Question

In a population, patients who have high cholesterol also have high blood-pressure (BP). Some patients with high BP also have diabetes. There are no patients who have both high cholesterol and diabetes. Furthermore,
1. the total number of patients with at least one of these conditions is 75,
2. the number of patients with high cholesterol is 10,
3. the number of patients with high BP is 45, and
4. the number of patients with only high BP and no other conditions is 20.
Then the number of patients who have both diabetes and high BP is _______

• A. 0
• B. 15
• C. 20
• D. 10

Hint:

Split the high BP group into cholesterol-overlap, BP-only and diabetes-overlap pieces that must sum to 45.

Answer 1

The Correct Option is B

Picture three overlapping circles for cholesterol, BP and diabetes. The clues say cholesterol sits fully inside BP, and cholesterol never touches diabetes, so BP splits cleanly into three pieces: cholesterol-and-BP, BP-only, and BP-and-diabetes.

1. Option (A), 0: if BP-and-diabetes were $0$, the BP circle would only total $10+20=30$, not the given $45$, so this is too low.
2. Option (B), 15: adding the known BP pieces, $10$ (cholesterol-and-BP) plus $20$ (BP-only) plus $15$ (BP-and-diabetes) gives exactly $45$, matching the stated high-BP total.
3. Option (C), 20: using $20$ here would push the BP total to $10+20+20=50$, which overshoots the given $45$.
4. Option (D), 10: using $10$ here gives a BP total of only $10+20+10=40$, which falls short of $45$.

Only $15$ makes the three BP pieces add up to the stated $45$ high-BP patients, so option (B) is correct.