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

Question

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 .

EMPOWERgmatRichC · Accepted Answer

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

anupamadw · Answer

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

Bunuel · Answer

The correct answer is A.

anupamadw · Answer

Thanks for explaination, +1 to you

BrentGMATPrepNow · Answer

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: https://www.gmatprepnow.com/articles/dat ... lug-values Answer: A Cheers, Brent

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