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# If set S consists of the positive integers w, x, y, and z,

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Manager
Joined: 24 Nov 2010
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Concentration: Technology, Entrepreneurship
Schools: Ross '15, Duke '15
If set S consists of the positive integers w, x, y, and z, [#permalink]

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01 Jun 2011, 19:52
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If set S consists of the positive integers w, x, y, and z, is the
range of the numbers in S greater than 6 ?
(1) No two numbers in set S are consecutive.
(2) None of the numbers in set S are multiples of 3.
Manager
Joined: 24 Nov 2010
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Location: United States (CA)
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Schools: Ross '15, Duke '15

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02 Jun 2011, 05:55
1
KUDOS
OA is C.
However, the question does not specify that the 4 numbers are different. What if the numbers are w=x=y=z=10. The range will be 0 in that case and the ans will be E. Can someone please clarify why we need to assume that the numbers could not be equal?
Manager
Joined: 04 Apr 2010
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04 Jun 2011, 14:44
1
KUDOS
1) 1, 3, 5, 7 (no)
1,3,5,10 (yes)
2)13, 13, 13, 13 (no)
11, 13, 17, 25 (yes)

Combining 1 and 2
13, 13, 13, 13 (no)
11, 13, 17, 25 (yes)

So i got E. (they have not stated the numbers are different)
Please correct me if i am wrong.

combining 1 and 2
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01 Jun 2011, 20:12
(1) No two numbers in set S are consecutive.
number could be 1,3,5,7 or 1,3,5,8 so the range could be either 6 or greater than 6. not sufficient.

(2) None of the numbers in set S are multiples of 3.
numbers in the set could be 1,2,4,5 or 1,2,4,8 so the range could be 6 or greater than 6 not sufficient.

combining both -
1,4,7,10 or it could be -2, 0, 2, 4 so the range could be 6 or greater than 6 not sufficient.

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02 Jun 2011, 00:03
agdimple333 wrote:
combining both -
1,4,7,10 or it could be -2, 0, 2, 4 so the range could be 6 or greater than 6 not sufficient.

Shouldn't it be all positive numbers?

Combining,
Set of number could be {1,4,7,10} range=9 > 6
or {11,13,16,19} range=8>6.

OA C.

Or am i missing something here?
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02 Jun 2011, 06:08
dreambeliever wrote:
OA is C.
However, the question does not specify that the 4 numbers are different. What if the numbers are w=x=y=z=10. The range will be 0 in that case and the ans will be E. Can someone please clarify why we need to assume that the numbers could not be equal?

Good point. The word "different" should be used in the question. Please notify the source.
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Manager
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02 Jun 2011, 09:00
dreambeliever wrote:
OA is C.
However, the question does not specify that the 4 numbers are different. What if the numbers are w=x=y=z=10. The range will be 0 in that case and the ans will be E. Can someone please clarify why we need to assume that the numbers could not be equal?

usually, in such type of questions when integers defined as $$x, y, z$$, it is assumed they are not equal.
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02 Jun 2011, 09:48
agdimple333 wrote:
combining both -
1,4,7,10 or it could be -2, 0, 2, 4 so the range could be 6 or greater than 6 not sufficient.

Shouldn't it be all positive numbers?

Combining,
Set of number could be {1,4,7,10} range=9 > 6
or {11,13,16,19} range=8>6.

OA C.

Or am i missing something here?

oops. you are very right. thanks for pointing the error.
Director
Joined: 01 Feb 2011
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02 Jun 2011, 15:34
1. Not sufficient

sequence could be as follows

1 3 5 7 =>range is 6

1 3 5 9 =>range >6

so on..

2. Not sufficient

sequence could be as follows

1 2 4 5 =>range is not greater than 6

1 2 4 7 =>range is not greater than 6

1 2 4 8 => range is greater than 6

together

sequence could be as follows

1 4 7 10 range >6

1 4 7 11 range >6

=> no matter what the sequence is range will at least be 6

Manager
Joined: 16 Mar 2011
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02 Jun 2011, 17:01
Can someone explain to me why the values chosen by anyone here contain only integers from 1-8.. Can't it be any other value for example 5, 11, 17, 23?
In this case range would be 18 right so C, sufficient!?
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03 Jun 2011, 04:49
@l0rrie, if all the integers are same (which is possible as per the wording of the question), then the range = 0, so answer is not C.
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06 Jun 2011, 03:30
considering w,x,y and Z have different values each.

a+b will give 1,4,7,9 or 2,4,7,9 or so. Thus range is always greater than 6.

Thus C.
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Re: Number prop question   [#permalink] 06 Jun 2011, 03:30
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