GMAT Question of the Day - Daily to your Mailbox; hard ones only

 It is currently 25 May 2019, 00:11 ### 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. ### Request Expert Reply # For any four digit number, abcd, *abcd*=3^a*5^b*7^c*11^d

 new topic post reply Question banks Downloads My Bookmarks Reviews Important topics
Author Message
TAGS:

### Hide Tags

Senior Manager  Status: Finally Done. Admitted in Kellogg for 2015 intake
Joined: 25 Jun 2011
Posts: 465
Location: United Kingdom
Concentration: International Business, Strategy
GMAT 1: 730 Q49 V45 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

6
43 00:00

Difficulty:   55% (hard)

Question Stats: 67% (02:07) correct 33% (02:31) wrong based on 455 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.

_________________
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
##### Most Helpful Expert Reply
Math Expert V
Joined: 02 Sep 2009
Posts: 55271
Re: *abcd*  [#permalink]

### Show Tags

13
18
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.
_________________
##### General Discussion
Senior Manager  Status: Finally Done. Admitted in Kellogg for 2015 intake
Joined: 25 Jun 2011
Posts: 465
Location: United Kingdom
Concentration: International Business, Strategy
GMAT 1: 730 Q49 V45 GPA: 2.9
WE: Information Technology (Consulting)
Re: *abcd*  [#permalink]

### Show Tags

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
Math Expert V
Joined: 02 Sep 2009
Posts: 55271
Re: *abcd*  [#permalink]

### Show Tags

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.
_________________
Senior Manager  Status: Finally Done. Admitted in Kellogg for 2015 intake
Joined: 25 Jun 2011
Posts: 465
Location: United Kingdom
Concentration: International Business, Strategy
GMAT 1: 730 Q49 V45 GPA: 2.9
WE: Information Technology (Consulting)
Re: *abcd*  [#permalink]

### Show Tags

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 D
Joined: 16 Oct 2010
Posts: 9239
Location: Pune, India
Re: For any four digit number, abcd, *abcd*=3^a*5^b*7^c*11^d  [#permalink]

### Show Tags

7
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 >
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

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
Senior Manager  S
Joined: 07 Sep 2014
Posts: 345
Concentration: Finance, Marketing
Re: For any four digit number, abcd, *abcd*=3^a*5^b*7^c*11^d  [#permalink]

### Show Tags

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 $$m$$: $$n-m=200$$.

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.

n-m = 24m
why 200 is not divisible by 24. What am i missing
Math Expert V
Joined: 02 Sep 2009
Posts: 55271
Re: For any four digit number, abcd, *abcd*=3^a*5^b*7^c*11^d  [#permalink]

### Show Tags

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 $$m$$: $$n-m=200$$.

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.

n-m = 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).
_________________
Intern  B
Joined: 26 Dec 2017
Posts: 44
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

This is a good question as it is tricky with many variables
Senior Manager  G
Status: Gathering chakra
Joined: 05 Feb 2018
Posts: 257
Re: For any four digit number, abcd, *abcd*=3^a*5^b*7^c*11^d  [#permalink]

### Show Tags

+1 for plugging in... once we get that the 5s are the hundreds place, just make every variable 0 so each place value is now 1.
So, we get n-m = 1(1+2)11 - 1111 = 200
Intern  B
Joined: 26 Mar 2018
Posts: 6
Re: For any four digit number, abcd, *abcd*=3^a*5^b*7^c*11^d  [#permalink]

### Show Tags

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.

n=25m
n-m=25m=m=24m= 8 * 3m
ie., m is a multiple of 8
2000 and 200 are multiples of 8
Now,
2000=250/3=(25*10)/3=(5^3)*2*(3^-1)
But m is not a factor of 2 as defined in the question.
200=25/3=(5^2)*(3^-1)
Therefore,
answer is B Re: For any four digit number, abcd, *abcd*=3^a*5^b*7^c*11^d   [#permalink] 23 Mar 2019, 09:22
Display posts from previous: Sort by

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

 new topic post reply Question banks Downloads My Bookmarks Reviews Important topics Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne 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®.

#### MBA Resources  