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

It is currently 19 Aug 2018, 23:57

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

Problem Solving Pack 4, Question 2) For every positive integer n...

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

Hide Tags

EMPOWERgmat Instructor
User avatar
V
Status: GMAT Assassin/Co-Founder
Affiliations: EMPOWERgmat
Joined: 19 Dec 2014
Posts: 12205
Location: United States (CA)
GMAT 1: 800 Q51 V49
GRE 1: Q170 V170
Problem Solving Pack 4, Question 2) For every positive integer n...  [#permalink]

Show Tags

New post 19 Nov 2015, 17:37
2
00:00
A
B
C
D
E

Difficulty:

  45% (medium)

Question Stats:

65% (01:24) correct 35% (01:43) wrong based on 150 sessions

HideShow timer Statistics

QUANT 4-PACK SERIES Problem Solving Pack 4 Question 2 For every positive integer n...

For every positive integer n that is greater than 1, the function g(n) is defined to be the sum of all of the odd integers from 1 to n, inclusive. The g(n) could have any of the following units digits except…?

A) 1
B) 2
C) 4
D) 6
E) 9


48 Hour Window Answer & Explanation Window
Earn KUDOS! Post your answer and explanation.
OA, and explanation will be posted after the 48 hour window closes.

This question is part of the Quant 4-Pack series

Scroll Down For Official Explanation

_________________

760+: Learn What GMAT Assassins Do to Score at the Highest Levels
Contact Rich at: Rich.C@empowergmat.com

Rich Cohen

Co-Founder & GMAT Assassin

Special Offer: Save $75 + GMAT Club Tests Free
  Official GMAT Exam Packs + 70 Pt. Improvement Guarantee
www.empowergmat.com/

***********************Select EMPOWERgmat Courses now include ALL 6 Official GMAC CATs!***********************

EMPOWERgmat Discount Codese-GMAT Discount CodesVeritas Prep GMAT Discount Codes
Senior Manager
Senior Manager
User avatar
B
Joined: 28 Feb 2014
Posts: 295
Location: United States
Concentration: Strategy, General Management
Reviews Badge
Re: Problem Solving Pack 4, Question 2) For every positive integer n...  [#permalink]

Show Tags

New post 19 Nov 2015, 19:08
1
For every positive integer n that is greater than 1, the function g(n) is defined to be the sum of all of the odd integers from 1 to n, inclusive. The g(n) could have any of the following units digits except…?

Used brute force on this one to calculate. Not sure if there is a quicker way.

1+3=4 C is out
1+3+....15= 81 A is out
1+3+5+7=16 D is out
1+3+5=9 E i out

Answer: B
CEO
CEO
User avatar
D
Joined: 12 Sep 2015
Posts: 2707
Location: Canada
Re: Problem Solving Pack 4, Question 2) For every positive integer n...  [#permalink]

Show Tags

New post 19 Nov 2015, 21:36
EMPOWERgmatRichC wrote:
For every positive integer n that is greater than 1, the function g(n) is defined to be the sum of all of the odd integers from 1 to n, inclusive. The g(n) could have any of the following units digits except…?

A) 1
B) 2
C) 4
D) 6
E) 9


Notice the pattern:
g(2) = 1
g(3) = 1 + 3 = 4
g(4) = 1 + 3 = 4
g(5) = 1 + 3 + 5 = 9
g(6) = 1 + 3 + 5 = 9
g(7) = 1 + 3 + 5 + 7 = 16

At this point, we've already eliminated A, C, D and E. So the answer is B.

Alternatively, we might notice that g(n) is always the square of an integer.
Since there is no integer that, when squared, has a units digit of 2, the answer must be B

Cheers,
Brent
_________________

Brent Hanneson – Founder of gmatprepnow.com

Image

Intern
Intern
avatar
Joined: 21 May 2015
Posts: 11
Concentration: Marketing, Nonprofit
GMAT 1: 720 Q48 V41
WE: Analyst (Non-Profit and Government)
Re: Problem Solving Pack 4, Question 2) For every positive integer n...  [#permalink]

Show Tags

New post 19 Nov 2015, 21:44
2
1
Sum of all odd numbers from 1 to n = n^2

Out of all those answers, only 2 is not the digit of any perfect square. So the answer is B.
EMPOWERgmat Instructor
User avatar
V
Status: GMAT Assassin/Co-Founder
Affiliations: EMPOWERgmat
Joined: 19 Dec 2014
Posts: 12205
Location: United States (CA)
GMAT 1: 800 Q51 V49
GRE 1: Q170 V170
Re: Problem Solving Pack 4, Question 2) For every positive integer n...  [#permalink]

Show Tags

New post 24 Nov 2015, 00:54
1
EMPOWERgmatRichC wrote:
QUANT 4-PACK SERIES Problem Solving Pack 4 Question 2 For every positive integer n...

For every positive integer n that is greater than 1, the function g(n) is defined to be the sum of all of the odd integers from 1 to n, inclusive. The g(n) could have any of the following units digits except…?

A) 1
B) 2
C) 4
D) 6
E) 9


Hi All,

GMAT Quant questions are built around patterns - whether you immediately spot (or know) the pattern or not. As such, even if you don't know the exact patterns involved, you can often PROVE what the pattern is by TESTing VALUES and doing some basic arithmetic.

Here, we're told that n is a positive integer greater than 1 and that the function g(n) is defined to be the sum of all of the ODD integers from 1 to n, inclusive. We're asked to find the digit that CAN'T be the unit's digit of any potential calculation that could be done using this function.

