7segmentdisplay - How can I make a 10 minute and 15 minute buzzer timer?

Basically, I have a big project going on in my campus which we were told to make digital counter. So when the timer counts reach at 10 minutes (by this case, the timer counts is shown by 7-segment display), it will produce alarm sound or buzzer sound, and when it continues and reach to 15 minutes, exactly doing the same by how the timer goes to 10 minutes. Any ideas guys on how to make the circuit? I'm kinda stuck here. (We aren't allowed using an IC NE555, but we are told to use 7-segment display, logic gates IC like IC 7408, any basic IC. And I'm on Digital Electronics course, I'm still learning about basic logic gates, boolean algebra, XOR and XNOR gates, multiplexer and duplexer. My reference book is Digital Electronics, a practical approach with VHDL by William Keiltz)