It is currently 21 Nov 2017, 19:10

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 a two-digit positive integer has its digits reversed, the

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

Hide Tags

2 KUDOS received
Manager
Manager
avatar
Joined: 03 Mar 2007
Posts: 162

Kudos [?]: 40 [2], given: 0

If a two-digit positive integer has its digits reversed, the [#permalink]

Show Tags

New post 14 Apr 2007, 17:54
2
This post received
KUDOS
8
This post was
BOOKMARKED
00:00
A
B
C
D
E

Difficulty:

  5% (low)

Question Stats:

86% (00:53) correct 14% (01:18) wrong based on 440 sessions

HideShow timer Statistics

If a two-digit positive integer has its digits reversed, the resulting integer differs from the original by 27. By how much do the two digits differ?

(A) 3
(B) 4
(C) 5
(D) 6
(E) 7
[Reveal] Spoiler: OA

Last edited by Bunuel on 12 Oct 2012, 10:22, edited 1 time in total.
Edited the question.

Kudos [?]: 40 [2], given: 0

9 KUDOS received
Senior Manager
Senior Manager
avatar
Joined: 11 Feb 2007
Posts: 350

Kudos [?]: 186 [9], given: 0

 [#permalink]

Show Tags

New post 14 Apr 2007, 19:33
9
This post received
KUDOS
3
This post was
BOOKMARKED
A?

Let x be the tenth digit and y be the units digit.

Then, the original number is 10x+y and the reversed number is 10y+x.

The difference between the two is 27. (reversed - original)

Thus, (10y+x)-(10x+y)=27
solve the above eq.
10y+x-10x-y=27
9y-9x=27
9(y-x)=27
y-x=3

Thus the two digits differ by 3.

:)

Kudos [?]: 186 [9], given: 0

Manager
Manager
avatar
Joined: 28 Feb 2007
Posts: 195

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

Location: California
 [#permalink]

Show Tags

New post 15 Apr 2007, 15:16
salr15 wrote:
ricokevin wrote:
A?

Let x be the tenth digit and y be the units digit.

Then, the original number is 10x+y and the reversed number is 10y+x.

The difference between the two is 27. (reversed - original)

Thus, (10y+x)-(10x+y)=27
solve the above eq.
10y+x-10x-y=27
9y-9x=27
9(y-x)=27
y-x=3

Thus the two digits differ by 3.

:)


how did you get 10x + y?


34 = (3 x 10) + 4
If xy = 34 then this explains it.
HTH

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

Manager
Manager
avatar
Joined: 03 Mar 2007
Posts: 162

Kudos [?]: 40 [0], given: 0

 [#permalink]

Show Tags

New post 15 Apr 2007, 16:25
techjanson wrote:
salr15 wrote:
ricokevin wrote:
A?

Let x be the tenth digit and y be the units digit.

Then, the original number is 10x+y and the reversed number is 10y+x.

The difference between the two is 27. (reversed - original)

Thus, (10y+x)-(10x+y)=27
solve the above eq.
10y+x-10x-y=27
9y-9x=27
9(y-x)=27
y-x=3

Thus the two digits differ by 3.

:)


how did you get 10x + y?


34 = (3 x 10) + 4
If xy = 34 then this explains it.
HTH


Great thanks! :oops:

Kudos [?]: 40 [0], given: 0

3 KUDOS received
SVP
SVP
User avatar
S
Joined: 14 Apr 2009
Posts: 2138

Kudos [?]: 1639 [3], given: 8

Location: New York, NY
Re: If a two-digit positive integer has its digits reversed, the [#permalink]

Show Tags

New post 12 Oct 2012, 09:32
3
This post received
KUDOS
1
This post was
BOOKMARKED
This is a tricky number properties question. Note that you can use two variables a and b to represent each of the digits.

In terms of expressing them in values - the total value would be (10a + b).

For example, for a number 37, a = 3 and b=7..then the expression 10a+b = 30 + 7 = 37.

Please refer to the video explanation here:
http://www.gmatpill.com/gmat-practice-t ... stion/2397

Kudos [?]: 1639 [3], given: 8

Non-Human User
User avatar
Joined: 09 Sep 2013
Posts: 15585

Kudos [?]: 283 [0], given: 0

Premium Member
Re: If a two-digit positive integer has its digits reversed, the [#permalink]

Show Tags

New post 08 Jan 2014, 21:10
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

Kudos [?]: 283 [0], given: 0

Non-Human User
User avatar
Joined: 09 Sep 2013
Posts: 15585

Kudos [?]: 283 [0], given: 0

Premium Member
Re: If a two-digit positive integer has its digits reversed, the [#permalink]

Show Tags

New post 15 Feb 2015, 10:42
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

Kudos [?]: 283 [0], given: 0

Expert Post
1 KUDOS received
EMPOWERgmat Instructor
User avatar
P
Status: GMAT Assassin/Co-Founder
Affiliations: EMPOWERgmat
Joined: 19 Dec 2014
Posts: 10158

Kudos [?]: 3523 [1], given: 173

Location: United States (CA)
GMAT 1: 800 Q51 V49
GRE 1: 340 Q170 V170
Re: If a two-digit positive integer has its digits reversed, the [#permalink]

Show Tags

New post 15 Feb 2015, 14:41
1
This post received
KUDOS
Expert's post
Hi All,

The "math" behind this question is such that there are several different numbers that "fit" the given "restrictions"; in that way, we can use a bit of "brute force" to quickly come up with the answer.

We're told that a two-digit positive integer will differ from its "reverse" by 27.

I'm going to 'play' with this math a bit.....

