The number of 3-digit numbers, formed using the digits 2, 3, 4, 5 and 7, when the repetition of digits is not allowed, and which are not divisible by 3, is equal to ________

Total 3-digit numbers (no repetition): $$^5P_3=5\times4\times3=60$$

Now, for a number to be divisible by 3, the sum of its digits must be divisible by 3.

So, classifying digits by mod 3:

Mod 0: {3}

Mod 1: {4, 7}

Mod 2: {2, 5}

For sum ≡ 0 (mod 3), possible valid combination:

(0, 1, 2)

Number of ways of choosing 1 from each group:   $$1\times2\times2=4$$ ways (digit sets)

Each set can be arranged in: $$3!=6$$ ways

So total numbers divisible by 3:$$4\times6=24$$