January 19, 2019 January 19, 2019 07:00 AM PST 09:00 AM PST Aiming to score 760+? Attend this FREE session to learn how to Define your GMAT Strategy, Create your Study Plan and Master the Core Skills to excel on the GMAT. January 20, 2019 January 20, 2019 07:00 AM PST 07:00 AM PST Get personalized insights on how to achieve your Target Quant Score.
Author 
Message 
TAGS:

Hide Tags

Intern
Joined: 20 Jun 2011
Posts: 44

All the terms in Set S are integers. Five terms in S are eve
[#permalink]
Show Tags
15 Jan 2013, 16:29
Question Stats:
49% (02:10) correct 51% (02:25) wrong based on 229 sessions
HideShow timer Statistics
All the terms in Set S are integers. Five terms in S are even, and four terms are multiples of 3. How many terms in S are even numbers that are not divisible by 3? (1) The product of all the even terms in Set S is a multiple of 9. (2) The integers in S are consecutive.
Official Answer and Stats are available only to registered users. Register/ Login.



Intern
Joined: 13 Mar 2011
Posts: 8

Re: All the terms in Set S are integers. Five terms in S are eve
[#permalink]
Show Tags
15 Jan 2013, 21:23
1) The product of all the even terms in Set S is a multiple of 9. the smallest even multiple of 9 which should be a product of 5 even terms is2x2x2x2x2x9, but there can other multiple of 9 too which should satisfy the basic criteria of the statementlike2x2x2x2x4x9, etcNot Sufficient 2) The integers in S are consecutive. lets take an example: 1, 2, 3, 4, 5, 6, 7, 8, 9, 10 this will have 5 even terms but only 3 terms which are multiple of 3 and since 3 is part of only 1 even number6, we cannot consider this 3, 4, 5, 6, 7, 8, 9, 10, 11, 12 now this will have 5 even terms and since 3 is now part of 2 even number6 and 12, the product of even number will be a multiple of 9hence sufficient Hence B!
_________________
How about some KUDOS...ey??!!



Intern
Joined: 27 Dec 2012
Posts: 13

Re: All the terms in Set S are integers. Five terms in S are eve
[#permalink]
Show Tags
05 May 2013, 04:58
I have a quick question.. Don't know someone has noticed it or not but the question never says that there are 9 elements in set S. It just says that there are 5 even numbers and 4 multiples of 3 which could overlap or even in one case there maybe other numbers besides these. Hence the answer should be E not B.... Posted from GMAT ToolKit



Verbal Forum Moderator
Joined: 10 Oct 2012
Posts: 611

Re: All the terms in Set S are integers. Five terms in S are eve
[#permalink]
Show Tags
Updated on: 07 May 2013, 09:52
Asishp wrote: I have a quick question.. Don't know someone has noticed it or not but the question never says that there are 9 elements in set S. It just says that there are 5 even numbers and 4 multiples of 3 which could overlap or even in one case there maybe other numbers besides these.
Hence the answer should be E not B.... From F.S 1,we can have a series like 2,4,6,9,12,15,20. Here the even nos, not divisible by 3 are 3. Again, we could have another series like 4,6,12,18,24 and the even nos, not divisible by 3 is only 1. Insufficient. From F.S 2, we know that the series is consecutive. For exactly 5 even integers, if our series starts with an even number, we need a total of 9 consecutive integers. 2k _ 2k+2 _ 2k+4 _ 2k+6 _ 2k+8 and we can have a maximum of three multiples of 3 as every 3 consecutive integers have one multiple of 3. Thus, our series has to start with a odd number, and for placing 5 consecutive even integers, the series would be _2k _ 2k+2 _ 2k+4 _ 2k+6 _ 2k+8 . Note that if the first integer is not a multiple of 3, we would still have 3 multiples of 3. Thus, the only way in which we can have 4 multiples is by having the first odd integer to be a multiple of 3. Thus, the number of even terms not divisible in such a case would be = 2k ,2k+4 and 2k+6. Sufficient. B.
_________________
All that is equal and notDeep Dive Inequality
Hit and Trial for Integral Solutions
Originally posted by mau5 on 05 May 2013, 05:56.
Last edited by mau5 on 07 May 2013, 09:52, edited 1 time in total.



Manager
Status: Trying.... & desperate for success.
Joined: 17 May 2012
Posts: 61
Location: India
Concentration: Leadership, Entrepreneurship
GPA: 2.92
WE: Analyst (Computer Software)

Re: All the terms in Set S are integers. Five terms in S are eve
[#permalink]
Show Tags
05 May 2013, 06:10
Asishp wrote: I have a quick question.. Don't know someone has noticed it or not but the question never says that there are 9 elements in set S. It just says that there are 5 even numbers and 4 multiples of 3 which could overlap or even in one case there maybe other numbers besides these. Hence the answer should be E not B.... Posted from GMAT ToolKitCorrect.. the wording of the question is wrong.



