now figured it out.
All attended atleast 12 concerts . as all attended atleast one concert per week.
so bottom 20 attended 12 concerts each. ( at least )
middle 170 have to attend atleast 1 more than the least number that is 12 and one less than the highest number. That is they attended 13 atleast.
top 10 has to attend atleast one more that the middle 170 that is they attended atleast 14 ..
Hence more that 6 people attended atleast 14 concers
Well explained, mandyrhtdm!
Inference problems--characterized by language in the question stem like "based on the evidence presented above"--ask you to accept the information in the stimulus as fact, and draw conclusions from it. When the facts are abstract or complex, it can be very difficult to predict an answer. But when there are numbers in the stem, it's often the case that the correct answer presents itself to a little mathematical reasoning!
Here, because we have "20" attending the "fewest" number of concerts, and "10 attending the "most" number of concerts, we have to have the remaining 170 somewhere in the middle. And since the fewest possible number of concerts is 12, the middle 170 must have each attended at least 13 concerts--and, accordingly, the remaining 10 have each attended an absolute floor of 14 concerts. (D) is correct.
For the record: (A) isn't supported--we have information on 30 out of 200, so there is no way we can support a "most" claim. (B) is out of scope; we don't know where the hours come from, not to mention that it's possible students are studying at the concerts! (C) also goes may beyond the scope of the stimulus. Finally, (E) speculates baselessly on the motivation of students. This is a reasonable supposition, but it's not actually based on anything in the text!
Best of luck studying!
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