GMAT Question of the Day: Daily via email | Daily via Instagram New to GMAT Club? Watch this Video
close
It is currently 13 May 2021, 11:52
Register
GMAT Club Tests
Decision Tracker
My Rewards
New posts
New comers' posts

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.

Go to My Error Log Learn more
Close

Request Expert Reply

Confirm Cancel
If x is a positive integer and x + 2 is divisible by 10, what is the
7 posts Go to First Unread Post
Print view
NEW TOPIC
POST REPLY
Downloads
My Bookmarks
Reviews
SORT BY:
Date
Kudos
Tags:
Find Similar Topics 

Show Tags
Hide Tags

User avatar
V
Bunuel
Math Expert
Joined: 02 Sep 2009
Posts: 74915
CAT Tests Top Member of the Month
If x is a positive integer and x + 2 is divisible by 10, what is the [#permalink] New post  22 Aug 2018, 02:07
5
Bookmarks
Expert Reply
Attempt only this question Same topic and source Same topic and difficulty Same source and difficulty Random Chronological Reverse chronological Learn more
00:00
A
B
C
D
E

Difficulty:

15% (low)

Question Stats:

79% (01:12) correct 21% (01:38) wrong based on 145 sessions

Hide Show timer Statistics

If x is a positive integer and x + 2 is divisible by 10, what is the remainder when x^2 + 4x + 9 is divided by 10?

A. 1
B. 3
C. 5
D. 7
E. 9
ShowHide Answer
Official Answer
Official Answer and Stats are available only to registered users. Register/Login.

_________________
New to the GMAT CLUB Forum?
Posting Rules: QUANTITATIVE | VERBAL. Guides and Resources: QUANTITATIVE | VERBAL | Ultimate GMAT Quantitative Megathread | All You Need for Quant

Questions' Banks and Collection:
PS: Standard deviation | Tough Problem Solving Questions With Solutions | Probability and Combinations Questions With Solutions | Tough and tricky exponents and roots questions | 12 Easy Pieces (or not?) | Bakers' Dozen | Algebra set | Mixed Questions | Fresh Meat
DS: DS Standard deviation | Inequalities | 700+ GMAT Data Sufficiency Questions With Explanations | Tough and tricky exponents and roots questions | The Discreet Charm of the DS | Devil's Dozen!!! | Number Properties set | New DS set
MIXED: GMAT Club's Complete Questions' Bank | SEVEN SAMURAI OF 2012 | Tricky questions from previous years. | Special Questions' Directory | Best Of The Best Of 2017 | The Best Of Quant of 2016 | 20 hardest and 20 best questions of 2015 | 15 best topics of 2015 | Seven Samurai of 2012 | GMAT Probability Questions

What are GMAT Club Tests?
Extra-hard Quant Tests with Brilliant Analytics
Signature Read More
Attempt only this question Same topic and source Same topic and difficulty Same source and difficulty Random Chronological Reverse chronological Learn more
avatar
V
Chethan92
IIM School Moderator
Joined: 18 Jul 2018
Posts: 1164
Location: India
Concentration: Operations, General Management
Schools: IIMB EPGP'22 (M)
GMAT 1: 590 Q46 V25
GMAT 2: 690 Q49 V34
WE:Engineering (Energy and Utilities)
Reviews Badge
Re: If x is a positive integer and x + 2 is divisible by 10, what is the [#permalink] New post  22 Aug 2018, 02:14
1
Kudos
Since X is a positive integer and x+2 is divisible by 10 then x can taje values 8,18,28,38....

For all these values of x, the remainder when x^2+4x+9 is divisible by 10 is 5.
For example, let's take x as 8
Then x^2+4x+9 = 64+32+9 = 105.
When 105 is divided by 10. Reaminder is 5

C is the answer.

Posted from my mobile device
User avatar
D
PKN
Director
Director
Joined: 01 Oct 2017
Status:Learning stage
Posts: 938
WE:Supply Chain Management (Energy and Utilities)
If x is a positive integer and x + 2 is divisible by 10, what is the [#permalink] New post  22 Aug 2018, 02:15
3
Kudos
1
Bookmarks
Bunuel wrote:
If x is a positive integer and x + 2 is divisible by 10, what is the remainder when x^2 + 4x + 9 is divided by 10?

A. 1
B. 3
C. 5
D. 7
E. 9


\(x^2 + 4x + 9\) can be written as
\(x^2 + 4x + 4+5=(x+2)^2+5\)
Since x+2 is divisible by 10, hence
Rem(\(\frac{(x+2)^2+5}{10}\))=Rem(\(\frac{(x+2)^2}{10}\))+Rem(\(\frac{5}{10}\))=0+5=5

Ans. (C)
_________________
Regards,

PKN

Rise above the storm, you will find the sunshine
Signature Read More
User avatar
D
KSBGC
VP
VP
Joined: 31 Oct 2013
Posts: 1489
Concentration: Accounting, Finance
GPA: 3.68
WE:Analyst (Accounting)
If x is a positive integer and x + 2 is divisible by 10, what is the [#permalink] New post  22 Aug 2018, 04:03
Bunuel wrote:
If x is a positive integer and x + 2 is divisible by 10, what is the remainder when x^2 + 4x + 9 is divided by 10?

