MGMAT CAT 6 - Gud Question

[ankur.agrawal]

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.

Oa after some discussion.

[smackmartine]

IMO B

Total scores (Pe+Pa+M )=78*3=234

1)Pe = 73 so Pa+M= 234-73 = 161

161 does not clarify individual scores of both Paul and Mary.
if Pa = 74 => M =161-74 = 87 (in this case median is 74 )

also if Pa= 72 ,M = 161- 72= 89 (in this case medial is 73)

so 1 is Insufficient

2) if M= 78

In order for average to be 78 one of the score should be less than 78 and other should be greater than 78 with the same difference . eg is if one is 75 then other should be 81 so median in any case is 78

So statement 2 is Sufficient.

So B

[Anurag@Gurome]

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.

Oa after some discussion.

That's a good question.

(1)Marks scored by Peter = 73, average of 3 scores = 78. This info is NOT SUFFICIENT as we don't know the scores of Paul and Mary.

(2)Mary scored a 78 on her exam, which is the same as the average. This means that one of Peter or Paul should have scored less than 78, and the other would have scored more than 78. Or it may be possible that all 3 of them scored 78. In either case, the median is 78.
So, (2) is SUFFICIENT.

The correct answer is B.

[M09]

IMO B

Total scores (Pe+Pa+M )=78*3=234

1)Pe = 73 so Pa+M= 234-73 = 161

161 does not clarify individual scores of both Paul and Mary.
if Pa = 74 => M =161-74 = 87 (in this case median is 74 )

also if Pa= 72 ,M = 161- 72= 89 (in this case medial is 73)

so 1 is Insufficient

2) if M= 78

In order for average to be 78 one of the score should be less than 78 and other should be greater than 78 with the same difference . eg is if one is 75 then other should be 81 so median in any case is 78

So statement 2 is Sufficient.

So B

@smackmartine: Just a thought here what if all scored 78? it's not necessary that if M=78 then one scored above 78 and other less than 78.
IMO E

[M09]

IMO B

Total scores (Pe+Pa+M )=78*3=234

1)Pe = 73 so Pa+M= 234-73 = 161

161 does not clarify individual scores of both Paul and Mary.
if Pa = 74 => M =161-74 = 87 (in this case median is 74 )

also if Pa= 72 ,M = 161- 72= 89 (in this case medial is 73)

so 1 is Insufficient

2) if M= 78

In order for average to be 78 one of the score should be less than 78 and other should be greater than 78 with the same difference . eg is if one is 75 then other should be 81 so median in any case is 78

So statement 2 is Sufficient.

So B

ohh.. Sorry B ..typing mistake