It is currently 20 Sep 2017, 04:24

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

Events & Promotions

Events & Promotions in June
Open Detailed Calendar

What is the remainder when the positive integer x is divided by 31?

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

Hide Tags

Expert Post
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 41631

Kudos [?]: 124106 [0], given: 12071

What is the remainder when the positive integer x is divided by 31? [#permalink]

Show Tags

New post 14 Aug 2017, 03:51
00:00
A
B
C
D
E

Difficulty:

  45% (medium)

Question Stats:

70% (01:23) correct 30% (01:44) wrong based on 66 sessions

HideShow timer Statistics

What is the remainder when the positive integer x is divided by 31?

(1) When x + 10 is divided by 31 the remainder is zero.
(2) When x + 33 is divided by 10 the remainder is zero.
[Reveal] Spoiler: OA

_________________

New to the Math Forum?
Please read this: Ultimate GMAT Quantitative Megathread | All You Need for Quant | PLEASE READ AND FOLLOW: 12 Rules for Posting!!!

Resources:
GMAT Math Book | Triangles | Polygons | Coordinate Geometry | Factorials | Circles | Number Theory | Remainders; 8. Overlapping Sets | PDF of Math Book; 10. Remainders | GMAT Prep Software Analysis | SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) | Tricky questions from previous years.

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?
Extra-hard Quant Tests with Brilliant Analytics

Kudos [?]: 124106 [0], given: 12071

2 KUDOS received
BSchool Forum Moderator
User avatar
P
Joined: 26 Feb 2016
Posts: 1321

Kudos [?]: 518 [2], given: 16

Location: India
Concentration: General Management, Leadership
WE: Sales (Retail)
Premium Member CAT Tests
Re: What is the remainder when the positive integer x is divided by 31? [#permalink]

Show Tags

New post 14 Aug 2017, 04:12
2
This post received
KUDOS
What is the remainder when the positive integer x is divided by 31?

1. When x + 10 is divided by 31 the remainder is zero.
The number x can take the value 21,52,83.... and so on seperated by 31.
The remainder of the numbers x when divided by 31 will always be 21(Sufficient)

2. When x + 33 is divided by 10 the remainder is zero.
The number x=7, gives a remainder of 0 when divided by 10.
7 divided by 31 gives a remainder of 7
If x=37, the remainder of x + 33 is 0 when divided by 10.
But, 37 divided by 31 will have a remainder of 6.(Insufficient)(Option A)
_________________

Stay hungry, Stay foolish

2017-2018 MBA Deadlines

Class of 2020: Rotman Thread | Schulich Thread
Class of 2019: Sauder Thread

Kudos [?]: 518 [2], given: 16

Intern
Intern
User avatar
B
Joined: 09 Mar 2016
Posts: 32

Kudos [?]: 1 [0], given: 20

Re: What is the remainder when the positive integer x is divided by 31? [#permalink]

Show Tags

New post 14 Aug 2017, 04:39
pushpitkc wrote:
What is the remainder when the positive integer x is divided by 31?

1. When x + 10 is divided by 31 the remainder is zero.
The number x can take the value 21,52,83.... and so on seperated by 31.
The remainder of the numbers x when divided by 31 will always be 21(Sufficient)

2. When x + 33 is divided by 10 the remainder is zero.
The number x=7, gives a remainder of 0 when divided by 10.
7 divided by 31 gives a remainder of 7
If x=37, the remainder of x + 33 is 0 when divided by 10.
But, 37 divided by 31 will have a remainder of 6.(Insufficient)(Option A)


but if I divide 21 by 31 the remainder is not 21 ?:)

Kudos [?]: 1 [0], given: 20

BSchool Forum Moderator
User avatar
P
Joined: 26 Feb 2016
Posts: 1321

Kudos [?]: 518 [0], given: 16

Location: India
Concentration: General Management, Leadership
WE: Sales (Retail)
Premium Member CAT Tests
Re: What is the remainder when the positive integer x is divided by 31? [#permalink]

Show Tags

New post 14 Aug 2017, 05:04
dave13 wrote:
pushpitkc wrote:
What is the remainder when the positive integer x is divided by 31?

1. When x + 10 is divided by 31 the remainder is zero.
The number x can take the value 21,52,83.... and so on seperated by 31.
The remainder of the numbers x when divided by 31 will always be 21(Sufficient)

2. When x + 33 is divided by 10 the remainder is zero.
The number x=7, gives a remainder of 0 when divided by 10.
7 divided by 31 gives a remainder of 7
If x=37, the remainder of x + 33 is 0 when divided by 10.
But, 37 divided by 31 will have a remainder of 6.(Insufficient)(Option A)


but if I divide 21 by 31 the remainder is not 21 ?:)


Hi dave13,

If the number is 21 and is divided by 31, the quotient is 0 and remainder is 21.
Hope it is clear!
_________________

Stay hungry, Stay foolish

2017-2018 MBA Deadlines

Class of 2020: Rotman Thread | Schulich Thread
Class of 2019: Sauder Thread

Kudos [?]: 518 [0], given: 16

Expert Post
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 41631

Kudos [?]: 124106 [0], given: 12071

Re: What is the remainder when the positive integer x is divided by 31? [#permalink]

Show Tags

New post 14 Aug 2017, 06:16
Bunuel wrote:
What is the remainder when the positive integer x is divided by 31?

