swerve 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.
The OA is B
Source: Manhattan Prep
Target question:
What was the median of the three scores?
Since there are 3 values, the median will be the middle-most value (when the values are arranged in ascending order).
We also know that: Total of all values = (median)(# of values)
So, the sum of all 3 scores = (78)(3) =
234
Statement 1: Peter scored a 73 on his exam.
There are several sets of scores that meet this condition. Here are two:
Case a: Peter:73, Paul:74, Mary:87, in which case
the median is 74
Case b: Peter:73, Paul:75, Mary:86, in which case
the median is 75
Since we cannot answer the
target question with certainty, statement 1 is NOT SUFFICIENT
Statement 2: Mary scored a 78 on her exam
NOTE: For scores above 78, I'll use the notation
78+ and for scores below 78, I'll use the notation
78-
If the mean is 78 and Mary scored a 78, then there are only 3 scenarios possible:
scenario 1: Peter:78, Mary:78, Paul:78, in which case
the median is 78
scenario 2: Peter:78-, Mary:78, Paul:78+, in which case
the median is 78
scenario 3: Peter:78+, Mary:78, Paul:78-, in which case
the median is 78
Notice that no other scenarios are possible. For example, consider this scenario:
Peter:78+, Mary:78, Paul:78+
This scenario is impossible, because the sum of all three values must be
234, and we know that 78+78+78=
234.
So, it is impossible for (78)+(78+)+(78+) to equal
234
Using similar logic and notation we can show that other scenarios are impossible.
As you can see, statement 2 consistently yields the same answer to the
target question.
So, statement 2 is SUFFICIENT
Answer: B
Cheers,
Brent
