CAT 2022 Slot 3 · DILR · Question 14

CAT 2022 Slot 3 previous year question on Caselet DI, with the answer and a step-by-step solution.

Caselet DIData InterpretationMultiple choiceMedium

Set 3: Grades in AI and ML Courses — this question belongs to a set. Read the full set with all 5 questions →

All the first-year students in the computer science (CS) department in a university take both the courses (i) AI and (ii) ML. Students from other departments (non-CS students) can also take one of these two courses, but not both. Students who fail in a course get an F grade; others pass and are awarded A or B or C grades depending on their performance. The following are some additional facts about the number of students who took these two courses this year and the grades they obtained.

1. The numbers of non-CS students who took AI and ML were in the ratio 2 : 5.

2. The number of non-CS students who took either AI or ML was equal to the number of CS students.

3. The numbers of non-CS students who failed in the two courses were the same and their total is equal to the number of CS students who got a C grade in ML.

4. In both the courses, 50% of the students who passed got a B grade. But, while the numbers of students who got A and C grades were the same for AI, they were in the ratio 3 : 2 for ML.

5. No CS student failed in AI, while no non-CS student got an A grade in AI.

6. The numbers of CS students who got A, B and C grades respectively in AI were in the ratio 3 : 5 : 2, while in ML the ratio was 4 : 5 : 2.

7. The ratio of the total number of non-CS students failing in one of the two courses to the number of CS students failing in one of the two courses was 3 : 1.

8. 30 students failed in ML.

How many students got A grade in AI?

A
99
B
42
C
84
D
63

Pick an option, then check.

Answer & solution

Answer: Option D

Solving the set

Step 1 – Let non-CS students in AI and ML be 2k and 5k (fact 1). The number of CS students equals 7k (fact 2), and every CS student takes both courses.

Step 2 – AI. No CS student fails AI and CS grades are A : B : C = 3 : 5 : 2, so CS AI = 10m (A 3m, B 5m, C 2m). No non-CS student gets A in AI, so all AI A grades are 3m; AI C = AI A = 3m ⇒ non-CS C = m; AI B = A + C = 6m ⇒ non-CS B = m.

Step 3 – Failures. Non-CS failures are f in AI and f in ML; 2f = CS C grades in ML (fact 3). CS ML grades are A : B : C = 4 : 5 : 2, so CS C in ML = 2f ⇒ CS ML: A 4f, B 5f, C 2f (passed 11f). Non-CS failures (2f) : CS failures = 3 : 1 ⇒ CS failures = 2f/3 (all in ML). ML failures f + 2f/3 = 30 ⇒ f = 18. CS ML failures = 12; CS passed ML = 11 × 18 = 198 (A 72, B 90, C 36).

Step 4 – CS students = 198 + 12 = 210 = 10m ⇒ m = 21; 7k = 210 ⇒ k = 30. Non-CS AI = 60 (B 21, C 21, F 18 ✓); non-CS ML = 150 (F 18, passed 132).

Step 5 – ML passed = 198 + 132 = 330: B = 165, A : C = 3 : 2 ⇒ A = 99, C = 66. Non-CS ML: A 27, B 75, C 30.

Group	Course	A	B	C	F	Total
CS	AI	63	105	42	0	210
Non-CS	AI	0	21	21	18	60
All	AI	63	126	63	18	270
CS	ML	72	90	36	12	210
Non-CS	ML	27	75	30	18	150
All	ML	99	165	66	30	360

This question

AI A grades are all CS: 3m = 63.

Hence, the answer is option 4.

CAT 2022 Slot 3 · DILR · Question 14

More Caselet DI questions