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m>0,n>0,k>0

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Carcass
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m>0,n>0,k>0 [#permalink] New post   14 May 2021, 10:08
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\(m>0,n>0,k>0\)


Quantity A
Quantity B
\(m + \frac{1}{n+\frac{1}{k}}\)
\(\frac{mnk++m+k}{nk+1 }\)



A)The quantity in Column A is greater.
B)The quantity in Column B is greater.
C)The two quantities are equal.
D)The relationship cannot be determined from the information given.
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C
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Re: m>0,n>0,k>0 [#permalink] New post   14 May 2021, 22:56
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Carcass wrote:
\(m>0,n>0,k>0\)


Quantity A
Quantity B
\(m + \frac{1}{n+\frac{1}{k}}\)
\(\frac{mnk+m+k}{nk+1 }\)



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


Col. A: \(m + \frac{1}{n+\frac{1}{k}}\)

Col. B: \(\frac{mnk+m+k}{nk+1 }\)

Col. A: \(m + \frac{1}{\frac{nk+1}{k}}\)

Col. B: \(\frac{mnk+m+k}{nk+1 }\)

Col. A: \(m + \frac{k}{nk+1}\)

Col. B: \(\frac{mnk+m+k}{nk+1 }\)

Col. A: \(\frac{mnk+m+k}{nk+1 }\)

Col. B: \(\frac{mnk+m+k}{nk+1 }\)

Hence, option C
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Re: m>0,n>0,k>0 [#permalink] New post   13 Jun 2022, 16:18
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m>0,n>0,k>0 [#permalink] New post   13 Jun 2022, 21:58
Put quantity A in a rational fraction form:
\(\frac{mnk+m}{k}+1*\frac{k}{nk+1}\)
\(\frac{mnk+m+k}{k}*\frac{k}{nk+1}\)
\(\frac{mnk+m+k}{nk+1}\)

which's equivelant to quantity B

Answer is (C)
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m>0,n>0,k>0 [#permalink]
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