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# If x is a positive integer greater than 1, which of the following has

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Math Expert
Joined: 02 Sep 2009
Posts: 49496
If x is a positive integer greater than 1, which of the following has  [#permalink]

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29 Jun 2018, 02:25
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87% (00:51) correct 13% (01:04) wrong based on 67 sessions

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If x is a positive integer greater than 1, which of the following has the greatest value?

A. $$\frac{1}{x}$$

B. $$\frac{1}{1+x}$$

C. $$\frac{x}{1+x}$$

D. $$\frac{x}{\frac{1}{1+x}}$$

E. $$\frac{x}{\frac{x}{1+x}}$$

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Posts: 627
Re: If x is a positive integer greater than 1, which of the following has  [#permalink]

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29 Jun 2018, 02:34
Bunuel wrote:
If x is a positive integer greater than 1, which of the following has the greatest value?

A. $$\frac{1}{x}$$

B. $$\frac{1}{1+x}$$

C. $$\frac{x}{1+x}$$

D. $$\frac{x}{\frac{1}{1+x}}$$

E. $$\frac{x}{\frac{x}{1+x}}$$

Since the answer must be true for any value of x, we'll pick an easy value and just calculate.
This is an Alternative approach.

Let's try the smallest possible value: 2.
Then (A) is 1/2, (B) is 1/3, (C) is 2/3, (D) is 2/(1/3) = 6, (E) is 2/(2/3) = 6/2 = 3.

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Re: If x is a positive integer greater than 1, which of the following has  [#permalink]

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29 Jun 2018, 07:28
Bunuel wrote:
If x is a positive integer greater than 1, which of the following has the greatest value?

A. $$\frac{1}{x}$$

B. $$\frac{1}{1+x}$$

C. $$\frac{x}{1+x}$$

D. $$\frac{x}{\frac{1}{1+x}}$$

E. $$\frac{x}{\frac{x}{1+x}}$$

Plugging in method fits this one.

In order to get the greatest value , keep the denominator smallest.

Note:
x is positive integer. x>1.

let the value of x be 2.

Option D gives us the greatest value as its denominator is the lowest among options.

Re: If x is a positive integer greater than 1, which of the following has &nbs [#permalink] 29 Jun 2018, 07:28
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# If x is a positive integer greater than 1, which of the following has

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