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If p, q, r, and s are non negative numbers. Which of the following bes

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Bunuel
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If p, q, r, and s are non negative numbers. Which of the following bes [#permalink] New post   14 Jan 2022, 03:15
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If p, q, r, and s are non negative numbers. Which of the following best describes the range of

\(\frac{p}{p+q+r}+\frac{q}{p+q+s}+\frac{r}{p+r+s}+\frac{s}{q+r+s}\)?

A. [1,3]
B. (0,2)
C. [1,2]
D. (2,4)
E. (1,3]



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C
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JerryAtDreamScore
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Re: If p, q, r, and s are non negative numbers. Which of the following bes [#permalink] New post   14 Jan 2022, 09:00
Bunuel wrote:
If p, q, r, and s are nonnegative numbers. Which of the following best describes the range of

\(\frac{p}{p+q+r}+\frac{q}{p+q+s}+\frac{r}{p+r+s}+\frac{s}{q+r+s}\)?

A. [1,3]
B. (0,2)
C. [1,2]
D. (2,4)
E. (1,3]



We can try a couple of different extreme cases to maximize/minimize the expression.

We can try {1, 1, 0, 0} to get \(0.5 + 0.5 + 0 + 0 = 1\)

Next, {1, 1, 1, 0} gives us \(\frac{1}{3} + \frac{1}{2} + \frac{1}{2} + 0\). Nothing interesting so we move on.

Then we can attempt to maximize this value. Start with p = 1, q = 0, r = 0 to make the first term as big as possible. Next, we can let s = 1 as well to make the last term as big as possible. Putting this together we have a total of 2. Then the range is between 1 and 2, inclusive.

Answer: C
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DrAnkita91
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Re: If p, q, r, and s are non negative numbers. Which of the following bes [#permalink] New post   27 Oct 2023, 22:26
What if all variables (pqrs) are zero? It's mentioned non negative integer
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Re: If p, q, r, and s are non negative numbers. Which of the following bes [#permalink] New post   27 Oct 2023, 23:36
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DrAnkita91 wrote:
What if all variables (pqrs) are zero? It's mentioned non negative integer


They cannot be zero because the each of the fractions in the equation will be undefined (with zero as denominator)

Hope that helps.

Posted from my mobile device
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Re: If p, q, r, and s are non negative numbers. Which of the following bes [#permalink] New post   28 Oct 2023, 04:03
Palpable wrote:
DrAnkita91 wrote:
What if all variables (pqrs) are zero? It's mentioned non negative integer


They cannot be zero because the each of the fractions in the equation will be undefined (with zero as denominator)

Hope that helps.

Posted from my mobile device


Thank you for the response :)
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Re: If p, q, r, and s are non negative numbers. Which of the following bes [#permalink]
28 Oct 2023, 04:03
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