(1) When x + 10 is divided by 31 the remainder is zero.
(2) When x + 33 is divided by 10 the remainder is zero.


What is the remainder when the positive integer x is divided by 31?

Now, we can solve this question algebraically or with number plugging, which in this case is easier:

(1) When x+10 is divided by 31 the remainder is zero.

Number picking approach:
x+10 to be multiple of 31 x must be 21, 52, 83, ... each yields a remainder of 21 upon division by 31. Sufficient.

Algebraic approach:
\(x+10=31q\) --> \(x=31q-10\) --> \(x=31q-31+21\) --> \(x=31(q-1)+21\) directly tells us that remainder upon division \(x\) by 31 is 21. Sufficient.

(2) When x+33 is divided by 10 the remainder is zero --> x+33 to be multiple of 10 x must be 7, 17, 27, ... 7 yields a remainder of 7 upon division by 31, but 17 yields a remainder of 17 upon division by 31. Not sufficient.

Answer: A.
_________________

New to the Math Forum?
Please read this: Ultimate GMAT Quantitative Megathread | All You Need for Quant | PLEASE READ AND FOLLOW: 12 Rules for Posting!!!

Resources:
GMAT Math Book | Triangles | Polygons | Coordinate Geometry | Factorials | Circles | Number Theory | Remainders; 8. Overlapping Sets | PDF of Math Book; 10. Remainders | GMAT Prep Software Analysis | SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) | Tricky questions from previous years.

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?
Extra-hard Quant Tests with Brilliant Analytics

Kudos [?]: 124106 [0], given: 12071

Manager
Manager
avatar
S
Joined: 06 Jul 2014
Posts: 101

Kudos [?]: 34 [0], given: 155

Location: India
Concentration: Finance, Entrepreneurship
GMAT 1: 640 Q48 V30
GMAT ToolKit User Reviews Badge
Re: What is the remainder when the positive integer x is divided by 31? [#permalink]

Show Tags

New post 14 Aug 2017, 07:10
which approach is more fool proof? number picking can be a bit difficult with more complicated questions?

Kudos [?]: 34 [0], given: 155

Expert Post
Target Test Prep Representative
User avatar
S
Status: Founder & CEO
Affiliations: Target Test Prep
Joined: 14 Oct 2015
Posts: 1503

Kudos [?]: 765 [0], given: 2

Location: United States (CA)
Re: What is the remainder when the positive integer x is divided by 31? [#permalink]

Show Tags

New post 24 Aug 2017, 13:37
Bunuel wrote:
What is the remainder when the positive integer x is divided by 31?

(1) When x + 10 is divided by 31 the remainder is zero.
(2) When x + 33 is divided by 10 the remainder is zero.


We use the “quotient remainder theorem,” which states: dividend = quotient x divisor + remainder.

We need to determine the remainder when the positive integer x is divided by 31. That is, if we express x as 31Q + R for some nonnegative integers Q and R where R < 31, then R is the remainder when x is divided by 31.

Statement One Alone:

When x + 10 is divided by 31, the remainder is zero.

Thus:

(x + 10)/31 = Q + 0/31

(x + 10)/31 = Q

x + 10 = 31Q

x = 31Q - 10

x = 31Q - 31 + 31 - 10

x = 31(Q - 1) + 21

Since Q - 1 is an integer and since 21 < 31, we see that when x is divided by 31, the remainder is 21.

Statement one alone is sufficient to answer the question.

Statement Two Alone:

When x + 33 is divided by 10, the remainder is zero.

Thus:

(x + 33)/10 = Q + 0/31

(x + 33)/10 = Q

x + 33 = 10Q

x = 10Q - 33

We see that if Q = 4, then x = 7 and the remainder when x is divided by 31 is 7. However, if Q = 5, then x = 17 and the remainder when x is divided by 31 is 17. Statement two is not sufficient to answer the question.

Answer: A
_________________

Scott Woodbury-Stewart
Founder and CEO

GMAT Quant Self-Study Course
500+ lessons 3000+ practice problems 800+ HD solutions

Kudos [?]: 765 [0], given: 2

Re: What is the remainder when the positive integer x is divided by 31?   [#permalink] 24 Aug 2017, 13:37
    Similar topics Author Replies Last post
Similar
Topics:
4 EXPERTS_POSTS_IN_THIS_TOPIC What is the remainder when the positive integer x is divided mybudgie 10 09 Jun 2015, 08:08
2 EXPERTS_POSTS_IN_THIS_TOPIC What is the remainder when positive integer x is divided by ronr34 3 22 Apr 2016, 07:41
30 EXPERTS_POSTS_IN_THIS_TOPIC What is the remainder when the positive integer x is divided enigma123 11 15 Jul 2017, 15:12
1 EXPERTS_POSTS_IN_THIS_TOPIC What is the remainder when the positive integer x is divided mydreammba 4 22 Jun 2016, 02:41
16 EXPERTS_POSTS_IN_THIS_TOPIC What is the remainder when the positive integer x is divided albany09 11 14 Sep 2017, 09:33
Display posts from previous: Sort by

What is the remainder when the positive integer x is divided by 31?

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


GMAT Club MBA Forum Home| About| Terms and Conditions| 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®.