Aug 25 08:00 PM PDT  11:00 PM PDT Exclusive offer! Get 400+ Practice Questions, 25 Video lessons and 6+ Webinars for FREE. Aug 25 09:00 AM PDT  12:00 PM PDT Join a FREE 1day verbal workshop and learn how to ace the Verbal section with the best tips and strategies. Limited for the first 99 registrants. Register today! Aug 28 08:00 AM PDT  09:00 AM PDT Join a FREE live webinar with examPAL and Admissionado and learn how to master GMAT Critical Reasoning questions and the 6pointed star of MBA application essay glory. Save your spot today! Aug 30 08:00 PM PDT  11:00 PM PDT We'll be posting questions in DS/PS/SC/CR in competition mode. Detailed and quickest solution will get kudos. Will be collecting new links to all questions in this topic. Here you can also check links to fresh questions posted. Aug 31 07:00 AM PDT  09:00 AM PDT Want to score 90 percentile or higher on GMAT CR? Attend this free webinar to learn how to prethink assumptions and solve the most challenging questions in less than 2 minutes. Sep 01 07:00 AM PDT  09:00 AM PDT Want to solve 700+ level Algebra questions within 2 minutes? Attend this free webinar to learn how to master the most challenging Inequalities and Absolute Values questions in GMAT Sep 02 08:00 PM PDT  11:00 PM PDT Sign Up, Get $49 Exam Pack 2 FREE. Train to be ready for Round 1 Deadlines with EMPOWERgmat's Score Booster Code: EP22019 Ends: September 2nd
Author 
Message 
TAGS:

Hide Tags

Ask GMAT Experts Forum Moderator
Status: Preparing for GMAT
Joined: 25 Nov 2015
Posts: 1038
Location: India
GPA: 3.64

Set A consists of consecutive integers. What is the median of all the
[#permalink]
Show Tags
28 Oct 2017, 23:09
Question Stats:
44% (01:23) correct 56% (01:17) wrong based on 285 sessions
HideShow timer Statistics
Set A consists of consecutive integers. What is the median of all the numbers in set A? (1) The smallest number in set A is 4. (2) The standard deviation of all the numbers in set A is \(\sqrt{2}\)
Official Answer and Stats are available only to registered users. Register/ Login.
_________________
Please give kudos, if you like my post
When the going gets tough, the tough gets going...




Math Expert
Joined: 02 Aug 2009
Posts: 7754

Set A consists of consecutive integers. What is the median of all the
[#permalink]
Show Tags
28 Oct 2017, 23:19
souvonik2k wrote: Set A consists of consecutive integers. What is the median of all the numbers in set A? (1) The smallest number in set A is 4. (2) The standard deviation of all the numbers in set A is \((2)^½\)
Please give kudos, if u liked my post! hi.. (1) The smallest number in set A is 4. we just know the smallest number . we require to know the number of items or the largest number to know the median insuff (2) The standard deviation of all the numbers in set A is \((2)^½\) since theterms are consecutive, we can know the number of elements in set.. \(\sqrt{2}=\sqrt{1^2+0+1^2}\), so 3 elements but where are these 3 elements... insuff combined 3 elements starting with 4.. 4,5,6 median 5 suff c souvonik2k, in response to your query mentioned in post below the consecutive numbers have a difference of 1 ... so two cases .. 1) ODD numbers in the list.. MEDIAN is also the MEAN.. SD depends on how each element is away from median.. If 3 elements, say 5,6,7,.... middle is 0 away from mean, the smaller and bigger are 1 away from mean so SD = \(\sqrt{1^2+0+1^2}=\sqrt{2}\) If 5 elements say 2,3,4,5,6... middle is 0 away, the biggest and smallest are 2 away from mean and other two 1 away, so SD =\(\sqrt{2^2+1^2+0+1^2+2^2}=\sqrt{10}\) and so on, it will keep increasing with more elements added 2) EVEN numbers in the list median=mean = average of centre two numbers if 2 elements.. 3,4...SD = \(\sqrt{(1/2)^2+(1/2)^2}=\sqrt{1/2}\)hope it helps
_________________




Ask GMAT Experts Forum Moderator
Status: Preparing for GMAT
Joined: 25 Nov 2015
Posts: 1038
Location: India
GPA: 3.64

