What we see: a Data Sufficiency question about population growth. The town had 10,000 people 8 years ago. People moved in, nobody left or died, and we must find how many babies were born in those 8 years.
Step 1. Write what makes up today's population.
What we see: only two things can add people: moving in and being born.
What it means: today's population \(= 10{,}000 + \text{movers} + \text{births}\). To find births we need either today's total and the movers, or a rule that gives births directly.
Step 2. Statement 1 alone.
What we see: 5,000 people moved in.
What it means: births \(= \text{today's population} - 15{,}000\). We do not know today's population.
What we do and why: any number of births fits. Not sufficient.
Step 3. Statement 2 alone.
What we see: from births alone, the population grew 5 percent every 2 years.
What it means: 5 percent of what? Of the population at that time, and that population includes the people who moved in. More movers means more births.
What we do and why: we do not know how many moved in, so we cannot find births. Not sufficient.
Step 4. Both statements together.
What we see: 5,000 movers, and births add 5 percent every 2 years.
What it means: the births still depend on when the 5,000 arrived. If they all came 8 years ago, they were in the population for all four 2-year periods and added to every round of births. If they all came last month, they added to none.
What we do and why: try two cases. All 5,000 at the start: births come from 15,000 people, \(15{,}000 \times (1.05^4 - 1) \approx 3{,}233\). All 5,000 at the end: births come from 10,000 people, \(10{,}000 \times (1.05^4 - 1) \approx 2{,}155\). Two different answers. Not sufficient.
The trap: picking C. With a start number, the movers and a growth rate, it looks like one formula. But the growth rate applies to a population that keeps changing as people arrive, and the arrival dates are never given.
Faster way: ask "does the growth rate apply to a number we know at every moment?" Here it does not, because the movers' timing is missing. That alone gives E.
Takeaway: a percent growth rate only gives a number when you know the exact base it grows from at each step. If people join along the way and you do not know when, the answer is not fixed.
Answer: E
