Check GMAT Club Decision Tracker for the Latest School Decision Releases https://gmatclub.com/AppTrack
GMAT Club

It is currently 23 Mar 2017, 05:35

R2 Decisions:

Yale SOM; Decision Tracker (Join Chat Room 4)  |  Berkeley Haas; Decision Tracker (Join Chat Room 5


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

If the tens digit x and the units digit y of a positive

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

Hide Tags

Senior Manager
Senior Manager
avatar
Joined: 31 Oct 2011
Posts: 323
Followers: 3

Kudos [?]: 939 [0], given: 18

If the tens digit x and the units digit y of a positive [#permalink]

Show Tags

New post 07 Mar 2012, 15:32
2
This post was
BOOKMARKED
00:00
A
B
C
D
E

Difficulty:

  35% (medium)

Question Stats:

61% (02:11) correct 39% (01:00) wrong based on 216 sessions

HideShow timer Statistics

If the tens digit x and the units digit y of a positive integer n are reversed, the resulting integer is 9 more than n. What is y in terms of x?

A. 10 - x
B. 9 - x
C. x + 9
D. x - 1
E. x + 1
[Reveal] Spoiler: OA

Last edited by Bunuel on 07 Mar 2012, 15:40, edited 1 time in total.
Edited the OA
Expert Post
1 KUDOS received
Math Expert
User avatar
G
Joined: 02 Sep 2009
Posts: 37553
Followers: 7391

Kudos [?]: 99232 [1] , given: 11010

Re: PT #11 PS 3 Q 15 [#permalink]

Show Tags

New post 07 Mar 2012, 15:39
1
This post received
KUDOS
Expert's post
2
This post was
BOOKMARKED
Intern
Intern
avatar
Joined: 06 Mar 2012
Posts: 29
Followers: 0

Kudos [?]: 17 [0], given: 31

GMAT ToolKit User
Re: If the tens digit x and the units digit y of a positive [#permalink]

Show Tags

New post 07 Mar 2012, 22:07
I plugged in with the numbers 23 and 32.

x=2, y=3 therefore y must be x+1.
____
Bunuel,

I followed your solution up until the last portion. Could you explain how you solved the equation into y=x+1? Thanks.
Expert Post
Math Expert
User avatar
G
Joined: 02 Sep 2009
Posts: 37553
Followers: 7391

Kudos [?]: 99232 [0], given: 11010

Re: If the tens digit x and the units digit y of a positive [#permalink]

Show Tags

New post 07 Mar 2012, 22:48
Expert's post
1
This post was
BOOKMARKED
damham17 wrote:
I plugged in with the numbers 23 and 32.

x=2, y=3 therefore y must be x+1.
____
Bunuel,

I followed your solution up until the last portion. Could you explain how you solved the equation into y=x+1? Thanks.


Welcome to GMAT Club.

First of all let me say that plug-in method is fine for this question and your approach is correct.

As for my solution: \(n'-n=(10y+x)-(10x+y)=9\) --> \(9y-9x=9\) --> \(y-x=1\) --> \(y=x+1\).

Hope it's clear.
_________________

New to the Math Forum?
Please read this: 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

Manager
Manager
avatar
B
Joined: 27 May 2012
Posts: 226
Followers: 2

Kudos [?]: 72 [0], given: 446

Re: PT #11 PS 3 Q 15 [#permalink]

Show Tags

New post 20 Jun 2012, 03:29
Bunuel wrote:
eybrj2 wrote:
If the tens digit x and the units digit y of a positive integer n are reversed, the resulting integer is 9 more than n. What is y in terms of x?

A. 10 - x
B. 9 - x
C. x + 9
D. x - 1
E. x + 1


\(n=10x+y\) and \(n'=10y+x\) --> \(n'-n=(10y+x)-(10x+y)=9\) --> \(y=x+1\).

Answer: E.