Re: Set A consists of consecutive integers. What is the median of all the
[#permalink]
Show Tags
28 Oct 2017, 23:27
chetan2u wrote: souvonik2k wrote: Set A consists of consecutive integers. What is the median of all the numbers in set A? (1) The smallest number in set A is 4. (2) The standard deviation of all the numbers in set A is \((2)^½\)
Please give kudos, if u liked my post! hi.. (1) The smallest number in set A is 4. we just know the smallest number . we require to know the number of items or the largest number to know the median insuff (2) The standard deviation of all the numbers in set A is \((2)^½\) since theterms are consecutive, we can know the number of elements in set.. \(\sqrt{2}=\sqrt{ 1^2+0+1^2}\), so 3 elementsbut where are these 3 elements... insuff combined 3 elements starting with 4.. 4,5,6 median 5 suff c Hi chetan2uI couldn't understand this highlighted part. Cannot there be any other possibility than 3 numbers. Please explain.
_________________
Please give kudos, if you like my post
When the going gets tough, the tough gets going...



Manager
Joined: 14 Sep 2016
Posts: 127

Re: Set A consists of consecutive integers. What is the median of all the
[#permalink]
Show Tags
09 Nov 2017, 00:12
niks18 ! some feedback on this one please !



Retired Moderator
Joined: 25 Feb 2013
Posts: 1192
Location: India
GPA: 3.82

Set A consists of consecutive integers. What is the median of all the
[#permalink]
Show Tags
09 Nov 2017, 02:14
souvonik2k wrote: Set A consists of consecutive integers. What is the median of all the numbers in set A?
(1) The smallest number in set A is 4. (2) The standard deviation of all the numbers in set A is \(\sqrt{2}\) Hi kunalsinghNSto find the median we need to know the number of elements in the set and as the set has consecutive elements, we need any one number from the set. Statement 1: provides one number from the set but we don't know the number of elements in the set. InsufficientStatement 2: let the number of elements in the set we \(n\) and \(a\) be the first number so our set will be {\(a, a+1, a+2.....a+(n1)\)} Use simple mathematical process to calculate st. deviation of this set. So average of the set will be \(= \frac{{a+a+1......a+(n1)}}{n}\) \(=\frac{{an+1+2...n1}}{n}\) \(= [an+n(n1)/2]/n\) [{1+2...{n1} this is a simple AP series with 1st term 1, last term n1, common difference 1 and number of terms n1. so you can easily calculate the sum in terms of n] so average of the set \(= a+\frac{(n1)}{2}\) to calculate standard deviation we need to reduce each element in the set by the average, then square it, then take the average of the resultant no and finally take the square root Step 1: \(aa\frac{(n1)}{2}\), \(a+1a\frac{(n1)}{2}\),.................., \(a+(n1)a\frac{(n1)}{2}\) \(= \frac{(n1)}{2}\), \(1\frac{(n1)}{2}\)........., \((n1)\frac{(n1)}{2}\) Step 2: now square each of the elements and add. On squaring & adding each of the elements, you will get something in terms of \(n^2\). let's call it \(kn^2\), where \(k\) is any constant resulting from the summation of the AP series Step 3: take the average of Step 2 \(= \frac{kn^2}{n} = kn\) Step 4: standard deviation \(= \sqrt{kn}\) so we have \(\sqrt{kn}=\sqrt{2}\) hence \(n=\frac{2}{k}\). So we get the value of \(n\) but we don't know any of the elements in the set. InsufficientCombining 1 & 2: we get all the required parameters. Statement 1 provides the 1st element in the set and Statement 2 provides the number of elements in the set. Hence CkunalsinghNS, instead of going for the mathematical derivation, you can test by using simple nos, for e.g 1,2,3 etc. to know that if you are given st. deviation/variance, then you can calculate the number of terms in the set because each element is consecutive. I have skipped some calculation because working with variables was becoming cumbersome . but the point is statement 2 will give you the number of elements in the set as the set is consecutive. Hope this helps



Manager
Joined: 14 Sep 2016
Posts: 127

Re: Set A consists of consecutive integers. What is the median of all the
[#permalink]
Show Tags
09 Nov 2017, 08:10
This seems to be a pretty long calculation !! approximation is the best option i guess ! but thank you !!



