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Why is the first statement marked “cannot be concluded”? The graph shows about 74% for South Dakota and 66% for the U.S. in 2007. Since 74% is clearly not twice 66%, can’t we conclude that the statement is false?
If we can conclude that the difference is not twice, that's concluding, right??

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Official Explanation

The first conclusion cannot be drawn, as while the relative heights of the bars may look like one is twice as large as the other, the scale at the left-hand side of the graph should show that it is a much more modest difference than double (75% vs. 65%).

The second conclusion cannot be drawn, as given a percentage/rate but no link to actual numbers we cannot draw an inference about actual numbers (suppose the state's population changed dramatically from one year to the next, the slight difference in percentage would be overwhelmed by the dramatic difference in overall number).

The third conclusion, however, is valid, as the graph clearly depicts labor force participation, the specific language of the question.

Answer: Cannot be concluded, Cannot be concluded and Can be concluded
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RaahiK
Why is the first statement marked “cannot be concluded”? The graph shows about 74% for South Dakota and 66% for the U.S. in 2007. Since 74% is clearly not twice 66%, can’t we conclude that the statement is false?
If we can conclude that the difference is not twice, that's concluding, right??


“Can be concluded” here means can this statement itself be concluded to be true from the graph?

We can determine that the statement is false, since 74% is not twice 66%. Therefore, the statement cannot be concluded from the graph.

So yes, we can conclude that it is false, but that is exactly why it belongs under “Cannot be concluded.”
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Hi RaahiK,

I love this question, because you've spotted something real: you're totally right that the graph lets you disprove Statement 1. In 2007 South Dakota reads about 73.7% and the U.S. reads about 66%, and twice 66% would be 132% - impossible, and nowhere near what the bars show. So yes, you can tell the statement is false.

Here's the subtle part. The prompt isn't asking "can you evaluate this statement?" It's asking "can this statement be concluded (drawn as a valid conclusion) from the graph?" In other words: is this a true conclusion the graph supports?

- "Can be concluded" = the statement is true and supported by the data.
- "Cannot be concluded" = the statement is not something the graph supports - because it's either false or unknowable.

Statement 1 is false, so it is not a conclusion you can draw from the graph - Cannot be concluded. You proved it's not twice - and that proof is exactly why it fails the "can be concluded" test, not a reason to pass it.

The trap in one line

Disproving a statement doesn't make it a valid conclusion. "Cannot be concluded" is the correct bucket for both "the graph shows this is false" (Statement 1) and "the graph can't tell us" (Statement 2). Only a statement the graph shows to be true - like Statement 3 - earns "Can be concluded."

Quick rehearsal: Suppose a chart shows a bar at 40 and another at 30.
- Claim A: "The first is double the second." - Graph shows it's not - Cannot be concluded (false).
- Claim B: "The first is larger than the second." - Graph shows it is - Can be concluded (true).

Same data, but only the true claim can be "concluded." That's the distinction Statement 1 is testing.

Answer: Statement 1: Cannot be concluded; Statement 2: Cannot be concluded; Statement 3: Can be concluded

RaahiK
Why is the first statement marked “cannot be concluded”? The graph shows about 74% for South Dakota and 66% for the U.S. in 2007. Since 74% is clearly not twice 66%, can’t we conclude that the statement is false?
If we can conclude that the difference is not twice, that's concluding, right??


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