adilka wrote:Peter, Paul, and Mary each received a passing score on his/her history midterm. The average (arithmetic mean) of the three scores was 78. What was the median of the three scores?

(1) Peter scored a 73 on his exam.

(2) Mary scored a 78 on her exam.

Source: Manhattan GMAT

You'd never see a question worded quite like this on the real GMAT - after all, what's a 'passing score'? In the US, it would likely be 50%; here in the UK, it would normally be 40%. The GMAT doesn't test your knowledge of American cultural conventions.

Still, the answer should be B. The first statement is not sufficient; if Peter scored a 73, there are many possible values for the median (the median could be 73 if the other two scores were 70 and 91, for example, but could be 78 if the other two scores were 78 and 83).

The second statement is sufficient; if Mary scored a 78, and the mean score was 78, the other two scores must add to 156. One of them must be less than or equal to 156/2 = 78, the other greater than equal to 156/2 = 78, and 78 must be the median.