At a particular university, every student receives a unique 4-digit identification number. The first digit of this number cannot be zero, while the last digit must be a prime number. How many unique identification numbers can be generated by the university?

Answer Choices

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8,000

3,600

Correct

2,400

2,160

1,728

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Explanation

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Official Explanation

Official

Let's break this down step by step. We denote the number as ABCD. 1) The first digit A can be any digit from 1 to 9 (it cannot be zero), giving us 9 options. 2) The second digit B can be any digit from 0 to 9, providing 10 options. 3) The third digit C can also…

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Comments

TaeikFeb 28, 2024

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SamriddhiMar 16, 2025

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What this question tests

What it tests

Whether you can count arrangements and selections correctly — permutations vs. combinations.

Common trap

Overcounting: treating a selection as ordered when order does not matter, or forgetting to divide by duplicates.