CAT 2026 Slot 1 DILR Q20: Table / Min-Max-Median

The set

In a fitness center, some members register for the Gym program, and some others register for the Yoga program. No member registers for both programs; hence the total registration number is the sum of Gym and Yoga registrations. The following facts and table pertain to these registration numbers for the five months—June to October of 2023. The table shows the minimum, maximum, and median registration numbers of these five months, separately for Gym, Yoga, and the total number of registrations.

Category	Median	Minimum	Maximum
Gym	45	15	70
Yoga	30	15	50
Total	75	60	85

Additional facts:

In every month, both Gym and Yoga registration numbers were multiples of 5.
In June, the number of Yoga registrations was thrice that of Gym registrations.
In September, the number of Gym registrations was twice that of Yoga registrations.
The number of Gym registrations in July was the same as the number of Yoga registrations in August.
The number of Gym registrations was the largest in October.

TITA (type the answer) · +3 / 0

What was the total number of registrations in September?

Your answer

Answer and solution

Correct answer: 75

Solution

October Gym $= 70$ (largest), so October Yoga $\le 15$ → 15 (total 85). Remaining Yoga values for Jul/Aug/Sep are $\{x, 30, 50\}$.
Sep Gym $= 2 \times$ Sep Yoga, so Sep Yoga $= x$; total $3x \ge 60$ and Gym median 45 force $x = 25$.
September $= 50 + 25 = 75$

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