May 24 10:00 PM PDT  11:00 PM PDT Join a FREE 1day workshop and learn how to ace the GMAT while keeping your fulltime job. Limited for the first 99 registrants. May 25 07:00 AM PDT  09:00 AM PDT Attend this webinar and master GMAT SC in 10 days by learning how meaning and logic can help you tackle 700+ level SC questions with ease. May 27 01:00 AM PDT  11:59 PM PDT All GMAT Club Tests are free and open on May 27th for Memorial Day! May 27 10:00 PM PDT  11:00 PM PDT Special savings are here for Magoosh GMAT Prep! Even better  save 20% on the plan of your choice, now through midnight on Tuesday, 5/27 May 30 10:00 PM PDT  11:00 PM PDT Application deadlines are just around the corner, so now’s the time to start studying for the GMAT! Start today and save 25% on your GMAT prep. Valid until May 30th.
Author 
Message 
TAGS:

Hide Tags

Math Expert
Joined: 02 Sep 2009
Posts: 55271

A certain list, L, contains a total of n numbers, not necessarily dist
[#permalink]
Show Tags
26 Apr 2019, 03:31
Question Stats:
51% (01:38) correct 49% (01:30) wrong based on 131 sessions
HideShow timer Statistics
A certain list, L, contains a total of n numbers, not necessarily distinct, that are arranged in increasing order. If \(L_1\) is the list consisting of the first \(n_1\) numbers in L and \(L_2\) is the list consisting of the last \(n_2\) numbers in L, is 17 a mode for L ? (1) 17 is a mode for \(L_1\) and 17 is a mode for \(L_2\). (2) \(n_1 + n_2 = n\) DS08091.01 OG2020 NEW QUESTION
Official Answer and Stats are available only to registered users. Register/ Login.
_________________



Math Expert
Joined: 02 Aug 2009
Posts: 7686

Re: A certain list, L, contains a total of n numbers, not necessarily dist
[#permalink]
Show Tags
26 Apr 2019, 04:29
A certain list, L, contains a total of n numbers, not necessarily distinct, that are arranged in increasing order. If \(L_1\) is the list consisting of the first \(n_1\) numbers in L and \(L_2\) is the list consisting of the last \(n_2\) numbers in L, is 17 a mode for L ? Say the list is a, b, c, c, d, e, f, h, h, h, k, l.. \(L_1\) could be just a, and \(L_2\) could be h,h,k,l OR \(L_1\) could be a,b,c,c,d and \(L_2\) could be c,c,d..h,h,k,l (1) 17 is a mode for \(L_1\) and 17 is a mode for \(L_2\). Since the list is in increasing order and mode is 17 in both cases, the list L1 and L2 either have all numbers within themselves OR only some other 17 are left. For example 1,3,5,17,17,17,17,17,20,25....L1 could be 1,3,5,17,17 and L2 could be 3,5,17,17,17,17,17,20,25 OR L1 could be 1,3,5,17,17 and L2 could be 17,17,20,25 So the mode of L will be 17 in each case. Suff (2) \(n_1 + n_2 = n\) We do not know the numbers. Insuff A
_________________



examPAL Representative
Joined: 07 Dec 2017
Posts: 1058

A certain list, L, contains a total of n numbers, not necessarily dist
[#permalink]
Show Tags
Updated on: 29 Apr 2019, 08:18
The Logical approach to this question will use the definition of 'mode'  the most frequent value of a set of data. In statement (1),if the number 17 appears more than all other numbers in both of the list, it must also appear more than any other number in the combined list as well. It is like saying that if a > x and b > y, then a + b > x + y: if 17 appears more than the second frequent number in both lists, it will appear more than the second greatest number in the combined list as well. This statement is enough on its own. Statement (2) does not tell us which numbers are in the set, so is insufficient. The correct answer is (A). Posted from my mobile deviceEDIT: *kudos to Shukhrat below for pointing out an error in my explanation of stmt (2) (which did not change the final answer)
_________________



Manager
Joined: 25 Jul 2018
Posts: 50
Location: Uzbekistan
Concentration: Finance, Organizational Behavior
GPA: 3.85
WE: Project Management (Investment Banking)

