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Math Expert V
Joined: 02 Sep 2009
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A, B and C have received their Math midterm scores today. They find th  [#permalink]

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Difficulty:   45% (medium)

Question Stats: 61% (01:28) correct 39% (01:37) wrong based on 196 sessions

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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?

(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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Re: A, B and C have received their Math midterm scores today. They find th  [#permalink]

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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
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Re: A, B and C have received their Math midterm scores today. They find th  [#permalink]

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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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Re: A, B and C have received their Math midterm scores today. They find th  [#permalink]

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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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Manager  B
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Re: A, B and C have received their Math midterm scores today. They find th  [#permalink]

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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
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Joined: 21 May 2013
Posts: 613
Re: A, B and C have received their Math midterm scores today. They find th  [#permalink]

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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.

+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
Math Expert V
Joined: 02 Sep 2009
Posts: 64134
Re: A, B and C have received their Math midterm scores today. They find th  [#permalink]

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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?

(1) A scored a 73 on her exam.

(2) C scored a 78 on her exam.

Kudos for a correct solution.

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.

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GRE 1: Q169 V154 Re: A, B and C have received their Math midterm scores today. They find th  [#permalink]

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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.

Hence Median must be 78.

Hence B

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Re: A, B and C have received their Math midterm scores today. They find th  [#permalink]

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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.
Math Expert V
Joined: 02 Sep 2009
Posts: 64134
Re: A, B and C have received their Math midterm scores today. They find th  [#permalink]

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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.

Not necessarily. For example, for {70, 78, 79, 79, 84} the average is 78 but the median is 79.
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Re: A, B and C have received their Math midterm scores today. They find th  [#permalink]

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_________________ Re: A, B and C have received their Math midterm scores today. They find th   [#permalink] 08 Jun 2019, 04:59

# A, B and C have received their Math midterm scores today. They find th  