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If a and b are both integers greater than 0 and the average (arithmeti
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03 Nov 2021, 07:21
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If a and b are both integers greater than 0 and the average (arithmetic mean) of the values above is 3, which of the following is a possible value for the median?
Re: If a and b are both integers greater than 0 and the average (arithmeti
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03 Nov 2021, 08:47
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Carcass wrote:
If a and b are both integers greater than 0 and the average (arithmetic mean) of the values above is 3, which of the following is a possible value for the median?
1, 4, a, 5, b, 4
(A) 1.5 (B) 2 (C) 2.5 (D) 3 (E) 4
The average (arithmetic mean) of the values above is 3
So, we can write: \(\frac{1 + 4 + a + 5 + b + 4}{6} = 3\)
Multiply both sides of the equation by \(6\) to get: \(1 + 4 + a + 5 + b + 4 = 18\)
Simplify: to get: \(a + b + 14 = 18\)
Subtract \(14\) from both sides: \(a + b = 4\)
Since we're told \(a\) and \(b\) are POSITIVE integers, there are only two possible pairs of values for \(a\) and \(b\). Let's examine each possible case....
Case i: The two numbers could be 1 and 3, in which case the six numbers (when displayed in ascending order) are {1, 1, 3, 4, 4, 5} In this case, the median = 3.5 Since 3.5 does not appear among the answer choices, we'll check case ii
Case ii: The two numbers could be 2 and 2, in which case the six numbers (when displayed in ascending order) are {1, 2, 2, 4, 4, 5} In this case, the median = 3
Re: If a and b are both integers greater than 0 and the average (arithmeti
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18 Jul 2024, 22:25
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Re: If a and b are both integers greater than 0 and the average (arithmeti [#permalink]