Find all School-related info fast with the new School-Specific MBA Forum

It is currently 03 Jul 2015, 20:18

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.

Events & Promotions

Events & Promotions in June
Open Detailed Calendar

A three-digit number is such that when its reverse is subtra

  Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:
7 KUDOS received
Manager
Manager
User avatar
Joined: 25 Jan 2010
Posts: 108
Location: Calicut, India
Followers: 7

Kudos [?]: 108 [7] , given: 40

A three-digit number is such that when its reverse is subtra [#permalink] New post 10 Feb 2010, 05:42
7
This post received
KUDOS
5
This post was
BOOKMARKED
00:00
A
B
C
D
E

Difficulty:

  75% (hard)

Question Stats:

60% (03:59) correct 41% (02:26) wrong based on 203 sessions
A three-digit number is such that when its reverse is subtracted from it, the result is 297. Also, thrice the tens digit is equal to the difference between its hundreds and units digits. How many possible values are there for the number?

(A) 4
(B) 5
(C) 7
(D) 8
[Reveal] Spoiler: OA

_________________

If u think this post is useful plz feed me with a kudo


Last edited by Bunuel on 25 Feb 2014, 06:16, edited 1 time in total.
Renamed the topic, edited the question and added the OA.
Expert Post
8 KUDOS received
Math Expert
User avatar
Joined: 02 Sep 2009
Posts: 28272
Followers: 4469

Kudos [?]: 45136 [8] , given: 6645

Re: Solve - Simple Equations Q#1 [#permalink] New post 10 Feb 2010, 06:00
8
This post received
KUDOS
Expert's post
5
This post was
BOOKMARKED
cleetus wrote:
Plz illustrate how to solve this equation question
1) A three-digit number is such that when its reverse is subtracted from it, the result is 297. Also, thrice the tens digit is equal to the difference between its hundreds and units digits. How many possible values are there for the number?

A) 4
B) 5
C) 7
D) 8


Hi, welcome to the Gmat Club.

Solution to your question is as follows:

Three digit number \(abc\) can be represented as \(100a+10b+c\), its reverse number would be \(cba\) or \(100c+10b+a\).

Given: \(100a+10b+c-(100c+10b+a)=297\) --> \(a-c=3\), this gives us 7 values for \(a\) and \(c\): {9,6}{8,5}{7,4}{6,3}{5,2}{4,1}{3,0}.

Also given: \(3b=a-c\), from above we know \(a-c=3\), hence \(3b=3\) --> \(b=1\), only one value for \(b\).

So total of 7 such numbers are possible: {916}{815}{714}{613}{512}{411}{310}.

Answer: C.
_________________

NEW TO MATH FORUM? PLEASE READ THIS: ALL YOU NEED FOR QUANT!!!

PLEASE READ AND FOLLOW: 11 Rules for Posting!!!

RESOURCES: [GMAT MATH BOOK]; 1. Triangles; 2. Polygons; 3. Coordinate Geometry; 4. Factorials; 5. Circles; 6. Number Theory; 7. Remainders; 8. Overlapping Sets; 9. PDF of Math Book; 10. Remainders; 11. GMAT Prep Software Analysis NEW!!!; 12. SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) NEW!!!; 12. Tricky questions from previous years. NEW!!!;

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?
25 extra-hard Quant Tests

GMAT Club Premium Membership - big benefits and savings

1 KUDOS received
GMAT Club Legend
GMAT Club Legend
User avatar
Joined: 09 Sep 2013
Posts: 5363
Followers: 310

Kudos [?]: 60 [1] , given: 0

Premium Member
Re: Solve - Simple Equations Q#1 [#permalink] New post 25 Feb 2014, 04:24
1
This post received
KUDOS
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

Current Student
avatar
Joined: 03 Aug 2012
Posts: 917
Concentration: General Management, General Management
GMAT 1: 630 Q47 V29
GMAT 2: 680 Q50 V32
GPA: 3.7
WE: Information Technology (Investment Banking)
Followers: 17

Kudos [?]: 349 [0], given: 322

Premium Member
Re: A three-digit number is such that when its reverse is subtra [#permalink] New post 19 Apr 2014, 07:39
abc - cba = 297

100a+10b+c - 100c - 10b - a = 297

99a-99c = 297

a-c = 3

also, 3b = a-c

b=1

Numbers abc

a1c

ac can take (9,6),(8,5),(7,4),(6,3),(5,2),(4,1),(3,0)

Hence 7
_________________

Rgds,
TGC!
_____________________________________________________________________
I Assisted You => KUDOS Please
_____________________________________________________________________________

GMAT Club Legend
GMAT Club Legend
User avatar
Joined: 09 Sep 2013
Posts: 5363
Followers: 310

Kudos [?]: 60 [0], given: 0

Premium Member
Re: A three-digit number is such that when its reverse is subtra [#permalink] New post 25 May 2015, 07:26
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

Expert Post
1 KUDOS received
Veritas Prep GMAT Instructor
User avatar
Joined: 16 Oct 2010
Posts: 5682
Location: Pune, India
Followers: 1413

Kudos [?]: 7334 [1] , given: 186

Re: A three-digit number is such that when its reverse is subtra [#permalink] New post 25 May 2015, 22:06
1
This post received
KUDOS
Expert's post
cleetus wrote:
A three-digit number is such that when its reverse is subtracted from it, the result is 297. Also, thrice the tens digit is equal to the difference between its hundreds and units digits. How many possible values are there for the number?

(A) 4
(B) 5
(C) 7
(D) 8


You can also use reasoning to solve it.

"thrice the tens digit is equal to the difference between its hundreds and units digits."

The difference between any two digits cannot be more than 9-0 = 9. So the tens digit can be 3 at most.
But if the difference between the other two digits is 9, their subtraction will give us something around 900. We need something around 300 so the tens digit must be 1 and the difference between the other two digits must be 3.

So the first such number you can have is 310. If you subtract 013 out of it, you get 297 - Correct.
Next you can have is 411. If you subtract 114 out of it, you will get 297 - Correct.
Next you can have is 512. If you subtract 215 out of it, you will get 297 - Correct.
and so on goes the pattern till you have 916.

So in all, you have 7 numbers.

Answer (C)
_________________

Karishma
Veritas Prep | GMAT Instructor
My Blog

Get started with Veritas Prep GMAT On Demand for $199

Veritas Prep Reviews

Re: A three-digit number is such that when its reverse is subtra   [#permalink] 25 May 2015, 22:06
    Similar topics Author Replies Last post
Similar
Topics:
13 Experts publish their posts in the topic If a two-digit positive integer has its digits reversed, the Walkabout 6 27 Dec 2012, 07:29
5 Experts publish their posts in the topic If n is a three-digit prime number and j is an integer Smita04 10 03 Apr 2012, 18:48
What is the greatest number of three-digit integers that dancinggeometry 7 15 Sep 2008, 03:14
14 Experts publish their posts in the topic If a two-digit positive integer has its digits reversed, the salr15 7 14 Apr 2007, 16:54
The numbers x and y are three-digit positive integers, and x TOUGH GUY 5 12 May 2006, 10:55
Display posts from previous: Sort by

A three-digit number is such that when its reverse is subtra

  Question banks Downloads My Bookmarks Reviews Important topics  


GMAT Club MBA Forum Home| About| Privacy Policy| 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®.