Great question for backsolving!
To get the smallest possible population in 1 district, we want the biggest possible populations in the other 10. We know that the total number of voters is 132000.
Let's look at the choices:
a) 10,700
b) 10,800
c) 10,900
d) 11,000
e) 11,100
When we backsolve, we usually start with either (b) or (d). (d) is a much easier number to work with, so let's start there.
Assuming (d) is correct, the smallest district has 11000 voters. The maximum size of every other district is 10% more than that, or 11000 + 1100 = 12,100.
So, we have 10 districts * 12,100 = 121,000 + 1 district of 11000 = 132000 people! 132000 is exactly what we wanted to get, so (d) is correct.
If we ended up with fewer than 132000, we'd know we needed a bigger number and that (e) was correct. If we ended up with more than 132000, we'd know that we neededa smaller number and we'd try (b). Using the same reasoning (i.e. too small, just right or too big), after our 2nd try we'd definitely know which answer is correct.
