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16 Sep 2014, 01:04
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What is the average (arithmetic mean) of set \(\{a, b, c\}\) ?
(1) The average (arithmetic mean) of set \(\{a + b, b + c, c + a\}\) is 30
(2) The average (arithmetic mean) of set \(\{a - b, b - c, c - a\}\) is 0
(1) The average (arithmetic mean) of set \(\{a + b, b + c, c + a\}\) is 30
(2) The average (arithmetic mean) of set \(\{a - b, b - c, c - a\}\) is 0
16 Sep 2014, 01:04
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Official Solution:
What is the mean of set \(\{a, b, c\}\) ?
The mean of set \(\{a, b, c\}\) is given by \(\frac{a + b + c}{3}\).
(1) The mean of set \(\{a + b, b + c, c + a\}\) is 30.
From this, we can derive:
\(\frac{(a + b) + (b + c) + (c + a)}{3} = 30\)
Which simplifies to:
\(\frac{2(a + b + c)}{3} = 30\)
And therefore:
\(\frac{a + b + c}{3} = 15\).
Sufficient.
(2) The mean of set \(\{a - b, b - c, c - a\}\) is 0:
The mean of \(\{a - b, b - c, c - a\}\) will always be 0 since \(\frac{(a - b) + (b - c) + (c - a)}{3} = \frac{0}{3} = 0\). Hence, the information in this statement does not add value.
Not Sufficient.
Answer: A
What is the mean of set \(\{a, b, c\}\) ?
The mean of set \(\{a, b, c\}\) is given by \(\frac{a + b + c}{3}\).
(1) The mean of set \(\{a + b, b + c, c + a\}\) is 30.
From this, we can derive:
\(\frac{(a + b) + (b + c) + (c + a)}{3} = 30\)
Which simplifies to:
\(\frac{2(a + b + c)}{3} = 30\)
And therefore:
\(\frac{a + b + c}{3} = 15\).
Sufficient.
(2) The mean of set \(\{a - b, b - c, c - a\}\) is 0:
The mean of \(\{a - b, b - c, c - a\}\) will always be 0 since \(\frac{(a - b) + (b - c) + (c - a)}{3} = \frac{0}{3} = 0\). Hence, the information in this statement does not add value.
Not Sufficient.
Answer: A
