7, 9, 6, 4, 5, x If x is a number in the list above

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7, 9, 6, 4, 5, x

If x is a number in the list above, what is the median of the list?

(1) x > 7
(2) The median of the list equals the arithmetic mean of the list.

A

Source: Official Guide 2020

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by GMATGuruNY » Sat May 04, 2019 2:09 am

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AbeNeedsAnswers wrote:7, 9, 6, 4, 5, x

If x is a number in the list above, what is the median of the list?

(1) x > 7
(2) The median of the list equals the arithmetic mean of the list.
Given numbers in ascending order:
4, 5, 6, 7, 9

Statement 1:
Smallest 3 numbers are 4, 5, and 6.
Greatest 3 numbers are 7, 9 and x, where x is any number greater than 7.
Thus:
Median = average of the 2 middle numbers =(6+7)/2 = 6.5.
SUFFICIENT.

Rule:
For any set that is SYMMETRICAL ABOUT THE MEDIAN, average = median.

Statement 2:
Case 1: x=2, so that the resulting set -- 2, 4, 5, 6, 7, 9 -- is symmetrical about the median of 5.5
Case 2: x=8, so that the resulting set -- 4, 5, 6, 7, 8, 9 -- is symmetrical about the median of 6.5
Since the median can be different values, INSUFFICIENT.

The correct answer is A.
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by [email protected] » Mon May 13, 2019 12:04 pm

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Hi All,

We're told that X is a number in the list (7, 9, 6, 5, 4, X). We're asked for the MEDIAN of the list. This question can be solved with Stats rules and TESTing VALUES. To start though, since there are six values in the list, the MEDIAN will be the AVERAGE of the two 'middle terms' (once we arrange the list from least to greatest). With a variable, we don't yet know which two values will be the 'middle two' values yet.

(1) X > 7

Fact 1 tells us that X is GREATER than 7, so it will either be the 5th value in the list or the 6th value in the list. For example:
IF....
X = 8, then the list is 4, 5, 6, 7, 8, 9 and the MEDIAN = (6+7)/2 = 13/2 = 6.5
X = 9, then the list is 4, 5, 6, 7, 9, 9 and the MEDIAN = (6+7)/2 = 13/2 = 6.5
X = 10, then the list is 4, 5, 6, 7, 9, 10 and the MEDIAN = (6+7)/2 = 13/2 = 6.5
Etc.
Thus, the answer to the question is ALWAYS 6.5
Fact 1 is SUFFICIENT

(2) The MEDIAN of the list equals the arithmetic MEAN of the list.

The information in Fact 2 requires a bit more work. To start, we can use one of the above TESTs (from Fact 1):
X = 8, then the list is 4, 5, 6, 7, 8, 9 and the MEDIAN = (6+7)/2 = 13/2 = 6.5

However, that's not the only way for the Median to EQUAL the Mean. If the numbers are equally 'spaced out' around the Mean, then the Median will equal the Mean. That can occur with another value of X...
IF... X = 2, then the list is 2, 4, 5, 6, 7, 9 and the MEDIAN = (5+6)/2 = 11/2 = 5.5
Fact 2 is INSUFFICIENT

Final Answer: A

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AbeNeedsAnswers wrote:
Fri May 03, 2019 4:10 pm
7, 9, 6, 4, 5, x

If x is a number in the list above, what is the median of the list?

(1) x > 7
(2) The median of the list equals the arithmetic mean of the list.

A

Source: Official Guide 2020
Solution:

Question Stem Analysis:


We need to determine the median of a list consisting of 6 numbers, including one unknown value.

Statement One Alone:

Since we know x > 7, arranging the numbers from smallest to largest, we have either:

4, 5, 6, 7, x, 9 or 4, 5, 6, 7, 9, x

We see that either way the median will be (6 + 7)/2 = 6.5. Statement alone is sufficient.

Statement Two Alone:

We can’t determine a unique value for the median, given the information in statement two. For example, if x = 8, then the median and mean are both 6.5. However, if x = 2, then the median and mean are both 5.5. Statement two alone is not sufficient.

Answer: A

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