CATSprint

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 establish a parametric framework using the normalized trade balance conditions, then anchor it using the critical constraint that P is the only country exporting to C — which immediately determines C's total import volume and unlocks the entire structure.

Steps:

  1. From the normalized trade balance definitions: For P (0%): Exports_P = Imports_P. Let both equal 10a. For X (10%): (E−I)/(E+I) = 10% → E/I = 11/9. Let Exports_X = 11b, Imports_X = 9b. For C (−20%): (E−I)/(E+I) = −20% → I/E = 3/2. Let Exports_C = 2c, Imports_C = 3c.
  2. Since P is the only country that exports to C, all imports of C come exclusively from P. From clue 5, P exports 1200 to C. Therefore, Imports_C = 1200 → 3c = 1200 → c = 400. Hence, total Exports_C = 2c = 800.
  3. From clue 3, exports of C are distributed as: 90% to P = 0.90 × 800 = 720, and 4% to ROW = 0.04 × 800 = 32. The remaining percentage goes to X: (100% − 90% − 4%) = 6% → Exports of C to X = 0.06 × 800 = 48.

Final Answer: 48

Question 2

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

Solution

Setup: With c = 400 and the export breakdown of C fully established, we now set up two simultaneous equations using the import-column totals for countries P and X. Both equations involve the unknowns b (the X-trade scale parameter) and n (total exports of ROW), allowing us to solve for P's total exports and isolate the ROW-directed portion.

Steps:

  1. From clue 2: exports of X to P = 40% × 11b = 4.4b; imports of P from X = 22% × 10a = 2.2a. Since these represent the same bilateral flow, 4.4b = 2.2a → a = 2b. Therefore, total exports of P = total imports of P = 10a = 20b.
  2. Let total exports of ROW = n. Set up the import equation for P: Imports_P = (from X) + (from C) + (from ROW) = 4.4b + 720 + 0.40n = 20b → 0.40n = 15.6b − 720 … (Equation 1). Set up the import equation for X: Imports_X = (from P) + (from C) + (from ROW) = 600 + 48 + 0.12n = 9b → 9b = 648 + 0.12n … (Equation 2).
  3. From Equation 2: b = (648 + 0.12n)/9. Substitute into Equation 1: 0.40n = 15.6 × (648 + 0.12n)/9 − 720 → 0.40n = 1123.2 + 0.208n − 720 → 0.192n = 403.2 → n = 2100. Substituting back: 9b = 648 + 0.12 × 2100 = 648 + 252 = 900 → b = 100.
  4. Total exports of P = 20b = 20 × 100 = 2000. Exports of P to X = 600, to C = 1200. Therefore, exports of P to ROW = 2000 − 600 − 1200 = 200.

Final Answer: 200

Question 3

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

Solution

Setup: With n = 2100 (total ROW exports) and b = 100 already determined, we use the percentage breakdown of ROW's exports (clue 4) to identify what ROW sends to P and X. The remainder — after accounting for all external destinations including C — represents the intra-ROW trade.

Steps:

  1. Total exports of ROW = n = 2100. From clue 4: exports of ROW to P = 40% × 2100 = 840. Exports of ROW to X = 12% × 2100 = 252.
  2. Exports of ROW to C = 0, because clue 5 states that P is the only country that exports to C. ROW cannot export to C.
  3. Exports of ROW to ROW (intra-ROW) = Total ROW exports − ROW→P − ROW→X − ROW→C = 2100 − 840 − 252 − 0 = 1008.

Final Answer: 1008

Question 4

What is the trade balance of ROW?

Solution

Setup: With the complete trade matrix resolved (b = 100, n = 2100, c = 400), we directly compute ROW's total exports and total imports by aggregating all bilateral flows directed toward ROW, then apply the trade balance formula: Trade Balance = Exports − Imports.

Steps:

  1. Total exports of ROW = n = 2100 (already established).
  2. Compute total imports of ROW by summing all flows directed toward ROW from every source: from P → 200 (solved in Q2), from X → total exports of X minus X's exports to P, C, and intra-X flows. Exports of X = 11b = 1100. X exports to P = 4.4b = 440, X exports to C = 0 (P is the only exporter to C). So X exports to ROW = 1100 − 440 − (any X to C, which is 0) = 660. From C → 32 (4% of 800, as established). From ROW itself (intra-ROW) → 1008.
  3. Total imports of ROW = 200 + 660 + 32 + 1008 = 1900. Trade balance of ROW = Exports − Imports = 2100 − 1900 = 200.

Final Answer: 200 (Option op4)

Question 5

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

Solution

Setup: With b = 100 and c = 400 fully determined, we compute total trade (Exports + Imports) for each of P, X, and C using their parametric expressions derived from the normalized trade balance conditions, then compare the three values.

Steps:

  1. Total trade of P = Exports_P + Imports_P = 10a + 10a = 20a. Since a = 2b = 200, total trade of P = 20 × 200 = 4000. Equivalently, 40b = 40 × 100 = 4000.
  2. Total trade of X = Exports_X + Imports_X = 11b + 9b = 20b = 20 × 100 = 2000.
  3. Total trade of C = Exports_C + Imports_C = 2c + 3c = 5c = 5 × 400 = 2000.
  4. Comparison: P = 4000, X = 2000, C = 2000. Both X and C are tied at the minimum total trade of 2000, which is exactly half of P's total trade.

Final Answer: Both X and C (Option op3)