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For any four digit number, abcd, *abcd*=3^a*5^b*7^c*11^d [#permalink]
24 Jan 2012, 16:12
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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.
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 \(1000r+100(s+2)+10t+u\) --> \(n-m=(1000r+100(s+2)+10t+u)-1000r+100s+10t+u=200\).
Re: For any four digit number, abcd, *abcd*=3^a*5^b*7^c*11^d [#permalink]
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
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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Re: For any four digit number, abcd, *abcd*=3^a*5^b*7^c*11^d [#permalink]
05 Apr 2015, 21:18
Hello from the GMAT Club BumpBot!
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For any four digit number, abcd, *abcd*= (3a)(5b)(7c)(11d). What is.. [#permalink]
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*)?
Re: For any four digit number, abcd, *abcd*=3^a*5^b*7^c*11^d [#permalink]
13 Dec 2015, 12:59
Expert's post
adityayagnik wrote:
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
Merging similar topics. Please refer to the solutions above. _________________
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
gmatclubot
For any four digit number, abcd, *abcd*=3^a*5^b*7^c*11^d
[#permalink]
14 Dec 2015, 07:33
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