positive integers

gmatnmein2010 wrote:Given distinct positive integers 1, 11, 3, x, 2, and 9, which of the following could be the median?


A)3
B)5
C)7
D)8
E)9

Since the integers are positive and distinct, x must be greater than 3. However, since we don’t know the exact value of x, we can start by ordering the given integers from least to greatest in the following possible scenarios:

Scenario 1: If the ordering is 1, 2, 3, x, 9, 11, then x is between 3 and 9

Scenario 2: If the ordering is 1, 2, 3, 9, x, 11, then x must be 10.

Scenario 3: If the ordering is 1, 2, 3, 9, 11, x, then x is greater than 11.

In the first scenario, the median is (3 + x)/2. In the latter two scenarios, the median is (3 + 9)/2 = 6. Since 6 is not an answer choice, the median must be (x + 3)/2 in which x is an integer between 3 and 9. Because x is an integer between 3 and 9, the median, (x + 3)/2, must be some value between 3 and 6. Thus:

3 < x < 9

6 < x + 3 < 12

3 < (x + 3)/2 < 6

The only number in the choices that satisfies this condition is 5, which is answer choice B.

Answer:B