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Manager  Joined: 19 Feb 2007
Posts: 223
k, n, 12, 6, 17 What is the value of n in the list above?  [#permalink]

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Difficulty:   25% (medium)

Question Stats: 72% (01:12) correct 28% (01:19) wrong based on 432 sessions

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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.

Originally posted by sidbidus on 05 Sep 2007, 08:41.
Last edited by Bunuel on 09 Dec 2019, 09:18, edited 2 times in total.
SVP  Joined: 24 Aug 2006
Posts: 2018
Re: k, n, 12, 6, 17 What is the value of n in the list above?  [#permalink]

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Assuming that k and n are integers, st1 tells us nothing about a value. st2 gives us some info, but k can equal 10 and n equal 7 or vice versa.

st1 and 2 combined tells us that n must be the median and 10.

I'll go with C

sidbidus 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.
Senior Manager  Joined: 22 Aug 2007
Posts: 440
Re: k, n, 12, 6, 17 What is the value of n in the list above?  [#permalink]

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sidbidus 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.

Vote for C

1 insuff
2 insuff

both, let`s start with 2nd statement, it says median is 10, that means 12 and 17 must come after 10, thus three numbers must be 10, 12 and 17. {median by deffinition is the middle number, when the number of numbers is odd, 5 in this case}, so we have: (some number), 6, 10, 12,17
"some number" can be either n or k, "some number" must be less than 10. Since the 1st statement says that k<n, n is 10, and k is "some number"...
VP  Joined: 07 Nov 2007
Posts: 1104
Location: New York
Re: k, n, 12, 6, 17 What is the value of n in the list above?  [#permalink]

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chan4312 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.

A. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
B. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
C. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
D. EACH statement ALONE is sufficient.
E. Statements (1) and (2) TOGETHER are NOT sufficient.

1) insuffciient (two variables..)
we don't the pattern

2) k, n, 12, 6, 17
re arrange in the ascending order.. following two combinations are possible.
either way n is median.. so n=10
6 ,k, n, 12,17
k,6, n, 12,17

VP  Joined: 28 Dec 2005
Posts: 1115
Re: k, n, 12, 6, 17 What is the value of n in the list above?  [#permalink]

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C for me.

It cant be B since you can have 6,k,n,12,17 or 6,n,k,12,17. Considering both statements together you effectively rule out the second case since k<n. Therefore n=median=10
VP  Joined: 07 Nov 2007
Posts: 1104
Location: New York
Re: k, n, 12, 6, 17 What is the value of n in the list above?  [#permalink]

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pmenon wrote:
C for me.

It cant be B since you can have 6,k,n,12,17 or 6,n,k,12,17. Considering both statements together you effectively rule out the second case since k<n. Therefore n=median=10

Yeap!! you are right..

for the second statment I combined both and answered B..

obvisiously it is C..
Oh!! God when will I stop the making care less mistakes..  Manager  Joined: 04 Jun 2008
Posts: 92
Re: k, n, 12, 6, 17 What is the value of n in the list above?  [#permalink]

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x2suresh wrote:
pmenon wrote:
C for me.

It cant be B since you can have 6,k,n,12,17 or 6,n,k,12,17. Considering both statements together you effectively rule out the second case since k<n. Therefore n=median=10

Yeap!! you are right..

for the second statment I combined both and answered B..

obvisiously it is C..
Oh!! God when will I stop the making care less mistakes..  OA is C.
I still can not understand how did you assess the value of k to find the value of n.
did you use your cognitive abilities to assess values..or do we have a formula to do it.

How did you find that n is 10.
VP  Joined: 07 Nov 2007
Posts: 1104
Location: New York
Re: k, n, 12, 6, 17 What is the value of n in the list above?  [#permalink]

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chan4312 wrote:
x2suresh wrote:
pmenon wrote:
C for me.

It cant be B since you can have 6,k,n,12,17 or 6,n,k,12,17. Considering both statements together you effectively rule out the second case since k<n. Therefore n=median=10

Yeap!! you are right..

for the second statment I combined both and answered B..

obvisiously it is C..
Oh!! God when will I stop the making care less mistakes..  OA is C.
I still can not understand how did you assess the value of k to find the value of n.
did you use your cognitive abilities to assess values..or do we have a formula to do it.

How did you find that n is 10.

median of x1,x2,x3,x4,x5
iss x3 ( when you arrange them in ascending order)

We have six numbers given.. k, n, 12, 6, 17
(to find the median arrange then in ascending order)
6,12,17 ( we don't know where k and n com in this order)
State 1) says k<n means k alsways comes before n.
series can be..
k,n,6,12,17
k,6,12,17,n
.... (you get more combinations)..

State 2) median is 10 (that means middle numbe must be 10)
__, __, 10,12,17
there are only two posibility with the above combinations
6,_,10,12,17
_,6,10,12,17
here other number_ must be k becaue k<n so 10 must be N.
assume that 10 is k then k<n is contradicting.

Manager  Joined: 23 May 2006
Posts: 184
Re: k, n, 12, 6, 17 What is the value of n in the list above?  [#permalink]

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Guys good explanantion. There is one more way to do this problem

S1. As mentioned it is a MAYBE case AD are out

S2. Median is 10. Since there are five numbers in this series the average must also be 10.
{6+12+17+(n+k)}/5 = 10
n+k = 15

Combine: Now we know that wither n or k is 10, but since k<n
n = 10

IMO C
Intern  Joined: 02 Aug 2008
Posts: 34
Re: k, n, 12, 6, 17 What is the value of n in the list above?  [#permalink]

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x97agarwal wrote:
Guys good explanantion. There is one more way to do this problem

S1. As mentioned it is a MAYBE case AD are out

S2. Median is 10. Since there are five numbers in this series the average must also be 10.
{6+12+17+(n+k)}/5 = 10
n+k = 15

Combine: Now we know that wither n or k is 10, but since k<n
n = 10

IMO C

How do you know that average(arithmetic mean) must also be 10?

