A list kept at Town Hall contains that town's average daily temperatur

Statement 1: The median temperature is 73.5
With even number of values, the median is in decimals. Eg: 2,3,4,5. Median=3.5
Sufficient
Statement 2:The sum of the average daily temperatures is divisible by 3: No use. If the sum of avg daily temparatures is 60,90 or 120 it wont tell us how many days are there in the month. Insufficient.

Answer A

Statement 1: The median temperature is 73.5.

Average Daily Temperatures are Integers so if there were 31 days then 16th Reading in ascending/descending of temperature would have been the Median which would have been Integer

But Since Median is in Decimal therefore certainly the Number of Days must be 30 as in that case the Median will be the average of 15th and 16th Reading of temperature written in ascending/descending order

Hence, SUFFICIENT

Statement 2: The sum of the average daily temperatures is divisible by 3.

Sum of the temperatures of 30 days as well as for 31 days can be divisible by 3 so it doesn't provide any information which can ascertain the number of days in month

Hence, NOT SUFFICIENT

Answer: Option

My work.

Option A: Sufficient.

All the numbers in the list are integers. No intergers when added give any decimal result. Hence the Median has to be something that was divided by 2. (Say 72 and 77, 73 and 74, 70, and 77)

So the series goes...................(14 numbers) 70, 77 (14 numbers)= hence 73.5. (So number of days=30)

If the number of days were 31, then 30 numbers would have been crossed off and we will be left with one value, which is definitely an integer.

Option B: Not sufficient

hence option A the answer.

Statement 1:
Sufficient. If the median of a set of integer is NOT an integer itself, then the set must have an even number of components. Therefore 30 days.

Statement 2:
Insufficient. Let's assume the average daily temperature was 9 Fahrenheit. If it was a month with 30 days: 30*9=270 is divisible by 3. If it was a month with 31 days: 31*9=279 which is divisible by 3.

Answer A

The median can only be either an integer or a fraction ending with .5
when we have odd number of integers(31); the central value(median) will be the n+1/2th(16th) term hence it'll be an integer
If we have even number of intergers(30); the central value(median) will be the mean of 2 integers hence if div by 2 will be an int or else value ending with .5
St 1 - tem = 73.5
again, If we have even number of intergers(30); the central value(median) will be the mean of 2 integers hence if div by 2 will be an int or else value ending with .5
Suff

St2
The sum of the average daily temperatures is divisible by 3.
doesnt tell us anything.

Answer - A

MANHATTAN GMAT OFFICIAL SOLUTION:

This question is really about evens and odds. A list of values contains either 30 or 31 elements. Does the list have an even or an odd number of elements?

(1) SUFFICIENT: Since every item in the list is an integer, the only way for the median to be a noninteger is if there is an even number of items in the list (and therefore no middle term— in this case, the median is calculated as the average of the two middle terms). Therefore, the month must have an even number of days, so it must contain 30 days.

(2) INSUFFICIENT: The sum of either 30 or 31 values is divisible by 3. Since there are no constraints on what the temperatures might be, it is perfectly possible to have a list of 30 values or a list of 31 values that add up to a multiple of 3. For example, if the temperature every day were 60 degrees, the sum of the temperatures would be divisible by 3 no matter how many days the month contained.

The correct answer is (A).
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Clearly A is sufficient . Since median is not integer means the set consist of even number of elements.

For B, sum divisible by 3 is not enough

If it is Feb it have 28 days also even????

Posted from my mobile device

Thank you for the explanation.

However one thing i couldnt understand is that where is it mentioned that the temperatures are consecutive integers. The concept of median not being an integer for even no. of numbers is true only for consecutive integers.
it would be of great help if you could share your views on the same.

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