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

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

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06 Mar 2011, 09:31
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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
[Reveal] Spoiler: OA
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06 Mar 2011, 09:48
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"
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06 Mar 2011, 23:55
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

So answer is B.

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07 Mar 2011, 03:09
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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.

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07 Mar 2011, 21:25
Temperatures should be positive.
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18 Apr 2011, 03:05
I followed the same strategy like Fluke.
OA is B.
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Re: If the average (arithmetic mean) of 5 positive temperatures [#permalink]

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06 Oct 2013, 21:50
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Expert's post
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.
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Get started with Veritas Prep GMAT On Demand for $199 Veritas Prep Reviews Veritas Prep GMAT Instructor Joined: 16 Oct 2010 Posts: 7377 Location: Pune, India Followers: 2288 Kudos [?]: 15136 [1] , given: 224 Re: If the average (arithmetic mean) of 5 positive temperatures [#permalink] ### Show Tags 06 Oct 2013, 21:52 1 This post received KUDOS Expert's post GMAT Club Legend Joined: 09 Sep 2013 Posts: 15491 Followers: 651 Kudos [?]: 210 [0], given: 0 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. _________________ GMAT Club Legend Joined: 09 Sep 2013 Posts: 15491 Followers: 651 Kudos [?]: 210 [0], given: 0 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. _________________ EMPOWERgmat Instructor Status: GMAT Assassin/Co-Founder Affiliations: EMPOWERgmat Joined: 19 Dec 2014 Posts: 9125 Location: United States (CA) GMAT 1: 800 Q51 V49 GRE 1: 340 Q170 V170 Followers: 445 Kudos [?]: 2875 [0], given: 169 Re: If the average (arithmetic mean) of 5 positive temperatures [#permalink] ### Show Tags 05 Dec 2015, 11:26 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 [Reveal] Spoiler: B 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 # Rich Cohen Co-Founder & GMAT Assassin # Special Offer: Save$75 + GMAT Club Tests

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

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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)

substituting x in the options gives the answer B
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Re: If the average (arithmetic mean) of 5 positive temperatures [#permalink]

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17 Dec 2016, 21:46
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.

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Re: If the average (arithmetic mean) of 5 positive temperatures   [#permalink] 17 Dec 2016, 21:46
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# If the average (arithmetic mean) of 5 positive temperatures

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