Summer is Coming! Join the Game of Timers Competition to Win Epic Prizes. Registration is Open. Game starts Mon July 1st.

 It is currently 16 Jul 2019, 13:40 ### 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.  # If the average (arithmetic mean) of 5 positive temperatures

Author Message
TAGS:

### Hide Tags

Intern  Joined: 26 Feb 2011
Posts: 31
If the average (arithmetic mean) of 5 positive temperatures  [#permalink]

### Show Tags

1
21 00:00

Difficulty:   25% (medium)

Question Stats: 72% (01:47) correct 28% (01:53) wrong based on 314 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:

A. 6x
B. 4x
C. 5x/3
D. 3x/2
E. 3x/5
Math Expert V
Joined: 02 Sep 2009
Posts: 56244

### Show Tags

3
5
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.

_________________
##### General Discussion
Retired Moderator Joined: 20 Dec 2010
Posts: 1736

### Show Tags

1
1
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.

Ans: "B"
_________________
Retired Moderator B
Joined: 16 Nov 2010
Posts: 1360
Location: United States (IN)
Concentration: Strategy, Technology

### Show Tags

1
I took 5 numbers and tried it out, because it's a "could be", so a possibility should be enough.

1, 2, 3, 4, 5 and mean = 15/5 = 3

so highest 3 = 3 + 4 + 5 = 12 = 4*3

_________________
Formula of Life -> Achievement/Potential = k * Happiness (where k is a constant)

GMAT Club Premium Membership - big benefits and savings
Intern  Status: Sophomore
Affiliations: President of Student Associoation
Joined: 09 Dec 2010
Posts: 35
Schools: HBS 2+2, IESE YTP

### Show Tags

Temperatures should be positive.
Veritas Prep GMAT Instructor D
Joined: 16 Oct 2010
Posts: 9433
Location: Pune, India
Re: If the average (arithmetic mean) of 5 positive temperatures  [#permalink]

### Show Tags

3
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.
_________________
Karishma
Veritas Prep GMAT Instructor

Veritas Prep GMAT Instructor D
Joined: 16 Oct 2010
Posts: 9433
Location: Pune, India
Re: If the average (arithmetic mean) of 5 positive temperatures  [#permalink]

### Show Tags

1
EMPOWERgmat Instructor V
Status: GMAT Assassin/Co-Founder
Affiliations: EMPOWERgmat
Joined: 19 Dec 2014
Posts: 14554
Location: United States (CA)
GMAT 1: 800 Q51 V49 GRE 1: Q170 V170 Re: If the average (arithmetic mean) of 5 positive temperatures  [#permalink]

### Show Tags

Hi All,

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 is a possibility, then you've answered the question (and you can stop).

GMAT assassins aren't born, they're made,
Rich
_________________
760+: Learn What GMAT Assassins Do to Score at the Highest Levels
Contact Rich at: Rich.C@empowergmat.com

*****Select EMPOWERgmat Courses now include ALL 6 Official GMAC CATs!*****

# Rich Cohen

Co-Founder & GMAT Assassin Follow
Special Offer: Save \$75 + GMAT Club Tests Free
Official GMAT Exam Packs + 70 Pt. Improvement Guarantee
www.empowergmat.com/
Manager  S
Joined: 24 Oct 2013
Posts: 130
Location: India
Concentration: General Management, Strategy
WE: Information Technology (Computer Software)
Re: If the average (arithmetic mean) of 5 positive temperatures  [#permalink]

### Show Tags

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)

substituting x in the options gives the answer B
Current Student D
Joined: 12 Aug 2015
Posts: 2609
Schools: Boston U '20 (M)
GRE 1: Q169 V154 Re: If the average (arithmetic mean) of 5 positive temperatures  [#permalink]

### Show Tags

Great Question.
I actually didnt solve it as a maxima minima question
I used brute Force to arrive at his set {x/2,x/2,4x/3,4x/3,4x/3} using Option B.

Quality Official Question

_________________
EMPOWERgmat Instructor V
Status: GMAT Assassin/Co-Founder
Affiliations: EMPOWERgmat
Joined: 19 Dec 2014
Posts: 14554
Location: United States (CA)
GMAT 1: 800 Q51 V49 GRE 1: Q170 V170 Re: If the average (arithmetic mean) of 5 positive temperatures  [#permalink]

### Show Tags

Hi All,

This question has a couple of great "concept" shortcuts built into it.

We're told that the average of 5 positive numbers is X, which means that the SUM of the 5 numbers is 5X.

The question asks us for a POSSIBLE sum of the greatest 3 values….

Since the values are all POSITIVE and they sum to 5X, there's no way for the sum of the greatest 3 to be bigger than that. 6X is NOT possible. Eliminate A.

IF all the values were the same (just call them all X), then the biggest 3 would sum to 3X. Changing the values would only INCREASE the sum of the biggest 3. This helps to eliminate C, D and E - they're all too small.

GMAT assassins aren't born, they're made,
Rich
_________________
760+: Learn What GMAT Assassins Do to Score at the Highest Levels
Contact Rich at: Rich.C@empowergmat.com

*****Select EMPOWERgmat Courses now include ALL 6 Official GMAC CATs!*****

# Rich Cohen

Co-Founder & GMAT Assassin Follow
Special Offer: Save \$75 + GMAT Club Tests Free
Official GMAT Exam Packs + 70 Pt. Improvement Guarantee
www.empowergmat.com/
Non-Human User Joined: 09 Sep 2013
Posts: 11659
Re: If the average (arithmetic mean) of 5 positive temperatures  [#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: If the average (arithmetic mean) of 5 positive temperatures   [#permalink] 09 Mar 2019, 01:52
Display posts from previous: Sort by

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