CAT 2026 Slot 1 DILR: Set 5: Fitness center — Gym and Yoga registrations, Jun–Oct 2023 with Solutions

4 questions: Q19, Q20, Q21, Q22. Solve each one here: tap the answer, press Check, then open the solution.

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.

Question 19Table / Min-Max-Median

MCQ · +3 / −1

What was the number of Gym registrations in June?

Answer and solution

Correct answer: C

Solution

June: Yoga $= 3 \times$ Gym. Gym $\ge 15$ (minimum) and Yoga $\le 50$ (maximum) → Gym $= 15$, Yoga $= 45$, total $60$.
Full table: Gym Jun 15, Jul 30, Aug 45, Sep 50, Oct 70; Yoga Jun 45, Jul 50, Aug 30, Sep 25, Oct 15.

Question 20Table / Min-Max-Median

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 $= 50 + 25 = 75$

Question 21Table / Min-Max-Median

MCQ · +3 / −1

What can be concluded about the number of Yoga registrations in August?

Answer and solution

Correct answer: D

Solution

If July Yoga were 30 and August Yoga 50, July Gym $= 50$ and August Gym $\le 35$ — the Gym median could not be 45. So July Yoga $= 50$, August Yoga $= 30 =$ July Gym, and August Gym $= 45$.

Question 22Table / Min-Max-Median

MCQ · +3 / −1

Which of the following statements can be true?
I. The number of Yoga registrations was the smallest in October.
II. The total number of registrations was the smallest in August.

Answer and solution

Correct answer: D

Solution

Yoga: Jun 45, Jul 50, Aug 30, Sep 25, Oct 15 → smallest in October: I is true.
Totals: Jun 60, Jul 80, Aug 75, Sep 75, Oct 85 → smallest in June: II is false.

An expected paper by Cetking, not the actual CAT paper. CAT is conducted by the IIMs.