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The average score in an examination of 10 students of a class is 60

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The average score in an examination of 10 students of a class is 60  [#permalink]

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New post 16 Sep 2016, 22:04
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The average score in an examination of 10 students of a class is 60. If the scores of the top five students are not considered, the average score of the remaining students falls by 5. The pass mark was 40 and the maximum mark was 100. It is also known that none of the students failed. If each of the top five scorers had distinct integral scores, the maximum possible score of the topper is

A) 87

B) 95

C) 99

D) 100

E) 103

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Re: The average score in an examination of 10 students of a class is 60  [#permalink]

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New post 17 Sep 2016, 00:00
GMATantidote wrote:
The average score in an examination of 10 students of a class is 60. If the scores of the top five students are not considered, the average score of the remaining students falls by 5. The pass mark was 40 and the maximum mark was 100. It is also known that none of the students failed. If each of the top five scorers had distinct integral scores, the maximum possible score of the topper is

A) 87

B) 95

C) 99

D) 100

E) 103


The average score in an examination of 10 students of a class is 60 --> the total score = 10*60 = 600;
The 5 smallest scores have an average of 55 --> the total score of the 5 smallest scores = 275.

From above, the total score of the 5 largest scores = 600 - 275 = 325.

Say the 5 largest scores are a, b, c, d, and e (where a<b<c<d<e, since each of the top five scorers had distinct scores). We want to maximize e. To maximize e, we need to minimize a, b, c, and d. The least value of a, is 55 (The least score of the top 5 , a, should be equal to the highest of the bottom 5 and to minimize the highest of the bottom 5, all scores from the bottom 5 should be equal). In this case the least values of b, c, and d are 56, 57, and 58 respectively:

a + b + c + d + e = 55 + 56 +57 + 58 + e = 325;
e = 99.

Answer: C.
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Re: The average score in an examination of 10 students of a class is 60  [#permalink]

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New post 17 Sep 2016, 00:03
GMATantidote wrote:
The average score in an examination of 10 students of a class is 60. If the scores of the top five students are not considered, the average score of the remaining students falls by 5. The pass mark was 40 and the maximum mark was 100. It is also known that none of the students failed. If each of the top five scorers had distinct integral scores, the maximum possible score of the topper is

A) 87

B) 95

C) 99

D) 100

E) 103


If the Maximum mark is 100 as per question, why is there a 103 in the answer choice ?
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Re: The average score in an examination of 10 students of a class is 60  [#permalink]

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New post 17 Sep 2016, 04:00
Senthil1981 wrote:
GMATantidote wrote:
The average score in an examination of 10 students of a class is 60. If the scores of the top five students are not considered, the average score of the remaining students falls by 5. The pass mark was 40 and the maximum mark was 100. It is also known that none of the students failed. If each of the top five scorers had distinct integral scores, the maximum possible score of the topper is

A) 87

B) 95

C) 99

D) 100

E) 103


If the Maximum mark is 100 as per question, why is there a 103 in the answer choice ?


Just to confuse those who do not read the question properly. :-D
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Re: The average score in an examination of 10 students of a class is 60  [#permalink]

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New post 17 Sep 2016, 06:33
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Can a be 55? Or can it start from 56 only? That's what I was not sure about


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Re: The average score in an examination of 10 students of a class is 60  [#permalink]

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New post 17 Sep 2016, 06:39
ProfX wrote:
Can a be 55? Or can it start from 56 only? That's what I was not sure about


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Look at Bunuel 's explanation above. It has to be 55 to make e the max.
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Re: The average score in an examination of 10 students of a class is 60  [#permalink]

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New post 17 Sep 2016, 07:18
GMATantidote wrote:
The average score in an examination of 10 students of a class is 60. If the scores of the top five students are not considered, the average score of the remaining students falls by 5. The pass mark was 40 and the maximum mark was 100. It is also known that none of the students failed. If each of the top five scorers had distinct integral scores, the maximum possible score of the topper is

A) 87

B) 95

C) 99

D) 100

E) 103


Hi,
Another method although logic is same as rhat used by Bunuel

If the value of all other except the largest is 55..
Largest will be 60*10-55*9=600-495=105..

However the top 5 are distinct and the smallest of these can be 55, so remaining THREE will be 1,2,&3 more so total combined value will be 1+2+3 or 6 more..
Therefore the largest will be 6 less than max possible..... 105-6=99
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Re: The average score in an examination of 10 students of a class is 60  [#permalink]

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New post 17 Sep 2016, 08:13
Bunuel wrote:
GMATantidote wrote:
The average score in an examination of 10 students of a class is 60. If the scores of the top five students are not considered, the average score of the remaining students falls by 5. The pass mark was 40 and the maximum mark was 100. It is also known that none of the students failed. If each of the top five scorers had distinct integral scores, the maximum possible score of the topper is

A) 87

B) 95

C) 99

D) 100

E) 103


The average score in an examination of 10 students of a class is 60 --> the total score = 10*60 = 600;
The 5 smallest scores have an average of 55 --> the total score of the 5 smallest scores = 275.

From above, the total score of the 5 largest scores = 600 - 275 = 325.

