$$. What is the value of $$f(100)$$?

$$A. 95$$
$$B. 100$$
$$C. 105$$
$$D. 120$$
$$E. 135$$

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Director  V
Joined: 27 May 2012
Posts: 898
Re: f(x) has the properties, f(x+y) = x + f(y) and f(0) = 5. What is the v  [#permalink]

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1
MathRevolution wrote:
[GMAT math practice question]

$$f(x)$$ has the properties, $$f(x+y) = x + f(y)$$ and $$f(0) = 5$$. What is the value of $$f(100)$$?

$$A. 95$$
$$B. 100$$
$$C. 105$$
$$D. 120$$
$$E. 135$$

Can be written as f(100+0) = 100 +f(0) -> 100+5 = 105.
Ans=c
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Joined: 18 Aug 2017
Posts: 4976
Location: India
Concentration: Sustainability, Marketing
GPA: 4
WE: Marketing (Energy and Utilities)
Re: f(x) has the properties, f(x+y) = x + f(y) and f(0) = 5. What is the v  [#permalink]

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MathRevolution wrote:
[GMAT math practice question]

$$f(x)$$ has the properties, $$f(x+y) = x + f(y)$$ and $$f(0) = 5$$. What is the value of $$f(100)$$?

$$A. 95$$
$$B. 100$$
$$C. 105$$
$$D. 120$$
$$E. 135$$

f(0)= o+f(y)
given f(0) =5
5=f(y)

so f(100) = 100+f(y)
f(100)= 100+5
= 105
IMO C
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Joined: 12 Sep 2015
Posts: 3990
Re: f(x) has the properties, f(x+y) = x + f(y) and f(0) = 5. What is the v  [#permalink]

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1
MathRevolution wrote:
[GMAT math practice question]

$$f(x)$$ has the properties, $$f(x+y) = x + f(y)$$ and $$f(0) = 5$$. What is the value of $$f(100)$$?

$$A. 95$$
$$B. 100$$
$$C. 105$$
$$D. 120$$
$$E. 135$$

Given: f(x+y) = x + f(y)

What is the value of f(100)?
We need to somehow use the fact that f(0) = 5 to help us determine the value of f(100).
Notice that we can rewrite 100 as 100 + 0

According to our the function f, we know that: f(100 + 0) = 100 + f(0)
= 100 + 5
= 105

Cheers,
Brent
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Math Revolution GMAT Instructor V
Joined: 16 Aug 2015
Posts: 7999
GMAT 1: 760 Q51 V42 GPA: 3.82
Re: f(x) has the properties, f(x+y) = x + f(y) and f(0) = 5. What is the v  [#permalink]

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=>

Using $$f(x +y ) = x + f(y)$$ yields
$$f(x) = f(x+0) = x + f(0)$$
Now, using $$f(0) = 5$$ yields
$$f(x) = x + 5.$$
Therefore,
$$f(100) = 100 + 5 = 105.$$

Therefore, the answer is C.
_________________ Re: f(x) has the properties, f(x+y) = x + f(y) and f(0) = 5. What is the v   [#permalink] 31 Jan 2019, 02:15
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