BREAKING: Target Test Prep releases Brand New 2026 On Demand GMAT prep course

Redeem
TTP OnDemand GMAT Video Course
Featured Course

Target Test Prep GMAT OnDemand

Scott Woodbury-Stewart’s private virtual classroom — 400 hours of master-class video lessons for the GMAT Focus Edition.

  • 715+ score guarantee — highest in the industry (99th percentile)
  • 52 chapters · 1,500+ lessons · 4,000+ practice questions
  • 400 hours of video · 1,500+ instructor-led HD smartboard lessons
  • 300,000+ students accepted to Harvard, Stanford, Wharton, Booth & Sloan & more
  • 24/7 live support + weekly Zoom office hours with GMAT instructors
  • TTP AI Assist — 24/7 AI-powered virtual tutor for instant help
  • 1,200+ flashcards + AI-powered study assistant & daily calendar
  • OnDemand, LiveTeach & GMAT Bootcamp formats available
  • Also: GRE, SAT Math & Executive Assessment courses
  • MBA Admissions Consulting now available
  • 🏆 2025 EdTech Breakthrough Award: Test Prep Solution Provider of the Year
  • 200,000+ students served
  • 5-day free trial — $0 to start, no auto-billing, cancel anytime
★★★★★ 5.0 (559 reviews)
130-pt guarantee
$0 to start then $127/mo
Start Free 5-Day Trial Read 559 Reviews →

By how much do the digits differ?

Expert replies
Post new topic Post Reply
Previous Topic Next Topic
Senior | Next Rank: 100 Posts
Posts: 85
Joined: Tue Mar 31, 2009 10:58 am
by GmatGreen » Thu Mar 13, 2014 12:30 pm

Timer

00:00

Answers

A

B

C

D

E

Stats

Difficulty—

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
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
Source: — Problem Solving |
User avatar
GMAT Instructor
Posts: 1052
Joined: Fri May 21, 2010 1:30 amFollowed by: 98 members
Thanked: 335 times

by Patrick_GMATFix » Thu Mar 13, 2014 12:44 pm
Any two-digit number (eg: 27) can be expressed as 10*tens + 1*units (eg: 10*2 + 7). This is the basis for how to solve this question quickly. The difference between 2 two-digit numbers with the same digits in reverse order can be expressed as (10t+u) - (10u+t) where t and u are the original tens and units digits.

The answer is A. I go through the question in detail in the full solution below (taken from the GMATFix App).

Image

-Patrick
  • Ask me about tutoring.
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
User avatar
GMAT Instructor
Posts: 15539
Joined: Tue May 25, 2010 12:04 pmFollowed by: 1906 members
Location: New York, NY
Thanked: 13060 times
GMAT Score:790

by GMATGuruNY » Thu Mar 13, 2014 1:47 pm
GmatGreen 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
TEST CASES between 10 and 20 until the required difference of 27 is yielded.

Case 1: 12 and 21
21-12 = 9.
Doesn't work.

Case 2: 13 and 31
31-13 = 18.
Doesn't work.

Case 3: 14 and 41
41-14 = 27.
Success!
Difference between the digits = 4-1 = 3.

The correct answer is A.
Private tutor exclusively for the GMAT and GRE, with over 20 years of experience.
Followed here and elsewhere by over 1900 test-takers.
I have worked with students based in the US, Australia, Taiwan, China, Tajikistan, Kuwait, Saudi Arabia -- a long list of countries.
My students have been admitted to HBS, CBS, Tuck, Yale, Stern, Fuqua -- a long list of top programs.

As a tutor, I don't simply teach you how I would approach problems.
I unlock the best way for YOU to solve problems.

For more information, please email me (Mitch Hunt) at [email protected].
Student Review #1
Student Review #2
Student Review #3
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
User avatar
Legendary Member
Posts: 1556
Joined: Tue Aug 14, 2012 11:18 pmFollowed by: 34 members
Thanked: 448 times
GMAT Score:650

by theCodeToGMAT » Thu Mar 13, 2014 10:30 pm
Original = (10X + y)
Reversed = 10Y + X

10Y + X - 10X - Y = 27
-9X + 9Y = 27
Y - X = 3
[spoiler]{A}[/spoiler]
R A H U L
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY

GMAT/MBA Expert

User avatar
Elite Legendary Member
Posts: 10392
Joined: Sun Jun 23, 2013 6:38 pmFollowed by: 511 members
Location: Palo Alto, CA
Thanked: 2867 times
GMAT Score:800

by [email protected] » Fri Mar 14, 2014 12:07 am
Hi GmatGreen,

You can actually TEST Values on this question (as Mitch's approach shows). One of the great aspects about this question is that there are a variety of options that you can use to find the correct answer.

