There are six numbers 5,6,6,7,7,x. Is the range greater than 2?
(1) Median of the 6 numbers is greater than mean.
(2) Median is 6.
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range 2
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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
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