Can anybody clear this for me

suppose I take first number as 10y + x and reverse it to get 10x + y

Then according to the equation (10x + y) - (10y + x ) = 9
9x -9y= 9
x-y=1
y= x-1

so why are we getting two different answers.

if I take first number to be 10x + y and reverse it to get 10y +x
then (10y + x) - (10x +y)= 9y- 9x=9
y-x=1
y= x+1

why two different answers ?
_________________

- Stne

Expert Post
Math Expert
User avatar
G
Joined: 02 Sep 2009
Posts: 37553
Followers: 7391

Kudos [?]: 99232 [0], given: 11010

Re: PT #11 PS 3 Q 15 [#permalink]

Show Tags

New post 20 Jun 2012, 03:37
stne wrote:
Bunuel wrote:
eybrj2 wrote:
If the tens digit x and the units digit y of a positive integer n are reversed, the resulting integer is 9 more than n. What is y in terms of x?

A. 10 - x
B. 9 - x
C. x + 9
D. x - 1
E. x + 1


\(n=10x+y\) and \(n'=10y+x\) --> \(n'-n=(10y+x)-(10x+y)=9\) --> \(y=x+1\).

Answer: E.


Can anybody clear this for me

suppose I take first number as 10y + x and reverse it to get 10x + y

Then according to the equation (10x + y) - (10y + x ) = 9
9x -9y= 9
x-y=1
y= x-1

so why are we getting two different answers.

if I take first number to be 10x + y and reverse it to get 10y +x
then (10y + x) - (10x +y)= 9y- 9x=9
y-x=1
y= x+1

why two different answers ?


You cannot arbitrary assign which will be the "first" number and which will be the "second", since the stem explicitly clears that.

Positive integer \(n\) has the tens digit x and the units digit y, so \(n=10x+y\);

Reversed integer, say \(n'\), has the tens digit y and the units digit x, so \(n'=10y+x\);

We are also told that " the resulting integer (so \(n'\)) is 9 more than \(n\)", which means \(n'-n=(10y+x)-(10x+y)=9\) --> \(y=x+1\).

Hope it's clear.
_________________

New to the Math Forum?
Please read this: 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

Manager
Manager
avatar
B
Joined: 27 May 2012
Posts: 226
Followers: 2

Kudos [?]: 72 [0], given: 446

Re: PT #11 PS 3 Q 15 [#permalink]

Show Tags

New post 20 Jun 2012, 03:44
Bunuel wrote:
stne wrote:
Bunuel wrote:
If the tens digit x and the units digit y of a positive integer n are reversed, the resulting integer is 9 more than n. What is y in terms of x?

A. 10 - x
B. 9 - x
C. x + 9
D. x - 1
E. x + 1

\(n=10x+y\) and \(n'=10y+x\) --> \(n'-n=(10y+x)-(10x+y)=9\) --> \(y=x+1\).

Answer: E.


Can anybody clear this for me

suppose I take first number as 10y + x and reverse it to get 10x + y

Then according to the equation (10x + y) - (10y + x ) = 9
9x -9y= 9
x-y=1
y= x-1

so why are we getting two different answers.

if I take first number to be 10x + y and reverse it to get 10y +x
then (10y + x) - (10x +y)= 9y- 9x=9
y-x=1
y= x+1

why two different answers ?


You cannot arbitrary assign which will be the "first" number and which will be the "second", since the stem explicitly clears that.

Positive integer \(n\) has the tens digit x and the units digit y, so \(n=10x+y\);

Reversed integer, say \(n'\), has the tens digit y and the units digit x, so \(n'=10y+x\);

We are also told that " the resulting integer (so \(n'\)) is 9 more than \(n\)", which means \(n'-n=(10y+x)-(10x+y)=9\) --> \(y=x+1\).

Hope it's clear.


