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# Algebra : Asteriscks Away

Author Message
Intern
Joined: 15 Oct 2017
Posts: 28
Schools: Northeastern '20

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01 Jan 2018, 06:41
00:00

Difficulty:

(N/A)

Question Stats:

0% (00:00) correct 0% (00:00) wrong based on 0 sessions

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Question:
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

According to the question, the “star function” is only applicable to four digit numbers. The function takes the thousands, hundreds, tens and units digits of a four-digit number and applies them as exponents for the bases 3, 5, 7 and 11, respectively, yielding a value which is the product of these exponential expressions.

Let’s illustrate with a few examples:
*2234* = (32)(52)(73)(114)
*3487* = (33)(54)(78)(117)

According to the question, the four-digit number m must have the digits of rstu, since *m* = (3r)(5s)(7t)(11u).

If *n* = (25)(*m*)
*n* = (52)(3r)(5s)(7t)(11u)
*n* = (3r)(5s+2)(7t)(11u)

n is also a four digit number, so we can use the *n* value to identify the digits of n:

thousands = r, hundreds = s + 2, tens = t, units = u.

All of the digits of n and m are identical except for the hundreds digits. The hundreds digits of n is two more than that of m, so n – m = 200.

I did not get it ...

--== Message from the GMAT Club Team ==--

THERE IS LIKELY A BETTER DISCUSSION OF THIS EXACT QUESTION.
This discussion does not meet community quality standards. It has been retired.

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Math Expert
Joined: 02 Sep 2009
Posts: 52285
Re: Algebra : Asteriscks Away  [#permalink]

### Show Tags

01 Jan 2018, 09:16
thegame12 wrote:
Question:
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

According to the question, the “star function” is only applicable to four digit numbers. The function takes the thousands, hundreds, tens and units digits of a four-digit number and applies them as exponents for the bases 3, 5, 7 and 11, respectively, yielding a value which is the product of these exponential expressions.

Let’s illustrate with a few examples:
*2234* = (32)(52)(73)(114)
*3487* = (33)(54)(78)(117)

According to the question, the four-digit number m must have the digits of rstu, since *m* = (3r)(5s)(7t)(11u).

If *n* = (25)(*m*)
*n* = (52)(3r)(5s)(7t)(11u)
*n* = (3r)(5s+2)(7t)(11u)

n is also a four digit number, so we can use the *n* value to identify the digits of n:

thousands = r, hundreds = s + 2, tens = t, units = u.

All of the digits of n and m are identical except for the hundreds digits. The hundreds digits of n is two more than that of m, so n – m = 200.

I did not get it ...

Discussed here: for-any-four-digit-number-abcd-abcd-3-a-5-b-7-c-11-d-126522.html

--== Message from the GMAT Club Team ==--

THERE IS LIKELY A BETTER DISCUSSION OF THIS EXACT QUESTION.
This discussion does not meet community quality standards. It has been retired.

If you would like to discuss this question please re-post it in the respective forum. Thank you!

To review the GMAT Club's Forums Posting Guidelines, please follow these links: Quantitative | Verbal Please note - we may remove posts that do not follow our posting guidelines. Thank you.

_________________
Re: Algebra : Asteriscks Away &nbs [#permalink] 01 Jan 2018, 09:16
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