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14 Jan 2022, 03:15
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C
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Difficulty:
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36% (02:10) correct
64%
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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]
Are You Up For the Challenge: 700 Level Questions
\(\frac{p}{p+q+r}+\frac{q}{p+q+s}+\frac{r}{p+r+s}+\frac{s}{q+r+s}\)?
A. [1,3]
B. (0,2)
C. [1,2]
D. (2,4)
E. (1,3]
Are You Up For the Challenge: 700 Level Questions
14 Jan 2022, 09:00
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Bunuel
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
27 Oct 2023, 22:26
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What if all variables (pqrs) are zero? It's mentioned non negative integer
