Beginning at noon yesterday, water was added to a partially filled water tank at the constant rate of 500 gallons...

Understanding the Question

Let's break down what we're being asked: Was there more than 1,000 gallons of water in the tank at noon yesterday?

This is a yes/no question - we need to definitively answer YES or NO.

Given Information

• Water was added starting at noon yesterday at a constant rate of 500 gallons per hour
• Water was added until the tank reached 2,000 gallons total
• Once the tank reached 2,000 gallons, no more water was added
• The tank was already partially filled at noon (but we don't know by how much)

What We Need to Determine

We need to find the initial amount in the tank at noon. Let's call this initial amount \(\mathrm{W_0}\).

To be sufficient, a statement (or combination of statements) must allow us to definitively determine whether \(\mathrm{W_0} > 1,000\) or \(\mathrm{W_0} \leq 1,000\).

Analyzing Statement 1

Statement 1: There were 1,700 gallons of water in the tank at 1:00 yesterday afternoon.

What This Reveals

From noon to 1:00 PM is exactly 1 hour. Since water was added at 500 gallons per hour:

• Water added in 1 hour = 500 gallons
• Amount at 1:00 PM = Initial amount + Water added
• \(1,700 = \mathrm{W_0} + 500\)
• Therefore: \(\mathrm{W_0} = 1,200\) gallons

Since \(1,200 > 1,000\), we can definitively answer YES to our question.

[STOP - Statement 1 is SUFFICIENT!]

This eliminates choices B, C, and E.

Analyzing Statement 2

Now let's forget Statement 1 completely and analyze Statement 2 independently.

Statement 2: There were 2,000 gallons of water in the tank at 3:00 yesterday afternoon.

The Key Uncertainty

Here's the critical insight: We know the tank had 2,000 gallons at 3:00 PM, but we don't know WHEN it first reached 2,000 gallons. Remember, once the tank hits 2,000 gallons, the filling stops immediately.

The tank could have reached 2,000 gallons anytime between noon and 3:00 PM!

Testing Different Scenarios

Let's explore what happens if the tank reached 2,000 gallons at different times:

Scenario 1: Tank reached 2,000 gallons after just 1 hour (at 1:00 PM)

• Water added: 500 gallons
• Initial amount: \(2,000 - 500 = 1,500\) gallons
• Is \(1,500 > 1,000\)? YES

Scenario 2: Tank reached 2,000 gallons after 2 hours (at 2:00 PM)

• Water added: \(500 \times 2 = 1,000\) gallons
• Initial amount: \(2,000 - 1,000 = 1,000\) gallons
• Is \(1,000 > 1,000\)? NO

Scenario 3: Tank reached 2,000 gallons after 3 hours (exactly at 3:00 PM)

• Water added: \(500 \times 3 = 1,500\) gallons
• Initial amount: \(2,000 - 1,500 = 500\) gallons
• Is \(500 > 1,000\)? NO

Since we get different answers (YES in Scenario 1, NO in Scenarios 2 and 3), we cannot definitively answer the question.

Statement 2 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."