Mean with 2 unknowns

[SaraLotfy]

if x and y are two positive unknown integers, is the mean of set {6,7,1,5,x,y} greater than the median of the set?
1)x+y=7
2)x-y=3

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Hi SaraLotfy,

These types of questions are perfect for TESTing values.

We're given 6 numbers: 1, 5, 6, 7, X?, Y? and we're told that X and Y are POSITIVE INTEGERS.

We're asked if the mean is > the median....this is a YES/NO question. The answer is clearly going to depend on the values of X and Y

Fact 1) X + Y = 7

Here, the group would have a sum of 26, so the mean = 4.333333

If X = 1, Y = 6 and we have 1,1,5,6,6,7 so the median = 5.5 and the answer is NO
If X = 2, Y = 5 and we have 1,2,5,5,6,7 so the median = 5 and the answer is NO
If X = 3, Y = 4 and we have 1,3,4,5,6,7 so the median = 4.5 and the answer is NO
Fact 1 is SUFFICIENT

Fact 2) X - Y = 3

If X = 4, Y = 1 and we have 1,1,4,5,6,7 so the mean = 4, the median = 4.5 and the answer is NO
If X = 100, Y = 97 and we have 1,5,6,7,97,100 so the mean = BIG, the median = 6.5 and the answer is YES
Fact 2 is INSUFFICIENT

Final Answer: A

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

[masoom j negi]

To find the mean of the sets we need to know the sum of x and y.
Statement 1. Mean of the set = (6 + 7 + 1 + 5 + 7)/6 = 26/6 = 4.33.
Since, x and y are positive integer, their possible values are (1,6), (2, 5), (3,4)
So, possible sets are {1, 1, 5, 6, 6, 7}. Median = (5+6)/2 = 5.5
{1, 2, 5, 5, 6, 7}. Median = 10/2 = 5
{1, 3, 4, 5, 6, 7}. Median = 9/2 = 4.5.
All possible values of median are greater than mean. Hence, Sufficient.
Statement 2. We need the sum of x and y to find the mean and not the difference of x and y. Hence, Insufficient.