Range = biggest value - smallest value
= 2a - 3.7
So, we must determine the possible values of 2a - 3.7

Since the values are listed in ascending order, we know that:
4.1 < a < 8.5 AND 9.2 < 2a

If 9.2 < 2a, then we can divide both sides by 2 to get: 4.6 < a

If 4.1 < a < 8.5 AND 4.6 < a, then it MUST be the case that 4.6 < a < 8.5

Multiply all sides by 2 to get: 9.2 < 2a < 17

Subtract 3.7 from all sides to get: 9.2 - 3.7 < 2a - 3.7 < 17 - 3.7

Simplify to get: 5.5 < 2a - 3.7 < 13.3

So, all answer choices between 5.5 and 13.3 are within the range of possibilities.

Answer: C, D and E

Cheers,
Brent
_________________

Explanation

The difference between the largest and smallest numbers in the list is the \(range\) of a list of numbers.
The smallest number is 3.7; the largest is 2a.

So our range is \(2a - 3.7\)

In order to figure \(a\) out we do need \(a\) itself and \(2a\)

Now. a is in the middle of 8.5 and 4.1. If we make the difference we do have 4.4 which is greater than the first choice A 4.0. This means that answer A is not possible. Cross off.

If we do have 2a and we multiply 2 for 4.4 (our \(a\) aforementioned) we do obtain 8.8 that is still in the range BUT if we multiply 2*8.8 is 17.6 which is impossible. Our maximum value must be 2a. So cross off answer choice F.

At this point, we do have as answers B, C, D, and E.

Considering that B is 5.2 that could easily be a so in the range BUT multiplying 2a, so 2*5.2 which is 10.4 it is not in the range. Cross off B as well.

Following the same reasoning, you arrive that our correct answers that are C, D, and E.

I do not understand why B is not possible?

Answer choice B says that 5.2 is a possible value of the range.
So, let's see what happens when the range = 5.2

We already know that 2a - 3.7 = the range
So, we get: 2a - 3.7 = 5.2
Add 3.7 to both sides to get: 2a = 8.9

So, in order for the range to equal 5.2, it must be the case that 2a = 8.9
HOWEVER, 2a CANNOT equal 8.9, since we're told that the values are listed in ascending order, which means 2a must be greater than 9.2
If 2a must be greater than 9.2, then 2a cannot equal 8.9

Does that help?

Cheers,
Brent
_________________

Yep, that's VERY tricky, and it was specifically put in there by the PSYCHOmetricians to deliberately trick you up.

Perhaps it could also be done this way:
Initial Notes
1. The problem doesn't say we don't have duplicates. That could be useful later on.

Process
1. Because 2a is at the end of the list and the list is ordered from lowest to highest, 9.2 <= 2a.
2. Therefore, 4.6 <= a.
3. a is also <= 8.5 based on its placement in the ordered list.
4. As a gets bigger, 2a gets bigger, and so the final term gets bigger, so the range gets bigger. That means the minimum value of a will define the minimum range of the set and the maximum value of a will define the maximum range of the set.
5. Let's try out the extremes of a within the parameters we're given:

Case 1: a = 4.6
2a = 9.2
range = 9.2 - 3.7 = 5.5

Case 2: a = 8.5
2a = 17
range = 17 - 3.7 = 13.3

So, the range could be anywhere between 5.5 and 13.3, inclusive.

C, D, and E fit the bill!