Each time Meg has visited a certain ice cream parlor with friends, she has bought chocolate ice cream, unless half...

Understanding the Question

We need to determine whether Meg bought chocolate ice cream.

Given Information

• Meg's rule: She always buys chocolate UNLESS half or more of her friends buy the same non-chocolate flavor
• In that case, Meg buys that same flavor instead
• Yesterday: Meg visited with 4 friends (Ann, Bart, Cathy, Derek)
• Ann bought chocolate ice cream

What We Need to Determine

Did Meg buy chocolate ice cream? This is a yes/no question.

Key Insight

For Meg to NOT buy chocolate, at least 2 friends (half of 4) must buy the same non-chocolate flavor. Since Ann already bought chocolate, we need at least 2 of the remaining 3 friends (Bart, Cathy, Derek) to buy the same non-chocolate flavor.

Remember: "Sufficient" means we can definitively answer whether Meg bought chocolate or not.

Analyzing Statement 1

Statement 1: Bart bought either vanilla or chocolate ice cream, and Cathy bought neither vanilla nor chocolate ice cream.

What Statement 1 Tells Us

• Ann: chocolate (given)
• Bart: vanilla OR chocolate
• Cathy: some other flavor (not vanilla, not chocolate)
• Derek: unknown

Testing Different Scenarios

Let's test what happens in each case:

Case 1: If Bart bought chocolate

• Chocolate count: Ann, Bart (2 people)
• Other flavors: Cathy (1 person), Derek (unknown)
• Since Cathy bought something else, no non-chocolate flavor can have 2+ people
• Result: Meg buys chocolate ✓

Case 2: If Bart bought vanilla

• Chocolate count: Ann (1 person)
• Vanilla count: Bart (1 person)
• Other flavor count: Cathy (1 person)
• Derek: unknown

Here's where it gets uncertain. If Derek bought vanilla, then vanilla would have 2 people (Bart and Derek), which is half the friends. Since vanilla isn't chocolate, Meg would buy vanilla. But if Derek bought anything else, no non-chocolate flavor has 2+ people, so Meg would buy chocolate.

Conclusion

Since Derek's choice creates different outcomes, we cannot definitively answer the question.

Statement 1 is NOT sufficient.

[STOP - Not Sufficient!] This eliminates choices A and D.

Analyzing Statement 2

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

Statement 2: Derek did not buy the same flavor as Bart.

What Statement 2 Provides

We know Derek and Bart bought different flavors, but we don't know what any specific flavors are (except Ann's chocolate).

Testing Possibilities

Without knowing the actual flavors, many scenarios are possible:

• Scenario 1: If Bart = vanilla, Cathy = vanilla, Derek = strawberry
  - Vanilla has 2 people → Meg buys vanilla
• Scenario 2: If Bart = vanilla, Cathy = strawberry, Derek = chocolate
  - No non-chocolate flavor has 2+ people → Meg buys chocolate

Different scenarios lead to different answers about whether Meg bought chocolate.

Conclusion

Statement 2 is NOT sufficient.

[STOP - Not Sufficient!] This eliminates choice B.

Combining Statements

Combined Information

Using both statements together:

• Ann: chocolate
• Bart: vanilla OR chocolate (Statement 1)
• Cathy: not vanilla, not chocolate - some other flavor (Statement 1)
• Derek: not the same as Bart (Statement 2)

Testing the Combined Cases

Case 1: Bart bought chocolate

• Derek ≠ chocolate (from Statement 2)
• Chocolate count: Ann, Bart (2 people)
• Cathy: some other flavor (not vanilla, not chocolate)
• Derek: must be vanilla or another non-chocolate flavor
• No non-chocolate flavor can reach 2+ people
• Result: Meg buys chocolate ✓

Case 2: Bart bought vanilla

• Derek ≠ vanilla (from Statement 2)
• Vanilla count: only Bart (1 person)
• Cathy: some specific other flavor (let's call it flavor X)
• Derek's options: chocolate, flavor X, or a different flavor Y

This is the crucial insight: If Derek bought the same flavor X as Cathy, then flavor X would have 2 people (half the friends). Since X isn't chocolate, Meg would buy flavor X instead of chocolate.

Why Together They Aren't Sufficient

We still can't determine what Meg bought because:

• In Case 1: Meg definitely buys chocolate
• In Case 2: Meg's choice depends on whether Derek matches Cathy's "other" flavor

Since we don't know if Derek chose the same non-chocolate, non-vanilla flavor as Cathy, we cannot definitively answer the question.

The statements together are NOT sufficient.

[STOP - Not Sufficient!] This eliminates choice C.

The Answer: E

Even with both statements combined, we cannot determine whether Meg bought chocolate ice cream. The uncertainty hinges on whether Derek bought the same non-chocolate, non-vanilla flavor as Cathy in the case where Bart bought vanilla.

Answer Choice E: The statements together are not sufficient.