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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?

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19 Aug 2015, 02:04

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Bunuel wrote:

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?[/b]

(1) A scored a 73 on her exam.

(2) C scored a 78 on her exam.

Ans: B

Statement 1) A scored 73 so remaining must be (78*3)-73 = B+C here B and C can have many different values which can give us the mean value of 78. [Not sufficient] Statement 2) C Score 78; this is exact the avg value means either all values are 78 or other two values are (less than 78, greater than 78) so median will always be 78 [Sufficient]
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19 Aug 2015, 02:07

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Bunuel wrote:

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?[/b]

(1) A scored a 73 on her exam.

(2) C scored a 78 on her exam.

Kudos for a correct solution.

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.

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19 Aug 2015, 04:31

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Bunuel wrote:

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?[/b]

(1) A scored a 73 on her exam.

(2) C scored a 78 on her exam.

Kudos for a correct solution.

Mean = 78 Total score = 78*3 = 234 Statement 1: A scored a 73 on her exam

If A scored 73 Thus B+C = 161. We can have multiple pairs of (B,C) satisfying this equation. Hence not suff

Statement 2 : C scored a 78 on her exam.

A-----B------C ?-----?------78 C= 78 which is also the mean.

Case 1: A and B both equal to 78 Then median = 78

Case 2: A and B both not equal to 78 Then among A and B, one must be >78 and another <78, so that mean is 78. Thus making C= 78 the middle value Hence for both cases median = 78 Sufficient _________________

I'm happy, if I make math for you slightly clearer And yes, I like kudos ¯\_(ツ)_/¯

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21 Aug 2015, 10:27

Bunuel wrote:

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?[/b]

(1) A scored a 73 on her exam.

(2) C scored a 78 on her exam.

Kudos for a correct solution.

+1 for B. Average=78. Sum of scores=234 Statement 1: A scores 73. Scores for 3 people can be 73,73,88 or 73,75 , 85 so on.. Insufficient Statement 2:C scored a 78. We can only have the 3 scores as 78,78,78. If we take 1st value as 78 and second value as 79, then 3rd value needs to be more than 78 which is not possible. So median is 78. Sufficient

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?

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.

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10 Dec 2016, 22:43

Excellent Question. Here is my solution to this one --> Given info --> Mean =78 We need to get the median. Here as mean of 3 numbers is 78=> Sum(3)= 78*3=234

Statement 1--> A=73

Hence B+C=234-73= 161 E.g=> 73,80,81 Or 78,78,78

Hence using the two above test cases => Not sufficient.

Statement 2--> B scored a 78. Now if B scored a 78 We have two cases to consider Case 1=> All scored 78 => Median =78 Case 2=> If one of them scored less than 78,then the other one must have score greater than 78 (Infact the two values will be equidistant from 78 for mean to be 78) Hence,In this case too => median will be 78.

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28 Dec 2017, 10:43

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