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

 It is currently 25 May 2019, 22:16 ### 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. ### Request Expert Reply # What is the sum of all numbers x for which the median of the numbers 4

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

### Hide Tags

Math Expert V
Joined: 02 Sep 2009
Posts: 55274
What is the sum of all numbers x for which the median of the numbers 4  [#permalink]

### Show Tags 00:00

Difficulty:   95% (hard)

Question Stats: 14% (01:49) correct 86% (02:44) wrong based on 22 sessions

### HideShow timer Statistics

What is the sum of all numbers x for which the median of the numbers 4, 6, 8, 17, and x is equal to the mean of those five numbers?

A. -5
B. 0
C. 5
D. 15/4
E. 35/4

_________________
Manager  B
Joined: 08 Dec 2013
Posts: 170
Location: India
Concentration: Nonprofit, Sustainability
GMAT 1: 630 Q47 V30 WE: Operations (Non-Profit and Government)
What is the sum of all numbers x for which the median of the numbers 4  [#permalink]

### Show Tags

1
Bunuel wrote:
What is the sum of all numbers x for which the median of the numbers 4, 6, 8, 17, and x is equal to the mean of those five numbers?

A. -5
B. 0
C. 5
D. 15/4
E. 35/4

Possible list:- (Medians marked in red)
1. 4 6 8 17 x
2. 4 6 8 x 17

3. 4 6 x 8 17

4. 4 x 6 8 17
5. x 4 6 8 17

Mean in all the above 6 cases= (35+x)/5. Equating Mean=Median

Case A, let's see if 8 can be a median:-
8 = (35+x)/5
5=x (Not possible for case# 1 and 2)

Case B Next, let's see when x is median
x= (35+x)/5
x=(35/4)= 8.something (Not possible for case#3)

Case C Finally let's see if 6 can be median
6=(35+x)/5
-5=x (Possible for case#5)

So Sum of all possible values of x= -5.

<Waiting for OA>
_________________
Kindly drop a '+1 Kudos' if you find this post helpful.

GMAT Math Book

-I never wanted what I gave up
I never gave up what I wanted-
Senior Manager  G
Joined: 19 Oct 2018
Posts: 293
Location: India
Re: What is the sum of all numbers x for which the median of the numbers 4  [#permalink]

### Show Tags

When x<6
(35+x)/5 =6
x= -5

When 6<x<8
(35+x)/5 =x
x= 8.75( not in our range)

When x>8
(35+x)/5 =8
x= 5( again not in our range)

Only value of x possible is -5
Intern  B
Joined: 07 Apr 2018
Posts: 1
Re: What is the sum of all numbers x for which the median of the numbers 4  [#permalink]

### Show Tags

Bunuel wrote:
What is the sum of all numbers x for which the median of the numbers 4, 6, 8, 17, and x is equal to the mean of those five numbers?

A. -5
B. 0
C. 5
D. 15/4
E. 35/4

mean= (sum of numbers)/5 = (35+x)/5
test no if x= -5 then Mean= 6 set = -5,4,6,8,17
median= 6

if x=0 then mean= 7 set = 0,4,6,8,17
median= 6 (not possible bcoz mean=median)
test rest of numbers but A will only fulfill the condition. So OA will be A
Senior Manager  G
Joined: 19 Oct 2018
Posts: 293
Location: India
Re: What is the sum of all numbers x for which the median of the numbers 4  [#permalink]

### Show Tags

'0' or any other option is not the value of x. It's actually the sum of all possible values of x. You can't substitute it for x.

rahul12988 wrote:
Bunuel wrote:
What is the sum of all numbers x for which the median of the numbers 4, 6, 8, 17, and x is equal to the mean of those five numbers?

A. -5
B. 0
C. 5
D. 15/4
E. 35/4

mean= (sum of numbers)/5 = (35+x)/5
test no if x= -5 then Mean= 6 set = -5,4,6,8,17
median= 6

if x=0 then mean= 7 set = 0,4,6,8,17
median= 6 (not possible bcoz mean=median)
test rest of numbers but A will only fulfill the condition. So OA will be A
Veritas Prep GMAT Instructor D
Joined: 16 Oct 2010
Posts: 9246
Location: Pune, India
Re: What is the sum of all numbers x for which the median of the numbers 4  [#permalink]

### Show Tags

Bunuel wrote:
What is the sum of all numbers x for which the median of the numbers 4, 6, 8, 17, and x is equal to the mean of those five numbers?

A. -5
B. 0
C. 5
D. 15/4
E. 35/4

The median of 4, 6, 8, 17 and x will be 6 or 8 or x (if x is between 6 and 8)

Assuming median is 6,
6 = (4 + 6 + 8 + 17 + x)/5
x = -5

Assuming median is 8,
8 = (4 + 6 + 8 + 17 + x)/5
x = 5
But x cannot be 5 because median must be 6 in the case.

Assuming median is x (between 6 and 8),
x = (4 + 6 + 8 + 17 + x)/5
x = 35/4
x is not between 6 and 8.

So x can be only -5.
Answer (A)
_________________
Karishma
Veritas Prep GMAT Instructor

Learn more about how Veritas Prep can help you achieve a great GMAT score by checking out their GMAT Prep Options >
Intern  B
Joined: 07 Mar 2019
Posts: 19
What is the sum of all numbers x for which the median of the numbers 4  [#permalink]

### Show Tags

I found this question to be poorly written. The question asks "What is the sum of all numbers x". The answer is not the sum of all 5 numbers. I also was very confused because I initially thought "x" was supposed to represent the sum of the 5 numbers.
Target Test Prep Representative D
Status: Founder & CEO
Affiliations: Target Test Prep
Joined: 14 Oct 2015
Posts: 6242
Location: United States (CA)
Re: What is the sum of all numbers x for which the median of the numbers 4  [#permalink]

### Show Tags

Bunuel wrote:
What is the sum of all numbers x for which the median of the numbers 4, 6, 8, 17, and x is equal to the mean of those five numbers?

A. -5
B. 0
C. 5
D. 15/4
E. 35/4

We can have 3 scenarios: 1) If x ≤ 6, then the median is 6; 2) if 6 < x < 8, then the median is x; and 3) if x ≥ 8, then the median is 8.

Scenario 1:

If the median is 6, we have:

(35 + x)/5 = 6

35 + x = 30

x = -5

Since -5 ≤ 6, x can be -5.

Scenario 2:

If the median is x, we have:

(35 + x)/5 = x

35 + x = 5x

35 = 4x

x = 35/4

Since 35/4 is not between 6 and 8, x can’t be 35/4.

Scenario 3:

If the median is 8, we have:

(35 + x)/5 = 8

35 + x = 40

x = 5

Since 5 is not greater than or equal to 8, x can’t be 5.

So x can only be -5.

Answer: A
_________________

# Scott Woodbury-Stewart

Founder and CEO

Scott@TargetTestPrep.com

See why Target Test Prep is the top rated GMAT quant course on GMAT Club. Read Our Reviews

If you find one of my posts helpful, please take a moment to click on the "Kudos" button. Re: What is the sum of all numbers x for which the median of the numbers 4   [#permalink] 20 May 2019, 18:58
Display posts from previous: Sort by

# What is the sum of all numbers x for which the median of the numbers 4

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

#### MBA Resources  