A. 1
B. 3
C. 5
D. 7
E. 9



x + 2 is divisible by 10. So, x + 2 is a multiple of 10.

thus x could be 8, 18, 28, 38, 48 and so on.


plug one of the value for x.

\(8^2 = 64\)
4*8 = 32

and 9.

64 + 32 + 9 = 105

105 / 10 = 10*10 + 5 .

So remainder is 5.

Thus the best answer is C.
User avatar
D
Abhishek009
Board of Directors
Joined: 11 Jun 2011
Status:QA & VA Forum Moderator
Posts: 5535
Location: India
GPA: 3.5
WE:Business Development (Commercial Banking)
GMAT ToolKit User
If x is a positive integer and x + 2 is divisible by 10, what is the [#permalink] New post  09 Sep 2019, 07:14
Bunuel wrote:
If x is a positive integer and x + 2 is divisible by 10, what is the remainder when x^2 + 4x + 9 is divided by 10?

A. 1
B. 3
C. 5
D. 7
E. 9

Least value of x to be divisible by 10 is x = 8

Now, \(\frac{x^2 + 4x + 9}{10} = \frac{8^2 + 4*8 +9}{10}=\frac{105}{10}\)

Thus, Remainder will be 5, Answer must be (C)
_________________
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 )
Signature Read More
User avatar
V
BrentGMATPrepNow
GMAT Club Legend
GMAT Club Legend
Joined: 11 Sep 2015
Posts: 5438
Location: Canada
Top Member of the Month
Re: If x is a positive integer and x + 2 is divisible by 10, what is the [#permalink] New post  04 Feb 2020, 09:32
1
Kudos
Expert Reply
Top Contributor
Bunuel wrote:
If x is a positive integer and x + 2 is divisible by 10, what is the remainder when x² + 4x + 9 is divided by 10?

A. 1
B. 3
C. 5
D. 7
E. 9


Given: x + 2 is divisible by 10
In other words x + 2 is a multiple of 10, which means we can write: x + 2 = 10k for some integer k

We want to know what the remainder will be when we divide x² + 4x + 9 by 10.

x² + 4x + 9 = x² + 4x + 4 + 5
= (x +2)(x +2) + 5
= (10k)(10k) + 5
= 100k² + 5
So now we want to know what the remainder will be when we divide 100k² + 5 by 10.

We can already see that 100k² [aka (10)(10k²)] is a MULTIPLE of 10
So, 100k² + 5 is 5 greater than a multiple of 10
So, the remainder will be 5 when we divide 100k² + 5 by 10

Answer: C

Cheers,
Brent
_________________
Image

A focused approach to GMAT mastery
Signature Read More
User avatar
V
ScottTargetTestPrep
Target Test Prep Representative
Joined: 14 Oct 2015
Status:Founder & CEO
Affiliations: Target Test Prep
Posts: 14035
Location: United States (CA)
Re: If x is a positive integer and x + 2 is divisible by 10, what is the [#permalink] New post  08 Feb 2020, 19:18
1
Kudos
Expert Reply
Bunuel wrote:
If x is a positive integer and x + 2 is divisible by 10, what is the remainder when x^2 + 4x + 9 is divided by 10?

A. 1
B. 3
C. 5
D. 7
E. 9



Since x + 2 is divisible by 10, then x + 2 could equal 10, and hence, x could equal 8. (Note, that x + 2 could also equal 20, or 30, or any positive multiple of 10).

We’ll choose x = 8, and we have:

8^2 + 4(8) + 9 = 64 + 32 + 9 = 105

Since 105/10 = 10 R 5, the remainder is 5.

Alternate Solution:

Let’s write x^2 + 4x + 9 = x^2 + 4x + 4 + 5 = (x + 2)^2 + 5.

Since x + 2 is divisible by 10, (x + 2)^2 is also divisible by 10. Hence, the remainder when x^2 + 4x + 9 = (x + 2)^2 + 5 is divided by 10 is 5.

Answer: C
_________________

★ ★ ★ ★ ★   350 REVIEWS

5-STAR RATED ONLINE GMAT QUANT SELF STUDY COURSE

NOW WITH GMAT VERBAL (Pre-Launch)

See why Target Test Prep is the top rated GMAT quant course on GMAT Club. Read Our Reviews

Signature Read More
GMAT Club Bot
gmatclubot
Re: If x is a positive integer and x + 2 is divisible by 10, what is the [#permalink]
08 Feb 2020, 19:18
NEW TOPIC
POST REPLY
Downloads
My Bookmarks
Reviews
Moderators:
chetan2u
Math Expert
9829 posts
Bunuel
Math Expert
74915 posts
yashikaaggarwal
Senior Moderator - Masters Forum
2468 posts
generis
Senior SC Moderator
4732 posts

cron

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

Main navigation

GMAT Resources

Partners

MBA Resources

www.gmac.com|www.mba.com | | GMAT Club Rules | Terms and Conditions