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

Question

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  3600.

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

blink005 · Answer

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.

MisterQ · Answer

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 !

preetimishra · Answer

ok.. ya got it. thanks

dumb me

kostyan5 · Answer

Agreed. 3600 is correct and so is the explanation.

pacifist85 · Answer

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.

OptimusPrepJanielle · Answer

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 -- Optimus Prep's GMAT On Demand course for only $299 covers all verbal and quant. concepts in detail. Visit the following link to get your 7 days free trial account: https://www.optimus-prep.com/gmat-on-demand-course

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