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

It is currently 24 Apr 2014, 18:48

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

For any four digit number, abcd, *abcd*=3^a*5^b*7^c*11^d

  Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:
1 KUDOS received
Director
Director
Status: Preparing for the 4th time -:(
Joined: 25 Jun 2011
Posts: 562
Location: United Kingdom
Concentration: International Business, Strategy
GMAT Date: 06-22-2012
GPA: 2.9
WE: Information Technology (Consulting)
Followers: 11

Kudos [?]: 129 [1] , given: 217

GMAT Tests User CAT Tests
For any four digit number, abcd, *abcd*=3^a*5^b*7^c*11^d [#permalink] New post 24 Jan 2012, 16:12
1
This post received
KUDOS
00:00
A
B
C
D
E

Difficulty:

  35% (medium)

Question Stats:

62% (02:43) correct 37% (01:52) wrong based on 69 sessions
For any four digit number, abcd, *abcd*= (3^a)(5^b)(7^c)(11^d). What is the value of (n – m) if m and n are four digit numbers for which *m* = (3^r)(5^s)(7^t)(11^u) and *n* = (25)(*m*)?

A. 2000
B. 200
C. 25
D. 20
E. 2

Guys - any idea how to solve this please? I am struggling and OA is not given either.
[Reveal] Spoiler: OA

_________________

Best Regards,
E.

MGMAT 1 --> 530
MGMAT 2--> 640
MGMAT 3 ---> 610 :-(


Last edited by Bunuel on 13 Feb 2012, 03:28, edited 2 times in total.
OA added
3 KUDOS received
Math Expert
User avatar
Joined: 02 Sep 2009
Posts: 17396
Followers: 2891

Kudos [?]: 18504 [3] , given: 2362

GMAT Tests User CAT Tests
Re: *abcd* [#permalink] New post 24 Jan 2012, 16:27
3
This post received
KUDOS
Expert's post
enigma123 wrote:
For any four digit number, abcd, *abcd*= (3^a)(5^b)(7^c)(11^d). What is the value of (n – m) if m and n are four digit numbers for which *m* = (3^r)(5^s)(7^t)(11^u) and *n* = (25)(*m*)?

A. 2000
B. 200
C. 25
D. 20
E. 2

Guys - any idea how to solve this please? I am struggling and OA is not given either.


Given for four digit number, abcd, *abcd*=3^a*5^b*7^c*11^d;

From above as *m*=3^r*5^s*7^t*11^u then four digits of m are rstu;

Next, *n*=25*\{*m*\}=5^2*(3^r*5^s*7^t*11^u)=3^r*5^{(s+2)}*7^t*11^u, hence four digits of n are r(s+2)tu, note that s+2 is hundreds digit of n;

You can notice that n has 2 more hundreds digits and other digits are the same, so n is 2 hundreds more than m: n-m=200.

Answer: B.

Or represent four digits integer rstu as 1000r+100s+10t+u and four digit integer r(s+2)tu as 1000r+100(s+2)+10t+u --> n-m=(1000r+100(s+2)+10t+u)-1000r+100s+10t+u=200.

Answer: B.
_________________

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

Director
Director
Status: Preparing for the 4th time -:(
Joined: 25 Jun 2011
Posts: 562
Location: United Kingdom
Concentration: International Business, Strategy
GMAT Date: 06-22-2012
GPA: 2.9
WE: Information Technology (Consulting)
Followers: 11

Kudos [?]: 129 [0], given: 217

GMAT Tests User CAT Tests
Re: *abcd* [#permalink] New post 24 Jan 2012, 16:31
Sorry buddy - apologies if I am missing something. But how did you get

four digits of m as r-s-t-u;
_________________

Best Regards,
E.

MGMAT 1 --> 530
MGMAT 2--> 640
MGMAT 3 ---> 610 :-(

Math Expert
User avatar
Joined: 02 Sep 2009
Posts: 17396
Followers: 2891

Kudos [?]: 18504 [0], given: 2362

GMAT Tests User CAT Tests
Re: *abcd* [#permalink] New post 24 Jan 2012, 16:37
Expert's post
enigma123 wrote:
Sorry buddy - apologies if I am missing something. But how did you get

four digits of m as r-s-t-u;


For four digit integer abcd some function, denoted by **, defined as *abcd*=3^a*5^b*7^c*11^d.

Now, as given that *m*=3^r*5^s*7^t*11^u then four digits of m are rstu, the same way as above: *rstu*=3^r*5^s*7^t*11^u

Hope it's clear.
_________________

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

Director
Director
Status: Preparing for the 4th time -:(
Joined: 25 Jun 2011
Posts: 562
Location: United Kingdom
Concentration: International Business, Strategy
GMAT Date: 06-22-2012
GPA: 2.9
WE: Information Technology (Consulting)
Followers: 11

Kudos [?]: 129 [0], given: 217

GMAT Tests User CAT Tests
Re: *abcd* [#permalink] New post 24 Jan 2012, 16:42
Ahhh - so four digits are r, s, t and u. And not r minus s minus t minus u. That's where I got confused.
_________________

Best Regards,
E.

