Q is a sequence of consecutive integers. Does set Q contain exactly one multiple of 7?
(1) There are at least six terms in Q.
(2) There are exactly eight terms in Q.
OE:
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(1) There are at least six terms in Q.
(2) There are exactly eight terms in Q.
OE:
[Reveal] Spoiler:
(1): If set Q has 6 terms beginning with 7, {7, 8, 9, 10, 11, 12}, it will have only one multiple of 7 yielding an answer of "Yes".
However, at least 6 terms also allows the possibility of set Q containing 1000 terms, with an answer of "No".
IS
(2): Set Q could begin with "1", containing only "7" as the single multiple of 7 (yielding an answer of "Yes"),
or it could begin with "7" and contain both "7" and "14" as multiples of 7 ("No").
IS
Combined: (1) does not add new information not already provided by stat. (2). Number of multiples of 7 in set Q still depends on set Q's initial term, which is yet unknown.
IS
However, at least 6 terms also allows the possibility of set Q containing 1000 terms, with an answer of "No".
IS
(2): Set Q could begin with "1", containing only "7" as the single multiple of 7 (yielding an answer of "Yes"),
or it could begin with "7" and contain both "7" and "14" as multiples of 7 ("No").
IS
Combined: (1) does not add new information not already provided by stat. (2). Number of multiples of 7 in set Q still depends on set Q's initial term, which is yet unknown.
IS