Say the 5 largest scores are a, b, c, d, and e (where a<b<c<d<e, since each of the top five scorers had distinct scores). We want to maximize e. To maximize e, we need to minimize a, b, c, and d. The least value of a, is 55 (The least score of the top 5 , a, should be equal to the highest of the bottom 5 and to minimize the highest of the bottom 5, all scores from the bottom 5 should be equal). In this case the least values of b, c, and d are 56, 57, and 58 respectively:

a + b + c + d + e = 55 + 56 +57 + 58 + e = 325;
e = 99.

Answer: C.


If the average of least 5 scores is 55, then is it allowed to have a score of 55 (a) in the top 5 set ?
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The average score in an examination of 10 students of a class is 60  [#permalink]

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New post 17 Sep 2016, 11:07
Senthil1981 wrote:
GMATantidote wrote:
The average score in an examination of 10 students of a class is 60. If the scores of the top five students are not considered, the average score of the remaining students falls by 5. The pass mark was 40 and the maximum mark was 100. It is also known that none of the students failed. If each of the top five scorers had distinct integral scores, the maximum possible score of the topper is

A) 87

B) 95

C) 99

D) 100

E) 103


If the Maximum mark is 100 as per question, why is there a 103 in the answer choice ?


May be to help the test takers by setting up the easiest answer choice to eliminate or for those who don't bother reading the question during time crunch. :-D
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The average score in an examination of 10 students of a class is 60  [#permalink]

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New post 18 Sep 2016, 04:58
Bunuel wrote:
GMATantidote wrote:
The average score in an examination of 10 students of a class is 60. If the scores of the top five students are not considered, the average score of the remaining students falls by 5. The pass mark was 40 and the maximum mark was 100. It is also known that none of the students failed. If each of the top five scorers had distinct integral scores, the maximum possible score of the topper is

A) 87

B) 95

C) 99

D) 100

E) 103


The average score in an examination of 10 students of a class is 60 --> the total score = 10*60 = 600;
The 5 smallest scores have an average of 55 --> the total score of the 5 smallest scores = 275.

From above, the total score of the 5 largest scores = 600 - 275 = 325.

Say the 5 largest scores are a, b, c, d, and e (where a<b<c<d<e, since each of the top five scorers had distinct scores). We want to maximize e. To maximize e, we need to minimize a, b, c, and d. The least value of a, is 55 (The least score of the top 5 , a, should be equal to the highest of the bottom 5 and to minimize the highest of the bottom 5, all scores from the bottom 5 should be equal). In this case the least values of b, c, and d are 56, 57, and 58 respectively:

a + b + c + d + e = 55 + 56 +57 + 58 + e = 325;
e = 99.

Answer: C.


Dear "Bunuel",

I have confusion on you solution.

The 5 smallest scores has an average of 55. For example: they could score 53,54,55,56,57 with total 275. In way of minimizing the the top 5 scores, you assumed that the lowest score is 55. However, in my example above, there at least 2 scores from the 5 smallest scores is larger that 2 scores in second group of top scores. Hence, I believe the smallest scores should not be 55, otherwise there are students in smallest group score higher than 2 students in top scores.

Where I go wrong?

Thanks
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Re: The average score in an examination of 10 students of a class is 60  [#permalink]

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New post 18 Sep 2016, 05:07
Mo2men wrote:
Bunuel wrote:
GMATantidote wrote:
The average score in an examination of 10 students of a class is 60. If the scores of the top five students are not considered, the average score of the remaining students falls by 5. The pass mark was 40 and the maximum mark was 100. It is also known that none of the students failed. If each of the top five scorers had distinct integral scores, the maximum possible score of the topper is

A) 87

B) 95

C) 99

D) 100

E) 103


The average score in an examination of 10 students of a class is 60 --> the total score = 10*60 = 600;
The 5 smallest scores have an average of 55 --> the total score of the 5 smallest scores = 275.

From above, the total score of the 5 largest scores = 600 - 275 = 325.

Say the 5 largest scores are a, b, c, d, and e (where a<b<c<d<e, since each of the top five scorers had distinct scores). We want to maximize e. To maximize e, we need to minimize a, b, c, and d. The least value of a, is 55 (The least score of the top 5 , a, should be equal to the highest of the bottom 5 and to minimize the highest of the bottom 5, all scores from the bottom 5 should be equal). In this case the least values of b, c, and d are 56, 57, and 58 respectively:

a + b + c + d + e = 55 + 56 +57 + 58 + e = 325;
e = 99.

Answer: C.


Dear "Bunuel",

I have confusion on you solution.

The 5 smallest scores has an average of 55. For example: they could score 53,54,55,56,57 with total 275. In way of minimizing the the top 5 scores, you assumed that the lowest score is 55. However, in my example above, there at least 2 scores from the 5 smallest scores is larger that 2 scores in second group of top scores. Hence, I believe the smallest scores should not be 55, otherwise there are students in smallest group score higher than 2 students in top scores.

Where I go wrong?

Thanks


Since, we need to find the maximum possible score of the topper, we need to make sure that the 5th person from the top should have the least score. So, if the average of last 5 is 275 and if we take all of those scores as 55, we can have the minimum value of the 5th also as 55. Hence, We need to take all the last 6 students to have a score of 55 so that we can maximize the topper student score. I hope it is clear now.
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