A certain list, L, contains a total of n numbers, not necessarily dist
[#permalink]
Show Tags
Updated on: 06 May 2019, 00:18
Bunuel wrote: A certain list, L, contains a total of n numbers, not necessarily distinct, that are arranged in increasing order. If \(L_1\) is the list consisting of the first \(n_1\) numbers in L and \(L_2\) is the list consisting of the last \(n_2\) numbers in L, is 17 a mode for L ?
(1) 17 is a mode for \(L_1\) and \(17\) is a mode for \(L_2\).
(2) \(n_1 + n_2 = n\)
DS08091.01 OG2020 NEW QUESTION Hola amigos I disagree with David from examPAL. Mode  is the number that occurs most often. If no number in the list is repeated, then there is no mode for the list. 1. \(17\) is a mode for \(L_1\) and \(17\) is a mode for \(L_2\).Most important thing to note is the numbers are in increasing order. That means that there are only \(2\) possible cases: Case 1: \(L_1\) and \(L_2\) togther include all the numbers \(L\) has. E.g. \(L\) = {1, 1, 3, 17, 17, 17, 19, 21,}, \(L_1\) = {1, 1, 3 , 17, 17, 17, 19} and \(L_2\) = {3, 17, 17, 17, 19, 21} Case 2: The numbers of \(L\) not included in \(L_1\) and \(L_2\) are all \(17\). E.g. \(L\) = {1, 1, 3, 17, 17, 17, 17, 17, 17, 17, 19, 21,}, \(L_1\) = {1, 1, 3, 17, 17, 17} and \(L_2\) = { 17, 17, 19, 21} Those two reds are leftover. In both cases \(17\) is the most repeated number and there is no other possible case, thus the mode of \(L\) is \(17\). Sufficient2. \(n_1+n_2=n\) The given information is not repeated in other words here. We already have seen that some \(17\) can be left. Though no info regarding numbers here. InsufficientThe answer is A
_________________
Let's help each other with kudos. Kudos will be payed back
Originally posted by ShukhratJon on 29 Apr 2019, 06:14.
Last edited by ShukhratJon on 06 May 2019, 00:18, edited 1 time in total.



Intern
Joined: 14 Apr 2017
Posts: 44
Location: Hungary
GMAT 1: 690 Q50 V34 GMAT 2: 760 Q50 V42 GMAT 3: 700 Q50 V33
WE: Education (Education)

Re: A certain list, L, contains a total of n numbers, not necessarily dist
[#permalink]
Show Tags
05 May 2019, 15:34
Bunuel wrote: A certain list, L, contains a total of n numbers, not necessarily distinct, that are arranged in increasing order. If \(L_1\) is the list consisting of the first \(n_1\) numbers in L and \(L_2\) is the list consisting of the last \(n_2\) numbers in L, is 17 a mode for L ?
(1) 17 is a mode for \(L_1\) and 17 is a mode for \(L_2\).
(2) \(n_1+n_2=n\)
DS08091.01 OG2020 NEW QUESTION Three cases are possible about the mode of a list of numbers. If the numbers are all distinct, then the list has no mode. If one number's frequency is greater than the frequencies of all other numbers, then the list has one mode. However, it's also possible that a list of not all distinct numbers has multiple modes if two or more numbers have the greatest frequency simultaneously. We know that \(L\) is a list of numbers, not necessarily distinct, that are arranged in increasing order. The original question: Is 17 a mode for \(L\)? 1) We can infer that in the list no number under 17 has greater frequency than that of 17. We can also infer that in the list no number above 17 has greater frequency than that of 17. Using that no number in the list has greater frequency than that of 17 and that 17 has a frequency of at least 2, we can answer the original question with a definite Yes. \(\implies\) Sufficient2) No information is given about the actual numbers. If all numbers in the list are 17, then the answer to the original question is Yes. However, if 17 is not even in the list, then the answer to the original question is No. Thus, we can't get a definite answer to the original question. \(\implies\) InsufficientAnswer: A
_________________



