It is currently 14 Dec 2017, 05:14

Decision(s) Day!:

CHAT Rooms | Wharton R1 | Stanford R1 | Tuck R1 | Ross R1 | Haas R1


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

The positive two-digit integers x and y have the same digits, but in

  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: 42604

Kudos [?]: 135613 [0], given: 12705

The positive two-digit integers x and y have the same digits, but in [#permalink]

Show Tags

New post 15 Oct 2015, 20:55
Expert's post
7
This post was
BOOKMARKED
00:00
A
B
C
D
E

Difficulty:

  5% (low)

Question Stats:

86% (00:42) correct 14% (00:54) wrong based on 707 sessions

HideShow timer Statistics

The positive two-digit integers x and y have the same digits, but in reverse order. Which of the following must be a factor of x + y?

(A) 6
(B) 9
(C) 10
(D) 11
(E) 14

Kudos for a correct solution.
[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 [?]: 135613 [0], given: 12705

3 KUDOS received
Director
Director
User avatar
Joined: 10 Mar 2013
Posts: 589

Kudos [?]: 493 [3], given: 200

Location: Germany
Concentration: Finance, Entrepreneurship
GMAT 1: 580 Q46 V24
GPA: 3.88
WE: Information Technology (Consulting)
GMAT ToolKit User
Re: The positive two-digit integers x and y have the same digits, but in [#permalink]

Show Tags

New post 15 Oct 2015, 23:00
3
This post received
KUDOS
2
This post was
BOOKMARKED
Bunuel wrote:
The positive two-digit integers x and y have the same digits, but in reverse order. Which of the following must be a factor of x + y?

(A) 6
(B) 9
(C) 10
(D) 11
(E) 14

Kudos for a correct solution.

10a+b+10b+a=11(a+b) Answer (D)
_________________

When you’re up, your friends know who you are. When you’re down, you know who your friends are.

Share some Kudos, if my posts help you. Thank you !

800Score ONLY QUANT CAT1 51, CAT2 50, CAT3 50
GMAT PREP 670
MGMAT CAT 630
KAPLAN CAT 660

Kudos [?]: 493 [3], given: 200

1 KUDOS received
Manager
Manager
User avatar
G
Joined: 13 Apr 2013
Posts: 217

Kudos [?]: 87 [1], given: 668

Location: India
Concentration: International Business, Operations
Schools: ISB '19
GMAT 1: 480 Q38 V22
GPA: 3.01
WE: Engineering (Consulting)
Premium Member CAT Tests
Re: The positive two-digit integers x and y have the same digits, but in [#permalink]

Show Tags

New post 15 Oct 2015, 23:26
1
This post received
KUDOS
3
This post was
BOOKMARKED
Bunuel wrote:
The positive two-digit integers x and y have the same digits, but in reverse order. Which of the following must be a factor of x + y?

(A) 6
(B) 9
(C) 10
(D) 11
(E) 14

Kudos for a correct solution.



My Solution:

Lets say integer x has two digits "ab" then as per question y has two digits in reverse i.e, "ba" ,

Then x+y will be,

(10a+b)+(10b+a)----> 11a+11b---->11(a+b)

Therefore 11 must be a factor of x+y

Answer D

_________________

"Success is not as glamorous as people tell you. It's a lot of hours spent in the darkness."

Kudos [?]: 87 [1], given: 668

1 KUDOS received
Manager
Manager
avatar
Status: tough ... ? Naaahhh !!!!
Joined: 07 Sep 2015
Posts: 66

Kudos [?]: 20 [1], given: 6

Location: India
Concentration: Marketing, Strategy
WE: Marketing (Computer Hardware)
GMAT ToolKit User
Re: The positive two-digit integers x and y have the same digits, but in [#permalink]

Show Tags

New post 16 Oct 2015, 00:00
1
This post received
KUDOS
10a+b+10b+a
11a+11b
11(a+b)....Ans: 11

Kudos [?]: 20 [1], given: 6

Expert Post
4 KUDOS received
EMPOWERgmat Instructor
User avatar
P
Status: GMAT Assassin/Co-Founder
Affiliations: EMPOWERgmat
Joined: 19 Dec 2014
Posts: 10391

