A bank has 2 paper shedding machines, one large and one small, to shred sheets of secure waste paper, all...

Understanding the Question

We need to find: How many minutes would it take the small machine, working alone at its constant shredding rate, to shred n sheets of paper?

What we know:

• Two machines: one large, one small
• Large machine shreds 5 times as fast as the small machine
• Both work at constant rates
• All sheets are the same size

This asks for a specific value - an exact number of minutes. We need enough information to calculate that precise time.

Key Insight

When machines work together, their contributions are proportional to their speeds. Since the large machine works 5 times as fast, in any time period:

• Small machine does \(\frac{1}{6}\) of the total work
• Large machine does \(\frac{5}{6}\) of the total work

Think of it like two workers where one is 5 times faster - the faster worker will complete 5 parts while the slower completes 1 part.

Analyzing Statement 1

Statement 1: Working together at their individual constant rates, the machines could shred n sheets in 40 minutes.

Let's reason through this step by step:

When the machines work together for 40 minutes:

• They complete all n sheets
• The work is split in a \(5:1\) ratio (because of their speed ratio)
• Small machine's share: \(\frac{1}{6}\) of n sheets
• Large machine's share: \(\frac{5}{6}\) of n sheets

Since the small machine completes \(\frac{n}{6}\) sheets in 40 minutes, how long would it need for all n sheets?

If you complete \(\frac{1}{6}\) of a job in 40 minutes, you need 6 times as long for the whole job:
Time = \(6 \times 40 = 240\) minutes

We can determine the exact time: 240 minutes.

[STOP - Sufficient!] Statement 1 alone is sufficient.

This eliminates choices B, C, and E.

Analyzing Statement 2

Forget Statement 1 completely. Look only at Statement 2.

Statement 2: \(n = 1,200\)

This tells us the quantity of sheets, but nothing about the machines' speeds.

Think of it this way: If I tell you that you need to shred 1,200 sheets, can you tell me how long it will take? No - because you don't know how fast you can shred.

Without knowing:

• The small machine's shredding rate, OR
• Any time/rate information about either machine

We cannot determine how long it takes the small machine to shred 1,200 sheets.

Statement 2 alone is NOT sufficient.

This eliminates choices B and D.

The Answer: A

Since Statement 1 alone is sufficient but Statement 2 alone is not sufficient, the answer is A.

Answer Choice A: "Statement 1 alone is sufficient, but Statement 2 alone is not sufficient."