Linda put an amount of money into each of two new investments, A and B, that pay simple annual interest....

Understanding the Question

Let's restate what we're looking for: What specific dollar amount did Linda invest in investment A?

Given Information

• Linda made two investments: A and B
• Both pay simple annual interest
• Investment B's interest rate = 1.5 × Investment A's interest rate
• We need the exact principal amount in investment A

What We Need to Determine

To find a specific dollar amount, we need either:

1. The actual interest rate AND the interest earned, OR
2. Some other constraint that uniquely determines the principal

Key insight: When a problem gives us relationships between variables but not actual values, it often signals insufficient information.

Analyzing Statement 1

What Statement 1 Tells Us

• Investment A earned \(\$50\) interest in one year
• Investment B earned \(\$150\) interest in one year

Testing Different Scenarios

Let's think about what this reveals. Investment B earned exactly 3× as much interest as A (\(\$150\) vs \(\$50\)). But wait—B's interest rate is only 1.5× A's rate. How can B earn 3× the interest with only 1.5× the rate?

The answer: B must have 2× as much principal invested!

But here's the crucial question: What's the actual interest rate? Let's test two scenarios:

Scenario 1: If A's rate = 5%

• Then A's principal = \(\$50 ÷ 0.05 = \$1,000\)
• Check: \(\$1,000 × 5\% = \$50\) ✓

Scenario 2: If A's rate = 10%

• Then A's principal = \(\$50 ÷ 0.10 = \$500\)
• Check: \(\$500 × 10\% = \$50\) ✓

Different rates give us different principal amounts. We cannot determine the exact amount Linda invested.

Conclusion

Statement 1 alone is NOT sufficient.

This eliminates answer choices A and D.

Analyzing Statement 2

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

What Statement 2 Provides

The amount Linda invested in B is twice the amount she invested in A.

Logical Analysis

This gives us a ratio: \(\mathrm{B} = 2\mathrm{A}\). But without knowing:

• The actual dollar amounts
• The interest rates
• The interest earned

We have infinite possibilities. For example, Linda could have invested:

• \(\$1,000\) in A and \(\$2,000\) in B
• \(\$5,000\) in A and \(\$10,000\) in B
• Any amount in A and twice that in B

Conclusion

Statement 2 alone is NOT sufficient.

This eliminates answer choice B.

Combining Both Statements

Combined Information

• From Statement 1, we deduced that B has 2× as much principal as A (because B earned 3× the interest with only 1.5× the rate)
• From Statement 2, we're explicitly told that B = 2A

The Critical Realization

Here's where it gets interesting: Statement 2 just confirms what we already figured out from Statement 1! It doesn't add any new information.

We still have the fundamental constraint from Statement 1:
Principal in A × Rate of A = \(\$50\)

Since we don't know the actual interest rate, this equation has infinite solutions:

• If rate = 1%, principal = \(\$5,000\)
• If rate = 2%, principal = \(\$2,500\)
• If rate = 5%, principal = \(\$1,000\)
• And so on...

Conclusion

Even combining both statements, we cannot determine the exact amount Linda invested in A. The statements together are NOT sufficient.

This eliminates answer choice C.

The Answer: E

The statements together are not sufficient because we still don't know the actual interest rate, leaving us with infinite possible values for the principal amount in investment A.

Answer Choice E: "The statements together are not sufficient."