A, B and C have received their Math midterm scores today. They find that the arithmetic mean of the three scores is 78. What is the median of the three scores?

(1) A scored a 73 on her exam.

(2) C scored a 78 on her exam.

Kudos for a correct solution.
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Statement-1: Since Average is 78. The sum will be 78*3= 234. And since A is 73 then the sum of other 2 numbers will be 161. But there are many combinations to add up this 161. And Median changes accordingly. For example Scores are 76 & 85. The median will be 76. And if 74 & 87. The median will be 74. So not sufficient.

Statement 2: C is 78 and since Average is 78. The other's score can't be below or above 78. So the median is 78.

The Correct answer is B.
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OA should be B

As B states C is 78 so other two should be equal to 78 or one less and one greater than 78
In either case mediun gonna be 78

VERITAS PREP OFFICIAL SOLUTION:

Recall from the arithmetic mean post that the sum of deviations of all scores from the mean is 0.
i.e. if one score is less than mean, there has to be one score that is more than the mean.
e.g. If mean is 78, one of the following must be true:
All scores are equal to 78.
At least one score is less than 78 and at least one is greater than 78.
For example, if one score is 70 i.e. 8 less than 78, another score has to make up this deficit of 8. Therefore, there could be a score that is 86 (8 more than 78) or there could be two scores of 82 each etc.

Statement 1: A scored 73 on her exam.

For the mean to be 78, there must be at least one score higher than 78. But what exactly are the other two scores? We have no idea! Various cases are possible:

73, 78, 83 or

73, 74, 87 or

70, 73, 91 etc.

In each case, the median will be different. Hence this statement alone is not sufficient.

Statement 2: C scored 78 on her exam.

Now we know that one score is 78. Either the other two will also be 78 or one will be less than 78 and the other will be greater than 78. In either case, 78 will be the middle number and hence will be the median. This statement alone is sufficient.

Answer (B)
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If there were 5 people and the average was 78 and one person's score was 78... thhe median would still be 78? Plz help me understand this concept.....Thanks so much.

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