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# Is the range of the integers 6, 3, y, 4, 5, and x greater

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Math Expert
Joined: 02 Sep 2009
Posts: 44419
Is the range of the integers 6, 3, y, 4, 5, and x greater [#permalink]

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25 Jun 2012, 03:03
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Difficulty:

55% (hard)

Question Stats:

61% (01:24) correct 39% (01:21) wrong based on 1045 sessions

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Is the range of the integers 6, 3, y, 4, 5, and x greater than 9?

(1) y > 3x
(2) y > x > 3

Diagnostic Test
Question: 32
Page: 25
Difficulty: 650
[Reveal] Spoiler: OA

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Math Expert
Joined: 02 Sep 2009
Posts: 44419
Re: Is the range of the integers 6, 3, y, 4, 5, and x greater [#permalink]

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25 Jun 2012, 03:04
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SOLUTION

Is the range of the integers 6, 3, y, 4, 5, and x greater than 9?

Given integers are: {3, 4, 5, 6, x, y}

(1) y > 3x. If $$x=1$$ and $$y=4$$ then the range=6-1=5<9 but if $$x=100$$ then the range>9. Not sufficient.

(2) y > x > 3. If $$x=4$$ and $$y=5$$ then the range=6-3=3<9 but if $$x=100$$ then the range>9. Not sufficient.

(1)+(2) From $$x > 3$$ we have that the least value of $$x$$ is 4, and from $$y > 3x=12$$ we have that the least value of $$y$$ is 13, hence the least value of the range is 13-3=10>9. Sufficient.

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Re: Is the range of the integers 6, 3, y, 4, 5, and x greater [#permalink]

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25 Jun 2012, 08:41
2
KUDOS
Hi,

Range = Largest value - smallest value.

6, 3, y, 4, 5, and x, where x & y are integers

Using (1),
y>3x, if x=1, then y = 4, 5,..100....
in each case range can be 5, 6,....So, range is greater than 5. Insufficient.

Using (2),
y>x>3.
Minimum value of x = 4,
y=5,6,7... We can't say whether range is greater than 9.

Combining both statements;
$$x_{min} = 4$$
& since, y > 3x, $$y_{min}=13,$$
thus, 3, 4, 4, 5, 6, & 13 has range (13-3)=10, which is greater than 9
and on increasing x, range will also increase.

Regards,
Math Expert
Joined: 02 Sep 2009
Posts: 44419
Re: Is the range of the integers 6, 3, y, 4, 5, and x greater [#permalink]

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29 Jun 2012, 04:36
1
KUDOS
Expert's post
SOLUTION

Is the range of the integers 6, 3, y, 4, 5, and x greater than 9?

Given integers are: {3, 4, 5, 6, x, y}

(1) y > 3x. If $$x=1$$ and $$y=4$$ then the range=6-1=5<9 but if $$x=100$$ then the range>9. Not sufficient.

(2) y > x > 3. If $$x=4$$ and $$y=5$$ then the range=6-3=3<9 but if $$x=100$$ then the range>9. Not sufficient.

(1)+(2) From $$x > 3$$ we have that the least value of $$x$$ is 4, and from $$y > 3x=12$$ we have that the least value of $$y$$ is 13, hence the least value of the range is 13-3=10>9. Sufficient.

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Re: Is the range of the integers 6, 3, y, 4, 5, and x greater [#permalink]

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27 Mar 2016, 19:25
1
KUDOS
Here is a visual that should help.
Attachments

Screen Shot 2016-03-27 at 7.23.57 PM.png [ 93.38 KiB | Viewed 6278 times ]

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Re: Is the range of the integers 6, 3, y, 4, 5, and x greater [#permalink]

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03 Nov 2016, 06:49
Bunuel wrote:
Is the range of the integers 6, 3, y, 4, 5, and x greater than 9?

(1) y > 3x
(2) y > x > 3

Diagnostic Test
Question: 32
Page: 25
Difficulty: 650

pretty easy for a 700 level question...

1. x can be 1, and y can be 4 - so the answer is NO
x can be 4, and y can be 13 - so the answer is YES.
1 alone is insufficient. A and D are out.

2. y>x>3.
x can be 4, y =5 - answer is no
x can be 4, y can be 20 - answer is YES.
2 alone is not sufficient. B is out.

1+2.
x>3
y>3x
minimum value for x is 4.
minimum value for y is 13
yes, the range is greater than 9.

sufficient.
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Re: Is the range of the integers 6, 3, y, 4, 5, and x greater [#permalink]

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07 Jan 2018, 04:50
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Re: Is the range of the integers 6, 3, y, 4, 5, and x greater   [#permalink] 07 Jan 2018, 04:50
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