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CAT 2018 Slot 1 · DILR · Data Interpretation · easy

CAT 2018 Slot 1 DILR: Test Series Scores

Four batsmen — Arjun, Bala, Chetan and Dev — played all four Tests of a series, batting once in each Test. The table shows some of their scores; the missing entries are marked '?'.

| Batsman | Test 1 | Test 2 | Test 3 | Test 4 |
|---|---|---|---|---|
| Arjun | 45 | ? | 88 | ? |
| Bala | ? | 102 | ? | 30 |
| Chetan | 67 | ? | 12 | ? |
| Dev | ? | 55 | ? | 91 |

The following additional information is known:

1. The combined scores of the four batsmen in Tests 1, 2, 3 and 4 were 206, 228, 176 and 295 respectively.
2. Arjun averaged exactly 55 runs per Test in the series.
3. Arjun's score in Test 4 was 41 more than his score in Test 2.
4. Chetan's series total was exactly 2 more than Dev's series total.
5. Dev scored exactly 53 more runs in Test 3 than in Test 1.

Question 1

Numerical answer

What was Chetan's score in Test 4?
Show answer and solution

Answer: 110

Arjun: total = 4 × 55 = 220, so Test 2 + Test 4 = 220 − 133 = 87. With Test 4 − Test 2 = 41: Test 2 = 23, Test 4 = 64.

Test 2 column: 23 + 102 + C2 + 55 = 228 → C2 = 48.
Test 4 column: 64 + 30 + C4 + 91 = 295 → C4 = 110.

(Chetan's total = 67 + 48 + 12 + 110 = 237.)

Full grid:

| | T1 | T2 | T3 | T4 | Total |
|---|---|---|---|---|---|
| Arjun | 45 | 23 | 88 | 64 | 220 |
| Bala | 76 | 102 | 5 | 30 | 213 |
| Chetan | 67 | 48 | 12 | 110 | 237 |
| Dev | 18 | 55 | 71 | 91 | 235 |

Question 2

Single correct option

What was the highest individual score in the series by any of the four batsmen?
  1. A. 110
  2. B. 88
  3. C. 91
  4. D. 102
Show answer and solution

Answer: (A) 110

Dev's total must be 237 − 2 = 235 (fact 4), so D1 + D3 = 235 − 146 = 89. With D3 − D1 = 53: D1 = 18, D3 = 71.

Then Bala: B1 = 206 − 45 − 67 − 18 = 76 and B3 = 176 − 88 − 12 − 71 = 5.

Individual scores: the largest are Chetan's 110 (Test 4), Bala's 102 (Test 2), Dev's 91 and Arjun's 88.

Highest = 110. The trap is 102, the largest score visible in the given table — Chetan's hidden Test 4 score is larger.

Question 3

Single correct option

In how many of the four Tests did Bala score more runs than Dev?
  1. A. 3
  2. B. 4
  3. C. 1
  4. D. 2
Show answer and solution

Answer: (D) 2

From the completed grid:

- Test 1: Bala 76, Dev 18 → Bala more
- Test 2: Bala 102, Dev 55 → Bala more
- Test 3: Bala 5, Dev 71 → Dev more
- Test 4: Bala 30, Dev 91 → Dev more

Answer: 2 Tests.

Key deduction: B1 and B3 follow from the column totals only after D1 and D3 are fixed using facts 4 and 5.

Question 4

Numerical answer

What is the difference between the highest and the lowest series totals among the four batsmen?
Show answer and solution

Answer: 24

Series totals from the completed grid:

- Chetan: 67 + 48 + 12 + 110 = 237
- Dev: 18 + 55 + 71 + 91 = 235
- Arjun: 45 + 23 + 88 + 64 = 220
- Bala: 76 + 102 + 5 + 30 = 213

Difference = 237 − 213 = 24.

Check: The four totals add to 905 = 206 + 228 + 176 + 295 ✓ — always cross-check row totals against column totals in grids like this.
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Original question written in the CAT 2018 Slot 1 pattern and checked twice for the correct answer. Not an official question paper. How we write and check questions · Corrections policy · Report a mistake