Kudos [?]: 3688 [4], given: 173

Location: United States (CA)
GMAT 1: 800 Q51 V49
GRE 1: 340 Q170 V170
Re: The positive two-digit integers x and y have the same digits, but in [#permalink]

Show Tags

New post 17 Oct 2015, 10:13
4
This post received
KUDOS
Expert's post
3
This post was
BOOKMARKED
Hi All,

This question can be solved by TESTing VALUES:

We're told that X and Y are both 2-digit positive integers with the digits reversed. We're asked for what MUST be a factor of X+Y

IF....
X=12
Y=21

X+Y = 12+21 = 33

Only one of the answers is a factor of 33...

Final Answer:
[Reveal] Spoiler:
D


GMAT assassins aren't born, they're made,
Rich
_________________

760+: Learn What GMAT Assassins Do to Score at the Highest Levels
Contact Rich at: Rich.C@empowergmat.com

Rich Cohen

Co-Founder & GMAT Assassin

Special Offer: Save $75 + GMAT Club Tests Free
  Official GMAT Exam Packs + 70 Pt. Improvement Guarantee
www.empowergmat.com/

***********************Select EMPOWERgmat Courses now include ALL 6 Official GMAC CATs!***********************

Kudos [?]: 3688 [4], given: 173

Intern
Intern
avatar
S
Joined: 12 Nov 2014
Posts: 21

Kudos [?]: 1 [0], given: 923

Re: The positive two-digit integers x and y have the same digits, but in [#permalink]

Show Tags

New post 18 Oct 2015, 10:05
WHy not 3,6. 36 and 63 are both divisible by 9.

Kudos [?]: 1 [0], given: 923

Expert Post
1 KUDOS received
EMPOWERgmat Instructor
User avatar
P
Status: GMAT Assassin/Co-Founder
Affiliations: EMPOWERgmat
Joined: 19 Dec 2014
Posts: 10391

Kudos [?]: 3688 [1], given: 173

Location: United States (CA)
GMAT 1: 800 Q51 V49
GRE 1: 340 Q170 V170
Re: The positive two-digit integers x and y have the same digits, but in [#permalink]

Show Tags

New post 18 Oct 2015, 11:08
1
This post received
KUDOS
Expert's post
Hi alice7,

The prompt asks us for what MUST be a factor of X+Y...

Using your example (36 and 63), we would have a total of 99. In this case, TWO of the answers 'fit' - both 9 and 11 are factors of 99. So one of these MUST be the solution, but we won't know which one until we find another example that is NOT divisible by one of the two options.

GMAT assassins aren't born, they're made,
Rich
_________________

760+: Learn What GMAT Assassins Do to Score at the Highest Levels
Contact Rich at: Rich.C@empowergmat.com

Rich Cohen

Co-Founder & GMAT Assassin

Special Offer: Save $75 + GMAT Club Tests Free
  Official GMAT Exam Packs + 70 Pt. Improvement Guarantee
www.empowergmat.com/

***********************Select EMPOWERgmat Courses now include ALL 6 Official GMAC CATs!***********************

Kudos [?]: 3688 [1], given: 173

Manager
Manager
avatar
Joined: 06 Jun 2014
Posts: 92

Kudos [?]: 96 [0], given: 109

Location: United States
Concentration: Finance, General Management
GMAT 1: 450 Q27 V21
GPA: 3.47
GMAT ToolKit User
Re: The positive two-digit integers x and y have the same digits, but in [#permalink]

Show Tags

New post 28 Oct 2015, 12:52
1
This post was
BOOKMARKED
Bunuel wrote:
The positive two-digit integers x and y have the same digits, but in reverse order. Which of the following must be a factor of x + y?

(A) 6
(B) 9
(C) 10
(D) 11
(E) 14

Kudos for a correct solution.


Remember: When you take the difference between the two, it will always be 9. e.g 23-32=9, 89-98=9
and when you add both integers, the sum will always be a multiple of 11 e.g 23+32=55, 89+98= 187

so the answer is 11

Kudos [?]: 96 [0], given: 109

Manager
Manager
avatar
Joined: 09 Jun 2015
Posts: 100

Kudos [?]: 9 [0], given: 0

Re: The positive two-digit integers x and y have the same digits, but in [#permalink]

Show Tags

New post 16 Mar 2016, 01:22
Bunuel wrote:
The positive two-digit integers x and y have the same digits, but in reverse order. Which of the following must be a factor of x + y?

