How many 5 existed in the 11 numbers?

How could the answer be B.

Median of 11 numbers is 5 doesn't confirm how many 5's do we have.

We could have numbers in the form of

1. 5,5,5,5,5,5,5,5,5,5,5
2. 1,2,3,4,5,6,7,8,9,10,11
3. 0,0,0,0,0,5,6,7,8,9,10,11

and so on.

Kindly confirm if the correct answer you mentioned is actually correct.

I read the question as asking, "How many 5's are in the set of 11 numbers?"
It's the only way I could make sense of the "how many" part.


Target question: How many 5's are in the set of 11 numbers?

Statement 1: The average (arithmetic mean) of the 11 numbers is 5
This statement doesn't FEEL sufficient, so I'll TEST some cases.
There are several sets of numbers that satisfy statement 1. Here are two:
Case a: {5,5,5,5,5,5,5,5,5,5,5} in which case there are ELEVEN 5's in the set
Case b: {0,1,2,3,4,5,6,7,8,9,10} in which case there is ONE 5 in the set
Since we cannot answer the target question with certainty, statement 1 is NOT SUFFICIENT

Aside: For more on this idea of plugging in values when a statement doesn't feel sufficient, you can read my article: https://www.gmatprepnow.com/articles/dat ... lug-values

Statement 2: The median of the 11 numbers is 5
There are several sets of numbers that satisfy statement 2. Here are two:
Case a: {5,5,5,5,5,5,5,5,5,5,5} in which case there are ELEVEN 5's in the set
Case b: {0,1,2,3,4,5,6,7,8,9,10} in which case there is ONE 5 in the set
Since we cannot answer the target question with certainty, statement 2 is NOT SUFFICIENT

Statements 1 and 2 combined
There are several sets of numbers that satisfy BOTH statements. Here are two:
Case a: {5,5,5,5,5,5,5,5,5,5,5} in which case there are ELEVEN 5's in the set
Case b: {0,1,2,3,4,5,6,7,8,9,10} in which case there is ONE 5 in the set
Since we cannot answer the target question with certainty, the combined statements are NOT SUFFICIENT

Answer =

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B?

I got the answer as E.

Median of 5 doesn mean only one 5 should be there :
--> 00011555666
--> 01234567899

It can have more than one 5 also.

I didn't get this, I assume the problem should specify that the numbers are in a set (and therefore distinct).

Under the assumption that the elements are in a set:

1) The average (arithmetic mean) of the 11 numbers is 5

No information about the distribution of the numbers, as long as the sum is 55.

Insufficient

2) The median of the 11 numbers is 5

There is an odd number of elements in the set, therefore the middle number is selected without average calculation.
Each element in the set is distinct.
We must have a 5 since the median is 5.

There is one 5 in the set

Sufficient

1) The average (arithmetic mean) of the 11 numbers is 5
There could be two possibilities:-
a) all numbers equal to 5
b) numbers are either >, < or = 5

Not Sufficient.

2) The median of the 11 numbers is 5
there is one 5 in the set, but we dont know about the other numbers. those can be equal to 5 or numbers to the left can be <5 and numbers to the right can be >5

Not sufficient.

Combining both statements is not sufficient.

Answer must be E

But DAllison2016 ..
How did you decide that all numbers are distinct. It is not specified in the question ?

If we modify the original condition and the question, since we have 11 numbers, the median exists in these numbers. Hence, if we look at the condition 2), since the median is 5, 5 is always a part of 11 numbers. The answer is yes and the answer is B.


- Forget conventional ways of solving math questions. In DS, Variable approach is the easiest and quickest way to find the answer without actually solving the problem. Remember equal number of variables and independent equations ensures a solution.

Q is How many 5 existed in the 11 numbers?
not that if 5 exists in the 11 numbers.

Bunuel : Can you please give our input.

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