Can someone help me out? Thank you, I rate well. A college survey claimed that 6

Question

Can someone help me out? Thank you, I rate well.

A college survey claimed that 62% of students took English composition, 45% took calculus, 15% took both, and 12% took neither. Show that these figures cannot be correct. The real percentage that took neither class is 8, not 12% as claimed by the survey. The real percentage that took neither class is 15, not 12% as claimed by the survey. The real percentage that took both classes is 12, not 15% as claimed by the survey. The real percentage that took both classes is 8, not 15% as claimed by the survey.

Explanation / Answer

n(e) denotes students who took english

n(c) denotes students who took calculus

n(c and e) denotes students who took both english and calculus

n(n) denotes those who took neither

according to the set theory, we can write

n(e) + n(c) - n(c and e) + n(n) = 100%

62 + 45 - 15 + 12 = 104, so there is an excess 4%, which is an error!

As per the options given, it could either be the students who took both or those who took neither which brought error in the statement.

Since it is an excess and n(c and e) has negative sign before it, n( c and e) has no error.

Therefore, it is clear that the excess perecentage is added the students who took neither. It should be 8% instead of 12%. Option A is the right answer.

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