gmatt1476 wrote:
Each of the five divisions of a certain company sent representatives to a conference. If the numbers of representatives sent by four of the divisions were 3, 4, 5, and 5, was the range of the numbers of representatives sent by the five divisions greater than 2 ?
(1) The median of the numbers of representatives sent by the five divisions was greater than the average (arithmetic mean) of these numbers.
(2) The median of the numbers of representatives sent by the five divisions was 4.
DS06110.01
Let integer x be the 5th number. The original question: Is R>2 ?
The range of the four known numbers is 5-3=2. The rephrased question: Is \(3\leq x\leq 5\) ?
1) We know that Me>A and can evaluate three possible cases.
Case 1: If \(x\leq 4\), then Me=4 and A=(17+x)/5.
4>(17+x)/5
x<3
The solution is x<3, which would give us a No answer to the rephrased question.
Case 2: If \(4<x\leq 5\), then Me=x.
x>(17+x)/5
4x>17
x>4.25
The solution is \(4.25<x\leq 5\), which would give us a Yes answer to the rephrased question.
Case 3: If x>5, then Me=5. We don't need to evaluate this case since we already have two different answers.
Thus, we can't get a definite answer to the rephrased question. \(\implies\)
Insufficient2) We know that Me=4, so \(x\leq 4\). If x is 4, then the answer to the rephrased question is Yes. However, if x is 1, then the answer to the rephrased question is No. Thus, we can't get a definite answer to the rephrased question. \(\implies\)
Insufficient1&2) Case 1 is the only valid case from statement 1). Thus, the answer to the rephrased question is a definite No. \(\implies\)
SufficientAnswer: C