Summer is Coming! Join the Game of Timers Competition to Win Epic Prizes. Registration is Open. Game starts Mon July 1st.

 It is currently 20 Jul 2019, 00:30 ### 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

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.  # For a certain set of n numbers, where n > 2, is the average (arithmet

Author Message
TAGS:

### Hide Tags

Math Expert V
Joined: 02 Sep 2009
Posts: 56300
For a certain set of n numbers, where n > 2, is the average (arithmet  [#permalink]

### Show Tags

1
6 00:00

Difficulty:   95% (hard)

Question Stats: 39% (01:49) correct 61% (01:40) wrong based on 154 sessions

### HideShow timer Statistics For a certain set of n numbers, where n > 2, is the average (arithmetic mean) equal to the median?

(1) The n numbers are positive, consecutive even integers.
(2) The average of the n numbers is equal to the average of the largest and smallest numbers in the set.

Kudos for a correct solution.

_________________
EMPOWERgmat Instructor V
Status: GMAT Assassin/Co-Founder
Affiliations: EMPOWERgmat
Joined: 19 Dec 2014
Posts: 14590
Location: United States (CA)
GMAT 1: 800 Q51 V49 GRE 1: Q170 V170 Re: For a certain set of n numbers, where n > 2, is the average (arithmet  [#permalink]

### Show Tags

6
1

Many DS questions include some type of "test" of your thoroughness - in other words, "do you 'see' more than just the 'obvious' answer?"

Here, your understanding of the concepts is strong when you're focused on positive integers. But what happens when the integers are NOT positive.....?

You properly assessed Fact 1, so I won't rehash any of that work here. Notice how Fact 1 "restricted" you to POSITIVE, CONSECUTIVE, EVEN integers? NONE of those restrictions exist in Fact 2...

Consider this set of numbers: {-1, 0, 6, 6, 9}

The average of the group = 4
The average of the smallest and biggest = 4
The median of the group = 6
Here, the average is NOT = to the median, so the answer to the question is NO.

You already have some examples that show that the answer could be YES.
Fact 2 is INSUFFICIENT.

To be fair, most DS questions don't require that you do too much to "break" a pattern in the possible answers, but you have to be ready to consider more than just the obvious. Here, the "obvious" was "positive integers and no duplicates."

GMAT assassins aren't born, they're made,
Rich
_________________
760+: Learn What GMAT Assassins Do to Score at the Highest Levels
Contact Rich at: Rich.C@empowergmat.com

*****Select EMPOWERgmat Courses now include ALL 6 Official GMAC CATs!*****

# Rich Cohen

Co-Founder & GMAT Assassin Follow
Special Offer: Save \$75 + GMAT Club Tests Free
Official GMAT Exam Packs + 70 Pt. Improvement Guarantee
www.empowergmat.com/
##### General Discussion
Manager  Joined: 31 Jul 2014
Posts: 127
GMAT 1: 630 Q48 V29 Re: For a certain set of n numbers, where n > 2, is the average (arithmet  [#permalink]

### Show Tags

Bunuel wrote:
For a certain set of n numbers, where n > 2, is the average (arithmetic mean) equal to the median?

(1) The n numbers are positive, consecutive even integers.
(2) The average of the n numbers is equal to the average of the largest and smallest numbers in the set.

Kudos for a correct solution.

stat1. The n numbers are positive, consecutive even integers.
For consecutive integers, arithmatic mean = Median
e.g. 2 4 6 8 am=5 and median = avg of middle 2 numbers = (4+6)/2 =5 --> am = median
e.g 2 4 6 8 10 am=30/5=6 and median = 6

suff

stat2
The average of the n numbers is equal to the average of the largest and smallest numbers in the set.
avg=(a1+an) / 2 --> This is also property of consecutive integers.
and for all consecutive integers --> am=median

suff

IMO : D

Pls correct me if I am wrong, Many Thanks
Math Expert V
Joined: 02 Sep 2009
Posts: 56300
Re: For a certain set of n numbers, where n > 2, is the average (arithmet  [#permalink]

### Show Tags

Bunuel wrote:
For a certain set of n numbers, where n > 2, is the average (arithmetic mean) equal to the median?

(1) The n numbers are positive, consecutive even integers.
(2) The average of the n numbers is equal to the average of the largest and smallest numbers in the set.

Kudos for a correct solution.

_________________
Manager  Joined: 31 Jul 2014
Posts: 127
GMAT 1: 630 Q48 V29 Re: For a certain set of n numbers, where n > 2, is the average (arithmet  [#permalink]

### Show Tags

EMPOWERgmatRichC wrote:

Many DS questions include some type of "test" of your thoroughness - in other words, "do you 'see' more than just the 'obvious' answer?"

Here, your understanding of the concepts is strong when you're focused on positive integers. But what happens when the integers are NOT positive.....?

You properly assessed Fact 1, so I won't rehash any of that work here. Notice how Fact 1 "restricted" you to POSITIVE, CONSECUTIVE, EVEN integers? NONE of those restrictions exist in Fact 2...

Consider this set of numbers: {-1, 0, 6, 6, 9}

The average of the group = 4
The average of the smallest and biggest = 4
The median of the group = 6
Here, the average is NOT = to the median, so the answer to the question is NO.

You already have some examples that show that the answer could be YES.
Fact 2 is INSUFFICIENT.

To be fair, most DS questions don't require that you do too much to "break" a pattern in the possible answers, but you have to be ready to consider more than just the obvious. Here, the "obvious" was "positive integers and no duplicates."

GMAT assassins aren't born, they're made,
Rich

Thanks for explaination, +1 to you
CEO  V
Joined: 12 Sep 2015
Posts: 3852
Re: For a certain set of n numbers, where n > 2, is the average (arithmet  [#permalink]

### Show Tags

Top Contributor
Bunuel wrote:
For a certain set of n numbers, where n > 2, is the average (arithmetic mean) equal to the median?

(1) The n numbers are positive, consecutive even integers.
(2) The average of the n numbers is equal to the average of the largest and smallest numbers in the set.

Kudos for a correct solution.

Target question: Is the average (arithmetic mean) EQUAL to the median?

Statement 1: The n numbers are positive, consecutive even integers.
There's a nice rule that says, "In a set where the numbers are equally spaced, the mean will equal the median."
For example, in each of the following sets, the mean and median are equal:
{7, 9, 11, 13, 15}
{-1, 4, 9, 14}
{3, 4, 5, 6}

Statement 1 tells us that the numbers are consecutive even integers, which means they are equally spaced.
As such, we can be certain that the mean and median are equal.
Since we can answer the target question with certainty, statement 1 is SUFFICIENT

Statement 2: The average of the n numbers is equal to the average of the largest and smallest numbers in the set.
This statement doesn't FEEL sufficient, so I'm going to try testing some different values.

There are several different sets that satisfy this condition. Here are two:
Case a: the numbers are {1, 2, 3}. Here, the mean is equal to the average of the biggest and smallest numbers. In this case the median and mean ARE equal
Case b: the numbers are {-3, -3, 1, 2, 3}. Here, the mean is equal to the average of the biggest and smallest numbers. In this case the median and mean are NOT equal
Since we cannot answer the target question with certainty, statement 2 is NOT SUFFICIENT

Aside: For more on this idea of testing values when a statement doesn't feel sufficient, you can read my article: http://www.gmatprepnow.com/articles/dat ... lug-values

Cheers,
Brent
_________________ Re: For a certain set of n numbers, where n > 2, is the average (arithmet   [#permalink] 28 Aug 2018, 14:39
Display posts from previous: Sort by

# For a certain set of n numbers, where n > 2, is the average (arithmet  