Question

In City X last April, was the average (arithmetic mean) daily high temperature greater than the median daily high temperature?
(1) In City X last April, the sum of the 30 daily high temperatures was 2,160°.
(2) In City X last April, 60 percent of the daily high temperatures were less than the average daily high temperature.

• 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

Hint:

For problems involving the median and mean, remember that if the mean is greater than the median, the data is skewed to the right.

Answer 1

The Correct Option is C

Step 1: Analyze statement (1).
Statement (1) tells us that the sum of the 30 daily high temperatures was 2,160°. The average (arithmetic mean) daily high temperature is: \[ \text{Average} = \frac{2160}{30} = 72^\circ \] However, this only gives us the average temperature, not the median temperature. We still don’t know if the average temperature is greater than the median. Therefore, statement (1) alone is insufficient.
Step 2: Analyze statement (2).
Statement (2) tells us that 60 percent of the daily high temperatures were less than the average daily high temperature. This means that the average temperature is greater than the median temperature, because the median is the middle value, and for the average to be higher, the data must be skewed towards the higher values. Therefore, statement (2) alone is sufficient to answer the question.
Step 3: Combine both statements.
When combining both statements, statement (2) alone is sufficient, so adding statement (1) does not change the sufficiency.
\[ \boxed{C} \]