Jul 20 07:00 AM PDT  09:00 AM PDT Attend this webinar and master GMAT SC in 10 days by learning how meaning and logic can help you tackle 700+ level SC questions with ease. Jul 21 07:00 AM PDT  09:00 AM PDT Attend this webinar to learn a structured approach to solve 700+ Number Properties question in less than 2 minutes Jul 26 08:00 AM PDT  09:00 AM PDT The Competition Continues  Game of Timers is a teambased competition based on solving GMAT questions to win epic prizes! Starting July 1st, compete to win prep materials while studying for GMAT! Registration is Open! Ends July 26th Jul 27 07:00 AM PDT  09:00 AM PDT Learn reading strategies that can help even nonvoracious reader to master GMAT RC
Author 
Message 
TAGS:

Hide Tags

Math Expert
Joined: 02 Sep 2009
Posts: 56300

For a certain set of n numbers, where n > 2, is the average (arithmet
[#permalink]
Show Tags
14 Jan 2015, 02:50
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.
Official Answer and Stats are available only to registered users. Register/ Login.
_________________




EMPOWERgmat Instructor
Status: GMAT Assassin/CoFounder
Affiliations: EMPOWERgmat
Joined: 19 Dec 2014
Posts: 14590
Location: United States (CA)

Re: For a certain set of n numbers, where n > 2, is the average (arithmet
[#permalink]
Show Tags
19 Jan 2015, 19:32
Hi anupamadw, 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
CoFounder & GMAT Assassin
Special Offer: Save $75 + GMAT Club Tests Free
Official GMAT Exam Packs + 70 Pt. Improvement Guarantee www.empowergmat.com/




Manager
Joined: 31 Jul 2014
Posts: 127

Re: For a certain set of n numbers, where n > 2, is the average (arithmet
[#permalink]
Show Tags
15 Jan 2015, 06:11
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
Joined: 02 Sep 2009
Posts: 56300

Re: For a certain set of n numbers, where n > 2, is the average (arithmet
[#permalink]
Show Tags
19 Jan 2015, 04:30
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. The correct answer is A.
_________________



Manager
Joined: 31 Jul 2014
Posts: 127

Re: For a certain set of n numbers, where n > 2, is the average (arithmet
[#permalink]
Show Tags
20 Jan 2015, 05:15
EMPOWERgmatRichC wrote: Hi anupamadw,
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
Joined: 12 Sep 2015
Posts: 3852
Location: Canada

Re: For a certain set of n numbers, where n > 2, is the average (arithmet
[#permalink]
Show Tags
28 Aug 2018, 14:39
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 equalCase 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 equalSince 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 ... lugvalues Answer: A Cheers, Brent
_________________
Test confidently with gmatprepnow.com




Re: For a certain set of n numbers, where n > 2, is the average (arithmet
[#permalink]
28 Aug 2018, 14:39






