What we see: a Data Sufficiency yes or no question. The average bill was $48 and each customer tipped either 15% or 20% of their own bill. Was the average tip more than $8?
Step 1. Turn $8 into a percent of the bills.
What we see: $8 per customer against an average bill of $48.
What it means: with \(n\) customers, total bills are \(48n\). The average tip is more than $8 when total tips are more than \(8n\), which is \(\tfrac{8}{48} = 16\tfrac{2}{3}\%\) of total bills.
What we do and why: now the question is only about percents: were total tips more than \(16\tfrac{2}{3}\%\) of total bills?
Step 2. Statement 1.
What we see: most customers left a 20% tip.
What it means: the overall tip percent is weighted by the size of each bill, not by the number of people. Test two cases with 3 customers and an average bill of $48.
Case yes: all three bills are $48, two tip 20% ($9.60 each), one tips 15% ($7.20). Average tip $8.80.
Case no: two $12 bills tip 20% ($2.40 each), one $120 bill tips 15% ($18). The bills still average $48, but the tips average \(\tfrac{22.80}{3} = \$7.60\).
What we do and why: yes in one case, no in the other, so statement 1 is not sufficient.
Step 3. Statement 2.
What we see: tips were more than 16% of the total amount paid.
What it means: the amount paid is the bills plus the tips. Call total tips \(T\) and total bills \(B = 48n\). Then \(T > 0.16(B + T)\), so \(0.84T > 0.16B\) and \(T > \tfrac{0.16}{0.84}B \approx 0.19B\). That is about \(0.19 \times 48 \approx \$9.14\) per customer, more than $8.
What we do and why: always yes, so statement 2 is sufficient.
The trap: reading "total amount paid" as the bills alone. Then tips are more than 16% of $48, only $7.68 per customer, which does not settle the $8 question, and you land on E. The amount paid includes the tips, and that makes the tips a bigger share of the bills.
Faster way: if tips are 16% of bill plus tip, they are \(\tfrac{16}{84}\), about 19%, of the bill. 19% of $48 is about $9, clearly over $8.
Takeaway: Always ask what a percent is "of." A percent of a total that includes the tip is a larger percent of the bill alone. And "most people" does not control an average when the amounts differ.
Answer: B
