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f(x) has the properties, f(x+y) = x + f(y) and f(0) = 5. Wha

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by Max@Math Revolution » Mon Jan 28, 2019 11:47 pm

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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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by fskilnik@GMATH » Tue Jan 29, 2019 3:53 am
Max@Math Revolution 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
$$\left( * \right)\,\,\,\left\{ \matrix{
f\left( 0 \right) = 5 \hfill \cr
f\left( {x + y} \right) = x + f\left( y \right) \hfill \cr} \right.$$
$$? = f\left( {100} \right)$$

$${\text{Take}}\,\,\left( {x,y} \right) = \left( {100,0} \right)\,\,\,\,\, \Rightarrow \,\,\,\,? = f\left( {100 + 0} \right)\,\,\mathop = \limits^{\left( * \right)} \,\,100 + f\left( 0 \right)\,\,\mathop = \limits^{\left( * \right)} \,\,105$$


We follow the notations and rationale taught in the GMATH method.

Regards,
Fabio.
Fabio Skilnik :: GMATH method creator ( Math for the GMAT)
English-speakers :: https://www.gmath.net
Portuguese-speakers :: https://www.gmath.com.br
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by Brent@GMATPrepNow » Tue Jan 29, 2019 5:54 am
Max@Math Revolution 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
Brent Hanneson - Creator of GMATPrepNow.com
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by Max@Math Revolution » Thu Jan 31, 2019 12:59 am
=>

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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