Mitch ended up using 14 and 41....

But you could also use...
25 and 52
36 and 63
47 and 74
58 and 85
69 and 96

Each of these possibilities fits the "rule" that the difference is 27 AND provides the exact same correct answer: 3

Final Answer: A

GMAT assassins aren't born, they're made,
Rich
Contact Rich at [email protected]
Image
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
User avatar
Master | Next Rank: 500 Posts
Posts: 359
Joined: Wed Mar 11, 2009 4:37 amFollowed by: 2 members
Location: Kolkata, India
Thanked: 50 times

by Abhishek009 » Fri Mar 14, 2014 8:52 am
theCodeToGMAT wrote:Original = (10X + y)
Reversed = 10Y + X

10Y + X - 10X - Y = 27
-9X + 9Y = 27
Y - X = 3
[spoiler]{A}[/spoiler]

There is a cute rule for solving these quickly ...

Remeber the form as any number ( having 2 digits ) when reversed forms -> 9y - 9x

Here 9y - 9x = 27

x - y = 3
Abhishek
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
User avatar
Legendary Member
Posts: 1556
Joined: Tue Aug 14, 2012 11:18 pmFollowed by: 34 members
Thanked: 448 times
GMAT Score:650

by theCodeToGMAT » Fri Mar 14, 2014 9:09 am
Abhishek009 wrote:
theCodeToGMAT wrote:Original = (10X + y)
Reversed = 10Y + X

10Y + X - 10X - Y = 27
-9X + 9Y = 27
Y - X = 3
[spoiler]{A}[/spoiler]

There is a cute rule for solving these quickly ...

Remeber the form as any number ( having 2 digits ) when reversed forms -> 9y - 9x

Here 9y - 9x = 27

x - y = 3
Will advise you to not to mug-up such shortcuts but rather spend 10 seconds more to reach to such solutions... Trust me, GMAT doesn't need such shortcuts..
R A H U L
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
User avatar
GMAT Instructor
Posts: 1462
Joined: Thu Apr 09, 2015 9:34 amFollowed by: 22 members
Location: New York, NY
Thanked: 39 times

by Jeff@TargetTestPrep » Tue Jul 28, 2015 2:19 pm
GmatGreen 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
Solution:

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 the idea of N = 10A + B is hard to see, let's use a sample number, say 24. We can say the following:

24 = (10 x 2) + 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

Because we know the resulting integer differs from the original integer by 27, we can say either one of the following:

(10B + A) - (10A + B) = 27 or (10A + B) - (10B + A) = 27

If it's the former, we have:

10B + A - 10A - B = 27

9B - 9A = 27

B - A = 3

If it's the latter, we have:

10A + B - 10B - A = 27

9A - 9B = 27

A - B = 3

In either case, we can see that the digits differ by 3.

The answer is A

Jeffrey Miller
Head of GMAT Instruction
[email protected]

Image

See why Target Test Prep is rated 5 out of 5 stars on BEAT the GMAT. Read our reviews
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
Legendary Member
Posts: 518
Joined: Tue May 12, 2015 8:25 pm
Thanked: 10 times

by nikhilgmat31 » Wed Jul 29, 2015 12:36 am
GMATGuruNY wrote:
GmatGreen 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
TEST CASES between 10 and 20 until the required difference of 27 is yielded.

Case 1: 12 and 21
21-12 = 9.
Doesn't work.

Case 2: 13 and 31
31-13 = 18.
Doesn't work.

Case 3: 14 and 41
41-14 = 27.
Success!
Difference between the digits = 4-1 = 3.

The correct answer is A.
36 & 63 is another good example.
25 & 52 is another good example.

difference is 3 always.
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
Post new topic Post Reply
• Page 1 of 1