Author 
Message 
TAGS:

Hide Tags

Senior Manager
Joined: 21 Oct 2013
Posts: 434

Q is a sequence of consecutive integers. Does set Q [#permalink]
Show Tags
24 Mar 2014, 15:23
2
This post received KUDOS
3
This post was BOOKMARKED
Question Stats:
56% (00:55) correct 44% (00:58) wrong based on 104 sessions
HideShow timer Statistics
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
Official Answer and Stats are available only to registered users. Register/ Login.



Math Expert
Joined: 02 Sep 2009
Posts: 44599

Re: Q is a sequence of consecutive integers. Does set Q [#permalink]
Show Tags
25 Mar 2014, 03:58
2
This post received KUDOS
Expert's post
2
This post was BOOKMARKED
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.
_________________
New to the Math Forum? Please read this: Ultimate GMAT Quantitative Megathread  All You Need for Quant  PLEASE READ AND FOLLOW: 12 Rules for Posting!!! Resources: GMAT Math Book  Triangles  Polygons  Coordinate Geometry  Factorials  Circles  Number Theory  Remainders; 8. Overlapping Sets  PDF of Math Book; 10. Remainders  GMAT Prep Software Analysis  SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS)  Tricky questions from previous years.
Collection of Questions: PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.
What are GMAT Club Tests? Extrahard Quant Tests with Brilliant Analytics



DS Forum Moderator
Joined: 22 Aug 2013
Posts: 1021
Location: India

Re: Q is a sequence of consecutive integers. Does set Q [#permalink]
Show Tags
16 Dec 2017, 10:49
[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




Re: Q is a sequence of consecutive integers. Does set Q
[#permalink]
16 Dec 2017, 10:49






