The number of elements in set K is an odd number. The minimum value of

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?

I spent a lot of time to deduce the reasoning of this problem.

Here is the breakdown.

Based on the information, we know that there would be odd number of terms.

Now let's try to identify the corner cases :
Number of elements under consideration is 13, hence corner cases would be 11, 15 (next available number of terms)

St. 1 => The total average of elements in set K is greater than 37

So, for 11 terms the minimum sum should be greater than (11*37) --> 407

However, if the max(Sum) of elements falls short of 407 then the minimum number of terms is greater than 11 ---> 13,15,17 - whatever
max(Sum) for 11 terms is = 22(1) + 37(5) + 40(5) = 407

However, since it's not more than 407, we can conclude number of elements in set is greater than 11.


Hence, A is sufficient.

Are we to assume that the elements of integers? Where is this stated?

1. No, we are not assuming the the terms are integers.

2. The wording of the question is bad, so I'd suggest ignoring it.

3. Pure algebraic questions are no longer a part of the DS syllabus of the GMAT.

DS questions in GMAT Focus encompass various types of word problems, such as:

• Word Problems
• Work Problems
• Distance Problems
• Mixture Problems
• Percent and Interest Problems
• Overlapping Sets Problems
• Statistics Problems
• Combination and Probability Problems

While these questions may involve or necessitate knowledge of algebra, arithmetic, inequalities, etc., they will always be presented in the form of word problems. You won’t encounter pure "algebra" questions like, "Is x > y?" or "A positive integer n has two prime factors..."

Check GMAT Syllabus for Focus Edition

You can also visit the Data Sufficiency forum and filter questions by OG 2024-2025, GMAT Prep (Focus), and Data Insights Review 2024-2025 sources to see the types of questions currently tested on the GMAT.

So, you can ignore this question.

Hope it helps.­