I think that is good Q, but if assumed they are not same, each should suffice

mosfad wrote: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.

Are w, x, y, and z implicitly distinct integers? If so, why?

The numbers w,x,y,z are only integers, distinct or not should be specified in the question or the question's statements (1,2). Why you start making such assumptions at all? let them be just integers.

given: w,x,y,z {integers} >0, r {r is range} >6?
st(1) 1,3,5,7 (7-1=6) No and 1,3,5,8 (8-1=7) Yes, Not Sufficient;
st(2) 1,2,4,5,7 (7-1=6) No and 1,2,4,5,8 (8-1=7) Yes, Not Sufficient;
Combined st(1&2) 1,5,7,9 (9-1=8) Yes, the range is always R>=8 Sufficient
IOM C

mosfad wrote: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.

Are w, x, y, and z implicitly distinct integers? If so, why?

Thanks guys but I'm still confused. The set S could be {1, 1, 4, 4} based on both statements, in which case the answer would be E.

Yea, I was a little confused by this one, too.

The phrasing is a bit ambiguous. There is no claim that the integers are UNIQUE, in which case the answer would be E.

However, if the question assumes that all variables represent unique integers, then the answer would have to be C, because statement 1 could imply any non-consecutive set of numbers, and so could statement two. However, if you combine the restrictions of non-consecutive and non-multiples of 3, then the absolute minimum range would be 7 (1, 4, 7, 8).

It's C so then you know it can be :

e.g. 1,4,7,9

with no consecutives and no mult's of 3