What we see: a Data Sufficiency question that asks for one value. The population doubles every week, so the only thing we are missing is how big the population is today.
Step 1. Decide what we need before reading the statements.
What we see: "doubles every week" and the goal "first exceed 1,000,000."
What it means: if today's population is \(P\), after \(n\) weeks it is \(P \cdot 2^n\). The growth rule is fixed, so the only unknown is \(P\).
What we do and why: any statement that tells us today's population is enough. We check the math once to be sure.
Step 2. Statement 1.
What we see: the population now is 65,536.
What it means: \(65{,}536 = 2^{16}\). After \(n\) weeks it is \(2^{16+n}\). \(2^{19} = 524{,}288\) is still under 1,000,000, and \(2^{20} = 1{,}048{,}576\) is over it. So it first exceeds 1,000,000 in 4 weeks.
What we do and why: one exact number of weeks, so statement 1 is sufficient.
Step 3. Statement 2.
What we see: fifteen weeks ago the population was 2.
What it means: 15 doublings from 2 gives \(2 \cdot 2^{15} = 2^{16} = 65{,}536\) today, the same number statement 1 gave.
What we do and why: it tells us today's population, so statement 2 is sufficient on its own too.
The trap: C. It feels like a growth question needs a starting value and a time, so students combine. But statement 2 already holds both: a value and how long ago it was.
Faster way: you never need to find the 4. Each statement fixes the population at a known moment, and a known value plus a fixed doubling rule always gives one answer.
Takeaway: Before reading the statements, name the one fact that would settle the question. Here, with a fixed growth rule, any statement that gives the population at a known time is enough.
Answer: D