CEO
Joined: 17 Nov 2007
Posts: 3438
Concentration: Entrepreneurship, Other
Schools: Chicago (Booth)  Class of 2011

Re: All the terms in Set S are integers. Five terms in S are eve
[#permalink]
Show Tags
05 May 2013, 06:18
The terms do overlap (even and multiple of 3). Here is my explanation for B:  If all terms are consecutive integers then 4 terms that are multiples of 3 follow each other too. If the first term is 3k (k is an integer) then the next one is 3(k+1) > 3K+3. So, if 3k is odd, then 3k + 3 is even and if 3k is even then 3k+3 is odd. There are only two combinations for those 4 terms: [even][odd][even][odd] (Example: 6, 9, 12, 15) or [odd][even][odd][even] (Example: 3, 6, 9, 12) it means that there are always 2 even terms that are multiple of 3 and (52) terms that are not multiple of 3. Sufficient.
_________________
HOT! GMAT TOOLKIT 2 (iOS) / GMAT TOOLKIT (Android)  The OFFICIAL GMAT CLUB PREP APP, a musthave app especially if you aim at 700+  Limited GMAT/GRE Math tutoring in Chicago



Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
Posts: 8789
Location: Pune, India

Re: All the terms in Set S are integers. Five terms in S are eve
[#permalink]
Show Tags
07 May 2013, 09:20
superpus07 wrote: All the terms in Set S are integers. Five terms in S are even, and four terms are multiples of 3. How many terms in S are even numbers that are not divisible by 3?
(1) The product of all the even terms in Set S is a multiple of 9. (2) The integers in S are consecutive. So we have 5 even terms (so rest are all odd) and 4 multiples of 3. There may or may not be overlap in these two number types. All we can say right now is that there must be at least one even number which is not a multiple of 3 (since there are 5 even numbers and only 4 multiples of 3). (1) The product of all the even terms in Set S is a multiple of 9. The product of all even terms is a multiple of 3 doesn't tell us how many even numbers are divisible by 3. It is possible that only one even number has 9 as a factor and none of the other 4 even numbers have 3 as a factor. It is also possible that 4 even numbers have 3 as a factor and the product is divisible by 81 too. This statement doesn't imply that the product of all even numbers is divisible only by 9 and no higher power of 3. Not sufficient. (2) The integers in S are consecutive. Since there are 5 even numbers, there must be either 4 or 5 or 6 odd numbers (s o that the numbers are consecutive) Out of 4 consecutive multiples of 3, two will be odd and 2 will be even. e.g. 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13. Every other multiple of 3 will be even and the rest will be odd. Hence, we have 2 even numbers which are multiples of 3 too. So, of the 5 even numbers, 2 must be multiples of 3 and 3 must not be multiples of 3 e.g. in our example, 6, 12 are multiples of 3 and 4, 8 and 10 will not be multiples of 3. Sufficient. Answer (B)
_________________
Karishma Veritas Prep GMAT Instructor
Learn more about how Veritas Prep can help you achieve a great GMAT score by checking out their GMAT Prep Options >



Manager
Status: Pushing Hard
Affiliations: GNGO2, SSCRB
Joined: 30 Sep 2012
Posts: 78
Location: India
Concentration: Finance, Entrepreneurship
GPA: 3.33
WE: Analyst (Health Care)

Re: All the terms in Set S are integers. Five terms in S are eve
[#permalink]
Show Tags
07 May 2013, 09:41
walker wrote: The terms do overlap (even and multiple of 3). Here is my explanation for B:
 If all terms are consecutive integers then 4 terms that are multiples of 3 follow each other too. If the first term is 3k (k is an integer) then the next one is 3(k+1) > 3K+3. So, if 3k is odd, then 3k + 3 is even and if 3k is even then 3k+3 is odd.
There are only two combinations for those 4 terms: [even][odd][even][odd] (Example: 6, 9, 12, 15) or [odd][even][odd][even] (Example: 3, 6, 9, 12)
it means that there are always 2 even terms that are multiple of 3 and (52) terms that are not multiple of 3. Sufficient. I really liked the way .. u explained Walker .Thanks !! .............................
_________________
If you don’t make mistakes, you’re not working hard. And Now that’s a Huge mistake.



