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

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preetimishra
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Each student at a certain business school is assigned a 4-digit studen [#permalink] New post   23 Oct 2011, 10:15
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 must be a prime number. How many student identification numbers can be created?

The OA is
Show Spoiler
3600.


Explanation given is:
Show Spoiler
Since first digit cannot be 0, therefore, it can be any of the remaining 9 digits.
there is no restriction on the second and third digits, so they can anything from 0-9, hence 10 choices.
and the last digit can be any from 2,3,5,7, hence 4 choices.
Therefore the number of identification numbers that can be created = 9X10X10X4 = 3600.


My doubt:
Show Spoiler
Since it is an IDENTIFICATION number. Shouldn't it be UNIQUE???
So in my opinion the ans should be: 9X10X9X4 = 2880.




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Re: Each student at a certain business school is assigned a 4-digit studen [#permalink] New post   23 Oct 2011, 10:33
No, the explanation is correct

e.g.
1002
1003
1115
6667
7777
7775

Repetition of a digit doesn't mean that entire 4-digit id no is not unique.
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MisterQ
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Re: Each student at a certain business school is assigned a 4-digit studen [#permalink] New post   23 Oct 2011, 10:39
Actually, I don't really get your point. Yes the ID number must be unique and yes the answer is 3600...

When we say 9x10x10x4, it gives the following unique combinations :

first number can be anything from 1 to 9
second number can be anything from 0 to 9
third number can be anything from 0 to 9
Last number must be 2,3,5 or 7

Saying that the third case must be "9" and so the answer is 9x10x9x4 actually means that the second number must be different than the third number in order to have a unique 4 digits number... it doesn't make sense :

For example : 1552, 1553 are unique (eventhough the second and the third number are identical, the four digits number is unique...)

Hope you get it... and good luck !
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preetimishra
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Re: Each student at a certain business school is assigned a 4-digit studen [#permalink] New post   23 Oct 2011, 11:31
ok.. ya got it.
thanks :)

dumb me :(
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Re: Each student at a certain business school is assigned a 4-digit studen [#permalink] New post   01 Nov 2011, 16:11
Agreed. 3600 is correct and so is the explanation.
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Re: Each student at a certain business school is assigned a 4-digit studen [#permalink] New post   24 Feb 2015, 14:21
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I used the slot method for this one, starting by drwing the 4 possible slots:

__ __ __ __

Starting with writing down all the possible choices, these are: 0,1,2,3,4,5,6,7,8,9

For the first slot, there are 9 choices (all minus 0)

9 __ __ __

For the last slot, there are 4 options (2,3,5,7)

9 __ __ 4

For the middle slots, all of the numbers can be used:

9 10 10 4

So, we are multiplying all the possible choices together and get 3600.
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Re: Each student at a certain business school is assigned a 4-digit studen [#permalink] New post   28 Feb 2015, 08:00
Expert Reply
preetimishra 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 must be a prime number. How many student identification numbers can be created?

The OA is
Show Spoiler
3600.


Explanation given is:
Show Spoiler
Since first digit cannot be 0, therefore, it can be any of the remaining 9 digits.
there is no restriction on the second and third digits, so they can anything from 0-9, hence 10 choices.
and the last digit can be any from 2,3,5,7, hence 4 choices.
Therefore the number of identification numbers that can be created = 9X10X10X4 = 3600.


My doubt:
Show Spoiler
Since it is an IDENTIFICATION number. Shouldn't it be UNIQUE???
So in my opinion the ans should be: 9X10X9X4 = 2880.


We are told that it is a 4 digit number.
First digit cannot be 0 => It can be any of 1-9. So 9 ways of selecting first digit.
Second digit can be any of 0-9. So 10 ways of selecting second digit.
Third digit can be any of 0-9. So 10 ways of selecting third digit. (We're NOT told that the number cannot be repeated)
Fourth digit can be only prime number. So fourth digit can be 2,3,5,7. So 4 ways of selecting fourth digit.
Total number of ways = 9 * 10 * 10 * 4
= 3600

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Re: Each student at a certain business school is assigned a 4-digit studen [#permalink]
28 Feb 2015, 08:00
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