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

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

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20 Apr 2008, 12:12
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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

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OPEN DISCUSSION OF THIS QUESTION IS HERE: is-the-range-of-the-integers-6-3-y-4-5-and-x-greater-134897.html
[Reveal] Spoiler: OA

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

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20 Apr 2008, 12:19
Statement 1: insuff
make x = -1 so y > -3 (range is or is not greater than 9 depending on what we pick)

Statement 2: insuff
make x = 4 so y > 4 (range is or is not greater than 9 depending on what we pick)

Combined Statements: sufficient
make x = 4 (most mitigating possibility) so y > 12
make y = 13 (most mitigating possibility)

--still, under greatest mitigation, range is from 3 to 13, which is greater than 9
--less mitigating choices for x and y would create even greater ranges

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

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20 Apr 2008, 12:21
jimmyjamesdonkey wrote:
Is the range of integers 6, 3, y, 4, 5, and x greater than 9?

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

1) Insuf. consider x=1 --> y>3. could be 4 or 10
2) Insuf. y>x>3 can be 5>4>3 or 100>5>3

Combined, we know x>3, which means y>12. take the next integer, y= 13 --> 13-3=10 which is greater than 9

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

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20 Apr 2008, 12:46
i get C as well.

from stat 1, we can have x=1 and therefore y=4, and range is not more than 9. Or, we can have x=1 and y=13, so range is more than 9. insuff.

from stat 2, we can have x=4 and y=5, and range is not more than 9. Or, we can have x=4 and y=13, so range is more than 9/ insuff.

Together. the minimum that x can be is 4, and so the minimum that y has to be is 13. this guarantees that range will always be greater than 9. suff.

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

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20 Oct 2014, 20:17
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Re: Is the range of integers 6, 3, y, 4, 5, and x greater than [#permalink]

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21 Oct 2014, 01:13
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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.

OPEN DISCUSSION OF THIS QUESTION IS HERE: is-the-range-of-the-integers-6-3-y-4-5-and-x-greater-134897.html
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Re: Is the range of integers 6, 3, y, 4, 5, and x greater than   [#permalink] 21 Oct 2014, 01:13
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