Last Updated on May 9, 2023
GMAT OFFICIAL GUIDE DS
Solution:
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 5 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 3 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.
Answer: C
