Peter, Paul, and Mary each received a passing score on

Question

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.

OPEN DISCUSSION OF THIS QUESTION IS HERE: peter-paul-and-mary-each-received-a-passing-score-on-135451.html

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Official Answer

B

nevergiveup · Accepted Answer

Since the average of 3 score is 78 so the total score is 234

Statement 1 says peter's score is 73, so the sum of the other 2 score is 161, it could be that one of the score is 72 and the other is 89 so the median is 73, or it could be that one of the other score is 75 and 86, so the median would be 75. So this is insufficient.

Statement 2 says Mary's score is 78, you know that since the average is 78, the other two score can not be all lower than 78 or all higher than 78. It could be that one other score is lower than 78 and the other one higher than 78. Or the other two score are 78 as well. Anyway, the median will be 78. So this is sufficient.

Answer B

gmatnub · Answer

C, but it depends on what a passing grade is.

FN · Answer

i too get B..

x+y+z=234

y+z=234-78=156

worst case one scored 100 the other scored 56..still median is 78

other case x=y=78..

median is still 78

tharunv · Answer

B is the answer - what is the OA? As mentioned, with Mary having 78, one is lower and the other is higher - whatever the case the median will be 78.

Vavali · Answer

I got C. variables X (Peter's score), Y (Paul's score) and Z (mary's score) (1) InSufficient 78 = 73 + y + z / 3 234 - 73 = y+ z y+z = 161. therefore the value of both y and z varies we need at least the value of two variables to find the third and the median. (2) Insufficient also. Mary scored 78 78 = x + Y + 78 / 3 234 - 78 = x + y Again same scenario ad statement 1. now combine the two statements. if Mary scored 78 and Peter's score is 73 then and the mean is 78 78 = 78 + 73 + Y (Paul's score) /3 234 - 151 = Y therefore Y = 83. So the scores are 73, 78, 83 therefore the median is 78. After a 2 month Hiatus it definitely feels good to be back 8-)

bsd_lover · Answer

B is enough.

If mean is 78 and one of the people gets 78 then there are 2 possibilities
All 3 got 78 (in which case median is 78)
One got less than 78, the other got more than 78 (in which case median is still 78)

Bunuel · Answer

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. If the other two scores are 73 and 78*3-73-73 (whatever it is) then the median is 73 but if the other two scores are 78 and 83 then the median is 78. Not sufficient.

(2) Mary scored a 78 on her exam. In order the average to be 78, one of the remaining scores (Peter or Paul) must be less than 78 and another must be more than 78 OR all three scores must be 78. In either case, the median is 78. Sufficient.

Answer: B.

OPEN DISCUSSION OF THIS QUESTION IS HERE: peter-paul-and-mary-each-received-a-passing-score-on-135451.html

Peter, Paul, and Mary each received a passing score on

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