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16 Sep 2014, 01:10
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65%
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Question Stats:
54% (01:59) correct
46%
(02:05)
wrong
based on 164
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What is the value of the median of data set \(S =\{a - b, b - a, a + b\}\) ?
(1) The average (arithmetic mean) of set \(S\) is equal to \(a + b\).
(2) The range of data set \(S\) is equal to \(2b\).
(1) The average (arithmetic mean) of set \(S\) is equal to \(a + b\).
(2) The range of data set \(S\) is equal to \(2b\).
16 Sep 2014, 01:10
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Official Solution:
What is the value of the median of data set \(S =\{a - b, b - a, a + b\}\) ?
(1) The average (arithmetic mean) of set \(S\) is equal to \(a + b\).
The above implies that \(\frac{(a - b)+(b - a)+(a + b)}{3}=a+b\), which leads to \(a+b=0\). In this case, \(a - b = a - (-a) = 2a\) and \(b - a = (-a) - a = -2a\). Hence, the data set becomes \(S =\{2a, -2a, 0\}\).
• If \(a < 0\), then \(2a\) will be negative and \(-2a\) will be positive, making data set S in ascending order \(\{negative, 0, positive\}\).
• If \(a = 0\), then both \(2a\) and \(-2a\) will be 0, making data set S \(\{0, 0, 0\}\).
• If \(a > 0\), then \(2a\) will be positive and \(-2a\) will be negative, making data set S in ascending order \(\{negative, 0, positive\}\).
In any case, the median of \(S\) is 0. Sufficient.
(2) The range of set \(S\) is equal to \(2b\).
If \(a=b=0\), then the median of \(S\) is 0, but if \(a=0\) and \(b=1\), then the median of \(S\) is 1. Not sufficient.
Answer: A
What is the value of the median of data set \(S =\{a - b, b - a, a + b\}\) ?
(1) The average (arithmetic mean) of set \(S\) is equal to \(a + b\).
The above implies that \(\frac{(a - b)+(b - a)+(a + b)}{3}=a+b\), which leads to \(a+b=0\). In this case, \(a - b = a - (-a) = 2a\) and \(b - a = (-a) - a = -2a\). Hence, the data set becomes \(S =\{2a, -2a, 0\}\).
• If \(a < 0\), then \(2a\) will be negative and \(-2a\) will be positive, making data set S in ascending order \(\{negative, 0, positive\}\).
• If \(a = 0\), then both \(2a\) and \(-2a\) will be 0, making data set S \(\{0, 0, 0\}\).
• If \(a > 0\), then \(2a\) will be positive and \(-2a\) will be negative, making data set S in ascending order \(\{negative, 0, positive\}\).
In any case, the median of \(S\) is 0. Sufficient.
(2) The range of set \(S\) is equal to \(2b\).
If \(a=b=0\), then the median of \(S\) is 0, but if \(a=0\) and \(b=1\), then the median of \(S\) is 1. Not sufficient.
Answer: A
11 Feb 2017, 12:15
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Judging by this question, you can't assume that the set provided to you is in ascending order? I'd feel more comfortable removing that assumption if anyone can provide an OG question which has a set of unknown variables not provided in ascending order.
