What we see: a Data Sufficiency remainder question. A box holds between \(50\) and \(60\) books. Exactly how many?
Step 1. Know what each statement lets us do.
What we see: each statement gives a remainder: "counted by three, one left over" means the number is \(1\) more than a multiple of \(3\).
What it means: we can list every number from \(50\) to \(60\) that fits. Sufficient means only one number is left.
What we do and why: listing is fast here because the range holds only about ten numbers.
Step 2. Statement 1 alone.
What we see: \(1\) more than a multiple of \(3\).
What it means: multiples of \(3\) in range are \(51, 54, 57\), so the box could hold \(52\), \(55\), or \(58\).
What we do and why: three possible counts. Not sufficient.
Step 3. Statement 2 alone.
What we see: \(1\) more than a multiple of \(6\).
What it means: multiples of \(6\) near the range are \(48, 54, 60\), so the counts \(49, 55, 61\) fit the remainder. Only \(55\) sits between \(50\) and \(60\).
What we do and why: one count, \(55\). Sufficient.
The trap: thinking the two statements say about the same thing and picking both together. Remainder \(1\) after dividing by \(6\) already gives remainder \(1\) after dividing by \(3\), because \(6\) is a multiple of \(3\). So Statement 2 is the stricter fact, and Statement 1 adds nothing to it.
Faster way: for Statement 2, find the one multiple of \(6\) in the range, \(54\), and add \(1\).
Takeaway: A remainder by a bigger number tells you more than the same remainder by one of its factors. In a small range, list the numbers that fit.
Answer: B