Retired Moderator
Joined: 25 Feb 2013
Posts: 1192
Location: India
GPA: 3.82

Re: Set A consists of consecutive integers. What is the median of all the
[#permalink]
Show Tags
09 Nov 2017, 08:18
kunalsinghNS wrote: This seems to be a pretty long calculation !! approximation is the best option i guess ! but thank you !! Yup. But you only need to visualise the process and need to note that if st. Deviation of consecutive nos is given we can calculate the number of terms in the set. Mathematical derivation is just for academics purposes Posted from my mobile device



Manager
Joined: 23 Aug 2017
Posts: 118

Re: Set A consists of consecutive integers. What is the median of all the
[#permalink]
Show Tags
23 Feb 2019, 02:37
we also need to divide the summation of the squares by the total no of elements. Can someone point out where are we dividing the summation before taking the square root?
Thanks in advance



Manager
Joined: 13 Oct 2018
Posts: 85
Location: India
GPA: 3.1
WE: Information Technology (Computer Software)

Re: Set A consists of consecutive integers. What is the median of all the
[#permalink]
Show Tags
23 Feb 2019, 03:15
Debashis Roy wrote: we also need to divide the summation of the squares by the total no of elements. Can someone point out where are we dividing the summation before taking the square root?
Thanks in advance Hello , In this step niks18 divided by n ( after approximation ) Step 3: take the average of Step 2 =kn2n=kn
_________________
Ankit GMAT is tough so I am ... Giving Kudos is the best way to encourage and appreciate people



Manager
Joined: 23 Aug 2017
Posts: 118

Set A consists of consecutive integers. What is the median of all the
[#permalink]
Show Tags
27 Feb 2019, 23:33
chetan2u VeritasKarishmaHi, In your explanation : √=1^2+0+1^2−−−−−−−−−√2=1^2+0+1^2, so 3 elements... shouldnt we divide the sum of the squares of the terms by the no of terms also... In gthat case for 3 terms 4,5,6... SD= √[(1^2+0+1^2)/3]...gives √(2/3)... Please explain..



Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
Posts: 9558
Location: Pune, India

Re: Set A consists of consecutive integers. What is the median of all the
[#permalink]
Show Tags
28 Feb 2019, 20:48
Debashis Roy wrote: chetan2u VeritasKarishmaHi, In your explanation : √=1^2+0+1^2−−−−−−−−−√2=1^2+0+1^2, so 3 elements... shouldnt we divide the sum of the squares of the terms by the no of terms also... In gthat case for 3 terms 4,5,6... SD= √[(1^2+0+1^2)/3]...gives √(2/3)... Please explain.. Yes, the SD will be \(\sqrt{2} = \sqrt{\frac{(2)^2 + (1)^2 + 0 + 1^2 + 2^2}{5}}\) In any case, the answer doesn't change. Each unique distribution will have a unique SD. For median, you will need the exact position where the distribution is placed on the number line so you need both statements to answer the question. Answer (C)
_________________
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: 23 Aug 2017
Posts: 118

Re: Set A consists of consecutive integers. What is the median of all the
[#permalink]
Show Tags
28 Feb 2019, 22:57
VeritasKarishmaTo quote an above explanation: (2) The standard deviation of all the numbers in set A is (2)½(2)½ since theterms are consecutive, we can know the number of elements in set.. 2√=12+0+12−−−−−−−−−√2=12+0+12, so 3 elements but where are these 3 elements... insuff combined 3 elements starting with 4.. 4,5,6 median 5 suff How come the SD is √2 for the set {4,5,6}... I am not getting this part as written in the explanation by chetan2u



