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Q is a sequence of consecutive integers. Does set Q

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Q is a sequence of consecutive integers. Does set Q  [#permalink]

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New post 24 Mar 2014, 14:23
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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:
(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
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Re: Q is a sequence of consecutive integers. Does set Q  [#permalink]

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New post 25 Mar 2014, 02:58
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2
goodyear2013 wrote:
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:
(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


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 --> if Q={0, 1, 2, 3, 4, 5, 6, 7}, then Q would contain two multiples of 7, namely 0 and 7 but if Q={1, 2, 3, 4, 5, 6, 7, 8}, then Q would contain only one multiple of 7, namely 7. Not sufficient.

(2) There are exactly eight terms in Q. Consider the same sets. Not sufficient.

(1)+(2) Consider the same sets. Not sufficient.

Answer: E.
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Re: Q is a sequence of consecutive integers. Does set Q  [#permalink]

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New post 16 Dec 2017, 09:49
[quote="goodyear2013"]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.

(1) if there are only 6 consecutive integers, then it might or might not contain a multiple of 7. Eg, {8, 9, 10, 11, 12, 13} does NOT contain a multiple of 7, while {9, 10, 11, 12, 13, 14} contains One multiple of 7. And the statement says there are at least six terms - there might be more. If there are 7 consecutive integers, then there will definitely be only ONE multiple of 7, no matter which 7 consecutive integers we look at. Eg, {8, 9, ...14} or {9, 10, ..15} or {15, 16, ..21} all contain exactly one multiple of 7. But if there are more terms say 20, then definitely there will be more than ONE multiples of 7. So not sufficient.

(2) Exactly 8 consecutive integers will Definitely contain at least one multiple of 7, BUT its also possible that they contain more than one multiple of 7. Eg, {8, 9, ..15} contains only one multiple of 7, but {7, 9, ..14} contains 2 multiples of 7. So not sufficient.

Even after combining the two statements, we know that there are eight terms - so we might have either only 1 multiple of 7, or 2 multiples of 7. So Insufficient.

Hence E answer
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Re: Q is a sequence of consecutive integers. Does set Q &nbs [#permalink] 16 Dec 2017, 09:49
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