Sofia will attend a sequence of daily training sessions for her job. On the last day of her training sessions...

Understanding the Question

Let's break down what's happening in Sofia's training program:

• She attends 2 sessions every day EXCEPT the last day
• On the last day, she attends either 1 OR 2 sessions
• We need to find: How many sessions remain after her third day?

What We Need to Determine

To answer this question, we need to know:

1. The total number of sessions in the program
2. How many sessions she completes by the end of day 3

Since Sofia always attends 2 sessions per day (except possibly the last day), by the end of day 3 she will have completed exactly 6 sessions (\(2 \text{ sessions/day} \times 3 \text{ days} = 6 \text{ sessions}\)).

Therefore, we really need to determine the total number of sessions in the program.

Analyzing Statement 1

Statement 1: The training lasts 6 days.

Let's think through what this means. If the training is 6 days long:

• Days 1-5: 2 sessions each = 10 sessions
• Day 6 (last day): Either 1 or 2 sessions
• Total: Either 11 or 12 sessions

By the end of day 3, Sofia has completed 6 sessions.

This gives us two possible scenarios:

• If total = 11 sessions → \(11 - 6 = 5\) → 5 sessions remaining
• If total = 12 sessions → \(12 - 6 = 6\) → 6 sessions remaining

Since we get two different answers (5 or 6), Statement 1 alone 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: There are exactly 11 training sessions total.

This is a powerful constraint. Let's work backwards to see what this tells us about the program structure.

If the last day has 1 session:

• Other days must have: \(11 - 1 = 10\) sessions
• At 2 sessions per day: \(10 \div 2 = 5\) days
• Total program length: \(5 + 1 = 6\) days ✓

If the last day has 2 sessions:

• Other days must have: \(11 - 2 = 9\) sessions
• At 2 sessions per day: \(9 \div 2 = 4.5\) days
• But we can't have half a day! ✗

The key insight: 11 total sessions forces exactly one possible structure - the program must be 6 days long with the last day having only 1 session.

By the end of day 3, Sofia completes 6 sessions.
Sessions remaining: \(11 - 6 = 5\) sessions

[STOP - Sufficient!] We get exactly one answer.

Statement 2 alone is sufficient.

This eliminates choices C and E.

The Answer: B

Statement 2 alone provides enough information to determine that exactly 5 sessions remain after Sofia's third day, while Statement 1 alone leaves us with two possible answers.

Answer Choice B: "Statement 2 alone is sufficient, but Statement 1 alone is not sufficient."