Author 
Message 
TAGS:

Hide Tags

eGMAT Representative
Joined: 04 Jan 2015
Posts: 1897

If the sum of the first 30 positive odd inte
[#permalink]
Show Tags
Updated on: 07 Aug 2018, 06:54
Question Stats:
45% (01:25) correct 55% (01:14) wrong based on 287 sessions
HideShow timer Statistics
Q. If the sum of the first 30 positive odd integers is k, what is the sum of first 30 nonnegative even integers? Answer Choices A. k29 B. k30 C. k D. k+29 E. k+30 To read all our articles:Must Read articles to reach Q51To solve question of the week:Question of the WeekThanks, Saquib Quant Expert eGMATRegister for our Free Session on Number Properties (held every 3rd week) to solve exciting 700+ Level Questions in a classroom environment under the realtime guidance of our Experts
Official Answer and Stats are available only to registered users. Register/ Login.
_________________
Register for free sessions Number Properties  Algebra Quant Workshop
Success Stories Guillermo's Success Story  Carrie's Success Story
Ace GMAT quant Articles and Question to reach Q51  Question of the week
Must Read Articles Number Properties – Even Odd  LCM GCD Word Problems – Percentage 1  Percentage 2  Time and Work 1  Time and Work 2  Time, Speed and Distance 1  Time, Speed and Distance 2 Advanced Topics Permutation and Combination 1  Permutation and Combination 2  Permutation and Combination 3  Probability Geometry Triangles 1  Triangles 2  Triangles 3  Common Mistakes in Geometry Algebra Wavy line Practice Questions Number Properties 1  Number Properties 2  Algebra 1  Geometry  Prime Numbers  Absolute value equations  Sets
 '4 out of Top 5' Instructors on gmatclub  70 point improvement guarantee  www.egmat.com



eGMAT Representative
Joined: 04 Jan 2015
Posts: 1897

Re: If the sum of the first 30 positive odd inte
[#permalink]
Show Tags
26 May 2017, 05:10



Intern
Status: GMAT tutor
Joined: 20 Apr 2017
Posts: 20

Re: If the sum of the first 30 positive odd inte
[#permalink]
Show Tags
26 May 2017, 06:20
EgmatQuantExpert wrote: Q. If the sum of the first 30 positive odd integers is k, what is the sum of first 30 nonnegative even integers? Answer Choices A. k29 B. k30 C. k D. k+29 E. k+30 Thanks, Saquib Quant Expert eGMATRegister for our Free Session on Number Properties (held every 3rd week) to solve exciting 700+ Level Questions in a classroom environment under the realtime guidance of our Experts Well, I'm going to start by running a scenario with the first 3 odd integers. Those would be 1, 3, and 5 for a total of 9. The first 3 nonnegative integers would be 0, 2, and 4 for a total of 6. It seems that each even integer is 1 less than its odd counterpart. So my sum is 3 less for the evens because I had 3 terms. So if I use 5 terms, it should be 5 less. Let's test that. 1 + 3 + 5 + 7 + 9 = 15 0 + 2 + 4 + 6 + 8 = 20 Sure enough, each even integer is 1 less than its counterpart. So the answer must be k30. I'll pick answer choice (B).
_________________
Elias Latour Verbal Specialist @ ApexGMAT blog.apexgmat.com +1 (646) 7367622



Director
Joined: 18 Aug 2016
Posts: 631
Concentration: Strategy, Technology
GMAT 1: 630 Q47 V29 GMAT 2: 740 Q51 V38

Re: If the sum of the first 30 positive odd inte
[#permalink]
Show Tags
26 May 2017, 06:34
EgmatQuantExpert wrote: Q. If the sum of the first 30 positive odd integers is k, what is the sum of first 30 nonnegative even integers? Answer Choices A. k29 B. k30 C. k D. k+29 E. k+30 Thanks, Saquib Quant Expert eGMATRegister for our Free Session on Number Properties (held every 3rd week) to solve exciting 700+ Level Questions in a classroom environment under the realtime guidance of our Experts Sum of First n +ve odd integers is n^2 Sum of First n +ve even integers is n(n+1) If we take the scenario for first 5 even/odd numbers First 5 +ve odd integers would be 25 which is K here First 5 +ve even integers would be 5(6) = 30 (Here "0" is not counted) "0" is considered as a nonpositive and nonnegative even integer. and hence will go with KN i.e. (B)
_________________
We must try to achieve the best within us
Thanks Luckisnoexcuse



Intern
Joined: 26 Jan 2017
Posts: 32

Re: If the sum of the first 30 positive odd inte
[#permalink]
Show Tags
26 May 2017, 09:24
mynamegoeson wrote: EgmatQuantExpert wrote: Q. If the sum of the first 30 positive odd integers is k, what is the sum of first 30 nonnegative even integers? Answer Choices A. k29 B. k30 C. k D. k+29 E. k+30 Thanks, Saquib Quant Expert eGMATRegister for our Free Session on Number Properties (held every 3rd week) to solve exciting 700+ Level Questions in a classroom environment under the realtime guidance of our Experts Sum of First n +ve odd integers is n^2 Sum of First n +ve even integers is n(n+1) If we take the scenario for first 5 even/odd numbers First 5 +ve odd integers would be 25 which is K here
First 5 +ve even integers would be 5(6) = 30 (Here "0" is not counted)"0" is considered as a nonpositive and nonnegative even integer. and hence will go with KN i.e. (B) Odd sum is 25 > This means k = 25 Even sum is 30. > This is 5 more than k. n = 5 (No. of elements) > This means Sum for even is k+5 > k+n When n is 30 > k+30



