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

It is currently 08 Feb 2016, 17:43
GMAT Club Tests

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:
4 KUDOS received
Director
Director
avatar
Status: Finally Done. Admitted in Kellogg for 2015 intake
Joined: 25 Jun 2011
Posts: 538
Location: United Kingdom
Concentration: International Business, Strategy
GMAT 1: 730 Q49 V40
GPA: 2.9
WE: Information Technology (Consulting)
Followers: 49

Kudos [?]: 1845 [4] , given: 217

For any four digit number, abcd, *abcd*=3^a*5^b*7^c*11^d [#permalink] New post 24 Jan 2012, 16:12
4
This post received
KUDOS
13
This post was
BOOKMARKED
00:00
A
B
C
D
E

Difficulty:

  55% (hard)

Question Stats:

64% (02:35) correct 36% (01:58) wrong based on 255 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
GMAT ==> 730


Last edited by Bunuel on 13 Feb 2012, 03:28, edited 2 times in total.
OA added
Expert Post
5 KUDOS received
Math Expert
User avatar
Joined: 02 Sep 2009
Posts: 31286
Followers: 5348

Kudos [?]: 62189 [5] , given: 9444

Re: *abcd* [#permalink] New post 24 Jan 2012, 16:27
5
This post received
KUDOS
Expert's post
7
This post was
BOOKMARKED
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 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

Director
Director
avatar
Status: Finally Done. Admitted in Kellogg for 2015 intake
Joined: 25 Jun 2011
Posts: 538
Location: United Kingdom
Concentration: International Business, Strategy
GMAT 1: 730 Q49 V40
GPA: 2.9
WE: Information Technology (Consulting)
Followers: 49

Kudos [?]: 1845 [0], given: 217

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
GMAT ==> 730

Expert Post
Math Expert
User avatar
Joined: 02 Sep 2009
Posts: 31286
Followers: 5348

Kudos [?]: 62189 [0], given: 9444

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 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

Director
Director
avatar
Status: Finally Done. Admitted in Kellogg for 2015 intake
Joined: 25 Jun 2011
Posts: 538
Location: United Kingdom
Concentration: International Business, Strategy
GMAT 1: 730 Q49 V40
GPA: 2.9
WE: Information Technology (Consulting)
Followers: 49

Kudos [?]: 1845 [0], given: 217

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
GMAT ==> 730

Expert Post
5 KUDOS received
Veritas Prep GMAT Instructor
User avatar
Joined: 16 Oct 2010
Posts: 6219
Location: Pune, India
Followers: 1676

Kudos [?]: 9599 [5] , given: 197

Re: For any four digit number, abcd, *abcd*=3^a*5^b*7^c*11^d [#permalink] New post 25 Jan 2012, 03:28
5
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

Get started with Veritas Prep GMAT On Demand for $199

Veritas Prep Reviews

GMAT Club Legend
GMAT Club Legend
User avatar
Joined: 09 Sep 2013
Posts: 8178
Followers: 416

Kudos [?]: 111 [0], given: 0

Top 10 in overall
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

GMAT Club Legend
GMAT Club Legend
User avatar
Joined: 09 Sep 2013
Posts: 8178
Followers: 416

Kudos [?]: 111 [0], given: 0

Top 10 in overall
Re: For any four digit number, abcd, *abcd*=3^a*5^b*7^c*11^d [#permalink] New post 05 Apr 2015, 21:18
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
Joined: 03 Oct 2012
Posts: 10
Concentration: Strategy, Finance
Followers: 0

Kudos [?]: 3 [0], given: 11

For any four digit number, abcd, *abcd*= (3a)(5b)(7c)(11d). What is.. [#permalink] New post 13 Dec 2015, 12:53
For any four digit number, abcd, *abcd*= (3a)(5b)(7c)(11d). What is the value of (n – m) if m and n are four-digit numbers for which *m* = (3r)(5s)(7t)(11u) and *n* = (25)(*m*)?

A. 2000
B. 200
C. 25
D. 20
E. 2
Expert Post
Math Expert
User avatar
Joined: 02 Sep 2009
Posts: 31286
Followers: 5348

Kudos [?]: 62189 [0], given: 9444

Re: For any four digit number, abcd, *abcd*=3^a*5^b*7^c*11^d [#permalink] New post 13 Dec 2015, 12:59
Expert's post
Intern
Intern
User avatar
Joined: 12 Jul 2015
Posts: 25
Followers: 3

Kudos [?]: 8 [0], given: 454

GMAT ToolKit User
For any four digit number, abcd, *abcd*=3^a*5^b*7^c*11^d [#permalink] New post 14 Dec 2015, 07:33
Hi Bunuel

Can we arrive at the solution by the following approach ?

Given: *m* = 3^r*5^s*7^t*11^u
*n* = 25 (*m*)

To Solve: n - m

Sol: Substituting for n ,
n - m = 25 *m* - *m*
= *m* (25-1)
= *m* (24)
we know that, 24 = 3*2^3 and *m* = 3^r*5^s*7^t*11^u , does not have 2 value which implies the answer should have 2^3 as a factor.

1. 2000 = 5^3*2^4 - ( Only 2^3 is possible. as 24 has only 2^3 and *m* is not a factor of 2)
2. 200 = 5^2*2^3 - Correct
3. 25 = 5^2
4. 20 = 5 *2^2
5. 2 = 2
For any four digit number, abcd, *abcd*=3^a*5^b*7^c*11^d   [#permalink] 14 Dec 2015, 07:33
    Similar topics Author Replies Last post
Similar
Topics:
For any four digit number, abcd, *abcd*= (3a)(5b)(7c)(11d). What is.. adityayagnik 0 13 Dec 2015, 12:53
6 Experts publish their posts in the topic If A,BCD is a four-digit positive integer such that A,BCD is equal to Bunuel 3 30 Aug 2015, 09:52
How many four digit numbers ankitranjan 1 27 Oct 2010, 02:49
7 Experts publish their posts in the topic How many four-digit odd numbers do not use any digit more than once? EnergySP 14 09 Jun 2009, 07:31
4 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
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| 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®.