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

It is currently 18 Sep 2014, 00:18

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

If x and y are positive integer, what is the remainder when

  Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:
Intern
Intern
avatar
Joined: 19 Oct 2009
Posts: 44
Followers: 0

Kudos [?]: 12 [0], given: 4

If x and y are positive integer, what is the remainder when [#permalink] New post 02 Nov 2009, 06:15
00:00
A
B
C
D
E

Difficulty:

(N/A)

Question Stats:

100% (00:00) correct 0% (00:00) wrong based on 4 sessions
If x and y are positive integer, what is the remainder when x is divided by y ?

(1) When x is divided by 2x, the remainder is 4.
(2) When x + y is divided by y, the remainder is 4.

OA: B
Expert Post
1 KUDOS received
Math Expert
User avatar
Joined: 02 Sep 2009
Posts: 29673
Followers: 3495

Kudos [?]: 26309 [1] , given: 2709

Re: Tough DS: please help [#permalink] New post 02 Nov 2009, 11:13
1
This post received
KUDOS
Expert's post
Hussain15 wrote:
Bunuel wrote:
gmat620 wrote:
If x and y are positive integer, what is the remainder when x is divided by y ?

(1) When x is divided by 2x, the remainder is 4.
(2) When x + y is divided by y, the remainder is 4.

OA: B


x=yn+r. Question is r=?

(1) This statement is clearly insufficient, no info about y.
Maybe there is a typo? If it were: "When x is divided by 2y, the remainder is 4." It would make more sense, though still would be insufficient.

But still let's consider this case too:
x=2yk+4. x=20 y=8 --> x/2y=20/16 remainder 4 and x/y=20/8 remainder also 4, BUT x=10 y=3 --> x/2y=10/6 remainder 4 and x/y=10/3 remainder 1. Two different remainders: not sufficient.

(2) x+y=yp+4 --> x=y(p-1)+4 --> this statement directly gives a remainder of 4 upon dividing x by y. Sufficient.

Answer: B.


Hi Bunuel!,

Look at the red coloured equation above.

x= 2yk + 4
=> x= y(2k) + 4
=> x divided by y has a remainder of 4. Is my understanding correct?

2nd query: For first equation (the red one mentioned above) x= 2yk + 4, you solved it by plugging in the numbers while for second correct equation x= y(p-1) + 4 you didn't solve it by plugging the numbers. Why did you not plug the numbers in equation 2? I mean how did you find out without counter checking that equation 2 will be true for all positive integers???

Thanks in Advance!!!


That's a good question.
A. x=y(2k)+4, k any integer >=0.
B. x=y(p-1)+4, p any integer >=0.

Why A is not sufficient to determine the remainder and B is? Why did I use number plugging to show this in the first case and didn't in the second?

If we are told that x divided by y gives a remainder of 4, means x=yp+4 where p is integer >=0. We don't know x and y so p (coefficient) can be any integer.

Look at equation A, the coefficient is 2k, 2k is even. It can be rephrased as x divided by y will give the remainder of 4 IF coefficient is even. But what about the cases when coefficient is odd? We don't know that so we must check to determine this.

As for B. Coefficient here is (p-1), which for integer values of p can give us ANY value: any even as well as any odd. So basically x=y(p-1)+4 is the same as x=yp+4. No need for double checking.

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

1 KUDOS received
Retired Moderator
User avatar
Status: The last round
Joined: 18 Jun 2009
Posts: 1318
Concentration: Strategy, General Management
GMAT 1: 680 Q48 V34
Followers: 56

Kudos [?]: 484 [1] , given: 157

GMAT ToolKit User GMAT Tests User
Re: Tough DS: please help [#permalink] New post 02 Nov 2009, 12:16
1
This post received
KUDOS
Expert Post
Math Expert
User avatar
Joined: 02 Sep 2009
Posts: 29673
Followers: 3495

Kudos [?]: 26309 [0], given: 2709

Re: Tough DS: please help [#permalink] New post 02 Nov 2009, 08:00
Expert's post
gmat620 wrote:
If x and y are positive integer, what is the remainder when x is divided by y ?

