Author 
Message 
TAGS:

Hide Tags

Senior Manager
Status: Final Lap
Joined: 25 Oct 2012
Posts: 281
Concentration: General Management, Entrepreneurship
GPA: 3.54
WE: Project Management (Retail Banking)

If list S contains nine distinct integers, at least one of w [#permalink]
Show Tags
24 Jun 2013, 02:07
2
This post received KUDOS
20
This post was BOOKMARKED
Question Stats:
37% (00:52) correct 63% (01:17) wrong based on 398 sessions
HideShow timer Statistics
If list S contains nine distinct integers, at least one of which is negative, is the median of the integers in list S positive? (1) The product of the nine integers in list S is equal to the median of list S. (2) The sum of all nine integers in list S is equal to the median of list S.
Official Answer and Stats are available only to registered users. Register/ Login.
_________________
KUDOS is the good manner to help the entire community.
"If you don't change your life, your life will change you"



Verbal Forum Moderator
Joined: 10 Oct 2012
Posts: 625

Re: If list S contains nine distinct integers, at least one of w [#permalink]
Show Tags
24 Jun 2013, 08:43
9
This post received KUDOS
4
This post was BOOKMARKED
Rock750 wrote: If list S contains nine distinct integers, at least one of which is negative, is the median of the integers in list S positive? (1) The product of the nine integers in list S is equal to the median of list S. (2) The sum of all nine integers in list S is equal to the median of list S. Let the set of 9 distinct integers in increasing order be\(a_1\) , \(a_2\) ... \(a_9\). From F.S 1, we know that \(a_1*a_2*....a_4*a_5....a_9\) = \(a_5\) \(\to\) \(a_5(a_1*a_2*...a_4....a_91)\) = 0. Thus, either \(a_5\) = 0 OR \((a_1*a_2*...*a_5....a_91)\) = 0, the latter is not possible as no product of 8 distinct integers can ever equal 1. Thus, the median,\(a_5\) = 0 and not positive. Sufficient. From F. S 2, for 4,3,2,1,0,1,2,3,4,the median is 0 and a NO for the question stem. Again, for the series 10,3,1,0,1,2,3,4,5, the median is 1, which is positive, and hence a YES for the question stem. Thus, Insufficient. A.
_________________
All that is equal and notDeep Dive Inequality
Hit and Trial for Integral Solutions



Senior Manager
Status: Final Lap
Joined: 25 Oct 2012
Posts: 281
Concentration: General Management, Entrepreneurship
GPA: 3.54
WE: Project Management (Retail Banking)

Re: If list S contains nine distinct integers, at least one of w [#permalink]
Show Tags
24 Jun 2013, 13:05
mau5 wrote: Rock750 wrote: If list S contains nine distinct integers, at least one of which is negative, is the median of the integers in list S positive? (1) The product of the nine integers in list S is equal to the median of list S. (2) The sum of all nine integers in list S is equal to the median of list S. Let the set of 9 distinct integers be\(a_1\) , \(a_2\) ... \(a_9\). From F.S 1, we know that \(a_1*a_2*....a_4*a_5....a_9\) = \(a_5\) \(\to\) \(a_5(a_1*a_2*...a_5....a_91)\) = 0. Thus, either \(a_5\) = 0 OR \((a_1*a_2*...*a_4....a_91)\) = 0, the latter is not possible as no product of 8 distinct integers can ever equal 1. Thus, the median,\(a_5\) = 0 and not positive. Sufficient. From F. S 2, for 4,3,2,1,0,1,2,3,4,the median is 0 and a NO for the question stem. Again, for the series 10,3,1,0,1,2,3,4,5, the median is 1, which is positive, and hence a YES for the question stem. Thus, Insufficient. A. How did u come up with this : \(a_1*a_2*....a_4*a_5....a_9\) = \(a_5\) \(\to\) \(a_5(a_1*a_2*...a_4....a_91)\) = 0. ?
_________________
KUDOS is the good manner to help the entire community.
"If you don't change your life, your life will change you"



Verbal Forum Moderator
Joined: 10 Oct 2012
Posts: 625

Re: If list S contains nine distinct integers, at least one of w [#permalink]
Show Tags
24 Jun 2013, 23:28
Rock750 wrote: How did u come up with this : \(a_1*a_2*....a_4*a_5....a_9\) = \(a_5\) \(\to\) \(a_5(a_1*a_2*...a_4....a_91)\) = 0. ? Could you elaborate on your doubt? The above equation is what is given in the Fact Statement.
_________________
All that is equal and notDeep Dive Inequality
Hit and Trial for Integral Solutions



Senior Manager
Status: Final Lap
Joined: 25 Oct 2012
Posts: 281
Concentration: General Management, Entrepreneurship
GPA: 3.54
WE: Project Management (Retail Banking)

Re: If list S contains nine distinct integers, at least one of w [#permalink]
Show Tags
25 Jun 2013, 00:10
mau5 wrote: Rock750 wrote: How did u come up with this : \(a_1*a_2*....a_4*a_5....a_9\) = \(a_5\) \(\to\) \(a_5(a_1*a_2*...a_5....a_91)\) = 0. ? Could you elaborate on your doubt? The above equation is what is given in the Fact Statement. The first equation is given in the fact statement OK But what about the transition from the first to the second ? I think u factorized by a_5 from both the two parts of the equation which must lead to the following : \(a_1*a_2*....a_4*a_5....a_9\) = \(a_5\) \(\to\) \((a_1*a_2*...a_4....a_9)\) = 1. Am I missing something here ?
_________________
KUDOS is the good manner to help the entire community.
"If you don't change your life, your life will change you"



