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

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For any four digit number, abcd, *abcd*=3^a*5^b*7^c*11^d [#permalink] New post 24 Jan 2012, 16:12
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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

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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
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Re: *abcd* [#permalink] New post 24 Jan 2012, 16:27
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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.
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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;
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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.
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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.
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Re: For any four digit number, abcd, *abcd*=3^a*5^b*7^c*11^d [#permalink] New post 25 Jan 2012, 03:28
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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
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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
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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.
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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.


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