Rather than stare at the screen or do math in our heads, let's TEST VALUES and seek out the pattern.

Since n is GREATER than 1, let's start with 2...

g(2) = 1
So the unit's digit COULD be 1.
Eliminate Answer A.

g(3) = 1 + 3 = 4
So the unit's digit COULD be 4.
Eliminate Answer C.

g(5) = 1 + 3 + 5 = 9
So the unit's digit COULD be 9.
Eliminate Answer E.

g(7) = 1 + 3 + 5 + 7 = 16
So the unit's digit COULD be 6.
Eliminate Answer D.

With 4 answers eliminated, there's just one answer left...

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

Rich Cohen

Co-Founder & GMAT Assassin

Special Offer: Save $75 + GMAT Club Tests Free
  Official GMAT Exam Packs + 70 Pt. Improvement Guarantee
www.empowergmat.com/

***********************Select EMPOWERgmat Courses now include ALL 6 Official GMAC CATs!***********************

Senior Manager
Senior Manager
User avatar
G
Joined: 03 Apr 2013
Posts: 290
Location: India
Concentration: Marketing, Finance
Schools: Simon '20
GMAT 1: 740 Q50 V41
GPA: 3
GMAT ToolKit User
Re: Problem Solving Pack 4, Question 2) For every positive integer n...  [#permalink]

Show Tags

New post 01 Jul 2016, 23:50
EMPOWERgmatRichC wrote:
QUANT 4-PACK SERIES Problem Solving Pack 4 Question 2 For every positive integer n...

For every positive integer n that is greater than 1, the function g(n) is defined to be the sum of all of the odd integers from 1 to n, inclusive. The g(n) could have any of the following units digits except…?

A) 1
B) 2
C) 4
D) 6
E) 9


48 Hour Window Answer & Explanation Window
Earn KUDOS! Post your answer and explanation.
OA, and explanation will be posted after the 48 hour window closes.

This question is part of the Quant 4-Pack series

Scroll Down For Official Explanation


Sum of the first n positive integers upto n is given by

\(n^2\)

now these can be either even number of odd numbers or odd number of odd numbers.

Thus the question is "Which of the following cannot be the units digit of a perfect square".

Answer (B). :)
_________________

Spread some love..Like = +1 Kudos :)

Board of Directors
User avatar
P
Joined: 17 Jul 2014
Posts: 2717
Location: United States (IL)
Concentration: Finance, Economics
GMAT 1: 650 Q49 V30
GPA: 3.92
WE: General Management (Transportation)
GMAT ToolKit User Premium Member Reviews Badge
Re: Problem Solving Pack 4, Question 2) For every positive integer n...  [#permalink]

Show Tags

New post 21 Oct 2016, 07:18
EMPOWERgmatRichC wrote:
QUANT 4-PACK SERIES Problem Solving Pack 4 Question 2 For every positive integer n...

For every positive integer n that is greater than 1, the function g(n) is defined to be the sum of all of the odd integers from 1 to n, inclusive. The g(n) could have any of the following units digits except…?

A) 1
B) 2
C) 4
D) 6
E) 9


1+3 = 4 -> C is out
4+5 = 9 -> E is out
9+7 = 16 -> D is out
16+9 = 25.
25+11 = 36
36+13 = 49
49+15 = 64
64+17 = 81 - A is out

only left - B!
Board of Directors
User avatar
P
Status: QA & VA Forum Moderator
Joined: 11 Jun 2011
Posts: 3789
Location: India
GPA: 3.5
WE: Business Development (Commercial Banking)
GMAT ToolKit User Premium Member
Re: Problem Solving Pack 4, Question 2) For every positive integer n...  [#permalink]

Show Tags

New post 21 Oct 2016, 09:36
EMPOWERgmatRichC wrote:
For every positive integer n that is greater than 1, the function g(n) is defined to be the sum of all of the odd integers from 1 to n, inclusive. The g(n) could have any of the following units digits except…?

A) 1
B) 2
C) 4
D) 6
E) 9


\(
No need of even a single calculation
\)

Function \(g(n) =\) \(n^2\) { Sum of odd integers }

Since \(n^2\) is a square number it must end in 1 , 2 , 4 , 6 , 9 and 0


Since Units digit of \(n^2\) can not be 2, our answer will be (B)
_________________

Thanks and Regards

Abhishek....

PLEASE FOLLOW THE RULES FOR POSTING IN QA AND VA FORUM AND USE SEARCH FUNCTION BEFORE POSTING NEW QUESTIONS

How to use Search Function in GMAT Club | Rules for Posting in QA forum | Writing Mathematical Formulas |Rules for Posting in VA forum | Request Expert's Reply ( VA Forum Only )

Non-Human User
User avatar
Joined: 09 Sep 2013
Posts: 7773
Premium Member
Re: Problem Solving Pack 4, Question 2) For every positive integer n...  [#permalink]

Show Tags

New post 29 Jul 2018, 21:58
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________

GMAT Books | GMAT Club Tests | Best Prices on GMAT Courses | GMAT Mobile App | Math Resources | Verbal Resources

Re: Problem Solving Pack 4, Question 2) For every positive integer n... &nbs [#permalink] 29 Jul 2018, 21:58
Display posts from previous: Sort by

Problem Solving Pack 4, Question 2) For every positive integer n...

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

Events & Promotions

PREV
NEXT


cron

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®.