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If x is an integer greater than 2, the function f(x)

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If x is an integer greater than 2, the function f(x)

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If x is an integer greater than 2, the function f(x) represents the product of all even integers between 2 and x, inclusive. What is f(51) -f(50)?

a) (51)50!
b) (502)49!
c) 50
d) 1
e) 0

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DivyaD wrote:
If x is an integer greater than 2, the function f(x) represents the product of all even integers between 2 and x, inclusive. What is f(51) - f(50)?

a) (51)50!
b) (502)49!
c) 50
d) 1
e) 0
The key here is that f(51) is EQUAL to f(50)
Here's why:
According to the definition of the function f, f(51) = (2)(4)(6). . . (48)(50), and f(50) = (2)(4)(6). . . (48)(50)
So, f(51) - f(50) = (2)(4)(6). . . (48)(50) - (2)(4)(6). . . (48)(50)
= 0

Answer: E

Cheers,
Brent

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Post
DivyaD wrote:
If x is an integer greater than 2, the function f(x) represents the product of all even integers between 2 and x, inclusive. What is f(51) -f(50)?

a) (51)50!
b) (502)49!
c) 50
d) 1
e) 0
$$f\left( x \right) = \left\{ \matrix{
\,2 \cdot 4 \cdot 6 \cdot \ldots \cdot x\,\,\,\,,\,\,\,\,x\,\,{\rm{even}}\,\,\,\,\left( * \right) \hfill \cr
\,2 \cdot 4 \cdot 6 \cdot \ldots \cdot \left( {x - 1} \right)\,\,\,\,,\,\,\,\,x\,\,{\rm{odd}}\,\,\,\,\left( {**} \right) \hfill \cr} \right.\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\left[ {\,x \ge 3\,\,{\mathop{\rm int}} \,} \right]$$
$$? = f\left( {51} \right) - f\left( {50} \right)$$
$$f\left( {51} \right)\,\,\,\mathop = \limits^{\left( {**} \right)} \,\,\,2 \cdot 4 \cdot 6 \cdot \ldots \cdot \left( {51 - 1} \right)\,\,\,\mathop = \limits^{\left( * \right)} \,\,\,f\left( {50} \right)\,\,\,\,\,\,\,\,\, \Rightarrow \,\,\,\,\,\,? = 0$$


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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