GMAT Club Olympics 2024 (Day 5): What is the median age of athletes

Question

What is the median age of the athletes in Team A?

(1) No athlete's age in Team A is less than the average (arithmetic mean) age of the athletes in Team A.

(2) The mode age for the athletes in Team A is 21 years.

A. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question asked.
B. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question asked.
C. BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficient to answer the question asked.
D. EACH statement ALONE is sufficient to answer the question asked.
E. Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data specific to the problem are needed.

Bunuel · Accepted Answer

GMAT Club Official Explanation:

What is the median age of the athletes in Team A?

(1) No athlete's age in Team A is less than the average (arithmetic mean) age of the athletes in Team A.

Since no athlete's age is less than the average, it follows that no athlete's age is more than the average, suggesting that all ages in the team are the same. This implies that the average equals the median. However, the actual values remain unknown, so this statement is insufficient.

(2) The mode age for the athletes in Team A is 21 years.

The mode is the number that occurs the most frequently in a list. Hence, this statement simply says that the most common age in the team is 21 years. However, this does not mean that the median is also 21 years. For example, consider the list {21, 21, 22, 23, 24}, which has a mode of 21 but a median of 22. Therefore, this statement is insufficient.

(1)+(2) Since from (1) all ages in the team are the same, and from (2) the most frequent age is 21, it must be true that all athletes are 21 years old, making the median age also 21 years. Sufficient.

Answer: C.

xhym · Answer

Statement 1

If no athlete's age is less than the average, that means that there can be no athlete's age which is higher than the average either. Therefore, all age's are the same BUT we do not know what that age is.

-> Statement 1 alone is not sufficient.

Statement 2

If the mode is 21, that is the number that appears most often but we cannot know if it is the median (i.e., if the ages are 21, 21, 23, 24, 25 then the median would be 23 even though the mode is 21)

-> Statement 2 alone is not sufficient.

Both statements combined

If no age can differ (statement 1), and the mode is 21 (statement 2), then that means that everyone must be 21 years old!

-> Both statements combined are sufficient.

Answer is  C. BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficient to answer the question asked.

captain0612 · Answer

Choice C

Find median age of team A.

Statement 1:

No team member age is less than the average => all team member ages equal
But we don't know what that age is. Hence  Not Sufficient

Statement 2:

Mode of age for athletes in Team A = 21 years.
But we don't the total number of athletes to trace the median. Hence  Not Sufficient

Statement 1 and Statement 2:

From 1 and 2:
we can say that all atheletes in Team are of same age, and the age = 21 ( since mode of the athletes age is 21)
 Sufficient

Hence C

DG1989 · Answer

What is the median age of the athletes in Team A?

Statement 1:    No athlete's age in Team A is less than the average (arithmetic mean) age of the athletes in Team A. 
 Solution:  Since no athlete's age is less than the average age, the minimum age is the average age and the age of all the athletes is the same. Only then the above condition can be met. The median age will then be the average age. However, this information alone doesn't tell us the median age.
  INSUFFICIENT

Statement 2:    The mode age for the athletes in Team A is 21 years. 
Mode is the most frequently occurring value in a list. This means, most athletes are 21 years old. However, we don't know the distribution or the total number of athletes on the team.
Hence we cannot determine the median age just with this information alone.
  INSUFFICIENT

Combining Statements 1 and 2,
Mode = 21
Average age = Median Age
Age is the same for all the athletes.
Hence the median age = 21
  SUFFICIENT

The correct answer is C

OmerKor · Answer

Ok, We need to fight back if we want to WIN.
Green team, it's time to wake up!
Fifth Day, Here we go:
Let's get started with our explanation for this topic:

Glance - the Question:  
 Question:  We have here kind of statistics question.
Illustrate the given information to clarify the story.

Rephrase - Reading and Understanding the question:  
No Given information.
  :  We are asked what is ve value of the median of team A ?
ok, if we have a 1 value = Sufficient. if we can come up with 2 values = Insufficient.

Solve:  
 (1)  that means All ages are the same.
2 scenarios:
A)   19 , 19 , 19 , 19   - median = 19
B)   21 , 21 , 21 , 21   - median = 21 
 Insufficient

(2)  mode=21
2 scenarios:
A)   19 , 20 , 21 , 21   - median = 20.5
B)   19 , 21 , 21 , 21   - median = 21 
 Insufficient

(1)+(2)
if the mode is 21. all ages must be 21. so the median is 21.
B)   21 , 21 , 21 , 21 ...  - median = 21 
  Sufficient - C

THE END  
I hope you liked the explanation, I have tried my best here.
Let me know if you have any questions about this question or my explanation.
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VivekSri · Answer

To determine the median age of the athletes in Team A.

