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

Question

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.

achuepnlx · Answer

Can somebody help with how A is sufficient?

kolodits · Answer

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

Kurtosis · Answer

Number of elements = odd
Min = 22, Median = 37 and Max = 40

Question: Number of elements >= 13?

St1: Average > 37
Our goal is to find the minimum number of elements for which the max possible average is greater than 37.
Let's assume the number of elements = 13
Set = {22, 37, 37, 37, 37, 37, 37, 40, 40, 40, 40, 40, 40}
Average = 37 + (-15 + 18)/13 = 37 + 3/13 > 37
So max possible average for 13 elements just crosses 37 and hence the number of elements must be atleast 13. If you lower the values we need more number of elements for the average to cross 37.
Sufficient

St2: Sum > 407
Lets consider only 11 elements and maximize the value of the set
22 + 37*5 + 40*5 = 22 + 185 + 200 = 407 
Since sum > 407, the set should have one more element. But the set contain odd number of elements. 
Hence number of elements in the set must be atleast 13
Sufficient

Answer: D

adityagupta2102 · Answer

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}  
average=36.07 , hence yes

Statement 1 : insufficient

Hence, B

But OA is D.

Am I missing something?

vikmahajan97 · Answer

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.

megadave · Answer

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

Bunuel · Answer

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.

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

Prep Toolkit

Top 5 GMAT Debrief Videos

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards