Set T consists of 3 numbers with only one mode. Does the range equal t

Question

Set T consists of 3 numbers with only one mode. Does the range equal the mode?
 
(1) The largest number is twice the value of the smallest number.

(2) The median equals the range.

Source: Barron's

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akansal211 · Answer

Can someone please explain why the answer is B and not C?

EncounterGMAT · Answer

Let set T= {x,y,z}. There is only one mode, which means that at least two of the three numbers must be the same.

Statement 1: the largest number is twice the value of the smallest number. So z=2x. Since there is only one mode, either y=x or y=z which is 2x

By plugging in numbers, this could be {2,2,4}, {0,0,0} or {2,4,4}. In each example, you can notice that in {2,2,4} and {0,0,0}, range = mode. However, in {2,4,4}, range does not equal to mode.
INSUFFICIENT!

Statement 2: median = range. Take the same examples from statement1.
In all the cases, where there is one mode in a set of three numbers and median=range,then the range does indeed equal the mode.
SUFFICIENT!

Answer is option B. Hope you got it by now!

surbhi1991 · Answer

Hi for statement 2 we get both yes and no

yes - 3,3,3,6,6
no - 4,5,8,12,12

According to me it should be C because when the largest term =2 smallest term, then the the smallest term will always be the mode for the range to be equal to the median.

IanStewart · Answer

This is a critically important DS strategy point: if you are generating scenarios for each DS statement, you can  never , when generating scenarios for Statement 2 alone, use  only  the examples that you used when looking at Statement 1. If you do that, you're implicitly assuming  both  Statements are true, because the only scenarios you're considering are ones that comply with both statements. You always must generate a scenario that agrees with Statement 2 but that does not agree with Statement 1. Otherwise any time the answer is C, you'll think the answer is B.

As for the question:

There are a few problems with it - for one thing, it misuses the word "consist", and for another, it misuses the word "set" (what is the source?), but if we take it to mean "the data set T has one mode", then Statement 1 is clearly not sufficient alone (just look at 1, 1, 2 and 1, 2, 2).

For Statement 2, we can use numbers - say the smallest value is 3, and the median is 5. Then if the range and median are equal, the largest value in the set will be 3+5 = 8, so we know we have these values:

3, 5, 8

Now we can easily insert values into this list to get both a 'yes' and a 'no' answer to the question:

3, 3, 5, 6, 8 --> here the mode is 3, and the range is 5
3, 5, 5, 5, 8 --> here the mode is 5 and the range is 5

So Statement 2 is not sufficient alone.

Using both statements, if the largest value is twice the smallest value, then if S is the smallest value, 2S is the largest value and 2S - S = S is the range. We're told that the range, S, is equal to the median of the list, and for the smallest value S in a list to be its median, more than half of the values in the list will need to be equal to S. But that ensures that S is the mode of the list.

Set T consists of 3 numbers with only one mode. Does the range equal t

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GMAT Data Sufficiency (DS) Questions

Set T consists of 3 numbers with only one mode. Does the range equal t

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