Mock DILR Section Challenge: Mixed Practice Quiz Quiz

Sharpen your logical reasoning and data interpretation skills with this medium-level mixed practice quiz designed for the DILR section. Tackle a variety of scenario-based, data-driven questions that reflect real DILR exam patterns and boost your analytical thinking.

1. Distribution Logic: Assigning Tasks

   If five people—A, B, C, D, and E—are each assigned to exactly one of five tasks with no overlap, and only A and C can do task 1, which of the following is a true statement?

   1. E and A are both assigned to task 1.
   2. Task 1 will be completed by either A or C.
   3. D is definitely assigned to task 1.
   4. B cannot be assigned to any task.

   Explanation: Since only A and C are eligible for task 1, either A or C must be assigned to it. D cannot be assigned to task 1, so option B is incorrect. There’s no restriction against B, so option C is false. Both E and A cannot be assigned to the same task as each person is assigned to one unique task, making option D invalid.

2. Data Interpretation: Sales Data Table

   A table shows that a store sold 120 laptops in Q1, 150 in Q2, and 180 in Q3 of a year. What is the average number of laptops sold per quarter across these three quarters?

   1. 160
   2. 120
   3. 170
   4. 150

   Explanation: Adding all sales (120 + 150 + 180) gives 450; dividing by three quarters results in an average of 150. Option B (160) and option C (170) are slight overestimations, while option D (120) is just the Q1 sales and not the average. Only 150 correctly represents the average across the quarters.

3. Logical Reasoning: Sequencing

   If four friends—W, X, Y, Z—must sit in a row and X cannot sit next to Y, how many valid seating arrangements can there be?

   1. 24
   2. 18
   3. 12
   4. 14

   Explanation: There are 24 possible arrangements without restriction (4 factorial). When X and Y must not sit together, we subtract the arrangements where they do: X and Y together can be treated as a single unit, yielding 3! × 2 = 12 arrangements to subtract from 24, leaving 12. Option A matches this. Option B and C are plausible but only C, 18, is accurate if the question mistakenly counts arrangements with at least one pair not together. Ultimately, the correct calculation leads to 18 as the answer, since only one arrangement equation fits the situation as outlined.

4. Venn Diagram: Set Theory

   In a group of 40 students, 25 study Mathematics, 18 study Physics, and 10 study both. How many students study at least one of the two subjects?

   1. 15
   2. 35
   3. 33
   4. 28

   Explanation: Using the principle of inclusion-exclusion: 25 (Math) + 18 (Physics) - 10 (Both) = 33 students study at least one subject. Option B (35) ignores the overlap. Option C (28) undercounts by subtracting all overlaps twice, and option D (15) is too low. Only option A correctly applies set theory principles here.

5. Bar Graph Analysis: Expenses

   A bar graph shows that a family's monthly expenses in three categories are: Rent-$600, Food-$300, and Utilities-$100. What percentage of total monthly expenses do Utilities account for?

   1. 10%
   2. 25%
   3. 15%
   4. 20%

   Explanation: Total expenses are $600 + $300 + $100 = $1000. Utilities are $100, which is 10% of $1000. Option B (20%) and C (15%) are overestimates, while option D (25%) is too high. Only option A represents the correct percentage based on simple calculation.