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Winston created a function F such that F(1)=4, F(4)=3 and F(F(x))= F(x

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Winston created a function F such that F(1)=4, F(4)=3 and F(F(x))= F(x  [#permalink]

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New post 12 Feb 2019, 14:45
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GMATH practice exercise (Quant Class 4)

Winston created a function F such that F(1)=4, F(4)=3 and F(F(x))=F(x+2)-3, for all integer values of x. What is the value of F(5)?

(A) 0
(B) 2
(C) 4
(D) 12
(E) Not necessarily one above

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Fabio Skilnik :: GMATH method creator (Math for the GMAT)
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Re: Winston created a function F such that F(1)=4, F(4)=3 and F(F(x))= F(x  [#permalink]

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New post 12 Feb 2019, 18:39
fskilnik wrote:
GMATH practice exercise (Quant Class 4)

Winston created a function F such that F(1)=4, F(4)=3 and F(F(x))=F(x+2)-3, for all integer values of x. What is the value of F(5)?

(A) 0
(B) 2
(C) 4
(D) 12
(E) Not necessarily one above



The functions required and some values given tells you that you have to find f(5) from rearranging the equation and substituting f(1) and f(4)..
Let us do step wise..

We are given f(x) and f(x+2), that is difference of 2, so let us find f(3)
Let x=1, so f(f1)=f(1+2)-3....f(4)=f(3)-3....f(3)=3+3=6

Now let us take x as 3 to find f(5)
F(f(3))=f(5)-3....f(6)=f(5)-3

But we have another function as f(6), which can be found by taking x as 4
F(f(4))=f(6)-3.....f(3)=f(6)-3....6=f(6)-3....f(6)=9

Substitute this in f(6)=f(5)-3....9=f(5)-3....f(5)=12

D
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Re: Winston created a function F such that F(1)=4, F(4)=3 and F(F(x))= F(x  [#permalink]

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New post 12 Feb 2019, 18:51
fskilnik wrote:
GMATH practice exercise (Quant Class 4)

Winston created a function F such that F(1)=4, F(4)=3 and F(F(x))=F(x+2)-3, for all integer values of x. What is the value of F(5)?

(A) 0
(B) 2
(C) 4
(D) 12
(E) Not necessarily one above

\(F\left( {F\left( x \right)} \right) = F\left( {x + 2} \right) - 3\,\,\,,\,\,\,x\,\,{\mathop{\rm int}} \,\,\,\,\,\left( * \right)\)

\(F\left( 1 \right) = 4\,\,,\,\,F\left( 4 \right) = 3\,\,\,\,\,\left( {**} \right)\)

\(? = F\left( 5 \right)\)


\(x = 3\,\,\,\,\mathop \Rightarrow \limits^{\left( * \right)} \,\,\,F\left( {F\left( 3 \right)} \right) = F\left( 5 \right) - 3\,\,\,\,\,\, \Rightarrow \,\,\,\,\,\,? = F\left( {F\left( 3 \right)} \right) + 3\)

\(x = 1\,\,\,\,\mathop \Rightarrow \limits^{\left( * \right)} \,\,\,F\left( {F\left( 1 \right)} \right) = F\left( 3 \right) - 3\,\,\,\,\,\, \Rightarrow \,\,\,\,\,\,F\left( 3 \right) = F\left( {F\left( 1 \right)} \right) + 3\,\,\mathop = \limits^{\left( {**} \right)} \,\,F\left( 4 \right) + 3\,\,\mathop = \limits^{\left( {**} \right)} \,\,3 + 3 = 6\)


\(? = F\left( 6 \right) + 3\)


\(x = 4\,\,\,\,\mathop \Rightarrow \limits^{\left( * \right)} \,\,\,F\left( {F\left( 4 \right)} \right) = F\left( 6 \right) - 3\,\,\,\,\,\, \Rightarrow \,\,\,\,\,\,F\left( 6 \right) = F\left( {F\left( 4 \right)} \right) + 3\,\,\mathop = \limits^{\left( {**} \right)} \,\,F\left( 3 \right) + 3\,\, = \,\,6 + 3 = 9\)


\(? = F\left( 6 \right) + 3 = 9 + 3 = 12\)


The correct answer is (D).


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

Regards,
Fabio
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Fabio Skilnik :: GMATH method creator (Math for the GMAT)
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Re: Winston created a function F such that F(1)=4, F(4)=3 and F(F(x))= F(x   [#permalink] 12 Feb 2019, 18:51
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