EMPOWERgmat Instructor
Status: GMAT Assassin/CoFounder
Affiliations: EMPOWERgmat
Joined: 19 Dec 2014
Posts: 14198
Location: United States (CA)

Re: A certain list, L, contains a total of n numbers, not necessarily dist
[#permalink]
Show Tags
10 May 2019, 16:16
Hi All, We're told that List L contains a total of N numbers, NOT necessarily DISTINCT, that are arranged in INCREASING order and L1 is the list consisting of the first N1 numbers in L and L2 is the list consisting of the last N2 numbers in L. We're asked if 17 is a MODE for L. It's worth noting that the two sublists (L1 and L2 could potentially "overlap", meaning that some numbers of List L appear in BOTH groups). Every number in List L is accounted for though (again though, it's possible that some values appear in both sublists). To start, it's worth noting that a "mode" is a number that shows up the most often in a group of numbers (for example, the group 1, 2, 2, 3, 4 has a mode of 2). There can actually be more than one mode in a group though (for example, the group 1, 1, 2, 2, 3, 4 has two modes: 1 and 2). (1) 17 is a mode for L1 and 17 is a mode for L2. Fact1 tells us that 17 is a mode for both sublists. Note that the prompt did tell us that the list is arranged in INCREASING order... IF.... there is NO 'overlap', then some of the 17s appear in L1 and some appear in L2. Totaling all of those individual 17s would make the mode even larger than it is in the two individual sublists, meaning that no other value could appear more often in List L. there IS an 'overlap'  meaning one (or more) of the 17s appears in BOTH sublists, then that total number of 17s will still be a mode. There might be other values that are also modes, but those values could not show up more often than the 17s do, so none of them could "outnumber" the 17s. Fact 1 is SUFFICIENT (2) N1 + N2 = N Fact 2 tells us that the two sublists have no terms in common (meaning that there is no 'overlap'), but it does not tell us anything about the individual terms or what the mode(s) might be. Fact 2 is INSUFFICIENT Final Answer: GMAT assassins aren't born, they're made, Rich
_________________
760+: Learn What GMAT Assassins Do to Score at the Highest Levels Contact Rich at: Rich.C@empowergmat.com*****Select EMPOWERgmat Courses now include ALL 6 Official GMAC CATs!*****
Rich Cohen
CoFounder & GMAT Assassin
Special Offer: Save $75 + GMAT Club Tests Free
Official GMAT Exam Packs + 70 Pt. Improvement Guarantee www.empowergmat.com/



eGMAT Representative
Joined: 04 Jan 2015
Posts: 2873

Re: A certain list, L, contains a total of n numbers, not necessarily dist
[#permalink]
Show Tags
15 May 2019, 00:14
Solution Steps 1 & 2: Understand Question and Draw InferencesIn this question, we are given • A certain list, L, contains a total of n numbers, not necessarily distinct, that are arranged in increasing order. • L1 is the list consisting of the first n1 numbers in L. • L2 is the list consisting of the last n2 numbers in L. We need to determine • Whether 17 is a mode for L or not. Step 3: Analyse Statement 1As per the information given in statement 1, 17 is a mode for L1 and 17 is a mode for L2. Therefore, we can infer that • 17 must occur in L1, either same or a greater number of times as any other number in L1. • 17 must occur in L1, either same or a greater number of times as any other number in L2. As all elements in L are in ascending order, we can also conclude that • Each number between last occurrence of 17 in L1 and the first occurrence of 17 in L2 must be equal to 17 only. • Therefore, 17 occurs either same or greater number of times as any other number in L.
o Thus, 17 is a mode for L. Hence, statement 1 is sufficient to answer the question. Step 4: Analyse Statement 2As per the information given in statement 2, n1 + n2 = n. • However, from this statement, we cannot conclude anything about the mode of L1, L2, or L. Hence, statement 2 is not sufficient to answer the question. Step 5: Combine Both Statements Together (If Needed)Since we can determine the answer from statement 1 individually, this step is not required. Hence, the correct answer choice is option A.
_________________




Re: A certain list, L, contains a total of n numbers, not necessarily dist
[#permalink]
15 May 2019, 00:14






