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.
Peter, Paul, and Mary
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1) Peter scored a 73 on exam ... and average is 78.. insufficient to find out the mediangmatnmein2010 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.
2) Mary scored a 78 on her exam... Average is also 78. One of Peter and Paul must have scored more than 78 and other less than 78 or they all would have scored 78, in any case the median is 78; sufficient
B
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avearge 78, so total = 234gmatnmein2010 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.
St.1: peter score = 73 then also we can't find the median as we don't know other scores
St.2: mary score = 78 which is equal to avg. so peter and paul have scored equal amount more and less than marry
say 78-p , 78 +p so median score is 78 ..
Ans B
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s1) insuffgmatnmein2010 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.
tot=3*78=234
sum of other two scores=234-73=161
no further info
s2)mean=78
# of scores=3
so one wud be >78 and the other wud be <78
irrespective of value of peter and paul the median will be 78 only
hence suff
the problem is tricky and conceptual good one
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gmatnmein2010 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.
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