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19 Oct 2021, 08:15
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D
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
55%
(hard)
Question Stats:
60% (02:01) correct
40%
(02:00)
wrong
based on 243
sessions
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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?
1, 4, a, 5, b, 4
(A) 1.5
(B) 2
(C) 2.5
(D) 3
(E) 4
1, 4, a, 5, b, 4
(A) 1.5
(B) 2
(C) 2.5
(D) 3
(E) 4
19 Oct 2021, 11:37
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Bunuel
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
Answer: D
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General Discussion
19 Oct 2021, 16:42
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doesn’t average of values above mean the average of a and b?
sorry for the semantics but the actual list of all the values is below, not above.
sorry for the semantics but the actual list of all the values is below, not above.
