HI nahid078,
This DS question comes with some great pattern "shortcuts" to it, if you recognize how the question relates to given information. This question is perfect for TESTing Values.
We're given a set of 6 numbers: 5, 6, 6, 7, 7, and X. We're asked if the range is GREATER than 2.
The range of a group of numbers is the "biggest" - "smallest." Right now, we don't know what the exact range is, BUT we know that it's AT LEAST 2. If 7 ends up being the biggest number and 5 ends up being the smallest number, then the range = 2 exactly. If the X is EITHER bigger than 7 or smaller than 5, then the range will be GREATER THAN 2.
This deduction gives us a rather easy way to think about the question and how X impacts the answer:
If X is ANYTHING from 5 to 7, inclusive, then the answer to the question is NO.
If X is greater than 7 or less than 5, then the answer to the question is YES.
Fact 1: The median is greater than the mean
The median of a group of 6 numbers is the average of the "middle 2" numbers.
Let's work through the possibilities:
If X = 5, then the average is 36/6 = 6 and median is 6. This does NOT match the info, so X CANNOT be 5
If X = 6, then the average is 37/6 = 6.16 and median is 6. This does NOT match the info, so X CANNOT be 6
Making the X really small will make the average smaller, but will not affect the median (median will still be 6)
If X = 0, then the average is 31/6 = 5.16 and median is 6. This DOES match the info, and the answer to the question is YES.
Now there's one more value I'd want to TEST.
If X = 7, then the average is 38/6 = 6.33 and median is 6.5. This DOES match the info, and the answer to the question is NO.
Fact 1 is INSUFFICIENT.
Fact 2: The median = 6
This means that X must be 6 or lower.
If X = 6, then the answer to the question is NO
If X = 0, then the answer to the question is YES
Fact 2 is INSUFFICIENT
Combining facts, we have LOTS of information that we can use:
From Fact 2, we know that X has to be 6 or less.
From Fact 2, we know that X cannot be 5 or 6
So X MUST be less than 5, which means the answer to the question is ALWAYS YES.
Combined, SUFFICIENT
Final Answer: C
GMAT assassins aren't born, they're made,
Rich
