Peter, Paul, and Mary

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gmatnmein2010: Master | Next Rank: 500 Posts; Posts: 185; Joined: Thu Feb 04, 2010 3:06 am; Thanked: 6 times

by gmatnmein2010 » Sat Feb 20, 2010 3:08 am

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.

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Source: Beat The GMAT — Data Sufficiency | Sat Feb 20, 2010 3:08 am

ajith: Legendary Member; Posts: 1275; Joined: Thu Sep 21, 2006 11:13 pmFollowed by: 2 members; Location: Arabian Sea; Thanked: 125 times

by ajith » Sat Feb 20, 2010 3:32 am

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.

1) Peter scored a 73 on exam ... and average is 78.. insufficient to find out the median

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

Always borrow money from a pessimist, he doesn't expect to be paid back.

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shashank.ism: Legendary Member; Posts: 1022; Joined: Mon Jul 20, 2009 11:49 pmFollowed by: 2 members; Location: Gandhinagar; Thanked: 41 times

by shashank.ism » Sat Feb 20, 2010 1:03 pm

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.

avearge 78, so total = 234
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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thephoenix: Legendary Member; Posts: 1560; Joined: Tue Nov 17, 2009 2:38 amFollowed by: 5 members; Thanked: 137 times

by thephoenix » Sat Feb 20, 2010 6:40 pm

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.

s1) insuff

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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Brent@GMATPrepNow: GMAT Instructor; Posts: 16207; Joined: Mon Dec 08, 2008 6:26 pmFollowed by: 1268 members; Location: Vancouver, BC; Thanked: 5254 times; GMAT Score:770

by Brent@GMATPrepNow » Sun Nov 11, 2012 8:03 am

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

Brent Hanneson - Creator of GMATPrepNow.com

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