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The six numbers shown are listed in increasing order. Which

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The six numbers shown are listed in increasing order. Which [#permalink] New post 24 Jun 2016, 12:54
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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
C,D,E
[Reveal] Spoiler: OA
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Re: The six numbers shown are listed in increasing order. Which [#permalink] New post 04 Jul 2016, 21:27
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The minimum 2a can take is 9.2 and maximum value a can take is 8.5, hence 2a can take is 17. So the minimum range will be 9.2 - 3.7 = 5.5 and maximum range is 17 - 3.5 = 13.5; So C,D,E fits between 5.5 and 13.5, hence answers.
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Re: The six numbers shown are listed in increasing order. Which [#permalink] New post 23 Aug 2016, 14:56
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Kapoorritika 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


Let's examine the two EXTREME values of a.

Case a: The GREATEST value of a
If the values are strictly increasing (i.e., no values are equal), then a could be a little bit smaller than 8.5.
So, a could equal 8.499999999999
For all intents and purposes, let's just say that the a COULD equal 8.5
In this case, 2a = 2(8.5) = 17 which means the range = 17 - 3.7 = 13.3

Case b: The SMALLEST value of a
If the values are strictly increasing (i.e., no values are equal), then a could be a little bit bigger than 4.1.
So, a could equal 4.100000000000001
For all intents and purposes, let's just say that the a COULD equal 4.1
In this case, 2a = 2(4.1) = 8.2, ...... hold on!
Since the numbers are arranged in ascending order 2a must be greater than 9.2. So, it can't be the case that 2a = 8.2
If 2a must be greater than 9.2, a must be greater than 4.6
So, a could equal 4.6000000000000000000000001
So, let's say a = 4.6
In this case, 2a = 2(4.6) = 9.2, which means the range = 9.2 - 3.7 = 5.5


Now that we've examined the EXTREME cases, we can see that the range can be between 5.5 and 13.3

Answer: C, D and E

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Re: The six numbers shown are listed in increasing order. Which [#permalink] New post 12 Sep 2017, 07:00
GreenlightTestPrep wrote:

Let's examine the two EXTREME values of a.

Case a: The SMALLEST value of a
If the values are strictly increasing (i.e., no values are equal), then a could be a little bit smaller than 8.5.
So, a could equal 8.499999999999
For all intents and purposes, let's just say that the a COULD equal 8.5
In this case, 2a = 9.2, which means the range = 5.5

Case b: The GREATEST value of a
If the values are strictly increasing (i.e., no values are equal), then a could be a little bit bigger than 4.1.
So, a could equal 4.10000000001
For all intents and purposes, let's just say that the a COULD equal 4.1
In this case, 2a = 17, which means the range = 13.3

Now that we've examined the EXTREME cases, we can see that the range can be between 5.5 and 13.3

Answer(s):
[Reveal] Spoiler:
C, D and E



If in the first case a = 8.5, how could it be that 2a = 9.2? And the same is in the second case, a = 4.1, how 2a could be equal to 17?
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Re: The six numbers shown are listed in increasing order. Which [#permalink] New post 04 Sep 2018, 18:49
We need to find the range here.
the range will be bigger than 9.2 - 3.7 = 5.5
and smaller than 8.5*2 = 17 - 3.7 = 13.25.
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Re: The six numbers shown are listed in increasing order. Which [#permalink] New post 06 Jun 2020, 11:16
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Kapoorritika 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

[Reveal] Spoiler: OA
C,D,E


keep in mind that 4.1<a<8.5
so, 2a>9.2
A) 2a-3.7=4 gives a=7.7/2, which is defenitely less than 4 implies a<4.5 which is not possible.
b) 2a-3.7=5.2, gives a=8.9/2=4.45 which is valid. but 2*4.45=8.9 which is <9.2 so B is not correct
C) same way a=11/2=5.5 which is >4.1 and 2a>9.2 , C is valid.
.
E) 2a-3.7=12.9, a=16.6/2=8.3 which is valid and preety close to 8.5.
so, option E also saying 14.5 will be more than 8.5. neglect option F.
hence C,D,E
Re: The six numbers shown are listed in increasing order. Which   [#permalink] 06 Jun 2020, 11:16
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