Question 923·Hard·Math

The condition is who had an annual physical exam. So the denominator, the group you divide by, is the $70\%$ of adults who had an exam. We can use percentages of all $800$ adults because the $800$ would cancel from the top and bottom of the fraction.

Neither means no flu shot and no exam. Its complement is having at least one of them. Subtract the neither share from all adults:

So $85\%$ had a flu shot, an exam, or both.

Adding the $60\%$ flu-shot share and the $70\%$ exam share counts adults in both groups twice, but the $85\%$ with at least one counts them once. Subtract the at-least-one share to find the intersection, the adults in both groups. Type $60+70-85$ in Desmos; it shows $45$. So

of all adults had both.

The $45\%$ with both is the numerator, the part of the exam group you want. Divide by the $70\%$ with an exam. Type $\frac{45}{70}\times100$ on the next Desmos line; it shows about $64.2857$. To the nearest tenth, $64.3\%$ of adults who had an annual physical exam also received a flu shot. Choice C.