NEW HERE? LEARN MORE
closeclose
It is currently 28 Sep 2023, 09:41
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 and y are positive intergers, what is the remainder

6 posts Go to First Unread Post
Print view
NEW TOPIC
POST REPLY
Downloads
My Bookmarks
Reviews
SORT BY:
Date
Kudos
User avatar
P
MHIKER
VP
VP
Joined: 14 Jul 2010
Status:No dream is too large, no dreamer is too small
Posts: 1016
If x and y are positive intergers, what is the remainder [#permalink] New post  19 Feb 2011, 11:13
1
Kudos
20
Bookmarks
Quiz Dashboard 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:

75% (01:00) correct 25% (01:00) wrong based on 764 sessions

Hide Show timer Statistics

If x and y are positive intergers, what is the remainder when 10^x+y is divided by y?

(1) x=5
(2) y=2
ShowHide Answer
Official Answer
Official Answer and Stats are available only to registered users. Register/Login.

_________________
Collections:-
PSof OG solved by GC members: https://gmatclub.com/forum/collection-ps-with-solution-from-gmatclub-110005.html
DS of OG solved by GC members: https://gmatclub.com/forum/collection-ds-with-solution-from-gmatclub-110004.html
100 GMAT PREP Quantitative collection https://gmatclub.com/forum/gmat-prep-problem-collections-114358.html
Collections of work/rate problems with solutions https://gmatclub.com/forum/collections-of-work-rate-problem-with-solutions-118919.html
Mixture problems in a file with best solutions: https://gmatclub.com/forum/mixture-problems-with-best-and-easy-solutions-all-together-124644.html
Signature Read More
Quiz Dashboard Attempt only this question Same topic and source Same topic and difficulty Same source and difficulty Random Chronological Reverse chronological Learn more
Most Helpful Reply
User avatar
L
Bunuel
Math Expert
Joined: 02 Sep 2009
Posts: 89499
CAT Tests Forum Quiz Mode
Re: Remainder [#permalink] New post  19 Feb 2011, 11:22
5
Bookmarks
Expert Reply
Baten80 wrote:
If x and y are positive intergers, what is the remainder when 10^x+y is divided by y?

(1) x=5
(2) y=2


\(\frac{10^x+y}{y}=\frac{10^x}{y}+1\) --> so we basically need the remainder upon division 10^x by y (as in 10^x+y the second term y is divisible by y itself then only the first term matters for remainder).

(1) x=5 --> need the value of y. Not sufficient.
(2) y=2 --> as x is a positive integer then 10^x is an even number and 10^x=even divided by 2 yields the remainder of zero. Sufficient.

Answer: B.
_________________
New to the GMAT CLUB Forum?

My Signature Questions' Collection:


What are GMAT Club Tests?
Extra-hard Quant Tests with Brilliant Analytics
Signature Read More
General Discussion
User avatar
TGC
Director
Director
Joined: 03 Aug 2012
Posts: 598
Concentration: General Management, General Management
Schools: ISB '16 NUS '17 NTU '17 XLRI SMU '17 IIM Lucknow IPMX'16 (A)
GMAT 1: 630 Q47 V29
GMAT 2: 680 Q50 V32
GPA: 3.7
WE:Information Technology (Investment Banking)
Re: If x and y are positive intergers, what is the remainder [#permalink] New post  15 Aug 2013, 21:21
REM[10^(x+y)]/y

(1) x=5

REM[10^(5+y)]/y no information about y so REM is not consistent hence INSUFFICIENT.

(2) y=2

REM[10^(x+2)]/2

Any power of 10 is even => Divisible by 2 => REM =0

Hence SUFFICIENT

Hence (B) !
User avatar
L
BrentGMATPrepNow
GMAT Club Legend
GMAT Club Legend
Joined: 12 Sep 2015
Posts: 6881
Location: Canada
If x and y are positive intergers, what is the remainder [#permalink] New post  Updated on: 17 May 2021, 08:36
1
Bookmarks
Expert Reply
Top Contributor
Baten80 wrote:
If x and y are positive integers, what is the remainder when \(10^x + y\) is divided by y?

(1) x = 5
(2) y = 2


Given: x and y are positive integers

Target question: What is the remainder when \(10^x + y\) is divided by y?

Statement 1: x = 5
Since we have no information about y, we cannot answer the target question with certainty
Statement 1 is NOT SUFFICIENT

Statement 2: y = 2
Important: When we divide an integer by 2, the remainder will be EITHER 1 OR 0, depending on whether the integer is odd or even.
If the number is ODD, then we get a remainder of 1 after dividing by 2
If the number is EVEN, then we get a remainder of 0 after dividing by 2

Now that we know the value of y, our target question becomes, "What is the remainder when \(10^x + 2\) is divided by 2?"
Since \(10^x\) is EVEN for all positive integer values of x, we know that \(10^x + 2\) must be EVEN

So, our target question becomes, "What is the remainder when SOME EVEN NUMBER is divided by 2?"
The answer to this new target question is the remainder will be 0
Since we can answer the target question with certainty, statement 2 is SUFFICIENT

Answer: B

Cheers,
Brent

RELATED VIDEO

Originally posted by BrentGMATPrepNow on 12 Mar 2020, 08:00.
Last edited by BrentGMATPrepNow on 17 May 2021, 08:36, edited 1 time in total.
avatar
B
Tonkotsu
Intern
Intern
Joined: 10 Oct 2020
Posts: 44
Location: United States (TN)
Concentration: Strategy, Finance
Schools: Fuqua '23 Johnson'23 Yale '23
GPA: 3.74
WE:Analyst (Consumer Products)
Re: If x and y are positive intergers, what is the remainder [#permalink] New post  14 Oct 2020, 19:38
If x and y are positive intergers, what is the remainder when 10^x+y is divided by y?

Prior to looking at the items, I would first separate the 10^x and 10 ^y and divide them by y as shown below.

(10^x)(10^y)/y

This will tell us that if y is divisible by either item we would know that y is a divisor with no remainder.

(1) x=5
Tells us nothing about the divisor y.

(2) y=2

10^2 is even and divisible by 2. sufficient!
User avatar
bumpbot
Non-Human User
Joined: 09 Sep 2013
Posts: 29508
Re: If x and y are positive intergers, what is the remainder [#permalink] New post  20 Sep 2022, 04:33
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
Signature Read More
GMAT Club Bot
gmatclubot
Re: If x and y are positive intergers, what is the remainder [#permalink]
20 Sep 2022, 04:33
NEW TOPIC
POST REPLY
Downloads
My Bookmarks
Reviews
Moderator:
Bunuel
Math Expert
89499 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