List could be 6,7,10,12,17 (k=7, n=10, k<n) with an average(arithmetic mean) of 10.4.
VP  Joined: 07 Nov 2007
Posts: 1104
Location: New York
Re: k, n, 12, 6, 17 What is the value of n in the list above?  [#permalink]

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new2gmat wrote:
x97agarwal wrote:
Guys good explanantion. There is one more way to do this problem

S1. As mentioned it is a MAYBE case AD are out

S2. Median is 10. Since there are five numbers in this series the average must also be 10.
{6+12+17+(n+k)}/5 = 10
n+k = 15

Combine: Now we know that wither n or k is 10, but since k<n
n = 10

IMO C

How do you know that average(arithmetic mean) must also be 10?

List could be 6,7,10,12,17 (k=7, n=10, k<n) with an average(arithmetic mean) of 10.4.

good point..

Its median=10 not the mean=10...

So this approach is not correct.
Retired Moderator Joined: 18 Jul 2008
Posts: 662
Re: k, n, 12, 6, 17 What is the value of n in the list above?  [#permalink]

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Mean = median in a series.

We don't know that the numbers listed were a list of series.

x97agarwal wrote:
Guys good explanantion. There is one more way to do this problem

S1. As mentioned it is a MAYBE case AD are out

S2. Median is 10. Since there are five numbers in this series the average must also be 10.
{6+12+17+(n+k)}/5 = 10
n+k = 15

Combine: Now we know that wither n or k is 10, but since k<n
n = 10

IMO C
Director  Joined: 17 Jun 2008
Posts: 842
Re: k, n, 12, 6, 17 What is the value of n in the list above?  [#permalink]

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chan4312 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.

A. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
B. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
C. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
D. EACH statement ALONE is sufficient.
E. Statements (1) and (2) TOGETHER are NOT sufficient.

lets arrange the numbers in increasing order :
6 12 17 with k,n occurring anywhere

hence consider
(1) k < n --------> it does not help in finding n
(2) median of numbers is 10 => k,n can occur anywhere hence either k or n can be 10
(1) & (2) cannot help since k <n does not say whether k=10 or n=10

INSUFFI
IMO E Veritas Prep GMAT Instructor V
Joined: 16 Oct 2010
Posts: 9985
Location: Pune, India
Re: k, n, 12, 6, 17 What is the value of n in the list above?  [#permalink]

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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.

I thought n have numerous value here ? Can someone explain where i am going wrong

Perfect example of how simple looking statistics questions can be a little tricky.

k, n, 12, 6, 17

Stmnt 1: k < n
No idea what n is. Not sufficient.

Stmnt 2: The median of the list is 10.
Since the list has 5 numbers i.e. odd number of numbers, the median must be the middle number i.e. the 3rd number when the numbers in the list are in increasing/decreasing order. Since 10 has to be a number in the list, either k or n has to be 10. But we do not know yet whether k is 10 or n is 10. So we don't know the value of n. Not sufficient.

Using both together, we know one of k and n is 10. We also know that k < n.
If k = 10, n is 10.1/11/12/13/14......etc etc etc
But then the list becomes: 6, k(10), n, 12, 17 (whatever be the arrangement of last 3 elements). k will not be the middle number in this case and hence 10 will not be the median.
If n = 10, k < 10 so the list will look something like:
6, k, n(10), 12, 17 ... Here 10 is the median. n must be 10. Hence, both together are sufficient.
_________________
Karishma
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Manager  Joined: 28 Aug 2010
Posts: 146
Re: k, n, 12, 6, 17 What is the value of n in the list above?  [#permalink]

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Karishma,
Thanks a tonne. Awesome. I wasted a quite some time on this question. Could you please give some pointer as to how to deal with type of question in future.
Veritas Prep GMAT Instructor V
Joined: 16 Oct 2010
Posts: 9985
Location: Pune, India
Re: k, n, 12, 6, 17 What is the value of n in the list above?  [#permalink]

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ajit257 wrote:
Karishma,
Thanks a tonne. Awesome. I wasted a quite some time on this question. Could you please give some pointer as to how to deal with type of question in future.

Practice some questions based on Median. Tag search for some on this forum itself. Median is the most time consuming to figure out in case of missing values or new values. Sometimes range can also be fun. If you get stuck somewhere, let me know...

I intend to write a complete post on statistics concepts soon. Check out http://www.veritasprep.com/blog/ and search for 'Quarter Wit Quarter Wisdom' (That is the tag I use to put my posts.) Look for statistics post in the coming weeks.
_________________
Karishma
Veritas Prep GMAT Instructor

Manager  Joined: 13 Jul 2010
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Re: k, n, 12, 6, 17 What is the value of n in the list above?  [#permalink]

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wow very tricky. I selected the trap answer E by quickly coming to the conclusion that I couldn't tell even with both statements whether k or n was the median so would not N's value.
Math Expert V
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k, n, 12, 6, 17 What is the value of n in the list above?  [#permalink]

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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.

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