OG What is the value of n in the list above?

Hi AbeNeedsAnswers,

We're given a group of 5 values: K, N, 12, 6, 17. We're asked for the value of N. We can answer this question by TESTing VALUES.

1) K < N

IF...
K =1, N=2, then the answer to the question is 2.
K =2, N=3, then the answer to the question is 3.
Fact 1 is INSUFFICIENT

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

The 'median' of a group of 5 numbers will be the '3rd' number (when we put the numbers in order from least to greatest). Here though, we have two variables. Since three of the values (6, 12 and 17) are NOT 10, one of the two variables MUST be 10.

With 6, 10, 12 and 17, the last value would have to be 10 or less.
IF.... N=10, then K would be something LESS than or equal to 10
IF.... K=10, then N would be something LESS than or equal to 10
Fact 2 is INSUFFICIENT

Combined, we know:
K < N
K or N (or both) = 10 and 10 is the MEDIAN.

Since N is BIGGER than K, then N MUST be 10 and K MUST be less than 10.
Combined, SUFFICIENT.

Final Answer: C

GMAT assassins aren't born, they're made,
Rich

AbeNeedsAnswers 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.

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