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# The minimum of the integers x, y, and z is 10 and their avera

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Math Revolution GMAT Instructor
Joined: 16 Aug 2015
Posts: 6827
GMAT 1: 760 Q51 V42
GPA: 3.82
The minimum of the integers x, y, and z is 10 and their avera  [#permalink]

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26 Apr 2018, 00:22
00:00

Difficulty:

15% (low)

Question Stats:

77% (00:51) correct 23% (00:55) wrong based on 54 sessions

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[GMAT math practice question]

The minimum of the integers $$x, y$$, and $$z$$ is $$10$$ and their average is $$11$$. What is the greatest possible value of their maximum?

$$A. 10$$
$$B. 11$$
$$C. 12$$
$$D. 13$$
$$E. 14$$

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MathRevolution: Finish GMAT Quant Section with 10 minutes to spare
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"Only $149 for 3 month Online Course" "Free Resources-30 day online access & Diagnostic Test" "Unlimited Access to over 120 free video lessons - try it yourself" Director Joined: 04 Dec 2015 Posts: 739 Location: India Concentration: Technology, Strategy Schools: ISB '19, IIMA , IIMB, XLRI WE: Information Technology (Consulting) The minimum of the integers x, y, and z is 10 and their avera [#permalink] ### Show Tags 26 Apr 2018, 00:34 1 MathRevolution wrote: [GMAT math practice question] The minimum of the integers $$x, y$$, and $$z$$ is $$10$$ and their average is $$11$$. What is the greatest possible value of their maximum? $$A. 10$$ $$B. 11$$ $$C. 12$$ $$D. 13$$ $$E. 14$$ Given minimum integer is $$= 10$$ Average of $$3$$ integers $$x$$, $$y$$, and $$z$$ $$= 11$$ Therefore Total $$= 11*3 = 33$$ ie; $$x + y + z = 33$$ Greatest value is possible if the other two values are minimum. Let $$x$$ and $$y$$ $$= 10$$ Therefore greatest possible value of their maximum; $$x + y + z = 33$$ $$10 + 10 + z = 33$$ $$20 + z = 33$$ $$z = 33-20 = 13$$ Answer D Senior SC Moderator Joined: 22 May 2016 Posts: 2367 The minimum of the integers x, y, and z is 10 and their avera [#permalink] ### Show Tags 26 Apr 2018, 11:25 MathRevolution wrote: [GMAT math practice question] The minimum of the integers $$x, y$$, and $$z$$ is $$10$$ and their average is $$11$$. What is the greatest possible value of their maximum? $$A. 10$$ $$B. 11$$ $$C. 12$$ $$D. 13$$ $$E. 14$$ I could not understand the question. (Maybe that's the point?) REWRITE: Each of three integers $$x, y,$$ and $$z$$ has a minimum value of $$10$$. The integers' average is $$11.$$ What is the greatest possible value of any one variable? We know the sum, $$x + y + z$$: $$A*n = S$$ $$11*3 = 33$$ = Sum of all three In order to maximize one value, minimize the other two. Each integer must = at least 10 Let $$x=10, y=10$$ $$10, 10,$$ z? . . .They sum to $$33$$: $$10 + 10 + z = 33$$ $$z = (33 - 20) = 13$$ Maximum value of the third integer = $$13$$ Answer D _________________ Life’s like a movie. Write your own ending. Kermit the Frog Math Revolution GMAT Instructor Joined: 16 Aug 2015 Posts: 6827 GMAT 1: 760 Q51 V42 GPA: 3.82 Re: The minimum of the integers x, y, and z is 10 and their avera [#permalink] ### Show Tags 29 Apr 2018, 17:32 => Assume $$x ≤ y ≤ z.$$ $$\frac{( x + y + z )}{3} = 11$$ and $$x = 10$$ We have $$10 + y + z = 33$$ or $$y + z = 23.$$ In order to have the greatest maximum number, y must be the minimum which is $$10$$. $$10 + z = 23.$$ $$z = 13$$. Therefore, D is the answer. Answer : D _________________ MathRevolution: Finish GMAT Quant Section with 10 minutes to spare The one-and-only World’s First Variable Approach for DS and IVY Approach for PS with ease, speed and accuracy. "Only$149 for 3 month Online Course"
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Joined: 11 Sep 2015
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Re: The minimum of the integers x, y, and z is 10 and their avera  [#permalink]

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30 Apr 2018, 10:26
Top Contributor
MathRevolution wrote:
[GMAT math practice question]

The minimum of the integers $$x, y$$, and $$z$$ is $$10$$ and their average is $$11$$. What is the greatest possible value of their maximum?

$$A. 10$$
$$B. 11$$
$$C. 12$$
$$D. 13$$
$$E. 14$$

Key concept: If we know the sum of a set of numbers, and we want to MAXIMIZE the biggest number in the set, we must MINIMIZE all of the other numbers.

GIVEN: Average of x, y, and z is 11
So, (x + y + z)/3 = 33
This means x + y + z = 33
Great! We know the sum of the values.

In order to MAXIMIZE the biggest number in the set, we must MINIMIZE all of the other numbers.
We're told that 10 is the MINIMUM value in the set.
So, let's let TWO of the values equal 10
Say x = 10 and y = 10
We have now MINIMIZED two of the three values.

Since we know that x + y + z = 33, we can now write 10 + 10 + z = 33
Solve to get: z = 13
So, the MAXIMUM value is 13.

Cheers,
Brent
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Re: The minimum of the integers x, y, and z is 10 and their avera &nbs [#permalink] 30 Apr 2018, 10:26
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