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Question 979843: The number of students in a school increased by 100% during the year 2009. Which of the following could be the percent by which the number of students dropped in the year 2010, if the number of students in the year 2010 is less than that of the year 2008.
Options:47%, 48%, 49%, 50%, 51%
Answer by KMST(5328)   (Show Source):
You can put this solution on YOUR website! The wording is made fuzzy by the use of "in the year" and "during the year".
Presumably, students can join and leave the school at any time "during the year",
and if it is so the "number of students in the year" is not a well defined quantity.
However, I think I know what was meant.
I would have said that the number of students enrolled for 2009 was 100% more than the number enrolled for 2008,
but that the number enrolled for 2010 was less than the number enrolled for 2008,
and I would asked what was the enrollment drop from 2009 to 2010.
WHAT THE FIFTH GRADER SAYS:
The number of students enrolled for 2009 was twice the number enrolled for 2008.
It could be that all the students from 2008 came back for 2009,
and an equal number of new students enrolled for 2009.
WOW! The school must have run a very good advertising campaign,
and half of the students enrolled for 2009 were new students.
However, the new students must have been disappointed by the school,
because by the next year the enrollment for 2010 was less than the enrollment for 2008.
Probably all those new students left the school,
along with some of the "old" students who had been in the school for 2008 and 2009.
So more than half of the 2009 students (the new half) had left by 2010.
Half is 50%, so more than 50% left the school between 2009 and 2010.
Of the multiple choices given, the only choice that is more than 50% is  .
MAKING IT LOOK LIKE ALGEBRA:
 = number of students enrolled for 2008
  = = = == increase from 2008 to 2009
 = number of students enrolled for 2009.
 = number of students enrolled for 2010.
 <---> because the number enrolled for 2010 was less than the number enrolled for 2008.
 = enrollment drop from 2009 to 2010 (as number of students)
The percentage drop in enrollment from 2009 to 2010, expressed as a fraction or decimal, is
 = relative enrollment drop from 2009 to 2010 (enrollment drop as a fraction of the number enrolled for 2009).
---> --->
So, the relative enrollment drop is more than  ,
and the percent of that drop must vbe more than 50%,
so the only option that works is .
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