Intern
Joined: 20 Feb 2018
Posts: 46
Location: India

Re: Set A consists of consecutive integers. What is the median of all the
[#permalink]
Show Tags
14 Jun 2019, 00:06
chetan2u wrote: souvonik2k wrote: Set A consists of consecutive integers. What is the median of all the numbers in set A? (1) The smallest number in set A is 4. (2) The standard deviation of all the numbers in set A is \((2)^½\)
Please give kudos, if u liked my post! hi.. (1) The smallest number in set A is 4. we just know the smallest number . we require to know the number of items or the largest number to know the median insuff (2) The standard deviation of all the numbers in set A is \((2)^½\) since theterms are consecutive, we can know the number of elements in set.. \(\sqrt{2}=\sqrt{1^2+0+1^2}\), so 3 elements but where are these 3 elements... insuff combined 3 elements starting with 4.. 4,5,6 median 5 suff c souvonik2k, in response to your query mentioned in post below the consecutive numbers have a difference of 1 ... so two cases .. 1) ODD numbers in the list.. MEDIAN is also the MEAN.. SD depends on how each element is away from median.. If 3 elements, say 5,6,7,.... middle is 0 away from mean, the smaller and bigger are 1 away from mean so SD = \(\sqrt{1^2+0+1^2}=\sqrt{2}\) If 5 elements say 2,3,4,5,6... middle is 0 away, the biggest and smallest are 2 away from mean and other two 1 away, so SD =\(\sqrt{2^2+1^2+0+1^2+2^2}=\sqrt{10}\) and so on, it will keep increasing with more elements added 2) EVEN numbers in the list median=mean = average of centre two numbers if 2 elements.. 3,4...SD = \(\sqrt{(1/2)^2+(1/2)^2}=\sqrt{1/2}\)hope it helps Hi chetan2u, I agree with your explanation but if we go by the SD formula then it will be \(\sqrt{2}\)/3. 3 being the number of terms. Hence, answer should be E instead of C?



Manager
Joined: 27 Jun 2015
Posts: 52

Re: Set A consists of consecutive integers. What is the median of all the
[#permalink]
Show Tags
30 Jun 2019, 08:56
Hi chetan2uAs per your solution posted above , SD for 4,5,6 will never be root(2). It will be root(2/3). SD of 4,5,6,7,8 will be root(2). SD of any 5 consecutive positive integers is root(2). Thus median will be 6 not 5



Duke & Cornell Moderator
Joined: 29 May 2018
Posts: 88
Location: India
GMAT 1: 700 Q48 V38 GMAT 2: 720 Q49 V39
GPA: 4

Re: Set A consists of consecutive integers. What is the median of all the
[#permalink]
Show Tags
07 Aug 2019, 09:52
chetan2u wrote: souvonik2k wrote: Set A consists of consecutive integers. What is the median of all the numbers in set A? (1) The smallest number in set A is 4. (2) The standard deviation of all the numbers in set A is \((2)^½\)
Please give kudos, if u liked my post! hi.. (1) The smallest number in set A is 4. we just know the smallest number . we require to know the number of items or the largest number to know the median insuff (2) The standard deviation of all the numbers in set A is \((2)^½\) since theterms are consecutive, we can know the number of elements in set.. \(\sqrt{2}=\sqrt{1^2+0+1^2}\), so 3 elements but where are these 3 elements... insuff combined 3 elements starting with 4.. 4,5,6 median 5 suff c souvonik2k, in response to your query mentioned in post below the consecutive numbers have a difference of 1 ... so two cases .. 1) ODD numbers in the list.. MEDIAN is also the MEAN.. SD depends on how each element is away from median.. If 3 elements, say 5,6,7,.... middle is 0 away from mean, the smaller and bigger are 1 away from mean so SD = \(\sqrt{1^2+0+1^2}=\sqrt{2}\) If 5 elements say 2,3,4,5,6... middle is 0 away, the biggest and smallest are 2 away from mean and other two 1 away, so SD =\(\sqrt{2^2+1^2+0+1^2+2^2}=\sqrt{10}\) and so on, it will keep increasing with more elements added 2) EVEN numbers in the list median=mean = average of centre two numbers if 2 elements.. 3,4...SD = \(\sqrt{(1/2)^2+(1/2)^2}=\sqrt{1/2}\)hope it helps Please see that formula used for SD is incorrect. Statment 1: clearly insufficient Statement 2: for SD to be root2, we need any 5 consecutive integers. But we still dont know the starting point. Not sufficient Combined: we know the starting point and we know that there are 5 integers Sufficient. Answer C




Re: Set A consists of consecutive integers. What is the median of all the
[#permalink]
07 Aug 2019, 09:52