(A) 6
(B) 9
(C) 10
(D) 11
(E) 14

Kudos for a correct solution.

Supposing that the numbers are ab and ba, then ab can be written as 10a+b and ba can be written as 10b+a
Adding we get 11a+11b=11*(a+b)
Therefore, the sum is divisible by 11 as well as by sum of the digits.

Kudos [?]: 9 [0], given: 0

Expert Post
1 KUDOS received
Math Expert
User avatar
D
Joined: 02 Aug 2009
Posts: 5347

Kudos [?]: 6125 [1], given: 121

Re: The positive two-digit integers x and y [#permalink]

Show Tags

New post 02 May 2016, 18:21
1
This post received
KUDOS
Expert's post
macbookno wrote:
The positive two-digit integers x and y have the same digits, but in reverse order. Which of the following must be a factor of x + y?

A. 6
B. 9
C. 10
D. 11
E. 14



Pl post according to guidelines..
Provide OA, proper topic name and post in correct sub-forum..

as for your Q..
let x = ab, a 2-digit integer so y= ba..

x= ab = 10a+b
and y=ba=10b+a..

so \(x+y = 10a+b+10b+a = 11(a+b)\)..
therefore x+y will always have a factor 11..
D

_________________

Absolute modulus :http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html

Kudos [?]: 6125 [1], given: 121

Expert Post
1 KUDOS received
Veritas Prep GMAT Instructor
User avatar
G
Joined: 16 Oct 2010
Posts: 7796

Kudos [?]: 18128 [1], given: 236

Location: Pune, India
Re: The positive two-digit integers x and y [#permalink]

Show Tags

New post 02 May 2016, 19:09
1
This post received
KUDOS
Expert's post
macbookno wrote:
The positive two-digit integers x and y have the same digits, but in reverse order. Which of the following must be a factor of x + y?

A. 6
B. 9
C. 10
D. 11
E. 14


Take a simple example. Two integers could be 12 and 21.
x + y = 33.
Only 11 is a factor. So 11 must be a factor of (x+y)

Answer (D)
_________________

Karishma
Veritas Prep | GMAT Instructor
My Blog

Get started with Veritas Prep GMAT On Demand for $199

Veritas Prep Reviews

Kudos [?]: 18128 [1], given: 236

Expert Post
1 KUDOS received
Target Test Prep Representative
User avatar
S
Status: Founder & CEO
Affiliations: Target Test Prep
Joined: 14 Oct 2015
Posts: 1940

Kudos [?]: 1018 [1], given: 3

Location: United States (CA)
Re: The positive two-digit integers x and y have the same digits, but in [#permalink]

Show Tags

New post 03 May 2016, 04:16
1
This post received
KUDOS
Expert's post
Bunuel wrote:
The positive two-digit integers x and y have the same digits, but in reverse order. Which of the following must be a factor of x + y?

(A) 6
(B) 9
(C) 10
(D) 11
(E) 14

Kudos for a correct solution.


We can solve this question using the natural relationships that all two-digit numbers have. As an example, we can express 37 as (10 x 3) + 7. We multiply the digit in the tens position by 10 and then add the digit in the ones position.

If we let a = the tens digit of x and b = the ones digit of x, we know:

x = 10a + b

Since the digits of y are the reverse of those of x, we can express y as:

y = 10b + a

When we sum x and y we obtain:

x + y = 10a + b + 10b + a = 11a + 11b

x + y = 11(a + b)

The final expression 11(a + b) is a multiple of 11, and therefore 11 divides evenly into it.

We see, therefore, that 11 must be a factor of x + y.

