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3.7, 4.1, a, 8.5, 9.2, 2a The six numbers shown are list

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3.7, 4.1, a, 8.5, 9.2, 2a The six numbers shown are list [#permalink] New post 02 Mar 2018, 16:43
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3.7, 4.1, a, 8.5, 9.2, 2a

The six numbers shown are listed in increasing order. Which of the following values could be the range of the six numbers?

Indicate \(all\) such values.


A 4.0

B 5.2

C 7.3

D 11.6

E 12.9

F 14.1
[Reveal] Spoiler: OA

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Re: 3.7, 4.1, a, 8.5, 9.2, 2a The six numbers shown are list [#permalink] New post 02 Mar 2018, 17:02
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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.
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Re: 3.7, 4.1, a, 8.5, 9.2, 2a The six numbers shown are list [#permalink] New post 02 May 2018, 07:30
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Carcass wrote:
3.7, 4.1, a, 8.5, 9.2, 2a

The six numbers shown are listed in increasing order. Which of the following values could be the range of the six numbers?

Indicate \(all\) such values.


A 4.0

B 5.2

C 7.3

D 11.6

E 12.9

F 14.1


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
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Re: 3.7, 4.1, a, 8.5, 9.2, 2a The six numbers shown are list [#permalink] New post 02 May 2018, 11:56
I do not understand why B is not possible?
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Re: 3.7, 4.1, a, 8.5, 9.2, 2a The six numbers shown are list [#permalink] New post 02 May 2018, 13:12
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kruttikaaggarwal wrote:
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
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Re: 3.7, 4.1, a, 8.5, 9.2, 2a The six numbers shown are list   [#permalink] 02 May 2018, 13:12
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