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

It is currently 23 Oct 2018, 07:02

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

If the median and the average (arithmetic mean) of 4 different numbers

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

Hide Tags

Senior SC Moderator
User avatar
V
Joined: 14 Nov 2016
Posts: 1314
Location: Malaysia
GMAT ToolKit User Premium Member CAT Tests
If the median and the average (arithmetic mean) of 4 different numbers  [#permalink]

Show Tags

New post 21 Feb 2017, 17:48
2
00:00
A
B
C
D
E

Difficulty:

  85% (hard)

Question Stats:

52% (02:22) correct 48% (02:16) wrong based on 98 sessions

HideShow timer Statistics

If the median and the average (arithmetic mean) of 4 different numbers are both 50, what is the smallest number?

1) The range of the 4 numbers is 50

2) The sum of the smallest and the largest of the 4 number is 100

_________________

"Be challenged at EVERY MOMENT."

“Strength doesn’t come from what you can do. It comes from overcoming the things you once thought you couldn’t.”

"Each stage of the journey is crucial to attaining new heights of knowledge."

Rules for posting in verbal forum | Please DO NOT post short answer in your post!

Advanced Search : https://gmatclub.com/forum/advanced-search/

Senior Manager
Senior Manager
User avatar
S
Joined: 24 Oct 2016
Posts: 278
Location: India
Concentration: Finance, International Business
Schools: IIMB
GMAT 1: 550 Q42 V28
GPA: 3.96
WE: Human Resources (Retail Banking)
Re: If the median and the average (arithmetic mean) of 4 different numbers  [#permalink]

Show Tags

New post 03 Mar 2017, 04:11
can someone explain how A can be the answer ,although i am pretty sure that D can not be the answer but still unable to understand the OA
please explain with necessary example

thanks
Intern
Intern
avatar
B
Joined: 28 Jan 2017
Posts: 4
Location: India
Concentration: Finance, General Management
WE: Securities Sales and Trading (Mutual Funds and Brokerage)
GMAT ToolKit User
Re: If the median and the average (arithmetic mean) of 4 different numbers  [#permalink]

Show Tags

New post 03 Mar 2017, 20:08
1
ziyuen wrote:
If the median and the average (arithmetic mean) of 4 different numbers are both 50, what is the smallest number?

1) The range of the 4 numbers is 50

2) The sum of the smallest and the largest of the 4 number is 100


Here's how I solved it -
1) Even numbered set + Average AND Median 50 -> Numbers Equidistant from 50 in either direction (50-y, 50-x, 50+x, 50+y). They're like mirror images around the number 50.


1) -> 50+y-50+y = 50. Sufficient
2) We already know sum of smallest and largest is 100! Actually, sum of 2nd largest and 2nd smallest is also 100! That's the beauty of this series. :lol:

Therefore, A.
Senior Manager
Senior Manager
User avatar
B
Status: Come! Fall in Love with Learning!
Joined: 05 Jan 2017
Posts: 472
Location: India
Premium Member
Re: If the median and the average (arithmetic mean) of 4 different numbers  [#permalink]

Show Tags

New post 04 Mar 2017, 04:59
1
Prompt analysis
a,b,c,d are the numbers such that a<b<c<d and (a+b+c+d)/4 = 50 and (b+c)/2 = 50 therefore a+d = 100

Super set
the answer will be a positive real number

translation
In order to find the answer, we need
1# exact value of all a
2# another equation in a and d
3# any specific property of a the restrict the valuye

statement analysis
St 1: range is 100. or d-a =100. therefore d =100 and a =0. ANSWER
St 2: a+d =100. that is already inferred from the question statement. INSUFFICIENT

Option A
_________________

GMAT Mentors
Image

Senior Manager
Senior Manager
User avatar
S
Joined: 24 Oct 2016
Posts: 278
Location: India
Concentration: Finance, International Business
Schools: IIMB
GMAT 1: 550 Q42 V28
GPA: 3.96
WE: Human Resources (Retail Banking)
Re: If the median and the average (arithmetic mean) of 4 different numbers  [#permalink]

Show Tags

New post 04 Mar 2017, 22:08
thank you byjusclasses :)
i was missing that zero (0), well you made it clear now thanks
Manager
Manager
avatar
S
Joined: 13 Mar 2013
Posts: 166
Location: United States
Concentration: Leadership, Technology
GPA: 3.5
WE: Engineering (Telecommunications)
Re: If the median and the average (arithmetic mean) of 4 different numbers  [#permalink]

Show Tags

New post 04 Mar 2017, 22:41
If the median and the average (arithmetic mean) of 4 different numbers are both 50, what is the smallest number?

1) The range of the 4 numbers is 50

2) The sum of the smallest and the largest of the 4 number is 100

Let the number be a,b,c and d ( increasing order )
as the Question
median = mean
b+c / 2 = 50
b+c = 100

mean = 50 = a+b+c+d /4
therefore a+b+c+d = 200
hence a+d = 100 ( as b+c = 100 )

(1) d-a = 50
and we know that a+d = 100
hence sufficient as we can calculate a from the two statement .

(2) no new information a+d =100 . Not sufficient

Hence the ans is A

Regards,

Press Kudos , if it helps .
_________________

Regards ,

Magoosh GMAT Instructor
User avatar
G
Joined: 28 Dec 2011
Posts: 4494
Re: If the median and the average (arithmetic mean) of 4 different numbers  [#permalink]

Show Tags

New post 05 Mar 2017, 12:24
1
ByjusClasses wrote:
Prompt analysis
a,b,c,d are the numbers such that a<b<c<d and (a+b+c+d)/4 = 50 and (b+c)/2 = 50 therefore a+d = 100

Super set
the answer will be a positive real number

translation
In order to find the answer, we need
1# exact value of all a
2# another equation in a and d
3# any specific property of a the restrict the valuye

statement analysis
St 1: range is 100. or d-a =100. therefore d =100 and a =0. ANSWER
St 2: a+d =100. that is already inferred from the question statement. INSUFFICIENT

Option A

coolnuts wrote:
The range is 50. So as per the Q S1 should be d-a=50 and not 100 as stated by you.

Dear ByjusClasses,

My colleague, a good solution. I simply want to point out, as coolnuts pointed out, that the range is 50. Of course, this doesn't change the answer to the DS question, but it would if similar information were in a PS question.

In fact, d - a = 50 and a + d = 100, so d = 75 and a = 25.

Also, coolnuts, the "report a problem" feature is really to indicate, for example, that a problem has a typo or has been miscopied from its source. Reporting a problem requires an expert to address it. If you see a problem in what another user has written, respond and tell that user yourself. Initiative and responsibility are important qualities when you are a manager, so it's good to practice them now.

Does all this make sense?
Mike :-)
_________________

Mike McGarry
Magoosh Test Prep


Education is not the filling of a pail, but the lighting of a fire. — William Butler Yeats (1865 – 1939)

Non-Human User
User avatar
Joined: 09 Sep 2013
Posts: 8541
Premium Member
Re: If the median and the average (arithmetic mean) of 4 different numbers  [#permalink]

Show Tags

New post 17 Apr 2018, 10:53
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 Books | GMAT Club Tests | Best Prices on GMAT Courses | GMAT Mobile App | Math Resources | Verbal Resources

GMAT Club Bot
Re: If the median and the average (arithmetic mean) of 4 different numbers &nbs [#permalink] 17 Apr 2018, 10:53
Display posts from previous: Sort by

If the median and the average (arithmetic mean) of 4 different numbers

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


Copyright

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®.