GMAT Question of the Day - Daily to your Mailbox; hard ones only

It is currently 20 Aug 2018, 02:12

Close

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
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.

Close

Request Expert Reply

Confirm Cancel

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

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:

Hide Tags

Math Revolution GMAT Instructor
User avatar
V
Joined: 16 Aug 2015
Posts: 6038
GMAT 1: 760 Q51 V42
GPA: 3.82
Premium Member
The minimum of the integers x, y, and z is 10 and their avera  [#permalink]

Show Tags

New post 26 Apr 2018, 01:22
00:00
A
B
C
D
E

Difficulty:

  15% (low)

Question Stats:

73% (00:34) correct 27% (00:31) wrong based on 51 sessions

HideShow timer Statistics

[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?

\(A. 10\)
\(B. 11\)
\(C. 12\)
\(D. 13\)
\(E. 14\)

_________________

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 $99 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
Director
User avatar
D
Joined: 04 Dec 2015
Posts: 700
Location: India
Concentration: Technology, Strategy
Schools: ISB '19, IIMA , IIMB, XLRI
WE: Information Technology (Consulting)
GMAT ToolKit User
The minimum of the integers x, y, and z is 10 and their avera  [#permalink]

Show Tags

New post 26 Apr 2018, 01:34
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
SC Moderator
avatar
V
Joined: 22 May 2016
Posts: 1911
Premium Member CAT Tests
The minimum of the integers x, y, and z is 10 and their avera  [#permalink]

Show Tags

New post 26 Apr 2018, 12:25
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
_________________

In the depths of winter, I finally learned
that within me there lay an invincible summer.

-- Albert Camus, "Return to Tipasa"

Math Revolution GMAT Instructor
User avatar
V
Joined: 16 Aug 2015
Posts: 6038
GMAT 1: 760 Q51 V42
GPA: 3.82
Premium Member
Re: The minimum of the integers x, y, and z is 10 and their avera  [#permalink]

Show Tags

New post 29 Apr 2018, 18:32
=>

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 $99 for 3 month Online Course"
"Free Resources-30 day online access & Diagnostic Test"
"Unlimited Access to over 120 free video lessons - try it yourself"

CEO
CEO
User avatar
D
Joined: 12 Sep 2015
Posts: 2707
Location: Canada
Re: The minimum of the integers x, y, and z is 10 and their avera  [#permalink]

Show Tags

New post 30 Apr 2018, 11:26
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.

Answer: D

Cheers,
Brent
_________________

Brent Hanneson – Founder of gmatprepnow.com

Image

Re: The minimum of the integers x, y, and z is 10 and their avera &nbs [#permalink] 30 Apr 2018, 11:26
Display posts from previous: Sort by

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

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  

Events & Promotions

PREV
NEXT


GMAT Club MBA Forum Home| About| Terms and Conditions and Privacy Policy| GMAT Club Rules| Contact| Sitemap

Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne

Kindly note that the GMAT® test is a registered trademark of the Graduate Management Admission Council®, and this site has neither been reviewed nor endorsed by GMAC®.