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 _______
Options:
(A) 0
(B) 15
(C) 20
(D) 10
Official Answer Key:
B
Step-by-Step Solution & Explanation
From the conditions: Cholesterol set C ⊂ BP set B, and C ∩ Diabetes D = ∅.
The BP set therefore splits into exactly three disjoint parts:
n(B) = (only BP) + (BP ∩ C) + (BP ∩ D)
45 = 20 + 10 + x
x = 15
Consistency check: patients with at least one condition = n(B) + (diabetes only) = 45 + 30 = 75 ✔ (so 30 patients have diabetes alone).
Practice This in Real CBT Exam Interface
Test yourself with the official TCS-iON palette, virtual calculator, and immediate performance analytics.