(1) When x is divided by 2x, the remainder is 4.
(2) When x + y is divided by y, the remainder is 4.

OA: B


x=yn+r. Question is r=?

(1) This statement is clearly insufficient, no info about y.
Maybe there is a typo? If it were: "When x is divided by 2y, the remainder is 4." It would make more sense, though still would be insufficient.

But still let's consider this case too:
x=2yk+4. x=20 y=8 --> x/2y=20/16 remainder 4 and x/y=20/8 remainder also 4, BUT x=10 y=3 --> x/2y=10/6 remainder 4 and x/y=10/3 remainder 1. Two different remainders: not sufficient.

(2) x+y=yp+4 --> x=y(p-1)+4 --> this statement directly gives a remainder of 4 upon dividing x by y. Sufficient.

Answer: B.
_________________

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

Retired Moderator
User avatar
Status: The last round
Joined: 18 Jun 2009
Posts: 1318
Concentration: Strategy, General Management
GMAT 1: 680 Q48 V34
Followers: 56

Kudos [?]: 484 [0], given: 157

GMAT ToolKit User GMAT Tests User
Re: Tough DS: please help [#permalink] New post 02 Nov 2009, 10:32
Bunuel wrote:
gmat620 wrote:
If x and y are positive integer, what is the remainder when x is divided by y ?

(1) When x is divided by 2x, the remainder is 4.
(2) When x + y is divided by y, the remainder is 4.

OA: B


x=yn+r. Question is r=?

(1) This statement is clearly insufficient, no info about y.
Maybe there is a typo? If it were: "When x is divided by 2y, the remainder is 4." It would make more sense, though still would be insufficient.

But still let's consider this case too:
x=2yk+4. x=20 y=8 --> x/2y=20/16 remainder 4 and x/y=20/8 remainder also 4, BUT x=10 y=3 --> x/2y=10/6 remainder 4 and x/y=10/3 remainder 1. Two different remainders: not sufficient.

(2) x+y=yp+4 --> x=y(p-1)+4 --> this statement directly gives a remainder of 4 upon dividing x by y. Sufficient.

Answer: B.


Hi Bunuel!,

Look at the red coloured equation above.

x= 2yk + 4
=> x= y(2k) + 4
=> x divided by y has a remainder of 4. Is my understanding correct?

2nd query: For first equation (the red one mentioned above) x= 2yk + 4, you solved it by plugging in the numbers while for second correct equation x= y(p-1) + 4 you didn't solve it by plugging the numbers. Why did you not plug the numbers in equation 2? I mean how did you find out without counter checking that equation 2 will be true for all positive integers???

Thanks in Advance!!!
_________________

[ From 470 to 680-My Story ] [ My Last Month Before Test ]
[ GMAT Prep Analysis Tool ] [ US. Business School Dashboard ] [ Int. Business School Dashboard ]

I Can, I Will

Get the best GMAT Prep Resources with GMAT Club Premium Membership

Re: Tough DS: please help   [#permalink] 02 Nov 2009, 10:32
    Similar topics Author Replies Last post
Similar
Topics:
4 Experts publish their posts in the topic If x and y are positive integers, what is the remainder when dzodzo85 6 19 Mar 2012, 23:40
If x and y are positive integers, what is the remainder when jjhko 1 19 Jul 2008, 14:41
4 Experts publish their posts in the topic If x and y are positive integers, what is the remainder when xALIx 6 01 Jul 2008, 14:57
4 Experts publish their posts in the topic If x and y are positive integers, what is the remainder when raviatreya 9 22 Apr 2005, 09:46
If x and y are positive integers, what is the remainder when pb_india 7 10 Jan 2005, 11:26
Display posts from previous: Sort by

If x and y are positive integer, what is the remainder when

  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®.