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The question is asking about the next hop to host 10.0.1.15, which is the broadcast of 10.0.1.0/28.

I disagree with the explanation and it goes on to say "this is the only correct answer".

Why wouldn't 10.0.1.0/24 via 192.168.0.4 work?

I believe this question needs to be reviewed and the explanation updated/corrected.

Thanks,
James

Yes, 10.0.1.15 is the broadcast address for 10.0.1.0/28. But for this question, that doesn’t change the routing decision. Routers don’t say, "This is a broadcast address, let me ignore this route”. They do a plain longest-prefix match on the destination IP. The router chooses 10.0.1.0/28 via 192.168.0.7 because /28 is more specific than /24.

Whether the final router treats 10.0.1.15 as a broadcast is a separate behavior at the edge, not part of the route lookup on this router. Though in practice, this traffic would likely fail since it's destined to a broadcast address.