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

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Math Expert
Joined: 02 Sep 2009
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2, 4, 5, 5, 9, m For the list of numbers above, what is the median?  [#permalink]

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10 Jun 2015, 04:09
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45% (medium)

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63% (01:25) correct 37% (01:08) wrong based on 182 sessions

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

(1) The median is an integer.
(2) m = 8

Kudos for a correct solution.

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Re: 2, 4, 5, 5, 9, m For the list of numbers above, what is the median?  [#permalink]

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10 Jun 2015, 09:12
2
Answer should be D (Either statements)

This set of numbers is an even spaced set of numbers, therefore the median is the average of the two middle numbers.

However
1) says median is an integer -> this means that m > 4, because if m < 5 the median would be 4,5, however this is not an integer. as the average between 5 and 5 is 5. -> sufficient.
2) says m = 8. This makes the median still 5, since the two middle numbers are 5 - > Sufficient.
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2, 4, 5, 5, 9, m For the list of numbers above, what is the median?  [#permalink]

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10 Jun 2015, 10:57
1
Bunuel wrote:
2, 4, 5, 5, 9, m
For the list of numbers above, what is the median?

(1) The median is an integer.
(2) m = 8

Kudos for a correct solution.

Here the value of median depends on value of m.

Case 1: If m > 5 then Median must be (5+5)/2 = 5
Case 2: If m = 5 then Median must be (5+5)/2 = 5
Case 3: If 4 < m < 5 then Median will be (5+x)/2 which will be a Non-Integer value
Case 4: If m < 4 then Median will be (5+4)/2 = 4.5

Statement 1: The median is an integer.

Only Case 1 and Case 2 mentioned above are applicable and in each case median = 5

Hence, SUFFICIENT

Statement 2: m = 8

Case 1 is the only case applicable i.e. Median = 5

Hence, SUFFICIENT

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Re: 2, 4, 5, 5, 9, m For the list of numbers above, what is the median?  [#permalink]

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12 Jun 2015, 00:52
Bunuel wrote:
2, 4, 5, 5, 9, m
For the list of numbers above, what is the median?

(1) The median is an integer.
(2) m = 8

Kudos for a correct solution.

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.
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Posts: 55773
Re: 2, 4, 5, 5, 9, m For the list of numbers above, what is the median?  [#permalink]

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15 Jun 2015, 05:23
Bunuel wrote:
2, 4, 5, 5, 9, m
For the list of numbers above, what is the median?

(1) The median is an integer.
(2) m = 8

Kudos for a correct solution.

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.
Attachment:

2015-06-15_1621.png [ 9.1 KiB | Viewed 2298 times ]

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.

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Re: 2, 4, 5, 5, 9, m For the list of numbers above, what is the median?  [#permalink]

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13 Jul 2017, 17:08
Bunuel wrote:
2, 4, 5, 5, 9, m
For the list of numbers above, what is the median?

(1) The median is an integer.
(2) m = 8

Kudos for a correct solution.

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
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Re: 2, 4, 5, 5, 9, m For the list of numbers above, what is the median?  [#permalink]

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20 May 2019, 17:45
Bunuel wrote:
2, 4, 5, 5, 9, m
For the list of numbers above, what is the median?

(1) The median is an integer.
(2) m = 8

Kudos for a correct solution.

(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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Re: 2, 4, 5, 5, 9, m For the list of numbers above, what is the median?   [#permalink] 20 May 2019, 17:45
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