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

It is currently 16 Oct 2019, 01:06

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

M13-16

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

Hide Tags

Find Similar Topics 
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 58372
M13-16  [#permalink]

Show Tags

New post 16 Sep 2014, 00:49
1
2
00:00
A
B
C
D
E

Difficulty:

  65% (hard)

Question Stats:

49% (01:15) correct 51% (00:52) wrong based on 99 sessions

HideShow timer Statistics

Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 58372
Re M13-16  [#permalink]

Show Tags

New post 16 Sep 2014, 00:49
Official Solution:


The average (arithmetic mean) of four distinct positive integers is 10. If the average of the smaller two of these four integers is 8, which of the following represents the maximum possible value of the largest integer?


A. 12
B. 14
C. 15
D. 16
E. 17


Given: \(0 \lt a \lt b \lt c \lt d\). Notice that \(a, b, c\) and \(d\) are distinct positive integers.

The average of four distinct positive integers is 10: \(a+b+c+d=4*10=40\);

The average of the smaller two of these four integers is 8: \(a+b=2*8=16\). So, \(16+c+d=40\), which leads to \(c+d=24\).

We want to maximize \(d\), so we should minimize \(c\). The minimum value of \(c\) is 10, for \(a=7\) and \(b=9\). So, \(10+d=24\) and \(d=14\).


Answer: B
_________________
Intern
Intern
avatar
Joined: 09 Mar 2016
Posts: 2
Re: M13-16  [#permalink]

Show Tags

New post 15 Jun 2016, 00:07
Bunuel : Why we minimize C=10???
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 58372
Re: M13-16  [#permalink]

Show Tags

New post 15 Jun 2016, 02:41
Intern
Intern
avatar
Joined: 02 Feb 2010
Posts: 1
Re: M13-16  [#permalink]

Show Tags

New post 10 Oct 2016, 07:09
I'm sorry. Maybe I'm not following the whole logic. But wouldn't the set 6,10,11,13 do the trick? I didn't understand why you assume the values of a and b in that way.

Thanks
Math Expert
avatar
V
Joined: 02 Aug 2009
Posts: 7958
Re: M13-16  [#permalink]

Show Tags

New post 10 Oct 2016, 07:23
chambreau wrote:
I'm sorry. Maybe I'm not following the whole logic. But wouldn't the set 6,10,11,13 do the trick? I didn't understand why you assume the values of a and b in that way.

Thanks


Hi i
It is done to ensure that the largest number has maximum possible value
_________________
Senior Manager
Senior Manager
avatar
P
Joined: 09 Jun 2014
Posts: 352
Location: India
Concentration: General Management, Operations
Premium Member Reviews Badge
Re: M13-16  [#permalink]

Show Tags

New post 17 Mar 2018, 08:14
Channarong22 wrote:
Bunuel : Why we minimize C=10???


It is given a,b are smaller of the 4 integers ..so definitely C and D have to be greater than that..
Now since we know a and b are 7 and 9 from above explanation.C has to be greater than 9 and so it is 10.
GMAT Club Bot
Re: M13-16   [#permalink] 17 Mar 2018, 08:14
Display posts from previous: Sort by

M13-16

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

Moderators: chetan2u, Bunuel






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