Manager
Joined: 23 Sep 2015
Posts: 83
Concentration: General Management, Finance
GMAT 1: 680 Q46 V38 GMAT 2: 690 Q47 V38
GPA: 3.5

Re: All the terms in Set S are integers. Five terms in S are eve
[#permalink]
Show Tags
24 May 2016, 20:07
I am confused why using 2 to start the sequence does not rule out B
2, 3, 4, 5, 6, 7, 8, 9, 10
Evens  5 Odds  4
Evens not divisible by 3 = 4
6,7,8,9,10,11,12,13,14 gives us 3 evens not divisible by 3



Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
Posts: 8789
Location: Pune, India

Re: All the terms in Set S are integers. Five terms in S are eve
[#permalink]
Show Tags
24 May 2016, 20:46
GMATDemiGod wrote: I am confused why using 2 to start the sequence does not rule out B
2, 3, 4, 5, 6, 7, 8, 9, 10
Evens  5 Odds  4
Evens not divisible by 3 = 4
6,7,8,9,10,11,12,13,14 gives us 3 evens not divisible by 3 2, 3, 4, 5, 6, 7, 8, 9, 10 doesn't satisfy all conditions. We need four multiples of 3 but it has only three (3, 6 and 9) Same is the problem with this: 6,7,8,9,10,11,12,13,14 If you have consecutive integers and four of them are multiples of 3, two will be even and two will be odd. Hence, of the 5 even integers, only 2 will be multiples of 3.
_________________
Karishma Veritas Prep GMAT Instructor
Learn more about how Veritas Prep can help you achieve a great GMAT score by checking out their GMAT Prep Options >



Manager
Joined: 24 Apr 2014
Posts: 100
Location: India
Concentration: Strategy, Operations
GMAT 1: 730 Q50 V38 GMAT 2: 730 Q50 V38
GPA: 4
WE: Information Technology (Computer Software)

Re: All the terms in Set S are integers. Five terms in S are eve
[#permalink]
Show Tags
25 May 2016, 04:38
superpus07 wrote: All the terms in Set S are integers. Five terms in S are even, and four terms are multiples of 3. How many terms in S are even numbers that are not divisible by 3?
(1) The product of all the even terms in Set S is a multiple of 9. (2) The integers in S are consecutive. the correct answer should be E , Because In question it's mentioned that All terms in s are integer.....(I can be positive or negative) Thus, Even with with only B option we can come to an answer but this answer is ambiguous because I can be +ve or ve . thus , I go with E.
_________________
way to victory .....



Math Expert
Joined: 02 Sep 2009
Posts: 52278

Re: All the terms in Set S are integers. Five terms in S are eve
[#permalink]
Show Tags
25 May 2016, 05:38



Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
Posts: 8789
Location: Pune, India

Re: All the terms in Set S are integers. Five terms in S are eve
[#permalink]
Show Tags
25 May 2016, 21:15
Nick90 wrote: superpus07 wrote: All the terms in Set S are integers. Five terms in S are even, and four terms are multiples of 3. How many terms in S are even numbers that are not divisible by 3?
(1) The product of all the even terms in Set S is a multiple of 9. (2) The integers in S are consecutive. the correct answer should be E , Because In question it's mentioned that All terms in s are integer.....(I can be positive or negative) Thus, Even with with only B option we can come to an answer but this answer is ambiguous because I can be +ve or ve . thus , I go with E. Even and odd integers are defined for negative numbers too so it won't matter.
_________________
Karishma Veritas Prep GMAT Instructor
Learn more about how Veritas Prep can help you achieve a great GMAT score by checking out their GMAT Prep Options >



