GMAT Question of the Day: Daily via email | Daily via Instagram New to GMAT Club? Watch this Video

 It is currently 21 Jan 2020, 18:24 ### GMAT Club Daily Prep

#### Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

#### Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.  # The average score in an examination of 10 students of a class is 60

Author Message
TAGS:

### Hide Tags

SVP  V
Status: It's near - I can see.
Joined: 13 Apr 2013
Posts: 1698
Location: India
GPA: 3.01
WE: Engineering (Real Estate)
The average score in an examination of 10 students of a class is 60  [#permalink]

### Show Tags

7 00:00

Difficulty:   95% (hard)

Question Stats: 25% (02:59) correct 75% (03:08) wrong based on 111 sessions

### HideShow timer Statistics

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

_________________
"Do not watch clock; Do what it does. KEEP GOING."
Math Expert V
Joined: 02 Sep 2009
Posts: 60555
Re: The average score in an examination of 10 students of a class is 60  [#permalink]

### Show Tags

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.

_________________
Senior Manager  Joined: 23 Apr 2015
Posts: 274
Location: United States
WE: Engineering (Consulting)
Re: The average score in an examination of 10 students of a class is 60  [#permalink]

### Show Tags

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 ?
Board of Directors V
Status: Stepping into my 10 years long dream
Joined: 18 Jul 2015
Posts: 3554
Re: The average score in an examination of 10 students of a class is 60  [#permalink]

### Show Tags

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. _________________
My GMAT Story: From V21 to V40
My MBA Journey: My 10 years long MBA Dream
My Secret Hacks: Best way to use GMATClub | Importance of an Error Log!
Verbal Resources: All SC Resources at one place | All CR Resources at one place

GMAT Club Inbuilt Error Log Functionality - View More.
New Visa Forum - Ask all your Visa Related Questions - here.
New! Best Reply Functionality on GMAT Club!
Find a bug in the new email templates and get rewarded with 2 weeks of GMATClub Tests for free
Check our new About Us Page here.
Current Student B
Joined: 24 Jul 2016
Posts: 73
Location: United States (MI)
GMAT 1: 730 Q51 V40
GPA: 3.6
Re: The average score in an examination of 10 students of a class is 60  [#permalink]

### Show Tags

1
Can a be 55? Or can it start from 56 only? That's what I was not sure about

Sent from my iPhone using GMAT Club Forum mobile app
Board of Directors V
Status: Stepping into my 10 years long dream
Joined: 18 Jul 2015
Posts: 3554
Re: The average score in an examination of 10 students of a class is 60  [#permalink]

### Show Tags

ProfX wrote:
Can a be 55? Or can it start from 56 only? That's what I was not sure about

Sent from my iPhone using GMAT Club Forum mobile app

Look at Bunuel 's explanation above. It has to be 55 to make e the max.
_________________
My GMAT Story: From V21 to V40
My MBA Journey: My 10 years long MBA Dream
My Secret Hacks: Best way to use GMATClub | Importance of an Error Log!
Verbal Resources: All SC Resources at one place | All CR Resources at one place

GMAT Club Inbuilt Error Log Functionality - View More.
New Visa Forum - Ask all your Visa Related Questions - here.
New! Best Reply Functionality on GMAT Club!
Find a bug in the new email templates and get rewarded with 2 weeks of GMATClub Tests for free
Check our new About Us Page here.
Math Expert V
Joined: 02 Aug 2009
Posts: 8340
Re: The average score in an examination of 10 students of a class is 60  [#permalink]

### Show Tags

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
C
_________________
Senior Manager  Joined: 23 Apr 2015
Posts: 274
Location: United States
WE: Engineering (Consulting)
Re: The average score in an examination of 10 students of a class is 60  [#permalink]

### Show Tags

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.

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 ?
SVP  V
Status: It's near - I can see.
Joined: 13 Apr 2013
Posts: 1698
Location: India
GPA: 3.01
WE: Engineering (Real Estate)
The average score in an examination of 10 students of a class is 60  [#permalink]

### Show Tags

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. _________________
"Do not watch clock; Do what it does. KEEP GOING."
SVP  V
Joined: 26 Mar 2013
Posts: 2344
Concentration: Operations, Strategy
Schools: Erasmus '21 (M\$)
The average score in an examination of 10 students of a class is 60  [#permalink]

### Show Tags

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.

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
Board of Directors V
Status: Stepping into my 10 years long dream
Joined: 18 Jul 2015
Posts: 3554
Re: The average score in an examination of 10 students of a class is 60  [#permalink]

### Show Tags

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.

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.
_________________
My GMAT Story: From V21 to V40
My MBA Journey: My 10 years long MBA Dream
My Secret Hacks: Best way to use GMATClub | Importance of an Error Log!
Verbal Resources: All SC Resources at one place | All CR Resources at one place

GMAT Club Inbuilt Error Log Functionality - View More.
New Visa Forum - Ask all your Visa Related Questions - here.
New! Best Reply Functionality on GMAT Club!
Find a bug in the new email templates and get rewarded with 2 weeks of GMATClub Tests for free
Check our new About Us Page here.
Non-Human User Joined: 09 Sep 2013
Posts: 13993
Re: The average score in an examination of 10 students of a class is 60  [#permalink]

### Show Tags

Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________ Re: The average score in an examination of 10 students of a class is 60   [#permalink] 04 Apr 2019, 02:18
Display posts from previous: Sort by

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