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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) _________________

Re: k, n, 12, 6, 17 What is the value of n in the list above? [#permalink]
08 Feb 2012, 04:37

Expert's post

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)

Thanks for the Explanation Karishma .......!! _________________

If you don’t make mistakes, you’re not working hard. And Now that’s a Huge mistake.

Re: What is the value of n in the list above? [#permalink]
13 Jan 2014, 06:00

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.

So answer is C.

gmatclubot

Re: What is the value of n in the list above?
[#permalink]
13 Jan 2014, 06:00