Average

[heshamelaziry]

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 B

[mehravikas]

It should be 'B'

The thumb rule is if you have a list and one of the items in the list is equal to the mean, then you can find the remaining items or even the median.

[life is a test]

It should be 'B'

The thumb rule is if you have a list and one of the items in the list is equal to the mean, then you can find the remaining items or even the median.

I agree with your point on median but how can you calculate the remaining items, e.g. taking statement 2. we know that the middle item is 78, this could mean that the other 2 also have 78 as scores or one has 77 and the other has 79 as score...perhaps I misunderstood your explanation?

[tarun.kirla]

It should be 'B'

The thumb rule is if you have a list and one of the items in the list is equal to the mean, then you can find the remaining items or even the median.

I agree with your point on median but how can you calculate the remaining items, e.g. taking statement 2. we know that the middle item is 78, this could mean that the other 2 also have 78 as scores or one has 77 and the other has 79 as score...perhaps I misunderstood your explanation?

i think answer is C

[gdk]

Hi All,

Since v have been told to find the median, we must remember that median is the middle value for odd number of terms. In this case, since Mary scored 78.
the remaining score would be 234 - 78 = 156.

case 1: 156/2 = 78. thus peter n paul both scored 78.
Median is 78.

Case 2: Either of them could hav scored 77 and the other might have scored 79. In which case, the middle value remains same i.e 78. So thus median is 78.

Rule: If any of the value is equal to the mean, that value itself is the Median for an Odd term data.

[mehravikas]

Sorry I went a little overboard it should be median only.

It should be 'B'

The thumb rule is if you have a list and one of the items in the list is equal to the mean, then you can find the remaining items or even the median.

I agree with your point on median but how can you calculate the remaining items, e.g. taking statement 2. we know that the middle item is 78, this could mean that the other 2 also have 78 as scores or one has 77 and the other has 79 as score...perhaps I misunderstood your explanation?

[Brent@GMATPrepNow]

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