GMAT Question of the Day - Daily to your Mailbox; hard ones only

It is currently 13 Dec 2018, 00:38

Close

GMAT Club Daily Prep

Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track
Your Progress

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.

Close

Request Expert Reply

Confirm Cancel
Events & Promotions in December
PrevNext
SuMoTuWeThFrSa
2526272829301
2345678
9101112131415
16171819202122
23242526272829
303112345
Open Detailed Calendar
  • The winning strategy for 700+ on the GMAT

     December 13, 2018

     December 13, 2018

     08:00 AM PST

     09:00 AM PST

    What people who reach the high 700's do differently? We're going to share insights, tips and strategies from data we collected on over 50,000 students who used examPAL.
  • GMATbuster's Weekly GMAT Quant Quiz, Tomorrow, Saturday at 9 AM PST

     December 14, 2018

     December 14, 2018

     09:00 AM PST

     10:00 AM PST

    10 Questions will be posted on the forum and we will post a reply in this Topic with a link to each question. There are prizes for the winners.

If the sum of the first 30 positive odd inte

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:

Hide Tags

e-GMAT Representative
User avatar
D
Joined: 04 Jan 2015
Posts: 2296
If the sum of the first 30 positive odd inte  [#permalink]

Show Tags

New post Updated on: 07 Aug 2018, 05:54
1
10
00:00
A
B
C
D
E

Difficulty:

  85% (hard)

Question Stats:

47% (01:55) correct 53% (01:51) wrong based on 293 sessions

HideShow timer Statistics

Q.

If the sum of the first 30 positive odd integers is k, what is the sum of first 30 non-negative even integers?


Answer Choices



    A. k-29
    B. k-30
    C. k
    D. k+29
    E. k+30

To read all our articles:Must Read articles to reach Q51

To solve question of the week:Question of the Week

Thanks,
Saquib
Quant Expert
e-GMAT

Register for our Free Session on Number Properties (held every 3rd week) to solve exciting 700+ Level Questions in a classroom environment under the real-time guidance of our Experts :)

Image

_________________








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 | Statistics-1 | Statistics-2 | Remainders-1 | Remainders-2
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 | Inequalities

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.e-gmat.com


Originally posted by EgmatQuantExpert on 26 May 2017, 04:09.
Last edited by EgmatQuantExpert on 07 Aug 2018, 05:54, edited 1 time in total.
e-GMAT Representative
User avatar
D
Joined: 04 Jan 2015
Posts: 2296
Re: If the sum of the first 30 positive odd inte  [#permalink]

Show Tags

New post 26 May 2017, 04:10
Intern
Intern
User avatar
B
Status: GMAT tutor
Joined: 20 Apr 2017
Posts: 20
GMAT 1: 770 Q49 V47
Re: If the sum of the first 30 positive odd inte  [#permalink]

Show Tags

New post 26 May 2017, 05:20
1
EgmatQuantExpert wrote:
Q.

If the sum of the first 30 positive odd integers is k, what is the sum of first 30 non-negative even integers?


Answer Choices



    A. k-29
    B. k-30
    C. k
    D. k+29
    E. k+30

Thanks,
Saquib
Quant Expert
e-GMAT

Register for our Free Session on Number Properties (held every 3rd week) to solve exciting 700+ Level Questions in a classroom environment under the real-time guidance of our Experts :)

Image

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 non-negative 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 k-30.
I'll pick answer choice (B).
_________________

Elias Latour
Verbal Specialist @ ApexGMAT
blog.apexgmat.com
+1 (646) 736-7622

Director
Director
User avatar
P
Joined: 18 Aug 2016
Posts: 623
Concentration: Strategy, Technology
GMAT 1: 630 Q47 V29
GMAT 2: 740 Q51 V38
GMAT ToolKit User Premium Member Reviews Badge
Re: If the sum of the first 30 positive odd inte  [#permalink]

Show Tags

New post 26 May 2017, 05:34
EgmatQuantExpert wrote:
Q.

If the sum of the first 30 positive odd integers is k, what is the sum of first 30 non-negative even integers?


