The number of elements in set K is an odd number. The minimum value of set K is 22, the maximum value is 40, and the median value is 37. Is the number of elements in set K at least 13?

1) The total average of elements in set K is greater than 37.
2) The sum of the elements in set K is greater than 407.
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Can somebody help with how A is sufficient?

We have a set {22,_ _ _, 37, _ _ _ ,40}. We need to check minimum and maximum scenarios to calculate the number of elements in the set.
Currently we have 3 elements and according to the scenario we can add elements in pairs (since the number of elements is odd): one between 22 to 37 and the other between 37 to 40 inclusive.

1) The total average of elements in set K is greater than 37.
22 is 15 less than 37. 40 is only 3 above 37.We need to add elements that will raise the average to 37. In order to get the minimum elements scenario we will add pairs with maximum value (37,40). We get a set {22,37,37,37,37,37,40,40,40,40,40}. That's 11 elements, but we need average greater than 37, so we need an additional pair of elements which makes it at least 13 elements. Sufficient.

2) The sum of the elements in set K is greater than 407.
The minimum scenario from the previous statement fit for this statements as well. Again we need a sum which is greater than 407, which makes it at least 13 elements. Sufficient.

The answer is D.

By the way I selected E, since I missed the part of the "greater". LOL

Statement 2- The sum of the elements in set K is greater than 407
min =22, max=40,median =37 , number of elements =odd
Since , sum > 407, let it be 408
Sample set - { 22,37,37,37,37, 37,40,40,40,40,40} This set contains 11 elements. But sum=407
Therefore , set has to be greater that 11 . So it is at least 13.




Statement 1-The total average of elements in set K is smaller than 37
min =22, max=40,median =37 , number of elements =odd
Sample set 1- { 22,37,40}
average=33 , but the set has 3 elements ; hence NO

Sample set 1- { 22,37,37,37,37,37,37,37,37,37,37,37,40} [No. of elements =13]
average=36.07 , hence yes

Statement 1 : insufficient

Hence, B

But OA is D.

Am I missing something?

They are not identical. The condition first is changed to opposite.