In a study conducted on a sample of 360 economists, it was found that 75 percent of the economists had...

1. Translate the problem requirements: We have 360 economists total. 75% invest in stocks, 40% invest in bonds, and 15% invest in neither. We need to find how many invest in stocks but NOT in bonds - this means the portion of stock investors who don't also invest in bonds.
2. Calculate the overlap between stock and bond investors: Since we know the percentages for each category and those with neither investment, we can determine how many economists must have both types of investments.
3. Find the stock-only investors: Subtract the overlap (those with both stocks and bonds) from the total stock investors to get those who have stocks but not bonds.

Execution of Strategic Approach

1. Translate the problem requirements

Let's start by understanding what we have and what we need to find.

We have 360 economists in total. Think of this as our entire group.

\(75\% \text{ invest in stocks - this means } 75\% \text{ of } 360 = 0.75 \times 360 = 270\) economists invest in stocks.

\(40\% \text{ invest in bonds - this means } 40\% \text{ of } 360 = 0.40 \times 360 = 144\) economists invest in bonds.

\(15\% \text{ invest in neither stocks nor bonds - this means } 15\% \text{ of } 360 = 0.15 \times 360 = 54\) economists have no investments in either.

What we need to find: How many economists invest in stocks but NOT in bonds? In other words, we want the economists who are in the "stocks only" group.

Process Skill: TRANSLATE - Converting the percentage language into concrete numbers that we can work with

2. Calculate the overlap between stock and bond investors

Here's the key insight: if \(15\%\) have neither investment, then \(85\%\) must have at least one investment (either stocks, bonds, or both).

So \(85\% \text{ of } 360 = 0.85 \times 360 = 306\) economists have at least one investment.

Now, let's think about this logically. We know:

• 270 economists have stocks
• 144 economists have bonds
• If we simply add these: \(270 + 144 = 414\)

But wait! We only have 306 economists who invest in anything at all. This means we've counted some economists twice - specifically, those who have BOTH stocks and bonds.

The number we counted twice = \(414 - 306 = 108\)

So 108 economists must have investments in BOTH stocks and bonds.

Process Skill: INFER - Drawing the non-obvious conclusion that the "double-counting" reveals the overlap

3. Find the stock-only investors

Now we can find our answer easily.

We know:

• Total stock investors = 270
• Stock investors who ALSO have bonds = 108

Therefore:
Stock investors who do NOT have bonds = \(270 - 108 = 162\)

Let's verify this makes sense:

• Stocks only: 162
• Bonds only: \(144 - 108 = 36\)
• Both stocks and bonds: 108
• Neither: 54
• Total: \(162 + 36 + 108 + 54 = 360\) ✓

4. Final Answer

The number of economists who have investment in stocks but not in bonds is 162.

Looking at our answer choices, this matches choice D. 162.

Common Faltering Points

Errors while devising the approach

1. Misinterpreting "stocks but not bonds" as "stocks or bonds"
Students often confuse the requirement and try to find all investors who have either stocks or bonds, rather than specifically those who have stocks but exclude bonds. This fundamental misunderstanding leads them down the wrong path entirely.

2. Not recognizing the need to find the overlap
Many students attempt to solve this directly without realizing they first need to calculate how many people invest in BOTH stocks and bonds. They may try to subtract percentages directly (\(75\% - 40\%\)) without understanding that this approach ignores the constraint about people having neither investment.

3. Forgetting to use the "neither" constraint
Students may focus only on the stock and bond percentages and completely overlook the crucial information that \(15\%\) have neither investment. This constraint is essential for determining the overlap between the two groups.

Errors while executing the approach

1. Arithmetic errors in percentage calculations
Students may make calculation mistakes when converting percentages to actual numbers, such as calculating \(75\% \text{ of } 360\) as 250 instead of 270, or \(40\% \text{ of } 360\) as 140 instead of 144.

2. Incorrectly calculating the overlap
Even when students understand they need to find the overlap, they may make errors in the calculation. For example, they might subtract 306 from 414 incorrectly, or misunderstand that the "double-counting" represents the overlap.

3. Sign errors or incorrect subtraction
When finding stocks-only investors, students may add instead of subtract (\(270 + 108\) instead of \(270 - 108\)) or subtract in the wrong direction (\(108 - 270\)).

4. Errors while selecting the answer

No likely faltering points