This is a question I get asked often. While the quality of your writing is considered over the quantity, this is my opinion on how long/how many words should be in an essay or a writing piece for a selective school exam or scholarship test.
NSW Selective Schools High School Placement Test: The test gives you 20 minutes of writing time, I would write approximately 250 words give or take. I’d focus on the same things as per the Victorian Selective High School Entrance Exam.
Victorian Selective High School Entrance Exam (Melbourne High, MacRob, Suzanne Cory and Nossal): The exam gives you 15 minutes of writing time, I would write approximately 250 words in that time frame. Key things I’d focus on are structure, showing as opposed to telling and linking it to the question.
Usually I would write 4-5 paragraphs and within each paragraph, around 4 sentences.
The content of your writing matters most over quantity.