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f(x) has the properties, f(x+y) = x + f(y) and f(0) = 5. What is the v

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Math Revolution GMAT Instructor
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f(x) has the properties, f(x+y) = x + f(y) and f(0) = 5. What is the v  [#permalink]

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New post 29 Jan 2019, 01:02
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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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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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New post 29 Jan 2019, 01:10
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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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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New post 29 Jan 2019, 03:18
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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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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New post 29 Jan 2019, 07:07
Top Contributor
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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 \(f(100)\)?

\(A. 95\)
\(B. 100\)
\(C. 105\)
\(D. 120\)
\(E. 135\)


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

Answer: C

Cheers,
Brent
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Math Revolution GMAT Instructor
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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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New post 31 Jan 2019, 02:15
=>

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.
Answer: C
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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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