Lee has three separate savings accounts. What is the total amount of money in the three accounts? The total amount...

Understanding the Question

Let's break down what we're being asked. Lee has three separate savings accounts, and we need to find the exact total amount of money across all three accounts.

In simpler terms: If we call the three accounts A, B, and C, we need to determine the specific value of \(\mathrm{A + B + C}\).

For this value question to be sufficient, we need information that allows us to determine one unique total—not a range of possible totals, but one specific number.

Key Insight

The constraint in Statement 1—that ANY two accounts sum to \(\$8{,}000\)—is extremely restrictive. This type of universal constraint often forces all elements to be equal, which would make finding the total straightforward.

Analyzing Statement 1

Statement 1 tells us: The total amount of money in any two of the accounts is \(\$8{,}000\).

This means:

• \(\mathrm{Account\ A + Account\ B} = \$8{,}000\)
• \(\mathrm{Account\ A + Account\ C} = \$8{,}000\)
• \(\mathrm{Account\ B + Account\ C} = \$8{,}000\)

Here's the key insight: For all three pairs to sum to the same amount (\(\$8{,}000\)), the three accounts must contain equal amounts. Why? Let's think about this logically:

If Account A pairs with B to make \(\$8{,}000\), and A also pairs with C to make \(\$8{,}000\), then B and C must be equal (they both make up the same "gap" to reach \(\$8{,}000\) when paired with A). By the same reasoning, A must equal B and C.

Let's verify: If all accounts are equal and any two sum to \(\$8{,}000\), then each account must contain \(\$4{,}000\).

• Check: \(\$4{,}000 + \$4{,}000 = \$8{,}000\) ✓
• Total: \(\$4{,}000 + \$4{,}000 + \$4{,}000 = \$12{,}000\)

[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 tells us: At least one of the accounts contains \(\$4{,}000\).

This gives us minimal information. We know one account has \(\$4{,}000\), but we know nothing about the other two accounts. Let's test some scenarios to see if we can determine a unique total:

• Scenario 1: Account A = \(\$4{,}000\), Account B = \(\$0\), Account C = \(\$0\)
  Total = \(\$4{,}000\)
• Scenario 2: Account A = \(\$4{,}000\), Account B = \(\$1{,}000\), Account C = \(\$2{,}000\)
  Total = \(\$7{,}000\)
• Scenario 3: Account A = \(\$4{,}000\), Account B = \(\$4{,}000\), Account C = \(\$4{,}000\)
  Total = \(\$12{,}000\)

Since we can get different total amounts (\(\$4{,}000\), \(\$7{,}000\), \(\$12{,}000\), and many others), we cannot determine a unique total.

Statement 2 is NOT sufficient.

This eliminates choices B and D.

The Answer: A

Only Statement 1 provides enough information to determine the unique total amount in Lee's three accounts (\(\$12{,}000\)).

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