Verbal Forum Moderator
Joined: 10 Oct 2012
Posts: 625

Re: If list S contains nine distinct integers, at least one of w [#permalink]
Show Tags
25 Jun 2013, 00:59
Rock750 wrote: The first equation is given in the fact statement OK But what about the transition from the first to the second ?
I think u factorized by a_4 from both the two parts of the equation which must lead to the following :
\(a_1*a_2*....a_4*a_5....a_9\) = \(a_5\) \(\to\) \((a_1*a_2*...a_5....a_9)\) = 1.
Am I missing something here ?
Yes, we cannot cancel \(a_5\) from both sides because \(a_5\) can be zero.
_________________
All that is equal and notDeep Dive Inequality
Hit and Trial for Integral Solutions



Manager
Joined: 29 Mar 2010
Posts: 135
Location: United States
Concentration: Finance, International Business
GPA: 2.54
WE: Accounting (Hospitality and Tourism)

Re: If list S contains nine distinct integers, at least one of w [#permalink]
Show Tags
31 Oct 2013, 00:28
For statement 1) Can we deduce that since at least 1 member of the set must be negative, that would give a no answer to the stem of the question. Ie, since at least one member is negative, the only possible answers we could get are either are 0 or <0. Which would give a no answer to the question. Or is this reasoning incorrect for this exam. Thanks, hunter
_________________
4/28 GMATPrep 42Q 36V 640



Director
Joined: 12 Nov 2016
Posts: 790

Re: If list S contains nine distinct integers, at least one of w [#permalink]
Show Tags
19 Apr 2017, 17:39
Rock750 wrote: If list S contains nine distinct integers, at least one of which is negative, is the median of the integers in list S positive? (1) The product of the nine integers in list S is equal to the median of list S. (2) The sum of all nine integers in list S is equal to the median of list S. Statement 1: Two possible numbers to start with are 1 and 0. We cannot have a set of 9 numbers where product of all numbers equals the median if we use 1 (e.x 3 x 2 x 1 x 1 x 2 x 3 x4 ); however, any number times 0 is 0 so if we use 0 as a median we can simply take any product of four negative numbers and multiply them by the product of four positive numbers and then by zero to yield a number equal to the mean or vice versa the product of any four negative numbers times zero times the product of any four positive numbers equals 0 a.k.a the median Sufficient. Statement 2We could have a set of numbers where 0 is the median (1,2,3,4,0,1,2,3,4) the result of which would be the media however, we could also have 6,4,3,2,1,2,3,5,7 which would equal 1 which is also the median of that set and a negative number Insufficient



SVP
Joined: 08 Jul 2010
Posts: 1960
Location: India
GMAT: INSIGHT
WE: Education (Education)

Re: If list S contains nine distinct integers, at least one of w [#permalink]
Show Tags
03 Sep 2017, 01:42
Rock750 wrote: If list S contains nine distinct integers, at least one of which is negative, is the median of the integers in list S positive? (1) The product of the nine integers in list S is equal to the median of list S. (2) The sum of all nine integers in list S is equal to the median of list S. Statement 1: Product if integers = Median Which is true only if either all terms are 1 or ,1 or Median is zero Since integers are distinct so median has to be zero Sufficient Statement 2: set may be (5,4,3,2,1,2,3,4,5) Or (5,4,3,2,0,2,3,4,5) Hence median may be 1 or zero or likewise Not sufficient Answer Option A
_________________
Prosper!!! GMATinsight Bhoopendra Singh and Dr.Sushma Jha email: info@GMATinsight.com I Call us : +919999687183 / 9891333772 Online OneonOne Skype based classes and Classroom Coaching in South and West Delhi http://www.GMATinsight.com/testimonials.html
22 ONLINE FREE (FULL LENGTH) GMAT CAT (PRACTICE TESTS) LINK COLLECTION



Director
Joined: 12 Nov 2016
Posts: 790

Re: If list S contains nine distinct integers, at least one of w [#permalink]
Show Tags
11 Sep 2017, 01:32
Rock750 wrote: If list S contains nine distinct integers, at least one of which is negative, is the median of the integers in list S positive? (1) The product of the nine integers in list S is equal to the median of list S. (2) The sum of all nine integers in list S is equal to the median of list S. Tricky but you just to be mindful of the possibilities 9 integers all must be different St 1 The only way this scenario could hold true is if the median were 0 suff St 2 You could actually have different scenarios as demonstrated below 5,4,3,2,1,2,3,4,5 5,4,3,2,1,1,2,5,6 insuff A



Senior Manager
Joined: 02 Apr 2014
Posts: 417

If list S contains nine distinct integers, at least one of w [#permalink]
Show Tags
11 Feb 2018, 09:02
Statement 1: Prod of all integers is equal median Let prod = product of all integers except median.
given, \(prod\) * \(median\) = \(median\) \(prod\) * \(median\)  \(median\) = 0 \(median\) * (\(prod\)  1) = 0 => median = 0 or prod = 1 but product of all integers except median cannot be 1, as all are distinct => median = 0 => not positive => sufficient
Statement 2: Sum of all nine integers to equal to median. case 1: we can have median as positive, sum of left 4 integers and right 4 integers to cancel each other case 2: we can have median as negative, sum of left 4 integers and right 4 integers to cancel each other case 3: we can have median as 0, sum of left 4 integer and right 4 integers to cancel each other. insuff
(A)




If list S contains nine distinct integers, at least one of w
[#permalink]
11 Feb 2018, 09:02






