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Sofia will attend a sequence of daily training sessions for her job. On the last day of her training sessions she will attend either 1 session or 2 sessions. On each of the other days of her training sessions she will attend exactly 2 sessions. At the end of her third day of attending training sessions, how many sessions will Sofia have left to attend?
Let's break down what's happening in Sofia's training program:
To answer this question, we need to know:
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.
Statement 1: The training lasts 6 days.
Let's think through what this means. If the training is 6 days long:
By the end of day 3, Sofia has completed 6 sessions.
This gives us two possible scenarios:
Since we get two different answers (5 or 6), Statement 1 alone is NOT sufficient.
This eliminates choices A and D.
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:
If the last day has 2 sessions:
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.
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."