The GATE Grind

GATE 2026 IN – Question 8

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

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.
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 ________.

  1. 0
  2. 15
  3. 20
  4. 10

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Show answer and explanation

Correct answer: (B) 15

Explanation

All 10 high-cholesterol patients belong to the BP group. None of these 10 patients has diabetes, so the BP group splits into three disjoint parts: BP only (20), BP with cholesterol (10), and BP with diabetes ($x$).

Consequently, $20+10+x=45$, giving $x=15$. The union total of 75 is not needed to determine this overlap.

The correct answer is **15 (B)**.