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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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GMATH Teacher
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Joined: 12 Oct 2010
Posts: 935
Winston created a function F such that F(1)=4, F(4)=3 and F(F(x))= F(x  [#permalink]

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12 Feb 2019, 14:45
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Difficulty:

95% (hard)

Question Stats:

38% (02:35) correct 62% (02:48) wrong based on 45 sessions

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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

_________________
Fabio Skilnik :: GMATH method creator (Math for the GMAT)
Our high-level "quant" preparation starts here: https://gmath.net
Math Expert
Joined: 02 Aug 2009
Posts: 8199
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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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
_________________
GMATH Teacher
Status: GMATH founder
Joined: 12 Oct 2010
Posts: 935
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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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

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

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

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

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

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

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

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

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

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

Regards,
Fabio
_________________
Fabio Skilnik :: GMATH method creator (Math for the GMAT)
Our high-level "quant" preparation starts here: https://gmath.net
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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