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# Each student at a certain business school is assigned a 4-digit studen

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Math Expert
Joined: 02 Sep 2009
Posts: 58311
Each student at a certain business school is assigned a 4-digit studen  [#permalink]

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29 Feb 2016, 10:51
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Difficulty:

15% (low)

Question Stats:

85% (01:10) correct 15% (02:11) wrong based on 155 sessions

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Each student at a certain business school is assigned a 4-digit student identification number. The first digit of the identification number cannot be zero, and the last digit of the identification number must be prime. How many different student identification numbers can the school create?

A. 9,000
B. 3,600
C. 2,700
D. 2,592
E. 1,944

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Joined: 02 Aug 2009
Posts: 7954
Re: Each student at a certain business school is assigned a 4-digit studen  [#permalink]

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29 Feb 2016, 20:23
Bunuel wrote:
Each student at a certain business school is assigned a 4-digit student identification number. The first digit of the identification number cannot be zero, and the last digit of the identification number must be prime. How many different student identification numbers can the school create?

A. 9,000
B. 3,600
C. 2,700
D. 2,592
E. 1,944

Hi,
these are simple Combinations problems..
But the most important point here is to reread if the combination is of different digits or the same digit can be repeated..

Here, there is no restriction..
Let the number be ABCD..
1) A can be any of the 10 digits, 0-9, except 0, so 9 ways..
2) B and C can be any of the 10 digits, so 10 ways each..
3) D is a prime number, so 2,3,5,7 fit in--- 4 ways..

Total ways= 9*10*10*4=3600
B

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Each student at a certain business school is assigned a 4-digit studen  [#permalink]

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Updated on: 03 Mar 2016, 03:08
Bunuel wrote:
Each student at a certain business school is assigned a 4-digit student identification number. The first digit of the identification number cannot be zero, and the last digit of the identification number must be prime. How many different student identification numbers can the school create?

A. 9,000
B. 3,600
C. 2,700
D. 2,592
E. 1,944

The identification number is of the form _ _ _ _

1. First digit cannot be 0
2. Middle digits can be anything
3. Last digit has to be prime - 2, 3, 5, 7

We can have the following number of possibilities for each space
__ __ __ __
9 10 10 4
Total cases = 3600
Option B

Originally posted by TeamGMATIFY on 03 Mar 2016, 02:27.
Last edited by TeamGMATIFY on 03 Mar 2016, 03:08, edited 1 time in total.
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Joined: 25 Dec 2012
Posts: 116
Re: Each student at a certain business school is assigned a 4-digit studen  [#permalink]

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03 Mar 2016, 02:56
Bunuel wrote:
Each student at a certain business school is assigned a 4-digit student identification number. The first digit of the identification number cannot be zero, and the last digit of the identification number must be prime. How many different student identification numbers can the school create?

A. 9,000
B. 3,600
C. 2,700
D. 2,592
E. 1,944

__ __ __ __
9 10 10 4

9*10*10*4 = 3600.

Just for understanding, If the same question mentioned as no repetition allowed, then it would be

Always start with the most restrictive clause, which number should end with a prime - 4 options are available.
__ __ __ __
4

The next restrictive clause is the number should not start with a zero. Already one number has been placed in the unit position and now we cant include zero to. So we have remaining 8 numbers to put in first place.

__ __ __ __
8 4

Remaining two positions has not restrictions. Hence we have 8 numbers (including zero) for one position and 7 numbers for the other.

__ __ __ __
8 8 7 4

= 8*8*7*4
Senior Manager
Joined: 15 Sep 2011
Posts: 310
Location: United States
WE: Corporate Finance (Manufacturing)
Re: Each student at a certain business school is assigned a 4-digit studen  [#permalink]

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03 Mar 2016, 18:46
Using the slot method, there are four choices so four slots.

The first restriction is that the number must not begin with zero, thus 9 choices.
The follow two slots, or digits, do not have restrictions, thus 10 choices each.
The last slot must be a prime number, thus four choices (2,3,5, and 7).

Therefore,
$$9 * 10 * 10 * 4 = 3600$$
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Re: Each student at a certain business school is assigned a 4-digit studen  [#permalink]

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19 Mar 2018, 16:22
Bunuel wrote:
Each student at a certain business school is assigned a 4-digit student identification number. The first digit of the identification number cannot be zero, and the last digit of the identification number must be prime. How many different student identification numbers can the school create?

A. 9,000
B. 3,600
C. 2,700
D. 2,592
E. 1,944

There are 9 possible options for the first digit, 10 for the second digit, 10 for the third digit, and 4 for the last digit, since the prime digits are 2, 3, 5, and 7.

Thus, the number of codes that can be created is 9 x 10 x 10 x 4 = 3600.

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Re: Each student at a certain business school is assigned a 4-digit studen   [#permalink] 19 Mar 2018, 16:22
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