MGMAT CAT

[ankurmit]

If S is a finite set of consecutive even numbers, is the median of S an odd number?

(1) The mean of set S is an even number.

(2) The range of set S is divisible by 4.

OA later

[bblast]

If S is a finite set of consecutive even numbers, is the median of S an odd number?

(1) The mean of set S is an even number.

(2) The range of set S is divisible by 4.

OA later

stat:1
the mean is an even number,
therefore the set has an odd no of items
thus median is even ->sufficient
eg (2,4,6,8,10)

stat 2 :
range is divisible by 4.
this is just a rephrased statement 1.
you can check in the follwing sets :
{2,4,6,8,10} range/4 = Integer, thus statement holds-->median = even(not odd)
{2,4,6,8} range/4 is not equal to integer

thus answer is D

[MAAJ]

Here's what I think:
(1) The mean of set S is an even number

• Because this is a Evenly spaced set, the median = mean, so this is sufficient

(2) The range of set S is divisible by 4

• This is the largest number of the sequence minus the smallest one, is divisible by 4.
  
  Trying different scenarios:
  4 - 2 is not multiple of 4 (NO)
  6 - 2 is a multiple of 4 (YES)
  8 - 2 is not a multiple of 4 (NO)
  10 - 2 is a multiple of 4 (YES)
  
  So the sequence repeats when there is an ODD number of even numbers in the set. The AM and the median of an evenly spaced set is the average of the first and the last term. The sum of the first and the last term ill always yield an even number and if we divide by an ODD number, then the result will always be EVEN. So statement 2 is sufficient

IMO Correct Answer [spoiler](D)[/spoiler]

[ankur.agrawal]

Here's what I think:
(1) The mean of set S is an even number

• Because this is a Evenly spaced set, the median = mean, so this is sufficient

(2) The range of set S is divisible by 4

• This is the largest number of the sequence minus the smallest one, is divisible by 4.
  
  Trying different scenarios:
  4 - 2 is not multiple of 4 (NO)
  6 - 2 is a multiple of 4 (YES)
  8 - 2 is not a multiple of 4 (NO)
  10 - 2 is a multiple of 4 (YES)
  
  So the sequence repeats when there is an ODD number of even numbers in the set. The AM and the median of an evenly spaced set is the average of the first and the last term. The sum of the first and the last term ill always yield an even number and if we divide by an ODD number, then the result will always be EVEN. So statement 2 is sufficient

IMO Correct Answer [spoiler](D)[/spoiler]

GR8 Explaination Maaj. Really crystal clear answer.