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).
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Regards,
Fabio
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Fabio Skilnik ::
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