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CAT 2025Slot 3DILRQues & Sol

Data InterpretationHard

Data Set

Three countries — Pumpland (P), Xiland (X) and Cheeseland (C) — trade among themselves and with the (other countries in) Rest of World (ROW). All trade volumes are given in IC (international currency). The following terminology is used:
• Trade balance = Exports - Imports
• Total trade = Exports + Imports
• Normalized trade balance = Trade balance / Total trade, expressed in percentage terms

The following information is known.
1. The normalized trade balances of P, X and C are 0%, 10%, and -20%, respectively.
2. 40% of exports of X are to P. 22% of imports of P are from X.
3. 90% of exports of C are to P; 4% are to ROW.
4. 12% of exports of ROW are to X, 40% are to P.
5. The export volumes of P, in IC, to X and C are 600 and 1200, respectively. P is the only country that exports to C.

Question 1

How much is exported from C to X, in IC?

Solution

Setup: We use the normalized trade balance conditions to express exports and imports of P, X, and C in parametric form, then anchor the system using the known export values of P (600 to X, 1200 to C) and the constraint that P is the only country exporting to C.

Steps:

  1. From normalized trade balance formulas: For P (0%) → Exports = Imports = 10a. For X (10%) → 11I = 9E, so let Exports = 11b, Imports = 9b. For C (−20%) → 2I = 3E, so let Exports = 2c, Imports = 3c.
  2. Since P is the only exporter to C, imports of C come entirely from P → Total imports of C = 1200 → 3c = 1200 → c = 400. Therefore, total exports of C = 2c = 800.
  3. From clue 2: exports from X to P = 40% × 11b = 4.4b, and imports of P from X = 22% × 10a = 2.2a. Equating: 4.4b = 2.2a → a = 2b.
  4. From clue 3: exports of C to P = 90% × 800 = 720; exports of C to ROW = 4% × 800 = 32.
  5. Exports of C to X = Total exports of C − exports to P − exports to ROW = 800 − 720 − 32 = 48.

Final Answer: 48

Question 2

How much is exported from P to ROW, in IC?

Solution

Setup: After establishing the parametric framework (P: 10a each, X: 11b/9b, C: 2c/3c) and finding c = 400 and a = 2b, we use the import column equations for P and X (incorporating ROW exports variable n) to solve for b, then compute P's total exports and subtract known destinations.

Steps:

  1. From earlier deductions: c = 400, a = 2b, exports of C to X = 48, exports of C to ROW = 32, exports of C to P = 720. Let total exports of ROW = n.
  2. Set up equations using import totals: For P: imports = 4.4b (from X) + 720 (from C) + 0.4n (from ROW) = 10a = 20b → 15.6b = 720 + 0.4n … (1). For X: imports = 600 (from P) + 48 (from C) + 0.12n (from ROW) = 9b → 9b = 648 + 0.12n … (2).
  3. Solve simultaneously: From (2), b = (648 + 0.12n)/9. Substitute into (1): 15.6 × (648 + 0.12n)/9 = 720 + 0.4n → 10108.8 + 1.872n = 6480 + 3.6n → 3628.8 = 1.728n → n = 2100.
  4. From equation (1): 15.6b = 720 + 0.4(2100) = 720 + 840 = 1560 → b = 100.
  5. Total exports of P = 20b = 2000. Exports of P to ROW = 2000 − 600 (to X) − 1200 (to C) = 200.

Final Answer: 200

Question 3

How much is exported from ROW to ROW, in IC?

Solution

Setup: With b = 100 and n = 2100 already established, we know all inter-country ROW exports. The 'ROW to ROW' trade represents the internal trade within ROW — i.e., total ROW exports minus what ROW sends to P, X, and C.

Steps:

  1. From previous solutions: n = total exports of ROW = 2100, b = 100.
  2. Exports of ROW to P = 40% × 2100 = 840. Exports of ROW to X = 12% × 2100 = 252. Exports of ROW to C = 0 (since P is the only exporter to C).
  3. Exports of ROW to ROW = Total ROW exports − ROW→P − ROW→X − ROW→C = 2100 − 840 − 252 − 0 = 1008.
  4. Verification: Imports of ROW = exports from P to ROW (200) + exports from X to ROW (660) + exports from C to ROW (32) + exports from ROW to ROW (1008) = 1900. This is consistent and solvable.

Final Answer: 1008

Question 4

What is the trade balance of ROW?

Solution

Setup: With the complete trade table resolved (b = 100, n = 2100), we directly compute ROW's total exports and total imports, then apply the trade balance formula: Trade Balance = Exports − Imports.

Steps:

  1. Total exports of ROW (n) = 2100 (already solved).
  2. Imports of ROW = sum of all exports directed toward ROW from other entities: from P → 200, from X → 6.6b = 660, from C → 32, from ROW itself → 1008. Total imports of ROW = 200 + 660 + 32 + 1008 = 1900.
  3. Trade balance of ROW = Exports − Imports = 2100 − 1900 = 200.
  4. Intuition check: P has trade balance = 0, X has positive balance (exports > imports), C has negative balance (imports > exports). The net surplus in the P-X-C system must be absorbed by ROW, confirming ROW's positive trade balance of 200.

Final Answer: 200 (Option D)

Question 5

Which among the countries P, X, and C has/have the least total trade?

Solution

Setup: With b = 100 and c = 400 resolved, we compute total trade (Exports + Imports) for each of P, X, and C using their parametric expressions and compare.

Steps:

  1. Total trade of P = Exports + Imports = 10a + 10a = 20a = 20(2b) = 40b = 40 × 100 = 4000.
  2. Total trade of X = Exports + Imports = 11b + 9b = 20b = 20 × 100 = 2000.
  3. Total trade of C = Exports + Imports = 2c + 3c = 5c = 5 × 400 = 2000.
  4. Comparing: P has total trade of 4000, while both X and C have total trade of 2000. Therefore, X and C are tied for the least total trade among the three countries.

Final Answer: Both X and C (Option C)