Its clear now , great. Thank you
_________________

- Stne

GMAT Club Legend
GMAT Club Legend
User avatar
Joined: 09 Sep 2013
Posts: 14368
Followers: 601

Kudos [?]: 174 [0], given: 0

Premium Member
Re: If the tens digit x and the units digit y of a positive [#permalink]

Show Tags

New post 18 Jun 2014, 04:37
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

Intern
Intern
avatar
Status: Preparing for GMAT
Joined: 10 Dec 2013
Posts: 20
Location: India
Concentration: Marketing, Leadership
GMAT 1: 530 Q46 V18
WE: Other (Entertainment and Sports)
Followers: 0

Kudos [?]: 7 [0], given: 61

Re: If the tens digit x and the units digit y of a positive [#permalink]

Show Tags

New post 06 Aug 2014, 11:28
Bunuel!!!! Your solutions make us all speechless. You are like the "Salman Khan" (The Hedge fund analyst who is the founder of Khan Academy- Free & quality education for all) of Gmat club. And what makes you even more special is that your solutions effectively convey what a hundred videos do, without any audio voice-overs.
Manager
Manager
avatar
Joined: 11 Jun 2014
Posts: 57
Concentration: Technology, Marketing
GMAT 1: 770 Q50 V45
WE: Information Technology (Consulting)
Followers: 4

Kudos [?]: 33 [0], given: 3

Re: If the tens digit x and the units digit y of a positive [#permalink]

Show Tags

New post 06 Aug 2014, 21:26
n is 10x+y
reversed it is, 10y+x

10y+x - (10x+y) = 9

9y-9x=9 --> y-x=1 --> y=x+1
GMAT Club Legend
GMAT Club Legend
User avatar
Joined: 09 Sep 2013
Posts: 14368
Followers: 601

Kudos [?]: 174 [0], given: 0

Premium Member
Re: If the tens digit x and the units digit y of a positive [#permalink]

Show Tags

New post 11 May 2016, 04:30
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

BSchool Forum Moderator
User avatar
G
Joined: 12 Aug 2015
Posts: 1943
Followers: 61

Kudos [?]: 454 [0], given: 483

GMAT ToolKit User
Re: If the tens digit x and the units digit y of a positive [#permalink]

Show Tags

New post 24 Nov 2016, 01:37
NOTE=> This Question Should have specified that n is a two digit positive integer.
Nevertheless let us proceed =>
N=xy=> 10x+y (x,y are tens and units digit)
N'=yx=10y+x
hence N'=N+9
=> 9y-9x=9
y=1+x

Hence E
_________________

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

Senior Manager
Senior Manager
User avatar
S
Joined: 08 Dec 2015
Posts: 300
GMAT 1: 600 Q44 V27
Followers: 1

Kudos [?]: 16 [0], given: 36

Reviews Badge
Re: If the tens digit x and the units digit y of a positive [#permalink]

Show Tags

New post 01 Dec 2016, 10:55
Shouldnt this question specify that they want y in terms of x of the starting number? take 23 and 32. y=x+1 works for 23 but not for 32. Confusing question?..
Expert Post
Math Expert
User avatar
G
Joined: 02 Sep 2009
Posts: 37553
Followers: 7391

Kudos [?]: 99232 [0], given: 11010

Re: If the tens digit x and the units digit y of a positive [#permalink]

Show Tags

New post 02 Dec 2016, 03:41
Re: If the tens digit x and the units digit y of a positive   [#permalink] 02 Dec 2016, 03:41
    Similar topics Author Replies Last post
Similar
Topics:
8 IF x is a positive integer, what is the units digit of deepthit 5 07 Sep 2016, 10:02
4 Experts publish their posts in the topic If the tens digit of positive integers x, y are 6, how many values of MathRevolution 5 14 Mar 2016, 18:08
7 Experts publish their posts in the topic The integer x has a tens digit of 6 and a units digit of 7. The units shasadou 5 17 Nov 2015, 03:14
14 Experts publish their posts in the topic The positive two-digit integers x and y have the same digits, but in Bunuel 16 15 Oct 2015, 21:55
4 Experts publish their posts in the topic A and B are positive two-digit integers such that the tens digit in A RudeyboyZ 3 25 Jun 2015, 02:32
Display posts from previous: Sort by

If the tens digit x and the units digit y of a positive

  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 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®.