2, 4, 5, 5, 9, m For the list of numbers above, what is the median?

1: since there are 6 numbers, the median will be the average of the 3rd and 4th numbers. For this to be an integer, the 4th number - 3rd number has to be even. If \(m>5,\) the median is 5. If \(m < 4\) the median is 4.5. If \(4\leq{m}\leq{5}\) the median is \(\frac{m+5}{2}\). The only integer is 5. Therefore, the median is 5. Sufficient.
2: The median is 5. sufficient.
Both are sufficient: D.

MANHATTAN GMAT OFFICIAL SOLUTION:

To find the median of a set of numbers, we line them up in order of value. The question of interest to us is “Where is m relative to the other values?” This set has 6 values, an even number of terms, so the median is the average of the two middle terms.
There are three scenarios:

If m ≤ 4, then the two middle terms are 4 and 5, and the median is 4.5.

If 4 < m < 5, then the two middle terms are m and 5, and the median is (m + 5)/2.

If m ≥ 5, then the two middle terms are 5 and 5, and the median is 5.

(1) SUFFICIENT: For the case where 4 < m < 5, the median is (m + 5)/2= (non-integer + odd)/2 = non-integer. Thus, if the median is an integer, it must be 5.

(2) If m = 8, then m ≥ 5, and the median is 5.

The correct answer is D.

Statement 1
This statement is basically just telling us that because the median is an integer you cannot have a value in between 5 and 5- which would affect which numbers are calculated to find the median. Like if you have 5.5 then 5 +5.5 /2 would be the median but that cannot be the case so "m" has to be larger or greater than 5- in either case 5 +5 /2 is the median

Suff

Statement2

Clearly Suff


D

statement 2 is easy, let's start with 2.

(2) median, the middle number when numbers are arranged in ascending order. For even number of elements take the mean of two elements in the middle of the list.

2 4 5 5 8 9, definitely median= (5+5)/2 Sufficient.

(1) The median is an integer for the listed 6 numbers-
2 4 5 5 9 m, we see that one of the 5 is coming in the middle for any given possible position of m,

m24559, 2m4559, 245m59 etc.

So the median is (5+any number from the list)/2= Integer. only possible when (5+5)/2 = 5, Integer. So sufficient.
even if we put m=7, 245579, median is 5.

Either statement sufficient.

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