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Which of the following equals the average of x and 1/x ?

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Bunuel
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Which of the following equals the average of x and 1/x ? [#permalink] New post   09 Apr 2019, 04:01
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A
B
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E

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86% (00:53) correct 14% (01:52) wrong based on 50 sessions
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Which of the following equals the average of x and 1/x ?

(A) (x + 2)/x

(B) (x^2 + 1)/(2x)

(C) (x + 1)/x^2

(D) (2x^2 + 1)/x

(E) (x + 1)/x
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B
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Which of the following equals the average of x and 1/x ? [#permalink] New post   09 Apr 2019, 04:08
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Bunuel wrote:
Which of the following equals the average of x and 1/x ?

(A) (x + 2)/x

(B) (x^2 + 1)/(2x)

(C) (x + 1)/x^2

(D) (2x^2 + 1)/x

(E) (x + 1)/x


the average of x and 1/x \(= [x+(1/x)]/2 = \frac{{x^2 + 1}}{2x}\)

Answer: Option B
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Re: Which of the following equals the average of x and 1/x ? [#permalink] New post   09 Apr 2019, 04:34
\(\frac{x + \frac{1}{x}}{2}\)

\(\frac{x^2 + 1}{2x}\)

OPTION: B
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Re: Which of the following equals the average of x and 1/x ? [#permalink] New post   09 Apr 2019, 04:52
Bunuel wrote:
Which of the following equals the average of x and 1/x ?

(A) (x + 2)/x

(B) (x^2 + 1)/(2x)

(C) (x + 1)/x^2

(D) (2x^2 + 1)/x

(E) (x + 1)/x


the average of x and 1/x ==> \((x+(1/x))/2\) ===> \((x^2 + 1)/(2x)\)

Hence B
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Re: Which of the following equals the average of x and 1/x ? [#permalink] New post   09 Apr 2019, 08:14
sum of terms = x+1/x = (x^2+1)/x

number of terms = 2

So average = 1/2*((x^2+1)/x )


IMO B
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Re: Which of the following equals the average of x and 1/x ? [#permalink] New post   10 Apr 2019, 18:18
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Bunuel wrote:
Which of the following equals the average of x and 1/x ?

(A) (x + 2)/x

(B) (x^2 + 1)/(2x)

(C) (x + 1)/x^2

(D) (2x^2 + 1)/x

(E) (x + 1)/x


The average of x and 1/x is:

(x + 1/x)/2 = (x^2/x + 1/x)/2 = [(x^2 + 1)/x]/2 = (x^2 + 1)/(2x)

Answer: B
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Re: Which of the following equals the average of x and 1/x ? [#permalink]
10 Apr 2019, 18:18
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