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:

If the average (arithmetic mean) of 5 positive temperatures [#permalink]

Show Tags

06 Mar 2011, 09:31

12

This post was BOOKMARKED

00:00

A

B

C

D

E

Difficulty:

25% (medium)

Question Stats:

69% (01:19) correct
31% (01:20) wrong based on 244 sessions

HideShow timer Statistics

If the average (arithmetic mean) of 5 positive temperatures is x degrees Fahrenheit, then the sum of the 3 greatest of these temperatures, in degrees Fahrenheit, could be:

The sum of three greatest should be more than sum of two lowest.

The total sum is; 5x

A. 6x; 6x is more than 5x. Not possible. B. 4x; 5x-4x=x(Possible) C. 5x/3; 10x/3; 10x/3 > 5x/3. Not possible D. 3x/2; 7x/2; 7x/2 > 3x/2. Not possible E. 3x/5; 22x/5; 22x/5 > 3x/5. Not possible.

If the average (arithmetic mean) of 5 positive temperatures is x degrees Fahrenheit, then the sum of the 3 greatest of these temperatures, in degrees Fahrenheit, could be: A/ 6x B/ 4x C/ 5x/3 D/ 3x/2 E/ 3x/5

Note that we have 5 positive temperatures.

Next, as the average is x then the sum of the temperatures is 5x and as all the temperatures are positive then the sum of the 3 greatest must be more than (or equal to) 3x (as the average of the 3 greatest must be at least x) and less than 5x: 3x<SUM<5x --> only option B fits.

If the average (arithmetic mean) of 5 positive temperatures is x degrees Fahrenheit, then the sum of the 3 greatest of these temperatures, in degrees Fahrenheit, could be:

A. 6x B. 4x C. 5x/3 D. 3x/2 E. 3x/5

Responding to a pm:

Avg of 5 temperatures is x. So the sum of all 5 temperatures is 5x. Now what CAN be the sum of the 3 greatest temperatures?

Let's try to find the maximum value that the 'sum of the 3 greatest temperatures' can take and the minimum value that it can take.

Maximum: To make the sum of 3 greatest temperatures as large as possible, we make the 2 lowest temperatures as small as possible. The two lowest temperatures can be as small as 0.0000000000000001 i.e. anything slightly more than 0. So the sum of the 3 greatest temperatures will be slightly less than 5x.

Minimize: To minimize the sum of 3 greatest temperatures, we make the 2 lowest temperatures as high as possible. For the average to be x, either some values should be less than x and some more OR all values could be equal to x. That is, the temperatures could be x, x, x, x, x - in this case the two lowest temperatures are maximum (all temperatures are the same actually). So sum of 3 greatest temperatures will be at least 3x.

Note that only one value lies between 5x and 3x and that is 4x.

We don't really need to figure out the minimum sum. Once we know that maximum sum can be a little less than 5x, we see that the sum of 3 greatest temperatures can easily be 4x. We will be left with a sum of x for the two lowest temperatures. They can be x/2 each. The 3 greatest temperatures can be x, x and 2x or many other variations.
_________________

Re: If the average (arithmetic mean) of 5 positive temperatures [#permalink]

Show Tags

29 Nov 2014, 08:51

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: If the average (arithmetic mean) of 5 positive temperatures [#permalink]

Show Tags

04 Dec 2015, 04:22

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.
_________________

One of the great 'shortcuts' to this question is that it asks for what COULD be the sum of the three highest temperatures. As such, once you find an answer that COULD be the sum, you can STOP working. Once you prove that Answer

Re: If the average (arithmetic mean) of 5 positive temperatures [#permalink]

Show Tags

26 Sep 2016, 22:55

let x be 2 and total sum becomes 10 now using maximization and minimization the least values can be 1 and 1 equaling to 2 =>10-2 = 8 (rest of the temp)

We’ve given one of our favorite features a boost! You can now manage your profile photo, or avatar , right on WordPress.com. This avatar, powered by a service...

Sometimes it’s the extra touches that make all the difference; on your website, that’s the photos and video that give your content life. You asked for streamlined access...

A lot has been written recently about the big five technology giants (Microsoft, Google, Amazon, Apple, and Facebook) that dominate the technology sector. There are fears about the...

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...