Probalitiy Question

daniel-fabry wrote:There are 800 students at School Y. At the beginning of the first semester, 45% of the students have taken the math placement test, 15% have taken both the math and the verbal placement tests, and 10% have taken neither. By the end of the first semester, 60% of the students have taken the math placement test, 30% have taken both tests, and all students have taken at least one test. If no students have entered or left school Y, how many more students took the math placement test during the first semester than took the verbal placement test during the first semester?

How would you tackle this question

You would normally make a venn diagram or a table. I am trying to put it here without diagram to show how it would look like. Hopefully, if there is no mistake, it should guide you to solve the problem.

Beginning of first sem :

Students who took Math Test -> 45%
Students who took both tests -> 15 % (that also means 30% only took Math test)
Students who took neither -> 10%
Hence, students who took verbal test -> 60% (that also means who took only verbal = 45%)

After first sem :

Students who took Math Test -> 60%
Students who took both tests -> 30 % (that also means 30% only took Math test)
Students who took neither -> 0%
Hence, students who took verbal test -> 70% (that also means who took only verbal = 40%)

So, we can see that 15% (60%-45%) more students took the math test, whereas only 10%(70%-60%) of the students took the verbal test.
So the difference is 5% = 800*5/100 = 40.

at start M+MV =45% ( where MV =15)

at start (M +MV +V+10%) =100%
V=45 %
therefore now V +MV = 60%

at finish M +MV =60%

M+MV+V =100% (where MV =30 and M +MV =60%)
V=40%
V+MV=70%

question asked is what is diff between raise of M+MV and V+MV

for math the raise was from 45-->60 i.e 15%
for verbal the raise was from 60-->70-->10%

difference is 5% of 800 students which is 40 students...

Nice twister in the last part of the sentence "how many more students took the math placement test during the first semester than took the verbal placement test during the first semester"

I misinterpreted the word translation here.