GATE 2026 ES – Question 8

General Aptitude · Analytical Aptitude: Logical Reasoning, Deduction and Analogy · 2 marks · Multiple choice

In a population, every high-cholesterol patient also has high blood pressure (BP). Some high-BP patients have diabetes, but no patient has both high cholesterol and diabetes. There are 75 patients with at least one condition,10 with high cholesterol,45 with high BP, and 20 with only high BP. How many have both diabetes and high BP?

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Correct answer: (B) 15

Explanation

Partition the BP group into BP only, cholesterol with BP, and diabetes with BP. The cholesterol and diabetes groups do not overlap, so these are disjoint and exhaustive within BP. Thus 45=20+10+x, giving **x=15, B**. The union count of 75 is not needed for this overlap.

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