GMATH Teacher
Status: GMATH founder
Joined: 12 Oct 2010
Posts: 616

All the terms in Set S are integers. Five terms in S are eve
[#permalink]
Show Tags
18 Nov 2018, 07:40
superpus07 wrote: All the terms in Set S are integers. Five terms in S are even, and four terms are multiples of 3. How many terms in S are even numbers that are not divisible by 3?
(1) The product of all the even terms in Set S is a multiple of 9. (2) The integers in S are consecutive.
\(?\,\,\, = \,\,\,x\,\,\, = \,\,\,5  \left( {\# \,\,{\rm{multiples}}\,\,{\rm{of}}\,\,6} \right)\) \(\left( 1 \right)\,\,\left\{ \matrix{ \,{\rm{Take}}\,\,S = \left\{ {\,2\,,2 \cdot 3\,,2 \cdot {3^2},\,2 \cdot {3^{3\,}},2 \cdot {3^4}\,} \right\}\,\,\,\,\,\, \Rightarrow \,\,\,\,\,? = 5  4 = 1 \hfill \cr \,{\rm{Take}}\,\,S = \left\{ {\,2\,,{2^2}\,,2 \cdot {3^2},\,2 \cdot {3^{3\,}},2 \cdot {3^4},3\,} \right\}\,\,\,\,\,\, \Rightarrow \,\,\,\,\,? = 5  3 = 2 \hfill \cr} \right.\,\,\,\,\,\,\,\, \Rightarrow \,\,\,\,\,\,{\rm{INSUFF}}{\rm{.}}\) \(\left( 2 \right)\,\,\,{\rm{different}}\,\,{\rm{classes}}\,\,{\rm{of}}\,\,{\rm{remainders}}\,\,{\rm{by}}\,\,3\,\,{\rm{and}}\,\,5\,\,\left( {{\rm{with}}\,\,5\,\,{\rm{even}}\,\,{\rm{numbers}}} \right)\,\,{\rm{:}}\,\,\,0,2,4\,\,{\rm{for}}\,\,{\rm{the}}\,\,{\rm{smaller}}\,\,{\rm{even}}\,\,{\rm{in}}\,\,{\rm{S}}\) The idea is crucial: 0, 2 and 4 represent ALL possible scenarios for the first even integer belonging to S, even when negative integers are considered. (We have presented the 6, 8 and 10 "next group" so that the "repetition of the cyclic behavior" becomes clear!) \(\left. {\left\{ \matrix{ \,{\rm{0}}\,\,\, \to \,\,\,{\rm{odds}}:\,\,\left( {{\rm{possibly}}  1} \right),1,3,5,7\,\left( {{\rm{and}}\,\,{\rm{possibly}}\,\,9} \right)\,\, \to \,\,\,\,\,0,\,3,6,9\,\,{\rm{multiples}}\,\,{\rm{of}}\,\,3\,\,\,\,\,\, \Rightarrow \,\,\,\,\,? = 5  2 = 3 \hfill \cr \,{\rm{2}}\,\,\, \to \,\,\,{\rm{odds}}:\,\,\left( {{\rm{possibly}}\,{\rm{ }}1} \right),3,5,7,9\,\left( {{\rm{and}}\,\,{\rm{possibly}}\,\,11} \right)\,\, \to \,\,\,\,\,3,\,6,9\,\,{\rm{multiples}}\,\,{\rm{of}}\,\,3\,\,\,\,\,\, \Rightarrow \,\,\,{\rm{not}}\,\,{\rm{viable}} \hfill \cr \,{\rm{4}}\,\,\, \to \,\,\,{\rm{odds}}:\,\,\left( {{\rm{possibly}}\,{\rm{ }}3} \right),5,7,9,11\,\left( {{\rm{and}}\,\,{\rm{possibly}}\,\,13} \right)\,\, \to \,\,\,\,\,3,\,6,9,12\,\,{\rm{multiples}}\,\,{\rm{of}}\,\,3\,\,\,\,\,\, \Rightarrow \,\,\,? = 5  2 = 3 \hfill \cr \,{\rm{6}}\,\,\, \to \,\,\,{\rm{odds}}:\,\,\left( {{\rm{possibly}}\,{\rm{ }}5} \right),7,9,11,13\,\left( {{\rm{and}}\,\,{\rm{possibly}}\,\,15} \right)\,\, \to \,\,\,\,\,6,\,9,12,15\,\,{\rm{multiples}}\,\,{\rm{of}}\,\,3\,\,\,\,\,\, \Rightarrow \,\,\,? = 5  2 = 3 \hfill \cr \,{\rm{8}}\,\,\, \to \,\,\,{\rm{odds}}:\,\,\left( {{\rm{possibly}}\,{\rm{ }}7} \right),9,11,13,15\,\left( {{\rm{and}}\,\,{\rm{possibly}}\,\,17} \right)\,\, \to \,\,\,\,\,9,\,12,15\,\,{\rm{multiples}}\,\,{\rm{of}}\,\,3\,\,\,\,\,\, \Rightarrow \,\,\,{\rm{not}}\,\,{\rm{viable}} \hfill \cr {\rm{10}}\,\, \to \,\,\,{\rm{odds}}:\,\,\left( {{\rm{possibly}}\,{\rm{ }}9} \right),11,13,15,17\,\left( {{\rm{and}}\,\,{\rm{possibly}}\,\,19} \right)\,\, \to \,\,\,\,\,9,\,12,15,18\,\,{\rm{multiples}}\,\,{\rm{of}}\,\,3\,\,\,\,\,\, \Rightarrow \,\,\,? = 5  2 = 3 \hfill \cr} \right.\,\,\,} \right\}\,\,\,\,\,\,\, \Rightarrow \,\,\,\,\,\,? = 3\,\,\,\,\, \Rightarrow \,\,\,\,{\rm{SUFF}}{\rm{.}}\,\) This solution follows the notations and rationale taught in the GMATH method. Regards, Fabio.
_________________
Fabio Skilnik :: GMATH method creator (Math for the GMAT) Our highlevel "quant" preparation starts here: https://gmath.net




All the terms in Set S are integers. Five terms in S are eve &nbs
[#permalink]
18 Nov 2018, 07:40






