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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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Difficulty:

55% (hard)

Question Stats:

64% (02:39) correct
36% (01:56) wrong based on 193 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

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.

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

Challenging Digits Q [#permalink]
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*)?

Re: Challenging Digits Q [#permalink]
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. _________________

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!

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).

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