Exam P Practice Problem 81 – A Medical Survey

Problem 81-A

A medical researcher tracked a group of 10,000 patients with heart disease and diabetes. The researcher found that sixty five percent of these patients have health insurance coverage. She also found that thirty percent and twenty percent of the patients with health insurance coverage have heart disease and diabetes, respectively. Of the patients with health insurance coverage, ten percent have both heart disease and diabetes. Furthermore, the medical researcher found that forty percent and twenty five percent of the patients with no health insurance coverage have heart disease and diabetes, respectively. Twenty percent of the patients with no health insurance coverage have both heart disease and diabetes.

What is the number of patients that have neither heart disease nor diabetes?

$\displaystyle (A) \ \ \ \ \ \ \ \ \ \ \ \ 1500$

$\displaystyle (B) \ \ \ \ \ \ \ \ \ \ \ \ 2600$

$\displaystyle (C) \ \ \ \ \ \ \ \ \ \ \ \ 4175$

$\displaystyle (D) \ \ \ \ \ \ \ \ \ \ \ \ 5825$

$\displaystyle (E) \ \ \ \ \ \ \ \ \ \ \ \ 8500$

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Problem 81-B

A large high school offers three sporting activities – swimming, running and basketball. Thirty percent of the students participate in swimming. Of the students participating in swimming, fifty percent participate in running, thirty percent participate in basketball and five percent participate in both running and basketball. Of the students not participating in swimming, twenty percent participate in running, forty percent participate in basketball and ten percent participate in both running and basketball.

What is the percentage of the students that participate in exactly two of the sports?

$\displaystyle (A) \ \ \ \ \ \ \ \ \ \ \ \ 10 \%$

$\displaystyle (B) \ \ \ \ \ \ \ \ \ \ \ \ 22.5 \%$

$\displaystyle (C) \ \ \ \ \ \ \ \ \ \ \ \ 28 \%$

$\displaystyle (D) \ \ \ \ \ \ \ \ \ \ \ \ 35 \%$

$\displaystyle (E) \ \ \ \ \ \ \ \ \ \ \ \ 57.5 \%$

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