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k, n, 12, 6, 17 What is the value of n in the list above?

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

(1) k < n. Clearly insufficient. (2) The median of the numbers in the list is 10 --> now, the list contains odd # of terms, thus its median is the middle term and since no other term is 10 then either n or k must be 10, but we don't know which one. Not sufficient.

(1)+(2) Since from (1) k<n then k=10=median is not possible, because in this case 3 terms will be greater than k (n, 12, and 17) and it won't be the middle term (it'll be the second term), for example {6, k=10, n, 12, 17}. Thus n must be 10. Sufficient.

5. What is the value of n in the list above k, n, 12, 6, 17? (1) k < n (2) The median of the numbers in the list is 10.

My solution: 1. Says that k < n, there is no information given on the values of k or n, we can make a list of the set possibilities: k,n,6,12,17 6,k,n,12,17 6,k,12,n,17 6,k,12,17,n 6,12,k,n,17 6,12,k,17,n 6,12,17,k,n k,6,n,12,17 k,6,12,n,17 k,6,12,17,n (I think these are all of the possibilites if not please correct me) Insufficient

2. The median of the list is 10. There are 5 elements in the set therefore if we list the possibilities: k,6,10,12,17 6,k,10,12,17 n,6,10,12,17 6,n,10,12,17 (Insufficient)

1+2 => List the set, the only intersections: 6,k,10,12,17 k,6,10,12,17 There are two possibilities but in each case n = 10 Therefore answer is C

s1 insufficient s2 insufficient, k or n can be the median. As we have an odd number of distinct numbers in the set, the median is just one of them and not an average of two of them. The median is the third number in the set. With 12 and 17 being the the two numbers larger than the median 10. 6 and either k or n are the two numbers smaller than median 10. The median 10 is either k or n. as k < n, n has to be the median. N = 10.

5. What is the value of n in the list above k, n, 12, 6, 17? (1) k < n (2) The median of the numbers in the list is 10.

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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5. What is the value of n in the list above k, n, 12, 6, 17? (1) k < n (2) The median of the numbers in the list is 10.

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)

Thanks for the Explanation Karishma .......!!
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Re: What is the value of n in the list above? [#permalink]

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13 Jan 2014, 07:00

ajit257 wrote:

k, n, 12, 6, 17 What is the value of n in the list above?

(1) k < n (2) The median of the numbers in the list is 10.

1 + 2: Since we have odd number of values, the median is equal to one of these values, not the average of two. Since 10 is the median, that means that either k or n is 10, and since 1) tells us that k < n, that means that n is the median = 10.

Re: What is the value of n in the list above? [#permalink]

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20 Jul 2015, 19:23

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Re: What is the value of n in the list above? [#permalink]

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20 Aug 2015, 03:45

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?

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.

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.
_________________

Re: What is the value of n in the list above? [#permalink]

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21 Aug 2015, 02:59

VeritasPrepKarishma wrote:

noTh1ng wrote:

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.

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.

right... stupid me. It happens to often that I confuse median and mean, should pay more attention...

Re: What is the value of n in the list above? [#permalink]

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12 Oct 2016, 02:02

Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

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k, n, 12, 6, 17 What is the value of n in the list above?

(1) k < n (2) The median of the numbers in the list is 10.

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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