Answer Choices



    A. k-29
    B. k-30
    C. k
    D. k+29
    E. k+30

Thanks,
Saquib
Quant Expert
e-GMAT

Register for our Free Session on Number Properties (held every 3rd week) to solve exciting 700+ Level Questions in a classroom environment under the real-time guidance of our Experts :)

Image



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 non-positive and non-negative even integer. and hence will go with K-N i.e. (B)
_________________

We must try to achieve the best within us


Thanks
Luckisnoexcuse

Intern
Intern
avatar
B
Joined: 26 Jan 2017
Posts: 31
Re: If the sum of the first 30 positive odd inte  [#permalink]

Show Tags

New post 26 May 2017, 08:24
mynamegoeson wrote:
EgmatQuantExpert wrote:
Q.

If the sum of the first 30 positive odd integers is k, what is the sum of first 30 non-negative even integers?


Answer Choices



    A. k-29
    B. k-30
    C. k
    D. k+29
    E. k+30

Thanks,
Saquib
Quant Expert
e-GMAT

Register for our Free Session on Number Properties (held every 3rd week) to solve exciting 700+ Level Questions in a classroom environment under the real-time guidance of our Experts :)

Image



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 non-positive and non-negative even integer. and hence will go with K-N 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
avatar
P
Joined: 21 Aug 2013
Posts: 1412
Location: India
Premium Member
Re: If the sum of the first 30 positive odd inte  [#permalink]

Show Tags

New post Updated on: 26 May 2017, 20:10
2
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 = k-30

Hence B answer

Originally posted by amanvermagmat on 26 May 2017, 10:06.
Last edited by amanvermagmat on 26 May 2017, 20:10, edited 1 time in total.
Manager
Manager
avatar
B
Joined: 03 Oct 2013
Posts: 84
Re: If the sum of the first 30 positive odd inte  [#permalink]

Show Tags

New post 26 May 2017, 12:47
2
Answer, I think, is k-30 i.e. choice B.

Solution Attached.
Attachments

Untitled.png
Untitled.png [ 55.43 KiB | Viewed 3270 times ]


_________________

P.S. Don't forget to give Kudos on the left if you like the solution

Senior PS Moderator
User avatar
V
Joined: 26 Feb 2016
Posts: 3325
Location: India
GPA: 3.12
Premium Member CAT Tests
Re: If the sum of the first 30 positive odd inte  [#permalink]

Show Tags

New post 26 May 2017, 13:00
1
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*n-1
Also, the sum of the first 30 non-negative 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 k-30 to get the value
k-30 = 30^2 - 30 = 30(30-1) = 30*29
Hence, Option B is the correct answer
_________________

You've got what it takes, but it will take everything you've got

Intern
Intern
avatar
B
Joined: 11 Oct 2017
Posts: 22
Re: If the sum of the first 30 positive odd inte  [#permalink]

Show Tags

New post 11 Oct 2017, 18:14
Can someone tell me if this is another way of doing these kind of problems?

I saw pushpitkc use n(n-1) 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 non-negative even integers (Non-Negatives 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

900-30=870.....

Which is k-30..... (B).
Senior Manager
Senior Manager
avatar
G
Joined: 02 Apr 2014
Posts: 474
GMAT 1: 700 Q50 V34
Re: If the sum of the first 30 positive odd inte  [#permalink]

Show Tags

New post 17 Dec 2017, 01:54
3
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
Director
User avatar
D
Joined: 27 May 2012
Posts: 631
Premium Member
Re: If the sum of the first 30 positive odd inte  [#permalink]

Show Tags

New post 13 Feb 2018, 04:14
EgmatQuantExpert wrote:
Q.

If the sum of the first 30 positive odd integers is k, what is the sum of first 30 non-negative even integers?


Answer Choices



    A. k-29
    B. k-30
    C. k
    D. k+29
    E. k+30

Thanks,
Saquib
Quant Expert
e-GMAT

Register for our Free Session on Number Properties (held every 3rd week) to solve exciting 700+ Level Questions in a classroom environment under the real-time guidance of our Experts :)

Image


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 = K-30
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

GMAT Club Bot
Re: If the sum of the first 30 positive odd inte &nbs [#permalink] 13 Feb 2018, 04:14
Display posts from previous: Sort by

If the sum of the first 30 positive odd inte

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  


Copyright

GMAT Club MBA Forum Home| About| Terms and Conditions and Privacy Policy| GMAT Club Rules| Contact| Sitemap

Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne

Kindly note that the GMAT® test is a registered trademark of the Graduate Management Admission Council®, and this site has neither been reviewed nor endorsed by GMAC®.