What we see: a Data Sufficiency sequence question. Each bid is 100 dollars more than the one before. We need the last bid.
Step 1. Write any bid as a formula.
What we see: the bids go up by the same 100 each time.
What it means: if the first bid is \(F\), bid number \(k\) is \(F + 100(k - 1)\). If there were \(n\) bids, the last bid is \(F + 100(n - 1)\).
What we do and why: two unknowns, the first bid \(F\) and how many bids there were, \(n\). We need both.
Step 2. Statement 1 alone.
What we see: the first bid was 450 dollars.
What it means: we know \(F\), but not how many bids followed. With 3 bids the last is 650; with 10 bids it is 1,350.
What we do and why: not sufficient.
Step 3. Statement 2 alone.
What we see: the fourth bid was 300 dollars less than the last bid.
What it means: each step adds 100, so 300 is three steps. The last bid is three bids after the fourth, so it is the seventh bid, and \(n = 7\). But we still do not know where the bids started.
What we do and why: not sufficient.
Step 4. Both statements together.
What we see: \(F = 450\) and \(n = 7\).
What it means: the last bid is \(450 + 100 \times 6 = 1{,}050\) dollars. (Check: the bids are 450, 550, 650, 750, 850, 950, 1,050, and 1,050 minus the fourth bid, 750, is 300.)
What we do and why: one value. Sufficient.
The trap: (B). Statement 2 has a dollar amount, so it feels like it fixes a price. It only fixes how many bids there were; without the starting bid, the last bid can be anything.
Faster way: a sequence that grows by the same amount each time needs two facts: where it starts and how many steps it takes. Statement 1 gives the start, Statement 2 gives the count.
Takeaway: in an even-step sequence, a gap between two terms divided by the step size tells you how many places apart they are.
Answer: C
