A survey of 110 people revealed that 65 of those surveyed own stocks and 82 of those surveyed own bonds....

Understanding the Question

Let's break down what we're looking for. We have 110 people surveyed about their stock and bond ownership, and we need to find the exact number who own stocks but NOT bonds.

Given Information

• Total people surveyed: 110
• People who own stocks: 65
• People who own bonds: 82

What We Need to Determine

The specific number of people in the "stocks only" group.

Key Insight

Picture this as a Venn diagram problem with two overlapping circles—one for stock owners and one for bond owners. The 65 stock owners include both those who own only stocks AND those who own both stocks and bonds. To find the "stocks only" group, we need to know how many people are in the overlap (own both), then subtract that from 65.

The critical question: Can we determine how many people own BOTH stocks and bonds?

Analyzing Statement 1

Statement 1 tells us: 50 of the people surveyed own both stocks and bonds.

This directly gives us the overlap! Now we can calculate:

• Total stock owners = 65
• Stock owners who also own bonds = 50
• Therefore, stock owners who DON'T own bonds = \(65 - 50 = 15\)

[STOP - Statement 1 is SUFFICIENT!]

We can definitively answer that 15 people own stocks but not bonds.

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: 13 of the people surveyed do not own either stocks or bonds.

This means that \(110 - 13 = 97\) people own at least one type of investment (stocks, bonds, or both).

Here's where the "slot-filling" logic reveals the answer. Think of it this way:

• We need to place 97 people into our Venn diagram
• The stock circle has 65 slots to fill
• The bond circle has 82 slots to fill
• Total slots available: \(65 + 82 = 147\)

But wait—we only have 97 people to fill 147 slots!

The difference of \(147 - 97 = 50\) represents the people who are "double-counted" because they fill a slot in BOTH circles. These are the people who own both stocks and bonds.

Now we can calculate: Stock owners who don't own bonds = \(65 - 50 = 15\)

[STOP - Statement 2 is also SUFFICIENT!]

Statement 2 alone allows us to determine the answer.

The Answer: D

Both statements independently tell us that exactly 15 people own stocks but not bonds.

Answer Choice D: "Each statement alone is sufficient."

Quick Verification

• Statement 1: Directly gives us the overlap (50), leading to \(65 - 50 = 15\)
• Statement 2: Indirectly reveals the overlap (50) through the slot-filling logic, also leading to \(65 - 50 = 15\)

Both paths arrive at the same definitive answer, confirming that each statement is sufficient on its own.