A worked CAT DILR practice set: one LR set and one DI-LR hybrid, solved in full

Reading about DILR methods helps only up to a point. The rest comes from solving sets under time pressure and then reviewing them honestly. This page gives you two original sets to do exactly that: a logic grid of the kind CAT uses as its warm-up set, and a table with missing cells that mixes DI arithmetic with LR deduction.

Both sets were built for this page and checked by computer to have exactly one solution. Try each one before reading its solution. A reasonable target is 8 minutes for Set A and 12 for Set B.

How to use this page

1. Set a timer. Read the set once, draw your grid, then solve.
2. Answer every question before looking at the solutions.
3. Mark each answer right or wrong, and note where your time went: reading, setting up, solving or checking.
4. Read the working even for questions you got right. A lucky right answer is worth finding.

Set A: four employees (target 8 minutes)

Four employees, J, K, L and M, each work in a different department (Finance, HR, Marketing and Operations) and have different years of experience: 2, 4, 6 and 8.

1. The Finance employee has more experience than K.
2. L has 6 years of experience.
3. The HR employee has the least experience.
4. M works in Marketing and has more experience than L.
5. J does not work in HR.
6. The Operations employee has more experience than the Finance employee.

Questions.

• A1. Who works in Operations?
• A2. How many years of experience does the Finance employee have?
• A3. Who has the least experience?
• A4. What is the total experience of the HR and Marketing employees?

Set B: mock scores with missing cells (target 12 minutes)

Four aspirants, K, L, M and N, each took three mocks. The table shows some of their scores. Every score is a multiple of 10 from 50 to 100.

Two more facts are known.

• In Mock 3, exactly three aspirants got the same score.
• L scored less in Mock 2 than in Mock 1.

Questions.

• B1. What was N's score in Mock 1?
• B2. Who scored the highest in Mock 1?
• B3. How many aspirants scored more in Mock 3 than in Mock 1?
• B4 (TITA). By what percentage did N's score rise from Mock 1 to Mock 3?
• B5. If the last fact (about L) were not given, how many complete tables would fit the data?

Stop here and solve both sets before reading on.

Solution to Set A

Step 1: the fixed facts. L has 6 years (clue 2). M works in Marketing and has more than 6, so M has 8 years (clue 4).

Step 2: J and K. They share 2 and 4 years. The HR employee has 2 years (clue 3), and J is not in HR (clue 5). If J had 2 years, J would be the least experienced and therefore in HR. So J has 4 years and K has 2, and K is in HR.

Step 3: Finance and Operations. J and L take these two. Operations has more experience than Finance (clue 6), so L (6 years) is in Operations and J (4 years) in Finance.

Step 4: check clue 1. The Finance employee (J, 4 years) has more experience than K (2 years). It holds.

Answers. A1: L. A2: 4. A3: K. A4: 2 + 8 = 10.

Clue 1 was never needed to place anyone; it only confirmed the result. CAT sets sometimes include such clues, and they are useful as a check.

Solution to Set B

Step 1: list what each row allows. Every score is 50, 60, 70, 80, 90 or 100.

• K: Mock 2 + Mock 3 = 240 − 90 = 150.
• L: Mock 1 + Mock 2 = 210 − 100 = 110, so the pair is 50 and 60 in some order.
• M: Mock 1 + Mock 3 = 250 − 90 = 160.

Step 2: use the Mock 3 fact. The Mock 3 column totals 340, and L has 100, so K, M and N together have 240 in Mock 3. Three aspirants scored the same in Mock 3.

• If L's 100 were one of the three equal scores, two others would also have 100, and the third would have 240 − 200 = 40, below the minimum of 50. Impossible.
• So the three equal scores belong to K, M and N: 240 ÷ 3 = 80 each.

That gives K: Mock 2 = 150 − 80 = 70. M: Mock 1 = 160 − 80 = 80. N: Mock 1 + Mock 2 = 200 − 80 = 120.

Step 3: the column totals.

• Mock 1: 90 + L1 + 80 + N1 = 280, so L1 + N1 = 110.
• Mock 2: 70 + L2 + 90 + N2 = 280, so L2 + N2 = 120.

L1 is 50 or 60, so there are two cases.

Step 4: the fact about L. L scored less in Mock 2 than in Mock 1, so L2 < L1. Only the second case fits: L1 = 60, L2 = 50, N1 = 50, N2 = 70.

Every row and column total checks.

Answers.

• B1: 50.
• B2: K, with 90.
• B3: 2. L (60 to 100) and N (50 to 80) improved. K fell from 90 to 80, and M stayed at 80.
• B4: (80 − 50) ÷ 50 = 60.
• B5: 2. Without the fact about L, both cases in the step 3 table survive.

Reviewing your attempt

Fill this in honestly after checking.

Common mistakes on sets like these

• Assuming L's 100 is one of the three equal Mock 3 scores. It cannot be, and testing that case takes only a line.
• Forgetting the range of scores. "Multiples of 10 from 50 to 100" is what ruled out the 40.
• Reading "more experience than K" as "the next level above K". Clue 1 in Set A says only "more".
• Skipping the final check. Row and column totals take twenty seconds to confirm.

What to do next

• Redo both sets in three days, from a blank sheet, and compare your time.
• Log each set in your mock-analysis sheet using the review table above. See DILR mock analysis.
• Practise two more missing-value tables this week; see table-based DI.
• For choosing which sets to open first in a real paper, read DILR set selection.