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

 It is currently 22 Feb 2019, 19:06

### 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

## Events & Promotions

###### Events & Promotions in February
PrevNext
SuMoTuWeThFrSa
272829303112
3456789
10111213141516
17181920212223
242526272812
Open Detailed Calendar
• ### Free GMAT RC Webinar

February 23, 2019

February 23, 2019

07:00 AM PST

09:00 AM PST

Learn reading strategies that can help even non-voracious reader to master GMAT RC. Saturday, February 23rd at 7 AM PT
• ### FREE Quant Workshop by e-GMAT!

February 24, 2019

February 24, 2019

07:00 AM PST

09:00 AM PST

Get personalized insights on how to achieve your Target Quant Score.

# If the average (arithmetic mean) and the median of the set of numbers

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

### Hide Tags

Manager
Status: Gathering chakra
Joined: 05 Feb 2018
Posts: 65
If the average (arithmetic mean) and the median of the set of numbers  [#permalink]

### Show Tags

06 Feb 2019, 18:39
00:00

Difficulty:

15% (low)

Question Stats:

100% (01:14) correct 0% (00:00) wrong based on 12 sessions

### HideShow timer Statistics

{3, 5, 9, 13, y}

If the average (arithmetic mean) and the median of the set of numbers shown above are equal, then what is the value of y ?

A) 7
B) 8
C) 10
D) 15
E) 17

1) Find avg to find median, Avg = (30+y)/5 or 6+(5/y)
2) From this we know that y has to be divisible by 5, so C or D.
3) Pick C, if y=10 then the Avg is 40/5 = 8. Looking at the set, if y=10 then 9 is the median, not 8
4) Check D, if y=15 then the Avg is 45/5 = 9. Now the avg = med, thus D.

Official explanation:
This problem is a great opportunity to Plug In the Answers. Start with (C) and substitute 10 for y in the problem. The average of the numbers {3, 5, 9, 13, 10} is 8, but the median of those numbers is 9. Eliminate (C). The value of y needs to be greater, so try (D), 15. The average of the numbers {3, 5, 9, 13, 15} is 9, and the median of those numbers is also 9. We’re done. The correct answer is (D).
VP
Joined: 09 Mar 2018
Posts: 1002
Location: India
Re: If the average (arithmetic mean) and the median of the set of numbers  [#permalink]

### Show Tags

06 Feb 2019, 22:36
energetics wrote:
{3, 5, 9, 13, y}

If the average (arithmetic mean) and the median of the set of numbers shown above are equal, then what is the value of y ?

A) 7
B) 8
C) 10
D) 15
E) 17

average (arithmetic mean) and the median of the set of numbers shown above are equal

(30 + y)/ 5 = y

From the given options plug in values for y now

$$\frac{{30 + 15}}{5}$$ = 9

9 = 9

D
_________________

If you notice any discrepancy in my reasoning, please let me know. Lets improve together.

Quote which i can relate to.
Many of life's failures happen with people who do not realize how close they were to success when they gave up.

Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
Posts: 8895
Location: Pune, India
Re: If the average (arithmetic mean) and the median of the set of numbers  [#permalink]

### Show Tags

07 Feb 2019, 02:06
energetics wrote:
{3, 5, 9, 13, y}

If the average (arithmetic mean) and the median of the set of numbers shown above are equal, then what is the value of y ?

A) 7
B) 8
C) 10
D) 15
E) 17

1) Find avg to find median, Avg = (30+y)/5 or 6+(5/y)
2) From this we know that y has to be divisible by 5, so C or D.
3) Pick C, if y=10 then the Avg is 40/5 = 8. Looking at the set, if y=10 then 9 is the median, not 8
4) Check D, if y=15 then the Avg is 45/5 = 9. Now the avg = med, thus D.

Official explanation:
This problem is a great opportunity to Plug In the Answers. Start with (C) and substitute 10 for y in the problem. The average of the numbers {3, 5, 9, 13, 10} is 8, but the median of those numbers is 9. Eliminate (C). The value of y needs to be greater, so try (D), 15. The average of the numbers {3, 5, 9, 13, 15} is 9, and the median of those numbers is also 9. We’re done. The correct answer is (D).

If placed in increasing order, we have 3 possibilities for median
- y is less than 5 and median is 5
- y is between 5 and 9 and y is the median
- y is more than 9 and hence median is 9

There is no option with y less than 5 so ignore case 1.
If y is 7 or 8 median will be 7 or 8. But in neither case, can mean be 7 or 8 (check using the deviation method discussed in the link given below. It takes just a few secs)
If y is 10, median is 9 but it cannot again be the mean.
If y is 15, median is 9 and mean will be 9 too.

Answer (D)

For more on mean using deviation method, check: https://www.veritasprep.com/blog/2012/0 ... eviations/
_________________

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 >

Target Test Prep Representative
Status: Founder & CEO
Affiliations: Target Test Prep
Joined: 14 Oct 2015
Posts: 4972
Location: United States (CA)
Re: If the average (arithmetic mean) and the median of the set of numbers  [#permalink]

### Show Tags

10 Feb 2019, 07:46
energetics wrote:
{3, 5, 9, 13, y}

If the average (arithmetic mean) and the median of the set of numbers shown above are equal, then what is the value of y ?

A) 7
B) 8
C) 10
D) 15
E) 17

Looking at the numbers, we see that 5 is 4 less than 9, and 13 is 4 more than 9. We also see that 3 is 6 less than 9, so if y is 6 more than 9, then 9 would be both the mean and the median. In that case, y would be 9 + 6 = 15. Since 15 is one of the choices, it is the correct answer.

Alternate Solution:

We observe that depending on the value of y, the median is either 5 (if y is less than or equal to 5), y (if y is between 5 and 9) or 9 (if y is greater than or equal to y).

If the median is 5, then, since the mean is also 5, the sum of the five numbers must be 5 x 5 = 25. We see that this is not possible since the sum of the numbers without y is already 30 and there are no negative numbers in the answer choices.

If the median is y, then the sum of the five numbers must be 5 x y = 5y. Then, we get 3 + 5 + 9 + 13 + y = 5y; which simplifies to 30 + y = 5y. Then, 4y = 30 and y = 7.5. We see that this is not among the answer choices.

Finally, if the median is 9, then the sum of the five numbers must be 5 x 9 = 45. Then, we get 3 + 5 + 9 + 13 + y = 45; which simplifies to 30 + y = 45. This yields y = 15.

Answer: D
_________________

Scott Woodbury-Stewart
Founder and CEO

GMAT Quant Self-Study Course
500+ lessons 3000+ practice problems 800+ HD solutions

Re: If the average (arithmetic mean) and the median of the set of numbers   [#permalink] 10 Feb 2019, 07:46
Display posts from previous: Sort by

# If the average (arithmetic mean) and the median of the set of numbers

 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®.