IF we use....
12 and 21 then the difference is 21-12 = 9 This is NOT a match
13 and 31 then the difference is 31-13 = 18 This is NOT a match. Notice how the difference increases by 9 though!!!!!
14 and 41 then the difference is 41-14 = 27 This IS a match.

The question asks for the difference in the two digits involved. Using these values, the answer is 4-1 = 3

Final Answer:
[Reveal] Spoiler:
A


I mentioned at the beginning that there were several numbers that "fit" what this question was asking for. They are 14 and 41, 25 and 52, 36 and 63, 47 and 74, 58 and 85, 69 and 96.

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 [?]: 3523 [1], given: 173

Non-Human User
User avatar
Joined: 09 Sep 2013
Posts: 15585

Kudos [?]: 283 [0], given: 0

Premium Member
Re: If a two-digit positive integer has its digits reversed, the [#permalink]

Show Tags

New post 09 Jun 2016, 13:19
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

Kudos [?]: 283 [0], given: 0

Expert Post
2 KUDOS received
Target Test Prep Representative
User avatar
S
Status: Founder & CEO
Affiliations: Target Test Prep
Joined: 14 Oct 2015
Posts: 1821

Kudos [?]: 938 [2], given: 3

Location: United States (CA)
Re: If a two-digit positive integer has its digits reversed, the [#permalink]

Show Tags

New post 15 Jul 2016, 04:31
2
This post received
KUDOS
Expert's post
salr15 wrote:
If a two-digit positive integer has its digits reversed, the resulting integer differs from the original by 27. By how much do the two digits differ?

(A) 3
(B) 4
(C) 5
(D) 6
(E) 7


Let’s first label the original two-digit integer as N. We can then say that N = 10A + B, where A is the tens digit and B is the units digit of N.

If this is hard to see let’s try it with a sample number, say 24. We can say the following:

24 = (2 x 10) + 4

24 = 20 + 4

24 = 24

Getting back to the problem, we are given that if the integer N has its digits reversed the resulting integer differs from the original by 27. First let’s express the reversed number in a similar fashion to the way in which we expressed the original integer.

10B + A = reversed integer

Since we know the resulting integer differs from the original by 27 we can say:

10B + A – (10A + B) = 27

10B + A – 10A – B = 27

9B – 9A = 27

B – A = 3

Since B is the tens digit and A is the units digit, we can say that the digits differ by 3.

The answer is A.
_________________

Scott Woodbury-Stewart
Founder and CEO

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

Kudos [?]: 938 [2], given: 3

Intern
Intern
User avatar
B
Joined: 16 May 2017
Posts: 21

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

Re: If a two-digit positive integer has its digits reversed, the [#permalink]

Show Tags

New post 18 May 2017, 08:09
I find this problem simple and a little confusing.

So we have here
ab – ba = 27
Let’s say ab = N,
We can formulate it as N = 10a + b, a – is tenths digit, and b – unit digit. For example:
N = 4*10 +5 = 45
Now reversed number will be as follows:

10b+a

we know: ab – ba = 27 =>
10a + b – (10b +a) = 27
10a + b – 10b – a = 27
9a – 9b = 27
a – b = 3. => two digits differ by 3.

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

Board of Directors
User avatar
G
Status: QA & VA Forum Moderator
Joined: 11 Jun 2011
Posts: 3102

Kudos [?]: 1116 [0], given: 327

Location: India
GPA: 3.5
WE: Business Development (Commercial Banking)
GMAT ToolKit User Premium Member
Re: If a two-digit positive integer has its digits reversed, the [#permalink]

Show Tags

New post 18 May 2017, 09:03
salr15 wrote:
If a two-digit positive integer has its digits reversed, the resulting integer differs from the original by 27. By how much do the two digits differ?

(A) 3
(B) 4
(C) 5
(D) 6
(E) 7


Let the original number be 10x + y
After reversal of the digits the number is 10y + x

Difference : ( 10y + x ) - ( 10x + y ) = 27

Or, 9y - 9x = 27

Or, y - x = 3

Thus, the answer must be (A) 3
_________________

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 [?]: 1116 [0], given: 327

Director
Director
avatar
G
Joined: 02 Sep 2016
Posts: 788

Kudos [?]: 43 [0], given: 274

Premium Member CAT Tests
Re: If a two-digit positive integer has its digits reversed, the [#permalink]

Show Tags

New post 04 Sep 2017, 04:02
ScottTargetTestPrep wrote:
salr15 wrote:
If a two-digit positive integer has its digits reversed, the resulting integer differs from the original by 27. By how much do the two digits differ?

(A) 3
(B) 4
(C) 5
(D) 6
(E) 7


Let’s first label the original two-digit integer as N. We can then say that N = 10A + B, where A is the tens digit and B is the units digit of N.

If this is hard to see let’s try it with a sample number, say 24. We can say the following:

24 = (2 x 10) + 4

24 = 20 + 4

24 = 24

Getting back to the problem, we are given that if the integer N has its digits reversed the resulting integer differs from the original by 27. First let’s express the reversed number in a similar fashion to the way in which we expressed the original integer.

10B + A = reversed integer

Since we know the resulting integer differs from the original by 27 we can say:

10B + A – (10A + B) = 27

10B + A – 10A – B = 27

9B – 9A = 27

B – A = 3

Since B is the tens digit and A is the units digit, we can say that the digits differ by 3.

The answer is A.



Can we also write it as:

10A+B-10B-A= 27
9A-9B= 27
A-B= 3

Kudos [?]: 43 [0], given: 274

Re: If a two-digit positive integer has its digits reversed, the   [#permalink] 04 Sep 2017, 04:02
Display posts from previous: Sort by

If a two-digit positive integer has its digits reversed, the

  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®.