What is the value of n in the list above?

SOLUTION

n, 15, 12, 9, 20
What is the value of n in the list above?

(1) n> 12. n can be any number greater than 12. Not sufficient.
(2) The median of the numbers in the list is 13. We have a list of five (odd) numbers. The median of a set with odd number of elements is the middle element (when arranged in ascending/descending order). Since, no other number in the list is 13, then n must 13. Sufficient.

Answer: B.
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IMO B:
1) Not sufficient n can take any value above 12.
2) Sufficient: n=13. All are distinct numbers and 2 values are below 13 and 2 values are above 13.

Given list: k, n, 12, 6, 17

We need the value of n.

(1) k < n

No value for k or n. Not sufficient.

(2) The median of the numbers in the list is 10.

So either k or n must be 10. There are 5 numbers so the median must be the middle (third here) number when the numbers are arranged in increasing order. 10 must be in the list. But we don't know whether k or n is 10. Not sufficient.

Take both together:
If k = 10 and n is greater, say 11 or 13 or 28 etc, 10 will be the second number in the list, not the third. Hence k cannot be 10.
If n = 10, k will be smaller e.g. 3 or 7 etc. Hence 10 will be the third number and will be the median.
Sufficient.
Answer (C)
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I have a question:

I approached the second statement and the combined statements in another way:

2) If the median of the 5 numbers is 10, it follows that k+n+12+6+17 = 50. Therefore k+n = 15.
This is of course insufficient.

1&2) If we take that k < n and k+n = 15 it still leaves us a variety of choices for k+n to equal 15. I wonder why this is not enough to solve the question... I forgot to take the median into account, maybe someone can clarify for me?

You are confusing median with arithmetic mean. If mean of 5 numbers is 10, then the sum of the numbers is 50. Median is just the middle number. It has no bearing on the sum of the numbers.

Look at the explanations given above to see how to solve this question.
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This might be a very easy question but the info in statement 2 is a bit ambiguous to me.

We have the following list of numbers and we don't know what is the value of "n".
n, 15, 12, 9, 20

As per statement 2, "The median of the numbers in the list is 13". If we arrange the numbers in the ascending order, there are two possibilities:

(1) 9,12,15,20,n (since we don't know what is the value of "n", it is possible that n is a large number)
(2) n, 9,12,15,20 (again we don't know what is the value of "n", "n" could be a small number)

In the first case, the medium is 15 and in the second case the medium is 12.

How come the second statement is sufficient to answer this question?

The median of a set with odd number of elements is the middle element (when arranged in ascending/descending order). So, the median is one of the following 5 numbers: n, 15, 12, 9, or 20. (2) says that the median is 13 and since no number is 13 there then it must be n. Thus the set is {9, 12, n = 13, 15, 20}
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Statement 1: n can take any value above 12. not sufficient
Statement 2: n=13. All are distinct numbers and if arranged in increasing order makes it possible to solve the question

Hence B

We need to determine the value of n in the list: n, 15, 12, 9, 20.

Statement One Alone:

n > 12

Only knowing that n > 12 is not enough to determine the value of n. For example, n can be 13 or 14 (or some other number greater than 12). Statement one alone does not provide enough information to answer the question. We can eliminate answer choices A and D.

Statement Two Alone:

The median of the numbers in the list is 13.

We are given a list of 5 values: n, 15, 12, 9, and 20. Since we have 5 numbers in the list (an odd number of values), the median is equal to the middle value when the data are ordered from least to greatest. Using statement two, when the values are ordered from least to greatest, the list looks like the following:

9, 12, 13, 15, 20

Since 13 is not one of the four known values in the list, we see that 13 must be equal to n.

The answer is B.
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We are given the following list of numbers: k, n, 12, 6, 17, and we must determine the value of n.

Statement One Alone:

k < n

Only knowing that k is less than n is not enough information to determine the value of n. Statement one alone is not sufficient to answer the question. We can eliminate answer choices A and D.

Statement Two Alone:

The median of the numbers in the list is 10.

Since we have five numbers in the given list, we know that the median is the middle number, when the numbers in the list are ordered from least to greatest. Since 10 is not one of the three known values in the list we see that 10 must be either k or n. However, since we don’t know which value (k or n) must be 10, statement two is not sufficient to answer the question. We can eliminate answer choice B.

Statements One and Two Together:

From statements one and two we know that k is less than n and that the median of the numbers in the list is 10. Let’s re-construct our list, listing the values from least to greatest. When we re-construct the list, we see we have two possible placements for k and n, remembering that k must be less than n.

Option 1:

6, k, n, 12, 17

We see that n must equal the median of 10.

Option 2:

k, 6, n, 12, 17

We see that n must equal the median of 10.

Note: If we try to place n and/or k somewhere else, we will either have k > n or neither one will be the median of 10, which is contradicts the information from statements one and two. Thus, n = 10.

The answer is C.
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The list I am seeing in the book is k, n, 12, 6, 17. Is this the right question?

You are looking at another question: https://gmatclub.com/forum/what-is-the- ... 05889.html
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Bunuel hello regarding statement TWO why do you say we have a list of five (odd) numbers. But 20 is not odd number does the key to solution of the this DS question relates to ODD number property ?
have a great weekend

The number of elements in the list is five, which is an odd number.
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n, 15, 12, 9, 20
What is the value of n in the list above?

(1) n> 12
n can be any number greater than 12 - Not sufficient.

(2) The median of the numbers in the list is 13.
Since the number of items on the set is 5 , the median of odd number number of digits is always the middle digit. So 13 is the median. The value of n is 13.

Ans: B
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Hi Bunuel,

When I clink on the link to question 414 of DS in the OG 2020 Directory, it brings me to this question thread. It should link to the other question that you have linked above.

I also got confused because of this.

What if the question is a bit changed? Will it still be legit? i mean-will both statements contradict each other?
Here you go for changed version-->
\(n, 15, 12, 9, 20\)
What is the value of n in the list above?

(1) n> 13
(2) The median of the numbers in the list is 13.
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Dear TheUltimateWinner,
You cannot modify the statement 1 in such a way because statements will never contradict one another.

Hope it helps.