Please help to answer this question step by step.

Question

On a test, 15 students answered more than 10 questions correctly, and 8 students answered at least 12 questions correctly.  How many students answered 11 questions correctly?

 

Please tell me how to do this in steps.

 

Thank you.

Answer 1

Good morning, Lynne.  What comes into play here is a little thing that says the whole is the sum of its parts.

 

Let's think about this.  We have 15 students who got more than 10 right. That means that 15 students got 11, 12, 13, or more correct, right?

 

Now, we have 8 students who got at least 12 right, so they got 12, 13, 14 or more correct.  This also means that they got more than 11 correct, because they scored at least 12.

 

So, 8 out of 15 students that scored more than 10 scored more than 11.  How many got 11, then?  The rest!  The other 7 got 11 correct.

 

Hope this helps!