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 Your Progress

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.

It appears that you are browsing the GMAT Club forum unregistered!

Signing up is free, quick, and confidential.
Join other 500,000 members and get the full benefits of GMAT Club

Registration gives you:

Tests

Take 11 tests and quizzes from GMAT Club and leading GMAT prep companies such as Manhattan GMAT,
Knewton, and others. All are free for GMAT Club members.

Applicant Stats

View detailed applicant stats such as GPA, GMAT score, work experience, location, application
status, and more

Books/Downloads

Download thousands of study notes,
question collections, GMAT Club’s
Grammar and Math books.
All are free!

Thank you for using the timer!
We noticed you are actually not timing your practice. Click the START button first next time you use the timer.
There are many benefits to timing your practice, including:

20 students took the test. The arithmetic mean of the scores [#permalink]

Show Tags

04 Aug 2013, 04:00

1

This post received KUDOS

9

This post was BOOKMARKED

00:00

A

B

C

D

E

Difficulty:

55% (hard)

Question Stats:

65% (01:45) correct
35% (02:10) wrong based on 241 sessions

HideShow timer Statistics

20 students took the test. The arithmetic mean of the scores was 4.75 and the range was 2. If the only possible scores were {2,3,4,5}, what is the greatest possible number of excellent scores (5)? (A)19 (B)17 (C)14 (D)13 (E)12

Re: 20 students took the test. The arithmetic mean of the scores [#permalink]

Show Tags

04 Aug 2013, 04:13

1

This post received KUDOS

1

This post was BOOKMARKED

guerrero25 wrote:

20 students took the test. The arithmetic mean of the scores was 4.75 and the range was 2. If the only possible scores were {2,3,4,5}, what is the greatest possible number of excellent scores (5)? (A)19 (B)17 (C)14 (D)13 (E)12

As the range is 2, and we want to maximize the no of 5's, there can not be any 2 in the given test.Also, the total score = 20*4.75 = 95.

Now, let the no of 3's,4's and 5's be x,y,z repectively.

Thus, 3x+4y+5z = 95.Now, for x=2 and y=1, we get 5z = 95-10=85 and z =17.

Re: 20 students took the test. The arithmetic mean of the scores [#permalink]

Show Tags

04 Aug 2013, 04:13

1

This post received KUDOS

1

This post was BOOKMARKED

20 students took the test. The arithmetic mean of the scores was 4.75 and the range was 2. If the only possible scores were {2,3,4,5}, what is the greatest possible number of excellent scores (5)?

The sum of the scores is \(4.75*20=95\). If the range is 2 and we want to find the max number of 5s, the lowest score possible is 3. To maximize the 5s we have to reduce the 3s and the 4s.

5*x+4*z+3*y=95 and x+y+z=20.

So y=2 and z=1, 5*x+4+6=85 and x=17.
_________________

It is beyond a doubt that all our knowledge that begins with experience.

Re: 20 students took the test. The arithmetic mean of the scores [#permalink]

Show Tags

04 Aug 2013, 04:24

2

This post received KUDOS

1

This post was BOOKMARKED

guerrero25 wrote:

20 students took the test. The arithmetic mean of the scores was 4.75 and the range was 2. If the only possible scores were {2,3,4,5}, what is the greatest possible number of excellent scores (5)? (A)19 (B)17 (C)14 (D)13 (E)12

Total Score = 20 x 4.75 = 95 Range is 2 Possible scores {2,3,4,5}

Rather Than solving this question using algebra, i would prefer testing options directly. My purpose would be to maximize the no of scores that value 5 Option A - 19 x 5= 95 Possible but this option fails to satisfy range criteria. As per this option range would be 0, but the range is 2. Thus Incorrect

Option B - 17 x 5= 85 We are left with 3 scores that must sum to 10 Because the range is 2 we can not scores that value 2. Thus we can use only 3 & 4 remaining 3 scores - 3,3,4 Possible Thus correct

Answer B

Thus Incorrect
_________________

If you like my Question/Explanation or the contribution, Kindly appreciate by pressing KUDOS. Kudos always maximizes GMATCLUB worth-Game Theory

If you have any question regarding my post, kindly pm me or else I won't be able to reply

Re: 20 students took the test. The arithmetic mean of the scores [#permalink]

Show Tags

24 Nov 2014, 01:11

1

This post was BOOKMARKED

x1-x20 = 2 also we have to make the number of 5s max. so we have to reject the 2 and 4 pair. Hence max of the 20 numbers is 5 and the minimum is 3. Now x1+x2+.....x20 = 4.75*20 =95, or x2+x3+......+x19 = 95-(3+5) = 87 to find the maximum of 5s divide 87 by 5 and the whole number part will be the answer i.e 17

Re: 20 students took the test. The arithmetic mean of the scores [#permalink]

Show Tags

19 May 2016, 10:21

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.
_________________

WE: Medicine and Health (Pharmaceuticals and Biotech)

Re: 20 students took the test. The arithmetic mean of the scores [#permalink]

Show Tags

07 Aug 2017, 23:10

Since the only possible scores are 2,3,4,5 and the range is 2 wherein the max score should be 5 thus the lowest score should be 3 Now as we have the avg =4.75 and the no.of terms =20 we can find the sum of all the 20 scores = avg * no.of students=4.75*20=95 Now to find the max no.of students who scored 5 we will consider that only 1 student scored 3 and only 1 student scored 4 Thus 95-(3+4)=88 which is not divisible by 5 thus option A is incorrect. Likewise when we increase the no.of students who scored 3 or 4 we get that option B is correct.

Re: 20 students took the test. The arithmetic mean of the scores [#permalink]

Show Tags

12 Aug 2017, 07:58

guerrero25 wrote:

20 students took the test. The arithmetic mean of the scores was 4.75 and the range was 2. If the only possible scores were {2,3,4,5}, what is the greatest possible number of excellent scores (5)? (A)19 (B)17 (C)14 (D)13 (E)12

4.75*20= 17*5 +3*2+4
_________________

Believe you can and you are halfway there-Theodore Roosevelt

Version 8.1 of the WordPress for Android app is now available, with some great enhancements to publishing: background media uploading. Adding images to a post or page? Now...

Post today is short and sweet for my MBA batchmates! We survived Foundations term, and tomorrow's the start of our Term 1! I'm sharing my pre-MBA notes...

“Keep your head down, and work hard. Don’t attract any attention. You should be grateful to be here.” Why do we keep quiet? Being an immigrant is a constant...