Author 
Message 
TAGS:

Hide Tags

Director
Status: Finally Done. Admitted in Kellogg for 2015 intake
Joined: 25 Jun 2011
Posts: 505
Location: United Kingdom
Concentration: International Business, Strategy
GPA: 2.9
WE: Information Technology (Consulting)

For any four digit number, abcd, *abcd*=3^a*5^b*7^c*11^d
[#permalink]
Show Tags
Updated on: 13 Feb 2012, 04:28
Question Stats:
67% (02:06) correct 33% (02:30) wrong based on 567 sessions
HideShow timer Statistics
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.
Official Answer and Stats are available only to registered users. Register/ Login.
_________________
Best Regards, E.
MGMAT 1 > 530 MGMAT 2> 640 MGMAT 3 > 610 GMAT ==> 730
Originally posted by enigma123 on 24 Jan 2012, 17:12.
Last edited by Bunuel on 13 Feb 2012, 04:28, edited 2 times in total.
OA added




Math Expert
Joined: 02 Sep 2009
Posts: 49533

Re: *abcd*
[#permalink]
Show Tags
24 Jan 2012, 17:27
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 \(m\): \(nm=200\). Answer: B. Or represent four digits integer \(rstu\) as \(1000r+100s+10t+u\) and four digit integer \(r(s+2)tu\) as \(1000r+100(s+2)+10t+u\) > \(nm=(1000r+100(s+2)+10t+u)1000r+100s+10t+u=200\). Answer: B.
_________________
New to the Math Forum? Please read this: Ultimate GMAT Quantitative Megathread  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? Extrahard Quant Tests with Brilliant Analytics




Director
Status: Finally Done. Admitted in Kellogg for 2015 intake
Joined: 25 Jun 2011
Posts: 505
Location: United Kingdom
Concentration: International Business, Strategy
GPA: 2.9
WE: Information Technology (Consulting)

Re: *abcd*
[#permalink]
Show Tags
24 Jan 2012, 17:31
Sorry buddy  apologies if I am missing something. But how did you get four digits of m as rstu;
_________________
Best Regards, E.
MGMAT 1 > 530 MGMAT 2> 640 MGMAT 3 > 610 GMAT ==> 730



Math Expert
Joined: 02 Sep 2009
Posts: 49533

Re: *abcd*
[#permalink]
Show Tags
24 Jan 2012, 17:37



Director
Status: Finally Done. Admitted in Kellogg for 2015 intake
Joined: 25 Jun 2011
Posts: 505
Location: United Kingdom
Concentration: International Business, Strategy
GPA: 2.9
WE: Information Technology (Consulting)

Re: *abcd*
[#permalink]
Show Tags
24 Jan 2012, 17:42
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



Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
Posts: 8301
Location: Pune, India

Re: For any four digit number, abcd, *abcd*=3^a*5^b*7^c*11^d
[#permalink]
Show Tags
25 Jan 2012, 04:28
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
Learn more about how Veritas Prep can help you achieve a great GMAT score by checking out their GMAT Prep Options >
GMAT selfstudy has never been more personalized or more fun. Try ORION Free!



Intern
Joined: 12 Jul 2015
Posts: 25
Location: United States
Concentration: Strategy, General Management
WE: General Management (Pharmaceuticals and Biotech)

For any four digit number, abcd, *abcd*=3^a*5^b*7^c*11^d
[#permalink]
Show Tags
14 Dec 2015, 08:33
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* (251) = *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



Senior Manager
Joined: 07 Sep 2014
Posts: 395
Concentration: Finance, Marketing

Re: For any four digit number, abcd, *abcd*=3^a*5^b*7^c*11^d
[#permalink]
Show Tags
02 Sep 2017, 01:08
Bunuel wrote: 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 \(m\): \(nm=200\). Answer: B. Or represent four digits integer \(rstu\) as \(1000r+100s+10t+u\) and four digit integer \(r(s+2)tu\) as \(1000r+100(s+2)+10t+u\) > \(nm=(1000r+100(s+2)+10t+u)1000r+100s+10t+u=200\). Answer: B. nm = 24m why 200 is not divisible by 24. What am i missing



Math Expert
Joined: 02 Sep 2009
Posts: 49533

Re: For any four digit number, abcd, *abcd*=3^a*5^b*7^c*11^d
[#permalink]
Show Tags
02 Sep 2017, 03:16
abrakadabra21 wrote: Bunuel wrote: 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 \(m\): \(nm=200\). Answer: B. Or represent four digits integer \(rstu\) as \(1000r+100s+10t+u\) and four digit integer \(r(s+2)tu\) as \(1000r+100(s+2)+10t+u\) > \(nm=(1000r+100(s+2)+10t+u)1000r+100s+10t+u=200\). Answer: B. nm = 24m why 200 is not divisible by 24. What am i missing How did you get that n  m = 24? We are given that *n* = (25)(*m*), not that n = 25m. Notice that both n and m are functions (*n* and *m*, not n and m).
_________________
New to the Math Forum? Please read this: Ultimate GMAT Quantitative Megathread  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? Extrahard Quant Tests with Brilliant Analytics



Intern
Joined: 26 Dec 2017
Posts: 21
Location: India
Concentration: Technology, Marketing
WE: General Management (Internet and New Media)

Re: For any four digit number, abcd, *abcd*=3^a*5^b*7^c*11^d
[#permalink]
Show Tags
05 Sep 2018, 08:54
This is a good question as it is tricky with many variables




Re: For any four digit number, abcd, *abcd*=3^a*5^b*7^c*11^d &nbs
[#permalink]
05 Sep 2018, 08:54