DS Forum Moderator
Joined: 22 Aug 2013
Posts: 1342
Location: India

Re: If the sum of the first 30 positive odd inte
[#permalink]
Show Tags
Updated on: 26 May 2017, 21:10
We should know that in an evenly spaced set (Arithmetic Progression), Mean or average is always = Median Also, for a series having EVEN number of terms, Median = average of two middle terms
First 30 positive odd integers: 1,3,5,7,...59 This is an evenly spaced set hence mean = median = average of two middle terms = average of 15th and 16th terms = (29+31)/2 = 30 Mean=30, So sum = 30*30 (Sum = mean*n) Sum = 900, this is given as K.
Now, first 30 non negative even integers: 0,2,4,6,8,...58 This is again an evenly spaced set hence mean = median = average of 15th and 16th terms = (28+30)/2 = 29 Mean=29, So Sum = 29*30 Sum = 870
If K=900, we can clearly see that 870 = k30
Hence B answer
Originally posted by amanvermagmat on 26 May 2017, 11:06.
Last edited by amanvermagmat on 26 May 2017, 21:10, edited 1 time in total.



Manager
Joined: 03 Oct 2013
Posts: 84

Re: If the sum of the first 30 positive odd inte
[#permalink]
Show Tags
26 May 2017, 13:47
Answer, I think, is k30 i.e. choice B. Solution Attached.
Attachments
Untitled.png [ 55.43 KiB  Viewed 3070 times ]
_________________
P.S. Don't forget to give Kudos on the left if you like the solution



BSchool Forum Moderator
Joined: 26 Feb 2016
Posts: 3040
Location: India
GPA: 3.12

Re: If the sum of the first 30 positive odd inte
[#permalink]
Show Tags
26 May 2017, 14:00
Since the sum of n positive integers(odd) can be got by simple formula Sum(Odd positive numbers) = n^2, which is equal to k. We can deduce that k = 30^2 as we are asked the sum of 30 odd integers. Coming to the second part of the question, we have a formula Sum(Even positive numbers) = n*n1Also, the sum of the first 30 nonnegative even numbers is 30*29 Since we need to find it in form of k & we already know that k = 30^2, we can use k30 to get the value k30 = 30^2  30 = 30(301) = 30*29 Hence, Option B is the correct answer
_________________
You've got what it takes, but it will take everything you've got



Intern
Joined: 11 Oct 2017
Posts: 22

Re: If the sum of the first 30 positive odd inte
[#permalink]
Show Tags
11 Oct 2017, 19:14
Can someone tell me if this is another way of doing these kind of problems? I saw pushpitkc use n(n1) and was wondering if that was just a shortcut from what I did on 2 below.
N^2 = sum of odd numbers N(N+1) = sum of even numbers. To find n = (First Even + Last Even)/2
1. The sum of the first 30 positive odd integers (0 is not included).... N^2=k=30^2=900
2. The sum of first 30 nonnegative even integers (NonNegatives include 0)... 0,2,4,6,8,10,12,14,16,18,20,22,24,26,28,30,32,34,36,38,40,42,44,46,48,50,52,54,56,58... (58 + 0)/2 = 29 = n 29(29+1)= 870
3. 900  x = 870
90030=870.....
Which is k30..... (B).



Senior Manager
Joined: 02 Apr 2014
Posts: 484

Re: If the sum of the first 30 positive odd inte
[#permalink]
Show Tags
17 Dec 2017, 02:54
first 30 odd sequence: 1,3,5,7..........................................59 => sum = k subtracting one from 1 from each term we get first 30 even sequence: 0,2,4,6.............................58 => sum = k 30 kudos if you like my approach, i need them badly to unlock GMAT club tests. Thanks



Director
Joined: 27 May 2012
Posts: 532

Re: If the sum of the first 30 positive odd inte
[#permalink]
Show Tags
13 Feb 2018, 05:14
EgmatQuantExpert wrote: Q. If the sum of the first 30 positive odd integers is k, what is the sum of first 30 nonnegative even integers? Answer Choices A. k29 B. k30 C. k D. k+29 E. k+30 Thanks, Saquib Quant Expert eGMATRegister for our Free Session on Number Properties (held every 3rd week) to solve exciting 700+ Level Questions in a classroom environment under the realtime guidance of our Experts If one remembers the formula's here's another way: Sum of first n positive odd integers = \(n^2\) =\(30^2\) =K Sum of first n positive even integers = n(n+1) = 29 (30) > (30 1)30 > \(30^2\) 30 = K30 Answer :B Sum of the first 30 positive even integers =n(n+1) Please note this formula was derived taking 2 as the first even positive integer. Now if we are to include 0 as the first term then the 29th even integer is actually the 30th term in this question Hence we need the sum of the first 29 positive even integers = 29(30) ( which is actually the sum of first 30 non negative even integers,adding zero does not change the total.) Hope this helps !
_________________
 Stne




Re: If the sum of the first 30 positive odd inte &nbs
[#permalink]
13 Feb 2018, 05:14






