What we see: a yes or no Data Sufficiency question. A statement is enough if it forces one answer, always yes or always no.
Step 1. Write the question as math.
What we see: a table takes 100 pounds, a chair takes 25 pounds.
What it means: with \(T\) tables and \(C\) chairs, the wood used is \(100T + 25C\). The question is: is \(100T + 25C > 20{,}000\)?
What we do and why: we do not need the exact amount, only whether it is above 20,000. So we look for a lowest possible value that is already above 20,000.
Step 2. Statement (1): \(T + C > 800\).
What we see: more than 800 pieces of furniture in total.
What it means: every piece uses at least 25 pounds, because the cheapest piece is a chair. So the wood is at least \(25(T + C)\).
What we do and why: \(25(T + C) > 25 \times 800 = 20{,}000\). Even if every piece were a chair, the total is over 20,000. Tables only add more. The answer is always yes, so statement (1) is enough.
Step 3. Statement (2): \(T > C\).
What we see: more tables than chairs, but no counts.
What it means: the shop could have made very few or very many pieces.
What we do and why: test two cases. 2 tables and 1 chair use \(200 + 25 = 225\) pounds: no. 300 tables and 100 chairs use \(30{,}000 + 2{,}500 = 32{,}500\) pounds: yes. Two different answers, so statement (2) is not enough.
The trap: picking "both together." Statement (2) feels useful because tables use more wood, but statement (1) already settles the question by itself, so (2) adds nothing.
Faster way: ask "what is the least wood this could be?" For statement (1), the least is all chairs: \(801 \times 25 = 20{,}025\), already over 20,000.
Takeaway: On a "greater than" question, find the smallest case the statement allows. If even the smallest case is over the line, the statement is enough.
Answer: A
