Last summer, as with every summer, Oshin and Reena made exactly one long trip together to a town neither of...

Understanding the Question

Let's parse this logic puzzle step by step. We need to determine: Did Oshin and Reena visit one of these four towns (F, G, J, or K) last summer?

Given Information

- Every summer, Oshin and Reena make exactly one trip to a town neither had visited before
- They choose a town Reena would have liked to visit—unless Oshin had been there before (then they avoid it)
- Reena had previously visited Towns F and G
- Oshin had never visited Towns J or K

What We Need to Determine

For any town to be their destination, it must satisfy two conditions:
1. Eligibility: Neither person had visited it before
2. Selection: It follows their decision rule (Reena's preference, unless Oshin had been there)

Key Insight

Since Reena had already visited F and G, these towns are immediately eliminated—they fail the "neither had visited" requirement. This means we're really asking: Did they visit Town J or Town K?

To answer this, we need to know:
- Whether Reena had visited J or K before (determines eligibility)
- Whether eligible towns match their selection criteria (Reena's preferences)

Analyzing Statement 1

Statement 1 tells us: Reena had never visited Town J and Oshin had never visited Town F.

Let's map out what we now know about each town:

So Town J is definitely eligible as a possible destination. But we still don't know:
- Is Town K also eligible? (depends on whether Reena had visited it)
- Would Reena have liked to visit Town J?
- If K is eligible, would Reena have preferred J or K?

Without knowing Reena's preferences or K's eligibility, we can't determine if they visited one of these four towns.

Statement 1 is 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 provides: Oshin would have liked to visit either Town G or Town K.

This tells us about Oshin's preferences, but remember—Oshin's preferences only matter if he had previously visited a town (which would make them avoid it). Since we know:
- Oshin had never visited J or K → his preferences for these towns don't affect the decision
- We don't know if Oshin had visited G → his preference for G might or might not matter

What we still don't know from Statement 2 alone:
- Which towns are eligible (we need complete visitation histories)
- Whether Reena would have liked to visit any eligible towns
- Whether Oshin had visited Towns F or G

Without knowing which towns neither had visited, we can't determine their destination.

Statement 2 is NOT sufficient.

This eliminates choice B.

Combining Statements

With both statements together, let's compile our complete picture:

Eligibility Status:

Selection Rule Application:

Since Oshin had never visited J or K, the selection for these towns simplifies to: they choose based on Reena's preferences alone.

What We Still Don't Know:

1. Had Reena visited Town K? (determines if K is eligible)
2. Would Reena have liked to visit Town J?
3. If K is eligible, would Reena have liked to visit it?

These unknowns create multiple possible scenarios:

Scenario 1: Reena had visited K and didn't like J
→ No eligible towns they'd select → They visited none of these four towns

Scenario 2: Reena hadn't visited K and liked only K
→ They'd select K → They visited one of these four towns (K)

Scenario 3: Reena hadn't visited K and liked only J
→ They'd select J → They visited one of these four towns (J)

Since different scenarios lead to different answers (sometimes yes, sometimes no), the combined statements are NOT sufficient.

The Answer: E

Even with both statements, we cannot determine whether they visited one of these four towns because:
- We don't know if Town K is eligible (Reena's visitation history unknown)
- We don't know Reena's preferences for the eligible towns

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