Problem Solving

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?

[source: Veritas free practice test for GMAT]

zooki 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?

[source: Veritas free practice test for GMAT]

Please find the below solution.

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1) Given that 1st number not equal to zero
2) last number should be a prime number
Solution
Out of 9 numbers, we need to select 1 ----> 9C1
Out of 10 numbers including zero , we need to select one ----> 10C1
Out of 10 numbers including zero , we need to select one ----> 10C1
Last digit Out of 4 prime numbers, we need to select one ----> 4C1

Total ---> 9c1*10c1*10c1*4C1
----> 3600 ways of creating a 4 digit identification number

Well I think the question is asking for identification numbers (which should be unique?).
your method gives the answer 3600. which includes e. g. {9557) twice.
i think only 9C1*10C1*8C1*4C1=2880 can give unique numbers= identification numbers.

Can someone please verify and explain.

what's the OA?


IMO 9 * 10 * 10 * 4 = 3600

@zookie

3600 IS correct. A number like 9557 IS a unique number which will NOT appear more than once. Also, u may wanna check ur method for finding the total number of digits with no repetition. If repetition of digits was not allowed then the answer would be 1864 and not 2880.

OA is 3600.

Make sense now. Thanks.