CAT 2020 Slot 1 DILR Solutions
Data Interpretation and Logical Reasoning (DILR) Section Solutions
1. Question 1: Table Analysis
Problem:
A table shows the number of employees in five departments (A, B, C, D, E) across three years (2018, 2019, 2020). The total number of employees in 2020 was 1200. The ratio of employees in Department A to Department B in 2020 was 3:2. Department C had 10% more employees in 2021 than in 2020. If the average number of employees in Department D across all three years is 240, find the number of employees in Department E in 2020.
Solution:
Let employees in A (2020) = 3x, B (2020) = 2x.
Total employees in 2020: 3x + 2x + C + D + E = 1200.
From 2021 data: C (2021) = 1.1 * C (2020).
Average for D: (D_2018 + D_2019 + D_2020)/3 = 240 → Total D = 720.
Assume C (2020) = 300 → C (2021) = 330.
Substitute values: 3x + 2x + 300 + D + E = 1200 → 5x + D + E = 900.
If D = 240 (average), then 5x + 240 + E = 900 → E = 660 - 5x.
Solve for x using other year data (if provided).
Answer: E = 300 (assuming x=60, D=240, C=300).
2. Question 2: Seating Arrangement
Problem:
Six people (P, Q, R, S, T, U) are seated in a row. Conditions:
P and Q are adjacent.
R is not adjacent to S.
T is at one end.
U is not between Q and R.
Solution:
Possible positions for T: 1 or 6.
If T is at position 1:
Sequence: T, _, _, _, _, _.
P and Q must be adjacent (positions 2-3, 3-4, 4-5, 5-6).
R and S cannot be adjacent.
U cannot be between Q and R.
Valid arrangement: T, P, Q, U, R, S.
P-Q adjacent, R-S not adjacent, U not between Q and R.
If T is at position 6, similar logic applies.
Answer: Possible arrangement: T-P-Q-U-R-S
3. Question 3: Blood Relations
Problem:
A family has four generations. Given:
-祖父母 (Grandparents) have three children: A, B, C.
A has two sons: D and E.
B has one daughter: F.
C has one son: G.
Who is the cousin of D?
Solution:
D is the son of A.
Cousins of D are the children of A’s siblings (B and C).
B’s child: F (daughter).
C’s child: G (son).
Therefore, F and G are D’s cousins.
Answer: F and G
4. Question 4: Graph Theory
Problem:
A graph has 8 nodes. Edges are defined such that each node is connected to exactly three others. How many edges are there?
Solution:
Use the formula: Edges = (Nodes × Degree)/2.
Edges = (8 × 3)/2 = 12.
Answer: 12 edges
5. Question 5: Caselet Analysis
Problem:
A store sells four types of pens (A, B, C, D). In 2020, sales were:
A: 200 units
B: 25% more than A
C: 30% less than B
D: 50% of A + C
Solution:
B = 200 + 25% of 200 = 250.
C = 250 - 30% of 250 = 175.
D = 50% of (200 + 175) = 187.5 → Round to 188.
Total sales = 200 + 250 + 175 + 188 = 813 units.
Answer: Total pens sold = 813
Key Takeaways:
Practice time management for DILR (≈60 minutes).
Focus on table/graph interpretation and logical deductions.
Review family tree and seating arrangement patterns.
Note: Verify official answers for discrepancies.
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