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

 It is currently 24 Oct 2016, 03:05

### 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

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

# Events & Promotions

###### Events & Promotions in June
Open Detailed Calendar

# If x and yare positive integers , what is the remainder when

Author Message
TAGS:

### Hide Tags

Math Expert
Joined: 02 Sep 2009
Posts: 35270
Followers: 6635

Kudos [?]: 85499 [2] , given: 10236

If x and yare positive integers , what is the remainder when [#permalink]

### Show Tags

03 Jan 2014, 06:12
2
KUDOS
Expert's post
11
This post was
BOOKMARKED
00:00

Difficulty:

(N/A)

Question Stats:

67% (01:48) correct 33% (00:51) wrong based on 549 sessions

### HideShow timer Statistics

The Official Guide For GMAT® Quantitative Review, 2ND Edition

If x and y are positive integers, what is the remainder when 10^x + y is divided by 3 ?

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

Data Sufficiency
Question: 16
Category: Arithmetic Properties of numbers
Page: 154
Difficulty: 600

GMAT Club is introducing a new project: The Official Guide For GMAT® Quantitative Review, 2ND Edition - Quantitative Questions Project

Each week we'll be posting several questions from The Official Guide For GMAT® Quantitative Review, 2ND Edition and then after couple of days we'll provide Official Answer (OA) to them along with a slution.

We'll be glad if you participate in development of this project:
2. Please vote for the best solutions by pressing Kudos button;
3. Please vote for the questions themselves by pressing Kudos button;
4. Please share your views on difficulty level of the questions, so that we have most precise evaluation.

Thank you!
[Reveal] Spoiler: OA

_________________
Math Expert
Joined: 02 Sep 2009
Posts: 35270
Followers: 6635

Kudos [?]: 85499 [1] , given: 10236

Re: If x and yare positive integers , what is the remainder when [#permalink]

### Show Tags

03 Jan 2014, 06:12
1
KUDOS
Expert's post
3
This post was
BOOKMARKED
SOLUTION

If x and y are positive integers, what is the remainder when 10^x +y is divided by 3?

Since, the sum of the digits of 10^x is always 1 then the remainders when 10^x+y is divided by 3 is only dependant on the value of the number added to 10^x, so on y. If y is a multiple of 3 then 10^x+y will yield the remainder of 1 (since the sum of the digits of 10^x+y will be one more than a multiple of 3), if y is one more than a multiple of 3 then 10^x+y will yield the remainder of 2 and finally if y is two more than a multiple of 3 then 10^x+y will yield the remainder of 0,

(1) x = 5. Not sufficient.
(2) y = 2. Sufficient.

_________________
Manager
Joined: 27 May 2012
Posts: 216
Followers: 2

Kudos [?]: 65 [1] , given: 431

If x and yare positive integers , what is the remainder when [#permalink]

### Show Tags

04 Jan 2014, 02:05
1
KUDOS
Bunuel wrote:
The Official Guide For GMAT® Quantitative Review, 2ND Edition

If x and y are positive integers, what is the remainder when 10^x + y is divided by 3 ?

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

We can see that 10^x + y will always be of the form 10+y , or 100 +y or 1000+y etc depending on the power of x
so 1 is always going to be carried forward from the 10^x side to y

e.g.

if x= 1 and y = 1 then 10^x+y will give 10+1 =11, divided by 3 remainder 2
if x= 2 and y = 1 then we have 100+1 =101,divided by 3 remainder 2
if x=2 and y =2 then we have 100+2 =102,divided by 3 remainder 0
etc

hence the remainder really depends on the value of y

1) if y = 1 remainder is 2, if y is 2 remainder is 0, since no info about y hence insuff.

2)Y =2 , just what we were looking for , no matter what ever is the value of x remainder will always be 0.
as 10^x+y will always be of the form:

12
102
1002
10002
etc remainder in all cases is 0 hence B is suff
_________________

- Stne

Last edited by stne on 10 May 2015, 17:43, edited 1 time in total.
Current Student
Joined: 03 Feb 2013
Posts: 932
Location: India
Concentration: Operations, Strategy
GMAT 1: 760 Q49 V44
GPA: 3.88
WE: Engineering (Computer Software)
Followers: 126

Kudos [?]: 768 [0], given: 546

Re: If x and yare positive integers , what is the remainder when [#permalink]

### Show Tags

05 Jan 2014, 11:46
Bunuel wrote:
The Official Guide For GMAT® Quantitative Review, 2ND Edition

If x and y are positive integers, what is the remainder when 10^x + y is divided by 3 ?

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

Before diving into the statements, lets try to simplify the expression. (10^x + y) rem by 3 = (1^x + y) rem by 3 = y rem by 3. The rule of simplification is applicable only in case of remainders.

