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

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

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New post 25 Jun 2012, 03:03
5
20
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A
B
C
D
E

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  55% (hard)

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61% (01:24) correct 39% (01:19) wrong based on 1340 sessions

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

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New post 25 Jun 2012, 03:04
3
4
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.

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

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New post 25 Jun 2012, 08:41
2
1
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.

Thus, answer is (C),

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

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New post 29 Jun 2012, 04:36
1
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.

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

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New post 27 Mar 2016, 19:25
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Here is a visual that should help.
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Re: Is the range of the integers 6, 3, y, 4, 5, and x greater  [#permalink]

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New post 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.
answer is C.
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Re: Is the range of the integers 6, 3, y, 4, 5, and x greater  [#permalink]

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New post 29 May 2018, 16:31
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


Statement One Alone:

y > 3x

Statement one is not sufficient to answer the question. For example, if x = 0, y could be 1 and the range is 6 - 0 = 6, which is less than 9. However, if x = 10, y could be 31 and the range is 31 - 3 = 28, which is greater than 9.

Statement Two Alone:

y > x > 3

Statement two is not sufficient to answer the question. For example, if x = 4, y could be 5 and the range is 6 - 0 = 6, which is less than 9. However, if x = 14, y could be 15 and the range is 15 - 3 = 12, which is greater than 9.

Statements One and Two Together:

From the two statements, we know that x > 3 and y > 3x. So the smallest integer x can be is 4 and the smallest integer y can be is 3(4) + 1 = 13. Thus the smallest range of the integers is 13 - 3 = 10, which is greater 9. Since 10 is the smallest range, any other range of the integers will be greater than 10 and hence greater than 9.

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

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New post 12 Sep 2018, 10:35
In the solution of these questions it is not asked to take minimum value and x and y can take any numbers so why we have solved this by taking minimum values
Re: Is the range of the integers 6, 3, y, 4, 5, and x greater &nbs [#permalink] 12 Sep 2018, 10:35
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