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#### Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here. # The six numbers shown are listed in increasing order. Which  Question banks Downloads My Bookmarks Reviews Important topics
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TAGS: Intern Joined: 24 Feb 2016
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The six numbers shown are listed in increasing order. Which [#permalink]
1
KUDOS 00:00

Question Stats: 56% (01:10) correct 43% (01:40) wrong based on 37 sessions
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 Manager Joined: 23 Jan 2016
Posts: 133
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Kudos [?]: 150  , given: 15

Re: The six numbers shown are listed in increasing order. Which [#permalink]
2
KUDOS
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. GRE Instructor Joined: 10 Apr 2015
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Kudos [?]: 4776  , given: 70

Re: The six numbers shown are listed in increasing order. Which [#permalink]
1
KUDOS
Expert's post
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

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Re: The six numbers shown are listed in increasing order. Which [#permalink]
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

[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?
Intern Joined: 10 Jun 2018
Posts: 32
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Kudos [?]: 21 , given: 4

Re: The six numbers shown are listed in increasing order. Which [#permalink]
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. Intern Joined: 19 May 2020
Posts: 6
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Kudos [?]: 6  , given: 1

Re: The six numbers shown are listed in increasing order. Which [#permalink]
1
KUDOS
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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