Find all School-related info fast with the new School-Specific MBA Forum

It is currently 22 Jul 2014, 06:12

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.

Events & Promotions

Events & Promotions in June
Open Detailed Calendar

I dont understand this solution from MGMAT :(

  Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:
Intern
Intern
avatar
Joined: 18 Jan 2012
Posts: 9
Followers: 0

Kudos [?]: 0 [0], given: 0

I dont understand this solution from MGMAT :( [#permalink] New post 22 Jan 2012, 22:20
00:00
A
B
C
D
E

Difficulty:

  5% (low)

Question Stats:

0% (00:00) correct 100% (00:07) wrong based on 1 sessions
Hey guys and gals,

question: Is X^2 odd?

statement 2: The sum of x consecutive integers is divisible by x

the solution states that the sum divided by x is an integer and moreover the sum of x consecutive integers divided by x is the average of that set of x integers. this therefore proves that x^2 is odd....how does that make sense?


anyone care to explain? :)


C210
[Reveal] Spoiler: OA
1 KUDOS received
Senior Manager
Senior Manager
avatar
Joined: 12 Oct 2011
Posts: 276
Followers: 0

Kudos [?]: 20 [1] , given: 110

Re: I dont understand this solution from MGMAT :( [#permalink] New post 22 Jan 2012, 23:21
1
This post received
KUDOS
x^2 will be odd only when x is odd. Thus, you are basically asked whether x is odd.

Now, the given statement says that the sum of x consecutive integers is an integer divisible by x.

To interpret this, you have to know a basic rule:

For all positive integers
The sum of n consecutive integers divided by n will be an integer if n is odd.
The sum of n consecutive integers divided by n will NOT be an integer if n is even.


To verify, let us check.
For n = 2, take any 2 consecutive integers and find their average. The result will NEVER be an integer. The same applies for n = 4 and all even numbers.
For n = 3, take any 3 consecutive integers and find their average. The result will ALWAYS be an integer. The same applies for n = 5 and all odd numbers.

Thus, the given statement tells us that x is odd. Thus x^2 is odd.

Hope that helps.
_________________

Consider KUDOS if you feel the effort's worth it

Intern
Intern
avatar
Joined: 18 Jan 2012
Posts: 9
Followers: 0

Kudos [?]: 0 [0], given: 0

Re: I dont understand this solution from MGMAT :( [#permalink] New post 22 Jan 2012, 23:34
ooooh! thanks senior manager!


c210
Senior Manager
Senior Manager
avatar
Joined: 12 Oct 2011
Posts: 276
Followers: 0

Kudos [?]: 20 [0], given: 110

Re: I dont understand this solution from MGMAT :( [#permalink] New post 22 Jan 2012, 23:45
c210 wrote:
ooooh! thanks senior manager!


c210

I hope you meant my name. That's Siddharth, not Senior Manager. :D

Anyway, glad it helped. Consider KUDOS if you think it's worth the effort.
Expert Post
1 KUDOS received
Math Expert
User avatar
Joined: 02 Sep 2009
Posts: 18678
Followers: 3229

Kudos [?]: 22153 [1] , given: 2599

Re: I dont understand this solution from MGMAT :( [#permalink] New post 23 Jan 2012, 01:58
1
This post received
KUDOS
Expert's post
c210 wrote:
Hey guys and gals,

question: Is X^2 odd?

statement 2: The sum of x consecutive integers is divisible by x

the solution states that the sum divided by x is an integer and moreover the sum of x consecutive integers divided by x is the average of that set of x integers. this therefore proves that x^2 is odd....how does that make sense?


anyone care to explain? :)


C210


Hi there,

When posting a question in PS/DS subforums make sure that the question is complete. So, please edit the question you've posted and add statement (1).

As for your query, below are some tips about consecutive integers (for more on this topic see Number Theory Chapter of Math Book: math-number-theory-88376.html).

Consecutive Integers
Consecutive integers are integers that follow one another, without skipping any integers. 7, 8, 9, and -2, -1, 0, 1, are consecutive integers.
• Sum of n consecutive integers equals the mean multiplied by the number of terms, n. Given consecutive integers \{-3, -2, -1, 0, 1,2\}, mean=\frac{-3+2}{2}=-\frac{1}{2}, (mean equals to the average of the first and last terms), so the sum equals to -\frac{1}{2}*6=-3.
• If n is odd, the sum of consecutive integers is always divisible by n. Given \{9,10,11\}, we have n=3 consecutive integers. The sum of 9+10+11=30, therefore, is divisible by 3.
• If n is even, the sum of consecutive integers is never divisible by n. Given \{9,10,11,12\}, we have n=4 consecutive integers. The sum of 9+10+11+12=42, therefore, is not divisible by 4.
• The product of n consecutive integers is always divisible by n!.
Given n=4 consecutive integers: \{3,4,5,6\}. The product of 3*4*5*6 is 360, which is divisible by 4!=24.

So, if statement (2) says that "the sum of x consecutive integers is divisible by x", according to the second point above x is odd, which makes x^2 an odd number.

As for your second question:

A set of consecutive integers is an evenly spaced set (AP).
• In any evenly spaced set the arithmetic mean (average) is equal to the median.
• The sum of the elements in any evenly spaced set equals to the mean multiplied by the number of terms: {sum}={mean}*{# of terms}

Thus, for original question: sum/x must equal to the mean (and median) and as median of odd consecutive integers is an integer itself, then sum/x=mean=median=integer.

Hope it's clear.
_________________

NEW TO MATH FORUM? PLEASE READ THIS: ALL YOU NEED FOR QUANT!!!

PLEASE READ AND FOLLOW: 11 Rules for Posting!!!

RESOURCES: [GMAT MATH BOOK]; 1. Triangles; 2. Polygons; 3. Coordinate Geometry; 4. Factorials; 5. Circles; 6. Number Theory; 7. Remainders; 8. Overlapping Sets; 9. PDF of Math Book; 10. Remainders; 11. GMAT Prep Software Analysis NEW!!!; 12. SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) NEW!!!; 12. Tricky questions from previous years. NEW!!!;

COLLECTION OF QUESTIONS:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS ; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


What are GMAT Club Tests?
25 extra-hard Quant Tests

Get the best GMAT Prep Resources with GMAT Club Premium Membership

Re: I dont understand this solution from MGMAT :(   [#permalink] 23 Jan 2012, 01:58
    Similar topics Author Replies Last post
Similar
Topics:
Resolve the discrepancy - From MGMAT - Plz help understand SavedByNazar 0 20 Apr 2014, 07:04
1 Princeton Review Drill - I don't understand Nchoward 6 30 Aug 2011, 04:06
Experts publish their posts in the topic A couple of prep test questions I dont understand PhilosophusRex 2 14 Jun 2009, 10:04
I understand this problem, but the solution is based on the dariusbanasik 1 13 Jul 2008, 13:15
I just don't understand GMATPrep Verbal jimmyjamesdonkey 6 31 May 2008, 19:32
Display posts from previous: Sort by

I dont understand this solution from MGMAT :(

  Question banks Downloads My Bookmarks Reviews Important topics  


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

Powered by phpBB © phpBB Group and phpBB SEO

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®.