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# The function f is defined for all positive integers n as f(

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The function f is defined for all positive integers n as f( [#permalink]  14 May 2019, 01:15
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Question Stats:

90% (00:23) correct 10% (00:26) wrong based on 40 sessions
The function f is defined for all positive integers n as $$f(n)= \frac{n}{n+1}$$

 Quantity A Quantity B f(1) × f(2) f(2) × f(3)

A) Quantity A is greater.
B) Quantity B is greater.
C) The two quantities are equal.
D) The relationship cannot be determined from the information given.
[Reveal] Spoiler: OA

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Re: The function f is defined for all positive integers n as f( [#permalink]  14 May 2019, 07:28
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Expert's post
Carcass wrote:
The function f is defined for all positive integers n as $$f(n)= \frac{n}{n+1}$$

 Quantity A Quantity B f(1) × f(2) f(2) × f(3)

A) Quantity A is greater.
B) Quantity B is greater.
C) The two quantities are equal.
D) The relationship cannot be determined from the information given.

QUANTITY A
f(1) x f(2) $$=\frac{1}{1+1}$$x$$\frac{2}{2+1}$$

$$=\frac{1}{2}$$x$$\frac{2}{3}$$

$$= \frac{1}{3}$$

QUANTITY B
f(2) x f(3) $$=\frac{2}{2+1}$$x$$\frac{3}{3+1}$$

$$=\frac{2}{3}$$x$$\frac{3}{4}$$

$$= \frac{1}{2}$$

Since $$\frac{1}{2}>\frac{1}{3}$$, the correct answer is B

Cheers,
Brent
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Brent Hanneson – Creator of greenlighttestprep.com

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Re: The function f is defined for all positive integers n as f( [#permalink]  14 May 2019, 16:27
1
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Without doing much work at all, we can see that the larger n gets, the closer f(n) gets to 1. So higher numbers means greater value, even though it's always less than one.
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Re: The function f is defined for all positive integers n as f( [#permalink]  07 Jun 2019, 01:22
1
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Cancel f(2) from both the sides and then compare:
f(1)< f(3)
Re: The function f is defined for all positive integers n as f(   [#permalink] 07 Jun 2019, 01:22
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