MGMAT 1 --> 530
MGMAT 2--> 640
MGMAT 3 ---> 610 :-(

2 KUDOS received
Veritas Prep GMAT Instructor
User avatar
Joined: 16 Oct 2010
Posts: 4198
Location: Pune, India
Followers: 898

Kudos [?]: 3822 [2] , given: 148

Re: For any four digit number, abcd, *abcd*=3^a*5^b*7^c*11^d [#permalink] New post 25 Jan 2012, 03:28
2
This post received
KUDOS
Expert's post
enigma123 wrote:
For any four digit number, abcd, *abcd*= (3^a)(5^b)(7^c)(11^d). What is the value of (n – m) if m and n are four digit numbers for which *m* = (3^r)(5^s)(7^t)(11^u) and *n* = (25)(*m*)?

A. 2000
B. 200
C. 25
D. 20
E. 2

Guys - any idea how to solve this please? I am struggling and OA is not given either.


Also, if you find to difficult to grasp a question with many variables, try throwing in some values. It helps you handle the question.

abcd is a four digit number where a, b, c and d are the 4 digits.
*abcd*= (3^a)(5^b)(7^c)(11^d). The '**' act as an operator.

Given: *m* = (3^r)(5^s)(7^t)(11^u)
So m = rstu where r, s, t, and u are the 4 digits of m.
Say, r = 1 and s = 0, t = 0 and u = 0
m = 1000
Then *m* = 3

Now,
*n* = (25)(*m*) = 25(3) = (3^1)(5^2)(7^0)(11^0)
n = 1200

n - m = 1200 - 1000 = 200
_________________

Karishma
Veritas Prep | GMAT Instructor
My Blog

Save $100 on Veritas Prep GMAT Courses And Admissions Consulting
Enroll now. Pay later. Take advantage of Veritas Prep's flexible payment plan options.

Veritas Prep Reviews

Manager
Manager
Joined: 18 Oct 2011
Posts: 92
Location: United States
Concentration: Entrepreneurship, Marketing
GMAT Date: 01-30-2013
GPA: 3.3
Followers: 2

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

Challenging Digits Q [#permalink] New post 10 Jan 2013, 08:23
For any four digit number, abcd, *abcd*= (3^a)(5^b)(7^c)(11^d). What is the value of (n – m) if m and n are four digit
numbers for which *m* = (3^r)(5^s)(7^t)(11^u) and *n* = (25)(*m*)?

a. 2000
b. 200
c. 25
d. 20
e. 2
Math Expert
User avatar
Joined: 02 Sep 2009
Posts: 17396
Followers: 2891

Kudos [?]: 18504 [0], given: 2362

GMAT Tests User CAT Tests
Re: Challenging Digits Q [#permalink] New post 10 Jan 2013, 15:19
Expert's post
sambam wrote:
For any four digit number, abcd, *abcd*= (3^a)(5^b)(7^c)(11^d). What is the value of (n – m) if m and n are four digit
numbers for which *m* = (3^r)(5^s)(7^t)(11^u) and *n* = (25)(*m*)?

a. 2000
b. 200
c. 25
d. 20
e. 2


Merging similar topics. Please refer to the solutions above.

Also, please read carefully and follow: rules-for-posting-please-read-this-before-posting-133935.html Pay attention to the rule #3: the name of a topic (subject field) MUST be the first 40 characters (~the first two sentences) of the question.
_________________

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

VP
VP
User avatar
Joined: 09 Sep 2013
Posts: 1110
Followers: 121

Kudos [?]: 29 [0], given: 0

Premium Member
Re: For any four digit number, abcd, *abcd*=3^a*5^b*7^c*11^d [#permalink] New post 05 Mar 2014, 09:12
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

Re: For any four digit number, abcd, *abcd*=3^a*5^b*7^c*11^d   [#permalink] 05 Mar 2014, 09:12
    Similar topics Author Replies Last post
Similar
Topics:
This topic is locked, you cannot edit posts or make further replies. New 2 Experts publish their posts in the topic For any four digit number, abcd, *abcd*=3^a*5^b*7^c*11^d faifai0714 10 19 Mar 2007, 20:49
New posts 1 For any four digit number, abcd, *abcd*= beckee529 3 22 Sep 2007, 17:37
New posts What is the hundreds digit of the smallest four digit number yuefei 2 02 Nov 2007, 15:41
New posts How many four digit numbers ankitranjan 1 27 Oct 2010, 02:49
Popular new posts 8 Experts publish their posts in the topic For the four-digit number ABCD , where A, B, C, and D all fluke 14 15 May 2011, 14:01
Display posts from previous: Sort by

For any four digit number, abcd, *abcd*=3^a*5^b*7^c*11^d

  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®.