rohan2345 wrote:
Of the students in a class, 90% had taken a course in writing, or math, or both. What percent of the students had taken both a course in writing and a course in math?
(1) 55% of the students had taken a course in writing.
(2) 35% of the students had taken a course in only math.
Let's say we have 100 students. 90 of them have taken a course in Writing, or Math, or Both. I set up my Venn diagram to have the following:
\(x\) equal the number of students who only took Math
\(y\) equal the number of students who only took Writing
\(z\) equal the number of students who took both Math and Writing
So, from the prompt we know that \(x+y+z=90\). Now let's look at the statements:
(1) 55 students took a course in Writing
This means that \(x+z=55\) so we know that \(y=35\). However, we have no way of discerning what \(z\) is from the given info. Not Sufficient
(2) 35 students had a course only in Math
This means that \(y=35\), but no information on \(x\) or \(z\). Not Sufficient
(1+2) Together, the statements don't provide any new information, so (E) is the answer