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For a certain radio station in India, the table shows the songs ranked among the top 10 during Week W. The rankings are determined by the number of listener requests for each song, with rank 1 being the most requested, rank 2 the second-most requested, and so on. Lesser numbers constitute higher rankings. The table also gives, as of Week W, each song's rank for the previous week, the number of weeks it has been among the top 20, and its peak rank (the highest ranking it has achieved). In the column for Previous week's rank, "n/a" indicates that the song was not ranked in the week immediately prior to Week W.
| Week W rank | Song | Previous week's rank | Weeks in top 20 | Peak rank |
|---|---|---|---|---|
| 1 | A | 1 | 4 | 1 |
| 2 | B | 2 | 10 | 1 |
| 3 | C | 6 | 3 | 3 |
| 4 | D | 4 | 6 | 4 |
| 5 | E | 3 | 11 | 1 |
| 6 | F | n/a | 1 | 6 |
| 7 | G | 5 | 9 | 3 |
| 8 | H | 10 | 3 | 8 |
| 9 | I | 12 | 5 | 9 |
| 10 | J | 13 | 2 | 10 |
For each of the following questions, select Can be answered if that question can be answered using only the information in the table. Otherwise, select Cannot be answered.
How many of the top 5 songs for Week W had a higher rank for Week W than they did for the previous week?
How many of the top 10 songs for Week W were not among the top 10 in the previous week?
How many of the top 10 songs for the week immediately prior to Week W have ever been at ranking 1?
Let's start by understanding what we're working with. This table shows 10 songs currently in the top 10 for "Week W" along with their previous week's rankings and peak positions.
Key insights about this dataset:
Looking at one example row helps us understand the relationships:
| Song | Week W rank | Previous week's rank | Peak rank |
| A | 1 | 1 | 1 |
This shows Song A is currently #1, was also #1 last week, and has peaked at #1.
Note: This is a "one-way dataset" - we only see songs currently in the top 10, not songs that were in the top 10 last week but fell out. This insight will be crucial for our approach!
Statement 3 Translation:
Original: "At least one song that was among the top 10 songs last week is ranked lower than 10th in the current week."
What we're looking for:
In other words: Are any songs from last week's top 10 missing from this week's top 10?
Let's think about what we need to answer this. We'd need to know which songs were in the top 10 last week but aren't in the current top 10. However, our table only shows songs that are currently in the top 10!
Looking at the "Previous week's rank" column, we can quickly scan for values 1-10 to see which of last week's top 10 songs are still in the top 10:
But here's the key insight: We can't determine if those missing songs dropped below rank 10 or if they're simply no longer being tracked. The data doesn't tell us where those songs are now ranked.
Answer for Statement 3: CANNOT BE ANSWERED
Teaching callout: Notice how understanding the dataset limitations immediately saved us from a potential trap! In table analysis, recognizing what data you don't have is just as important as working with what you do have.
Statement 2 Translation:
Original: "Exactly 3 of the top 10 songs in the current week were not among the top 10 songs last week."
What we're looking for:
In other words: Are there exactly 3 songs in the current top 10 that are new to the top 10?
For this statement, let's use sorting to make our job easier.
First, let's sort by "Previous week's rank" to group similar values together. This instantly helps us identify which songs were not in the top 10 last week.
After sorting, we can see:
By sorting, we've instantly found that exactly 3 songs (F, I, and J) were not in the top 10 last week.
Answer for Statement 2: CAN BE ANSWERED
Teaching callout: Notice how sorting allowed us to see the answer at a glance! Instead of checking each song individually (which would take 10 separate checks), sorting grouped the relevant songs together for immediate recognition.
Statement 1 Translation:
Original: "Exactly 1 of the songs ranked in the top 5 positions in the current week had a better rank last week than in the current week."
What we're looking for:
In other words: Did exactly one of the current top 5 songs drop in ranking from last week?
Let's sort by "Week W rank" to focus only on the top 5 songs. Then we'll compare their current ranks with their previous ranks.
For songs ranked 1-5 this week:
Looking for songs where previous rank is better (lower number) than current rank, we find only Song E (previous 3, current 5) has dropped in ranking.
Answer for Statement 1: CAN BE ANSWERED
Teaching callout: By sorting first and focusing only on the top 5 songs, we dramatically reduced our workload. We also avoided unnecessary calculations by simply comparing the direction of change rather than calculating exact differences.
Looking at our analysis of all three statements:
The correct answer is (D): Statements 1 and 2 are CAN BE ANSWERED, Statement 3 CANNOT BE ANSWERED.
Remember: In table analysis questions, your approach matters just as much as your calculations. Always spend those first few seconds understanding what your dataset can and cannot tell you, and use sorting to transform complex data into visible patterns!
How many of the top 5 songs for Week W had a higher rank for Week W than they did for the previous week?
How many of the top 10 songs for Week W were not among the top 10 in the previous week?
How many of the top 10 songs for the week immediately prior to Week W have ever been at ranking 1?