So clearly Statement is Sufficient. hence Option B)
_________________

Thanks,
Kinjal
Struggling with GMAT ? Experience http://www.gmatify.com/

My Application Experience : http://gmatclub.com/forum/hardwork-never-gets-unrewarded-for-ever-189267-40.html#p1516961

Math Expert
Joined: 02 Sep 2009
Posts: 35270
Followers: 6635

Kudos [?]: 85499 [0], given: 10236

Re: If x and yare positive integers , what is the remainder when [#permalink]

### Show Tags

05 Jan 2014, 11:59
SOLUTION

If x and y are positive integers, what is the remainder when 10^x +y is divided by 3?

Since, the sum of the digits of 10^x is always 1 then the remainders when 10^x+y is divided by 3 is only dependant on the value of the number added to 10^x, so on y. If y is a multiple of 3 then 10^x+y will yield the remainder of 1 (since the sum of the digits of 10^x+y will be one more than a multiple of 3), if y is one more than a multiple of 3 then 10^x+y will yield the remainder of 2 and finally if y is two more than a multiple of 3 then 10^x+y will yield the remainder of 0,

(1) x = 5. Not sufficient.
(2) y = 2. Sufficient.

_________________
GMAT Club Legend
Joined: 09 Sep 2013
Posts: 12199
Followers: 541

Kudos [?]: 151 [0], given: 0

Re: If x and yare positive integers , what is the remainder when [#permalink]

### Show Tags

27 Jan 2015, 23:31
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.
_________________
Senior Manager
Status: Math is psycho-logical
Joined: 07 Apr 2014
Posts: 443
Location: Netherlands
GMAT Date: 02-11-2015
WE: Psychology and Counseling (Other)
Followers: 2

Kudos [?]: 98 [0], given: 169

Re: If x and yare positive integers , what is the remainder when [#permalink]

### Show Tags

07 Feb 2015, 07:09
Great, but it should be (10^x) + y. Otherwise it is as if x+y is the power of 10.
Math Expert
Joined: 02 Sep 2009
Posts: 35270
Followers: 6635

Kudos [?]: 85499 [1] , given: 10236

Re: If x and yare positive integers , what is the remainder when [#permalink]

### Show Tags

07 Feb 2015, 07:15
1
KUDOS
Expert's post
pacifist85 wrote:
Great, but it should be (10^x) + y. Otherwise it is as if x+y is the power of 10.

It should be as it is. If it were $$10^{x+y}$$, then it would be written as 10^(x+y).
_________________
Senior Manager
Joined: 02 Dec 2014
Posts: 382
Location: Russian Federation
Concentration: General Management, Economics
WE: Sales (Telecommunications)
Followers: 0

Kudos [?]: 72 [0], given: 348

Re: If x and yare positive integers , what is the remainder when [#permalink]

### Show Tags

10 May 2015, 14:51
stne wrote:
Bunuel wrote:
The Official Guide For GMAT® Quantitative Review, 2ND Edition

If x and y are positive integers, what is the remainder when 10^x + y is divided by 3 ?

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

We can see that 10^x + y will always be of the form 10+y , or 100 +y or 1000+y etc depending on the power of x
so 1 is always going to be carried forward from the 10^x side to y

e.g.

if x= 1 and y = 1 then 10^x+y will give 10+1 =11, divided by 3 remainder 2
if x= 2 and y = 1 then we have 100+1 =101,divided by 3 remainder 2
if x=2 and y =2 then we have 100+2 =102,divided by 3 remainder 0
etc

hence the remainder really depends on the value of y

1) if y = 1 remainder is 2, if y is 2 remainder is 0, since no info about y hence insuff.

2)X=2 , just what we were looking for , no matter what ever is the value of x remainder will always be 0.
as 10^x+y will always be of the form:

12
102
1002
10002
etc remainder in all cases is 0 hence B is suff

Not X=2, Y=2. Please correct a typo=))
_________________

"Are you gangsters?" - "No we are Russians!"

GMAT Club Legend
Joined: 09 Sep 2013
Posts: 12199
Followers: 541

Kudos [?]: 151 [0], given: 0

Re: If x and yare positive integers , what is the remainder when [#permalink]

### Show Tags

20 Jun 2016, 09:59
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.
_________________
Re: If x and yare positive integers , what is the remainder when   [#permalink] 20 Jun 2016, 09:59
Similar topics Replies Last post
Similar
Topics:
18 What is the remainder when the positive integer x is divided 8 21 Jan 2012, 18:24
41 If x and y are positive integers, what is the remainder when 22 04 Aug 2010, 15:17
12 If x and y are positive integer, what is the remainder when 6 02 Nov 2009, 07:15
13 What is the remainder when the positive integer x is divided 9 07 Oct 2008, 06:25
14 What is the remainder when the positive integer x is divided 12 15 Apr 2007, 05:57
Display posts from previous: Sort by