Statement (1): No athlete's age in Team A is less than the average (arithmetic mean) age of the athletes in Team A.

All athletes in Team A have ages that are at least equal to the average age of the team. Therefore, if the average age is m, every athlete's age is ≥m . Without knowing the actual ages or their distribution, we cannot determine the exact median age. Therefore, Statement (1) alone is not sufficient to determine the median age.

Statement (2): The mode age for the athletes in Team A is 21 years.

This statement tells us that the most frequently occuring age in Team A is 21 years. Mode does not provide enough information about the median, as distribution is not known.Therefore, Statement (2) alone is not sufficient to determine the median age.

Combining Statements (1) and (2):

If we combine both statements:
Given no athlete age is less than average, the average age must be at least 21 years as most frequent is 21. Since all ages are at least the average, and the most frequent age is 21, the median age must also be 21.  if 21 is the mode and all ages are at least 21, then 21 must be the median to satisfy the conditions given.

Thus, combining the two statements gives us enough information to determine that the median age is 21.

Therefore, the correct answer is: C

d_patel · Answer

We need to find median age of the athletes in Team A?

Statement-1 
No athlete's age in Team A is less than the average (arithmetic mean) age of the athletes in Team A.

This is a special case. It only happens when all of the observations have same value.
Like example,  {2,2,2,2}  has mean of  2 . 
Now, if we increase or decrease one of the observation, mean value will change and premise that no observation has value less than average age of the athletes in team-A  will no longer hold true.

But we cannot tell median age of athletes as no value for observation or mean is provided in statement. 
Could be anything.

Statement-1 is not sufficient

Statement-2 
The mode age for the athletes in Team A is 21 years.

We cannot guess median from this. Multiple observations can have mode of 21 but median different.
For example,

case-1  
 {21, 21, 24, 25, 27} 
Here mode= 21  but median= 24

case-1  
 {21, 21, 23, 25, 27} 
Here mode= 21  but median= 23

Statement-2 is not sufficient

Combining Statement-1 and Statement-2, 
We know that all ages are same from statement-1.
And we know that mode is 21.

So, all the players are 21 years old. 
Ex.  {21, 21}  or  {21, 21, 21}

This means median will always be  21 .

Combination of statements are sufficient.

Final answer -  C

Lizaza · Answer

The median age is the middle age if all players are arranged from youngest to oldest.

(1) 
If no age is less than the average, it means that all he athletes have the same age.
However, given we don't actually know this number, this is  inufficient by itself.

(2) 
While the mode is the most frequent number, the median doesn't have to be connected with it. 
For instance, let's say we have only one athlete of each age and two aged 21. Indeed, the mode is 21, but nothing is known of the median.
Therefore, this is  insuficient by itself.

(1) + (2) 
Together, we know that all athletes are aged the same and the mode is 21.
This effectively leaves no other option apart from the median being 21 as well as the average and the mode, which means the conditions are  sufficient together.

The correct answer is C.

anish0953 · Answer

Statement (1):  No athlete's age in Team A is less than the average (arithmetic mean) age of the athletes in Team A.

Statement (2):  The mode age for the athletes in Team A is 21 years.

Given both statements, we must ensure:

No athlete's age is less than the mean age. 
 The mode age (most frequently occurring age) is 21.  
 Example 1

Suppose there are 5 athletes in Team A.

Ages:   
 Mean: 21+21+21+21+21/5=21 
 Median: The middle value is 21. 
 No age is below the mean.  
 This satisfies both statements and the median is 21.

Example 2

Suppose there are 6 athletes in Team A.

Ages:   
 Mean: 21+21+21+21+23+23/6>21 
 Median: The average of the 3rd and 4th values is 21+21/2​=21. 
 No age is below the mean.  
 This satisfies both statements and the median is 21.

Conclusion

Given the condition that no athlete's age is less than the average age, the ages must all be the same if the mode is 21 and all ages are at least the mean. Therefore, in any valid scenario satisfying both statements, all athletes are 21 years old, and thus, the median age must be 21.

So, the correct answer is indeed: C. BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficient to answer the question asked.

GMAT Club Olympics 2024 (Day 5): What is the median age of athletes

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