Answer: D
_________________

Scott Woodbury-Stewart
Founder and CEO

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

Kudos [?]: 1018 [1], given: 3

Manager
Manager
avatar
Joined: 20 Mar 2015
Posts: 63

Kudos [?]: 32 [0], given: 9

GMAT ToolKit User
The positive two-digit integers x and y have the same digits, but in [#permalink]

Show Tags

New post 23 Jun 2016, 09:25
EMPOWERgmatRichC wrote:
Hi All,

This question can be solved by TESTing VALUES:

We're told that X and Y are both 2-digit positive integers with the digits reversed. We're asked for what MUST be a factor of X+Y

IF....
X=12
Y=21

X+Y = 12+21 = 33

Only one of the answers is a factor of 33...

Final Answer:
[Reveal] Spoiler:
D


GMAT assassins aren't born, they're made,
Rich



I thought same digits were 11, 22, 33, 44, 55, 66..... 99. I am confused now. :?:

Kudos [?]: 32 [0], given: 9

Board of Directors
User avatar
G
Status: QA & VA Forum Moderator
Joined: 11 Jun 2011
Posts: 3111

Kudos [?]: 1146 [0], given: 327

Location: India
GPA: 3.5
WE: Business Development (Commercial Banking)
GMAT ToolKit User Premium Member
Re: The positive two-digit integers x and y have the same digits, but in [#permalink]

Show Tags

New post 23 Jun 2016, 10:09
bimalr9 wrote:
I thought same digits were 11, 22, 33, 44, 55, 66..... 99. I am confused now. :?:


Ok Let me try once -

X = 14 , Y = 41

X + Y = 14 + 41 =>55

55 = 11 * 5

Check again -

X = 12 , Y = 21

X + Y = 12 + 21 =>33

33 = 11 * 3

Check again -

X = 16 , Y = 61

X + Y = 16 + 61 =>77

77 = 11 * 7


Check in each case the common factor is 11 , hence the answer must be 11......


Feel free to revert in case of the slightest doubt, I will love to explain it again...

PS: IMHO the best method for this problem will be (10a + b ) + (10b + a ) => 11(a+b) as posted earlier...

_________________

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 )

Kudos [?]: 1146 [0], given: 327

Retired Moderator
avatar
P
Joined: 12 Aug 2015
Posts: 2208

Kudos [?]: 902 [0], given: 607

GRE 1: 323 Q169 V154
GMAT ToolKit User Premium Member
Re: The positive two-digit integers x and y have the same digits, but in [#permalink]

Show Tags

New post 04 Dec 2016, 00:16
Here is my solution for this one =>
x=MN => 10M+N
y=NM=>10N+M
x+y=> Must be a multiple of 11
OR in other words => 11 must be a factor of x+y

Alternatively
Let x=23
y=32
x+y=55
Only option that is a factor of 55 is 11 i.e Option D

Hence D


Additionally
x-y will always be multiple of 9 :twisted: :shock:

_________________

Give me a hell yeah ...!!!!!

Kudos [?]: 902 [0], given: 607

Study Buddy Forum Moderator
avatar
G
Joined: 04 Sep 2016
Posts: 447

Kudos [?]: 104 [0], given: 261

Location: India
WE: Engineering (Other)
Premium Member CAT Tests
The positive two-digit integers x and y have the same digits, but in [#permalink]

Show Tags

New post 28 Sep 2017, 22:29
VeritasPrepKarishma
Bunuel Engr2012


Quote:
Take a simple example. Two integers could be 12 and 21.


Is not the question stem ambiguous, leaving scope for discrepancy ?

Ideal Q should be : no of digits are the same

if no if digits of x and y are same, x = y = 10x + y

Is q says reversing digits makes x and y same, it should be inferred as 10x + y = 10 y + x

Let me know your understanding.

Kudos [?]: 104 [0], given: 261

Intern
Intern
avatar
B
Joined: 20 Sep 2016
Posts: 26

Kudos [?]: [0], given: 115

Premium Member
Re: The positive two-digit integers x and y have the same digits, but in [#permalink]

Show Tags

New post 08 Oct 2017, 01:58
take x as 23 and y as 32
x+y= 55
prime factors of 55 is 5 and 11.
thus 11 is the answer!

Kudos [?]: [0], given: 115

Re: The positive two-digit integers x and y have the same digits, but in   [#permalink] 08 Oct 2017, 01:58
Display posts from previous: Sort by

The positive two-digit integers x and y have the same digits, but in

  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®.