If P is a set of integers, is the average of P equal to the median of

Question

If P is a set of integers, is the average of P equal to the median of P ?

(1.) There are an equal number of integers greater than and less than the median and average of Set P.

(2.) There are an odd number of integers in Set P

Bunuel · Answer

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.

NoeticImbecile · Answer

Hello, I understand this is out of syllabus but for the sake of conceptual clarity, why isn't S1 sufficient and why is S2 required? Thanks

francine8375 · Answer

I think the answer is wrong, it should be A, only (1) is sufficient.
Here is the explanation:

Statement (1) 
There are as many integers > the mean as < the mean.

Any point that splits a finite ordered list into equal “above” and “below” parts **must** coincide with its median. Hence the common value—namely the mean—**is** the median. 
- ⇒ **Mean = Median** 
- ⇒ (1) alone is **sufficient**.

---

Statement (2) 
Number of integers in P is odd.

Odd size alone doesn’t force symmetry of the data or equality of mean and median. 
- Example: P={1,2,4} has odd size, median = 2 but mean = 7/3 is not equal to 2. 
- ⇒ (2) is **not sufficient**.

---

Since (1) suffices and (2) does not, the correct choice is **(A)**.

quamhic · Answer

For me the correct answer is  E .

I worked with the following example:
P = { -2, -1, 2, 7, 9 }
Mean = 3
Median = 2

Of course, we can also prove the opposite:
P = { 1, 2, 3 }
Mean = 2
Median = 2

Let me know if I missed something. Thanks!

BadalDewani · Answer

in your eg, the numbers greater than mean are not equal to the numbers less than it

If P is a set of integers, is the average of P equal to the median of

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GMAT Data Sufficiency (DS) Questions

If P is a set of integers, is the average of P equal to the median of

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