The range of a set is the difference between the largest and smallest elements of a set.

Without x, the difference between the largest and smallest elements of a set is 14-3=11<12, which means that in order 12 to be the range of the set x must be either the smallest element so that 14-x=12 ---> x=2 OR x must the largest element so that x-3=12 --> x=15.

The the difference between the greatest possible value of x and least possible value of x is 15-2=13.

Answer: D.
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nice question. As in international student, the word "range" didnt say anything to me before that.

Thanks.

+1 from me.

The Range of the numbers without x is 14-3 = 11......
Now x changes the range to 12....

so x can be 1 greater than largest value or 1 lesser than eth smallest value....
so Range = 11+1+1 = 13
D
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Hi All,

The general category of 'statistics' will show up on the GMAT at least a couple of times on Test Day, so it's important to know the 'math definition' of each of the statistical words - "mean", "median", "mode", "range" and "standard deviation." Sometimes you'll be asked to calculate one (or more) of those terms; sometimes you'll use information given about one of those terms to figure out something else.

Here, we're told that the RANGE of six numbers is 12. Since range is 'the difference between the largest and smallest terms', it helps to list out the numbers...

Notice how one of the numbers is a VARIABLE though; I'm going to put that at the end of the list for convenience.

3, 4, 7, 10, 14...... X

The range of the first 5 numbers is 11, so we have to make the X some number that will make the range = 12.

We COULD make X = 15... since 15 - 3 = 12

We COULD make X = 2... since 14 - 2 = 12

Now we know the greatest and least possible values of X, so the answer to the question is 15 - 2 = 13

Final Answer:

GMAT assassins aren't born, they're made,
Rich
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Hi IKR9,

In this question, we are NOT told that X is 12, we are told that the RANGE of six numbers is 12. Since range is 'the difference between the largest and smallest terms', it helps to list out the numbers...

Notice how one of the numbers is a VARIABLE though; I'm going to put that at the end of the list for convenience.

3, 4, 7, 10, 14...... X

The range of the first 5 numbers is 11, but we're told the range is 12, so we have to make the X some number that will increase the range to 12.

We COULD make X = 15... since 15 - 3 = 12

We COULD make X = 2... since 14 - 2 = 12

Now we know the greatest and least possible values of X, so the answer to the question is 15 - 2 = 13

GMAT assassins aren't born, they're made,
Rich
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Answer: D.[/quote]

Hello Brunel, I got confused because I thought there was a hidden constraint indicating that x cannot be greater than 14 (based on the set given). In addition, if X is given as 12, I am not sure how to know when to use that information to then decipher that X can be either 15 or 13. I never put that together. Why is it OK in this situation to take givens (such as x=12) and then further solve for X? May you please help clarify? Thank you![/quote]

It is not given that x = 12. The stem says that the range of the six numbers {4, 3, 14, 7, 10, x} is 12.[/quote]


Thank you for the confirmation. That's odd because I am using the wiley efficient program that has the computer version of all GMAT questions, it appears its a bit different on that vs. the text book on this question.

Thanks!