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CAT 2025 Slot 3 DILR · Set 1 of 5Logical ReasoningHard DifficultyQ1–Q5 · 2 MCQ + 3 TITA

CAT 2025 Slot 3 DILR Set 1: Math Puzzles (5 Questions) with Solutions

The Math Puzzles set from the official CAT 2025 Slot 3 DILR paper: the caselet, all 5 questions, the official answer key and a step-by-step solution for each. 100% free, no sign-up.

The Set: Read the Caselet First

CAT 2025 Slot 3 DILR · Questions 1–5
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.

In the exam this set competed with 4 others for 40 minutes. Budget about 8 minutes if you attempt it.

Q1. Math Puzzles

TITA · +3 / 0
How much is exported from C to X, in IC?
Correct Answer
48
Step-by-step solution
📌 Core Concept
C's imports are known from clue 5, so the normalized trade balance in clue 1 gives C's total exports. Clue 3 then splits those exports by destination.
🔢 Step-by-Step Solution
1
Clue 5 says P is the only country that exports to C, so C's imports are 1200.
2
Let C's exports be EE. Its normalized balance is −20%-20\%, so E−1200E+1200=−0.2\frac{E-1200}{E+1200}=-0.2.
3
Then E−1200=−0.2E−240E-1200=-0.2E-240, so 1.2E=9601.2E=960 and E=800E=800.
4
By clue 3, 90% of 800 goes to P, which is 720. 4% goes to ROW, which is 32.
5
The remaining 6% goes to X. C cannot export to itself, so this is the only other destination: 0.06×800=480.06\times 800=48.
Quick Check
720+32+48=800720+32+48=800, which matches C's total exports.
Correct Answer: 48

Q2. Math Puzzles

TITA · +3 / 0
How much is exported from P to ROW, in IC?
Correct Answer
200
Step-by-step solution
📌 Core Concept
P's exports equal its imports because its normalized balance is 0%. Set up equations for the unknown total exports of ROW (call it RR) and solve them together.
🔢 Step-by-Step Solution
1
C's exports are 800, from the previous question. They go 720 to P, 32 to ROW and 48 to X.
2
Let P's imports be IPI_P. Clue 2 says X supplies 22% of this, so X's exports to P equal 0.22IP0.22I_P.
3
Clue 2 says 40% of X's exports go to P, so X's total exports are 0.22IP0.4=0.55IP\frac{0.22I_P}{0.4}=0.55I_P.
4
X's normalized balance is 10%, so EX=119IXE_X=\frac{11}{9}I_X. This gives IX=911×0.55IP=0.45IPI_X=\frac{9}{11}\times 0.55I_P=0.45I_P.
5
X's imports are 600 from P, 48 from C and 0.12R0.12R from ROW (clue 4). So IX=648+0.12RI_X=648+0.12R.
6
P's imports are 720 from C, 0.4R0.4R from ROW and 0.22IP0.22I_P from X. So 0.78IP=720+0.4R0.78I_P=720+0.4R.
7
Substitute IP=648+0.12R0.45=1440+0.2667RI_P=\frac{648+0.12R}{0.45}=1440+0.2667R into the equation from step 6. This gives 1123.2+0.208R=720+0.4R1123.2+0.208R=720+0.4R, so R=2100R=2100 and IP=2000I_P=2000.
8
P's exports are also 2000. P sends 600 to X and 1200 to C, so the remainder to ROW is 2000−1800=2002000-1800=200.
Quick Check
Then IX=648+252=900I_X=648+252=900 and EX=1100E_X=1100. Since 1100−9002000=10%\frac{1100-900}{2000}=10\%, X's balance condition holds.
Correct Answer: 200

Q3. Math Puzzles

TITA · +3 / 0
How much is exported from ROW to ROW, in IC?
Correct Answer
1008
Step-by-step solution
📌 Core Concept
ROW's total exports are 2100, from the earlier equations. ROW's exports to X and P are given as percentages, and ROW sends nothing to C. The rest goes to ROW itself.
🔢 Step-by-Step Solution
1
Solving P's and X's balance conditions gives ROW's total exports as 2100. Here IP=2000I_P=2000 and IX=648+0.12RI_X=648+0.12R with R=2100R=2100.
2
Clue 4 says 12% of ROW's exports go to X, which is 0.12×2100=2520.12\times 2100=252.
3
Clue 4 says 40% go to P, which is 0.4×2100=8400.4\times 2100=840.
4
Clue 5 says P is the only exporter to C, so ROW exports nothing to C.
5
The remaining share is 100%−12%−40%=48%100\%-12\%-40\%=48\%. This is the amount ROW exports within itself: 0.48×2100=10080.48\times 2100=1008.
Quick Check
252+840+1008=2100252+840+1008=2100, which matches ROW's total exports.
Correct Answer: 1008

Q4. Math Puzzles

MCQ · +3 / −1
What is the trade balance of ROW?
  1. A) 100
  2. B) -200
  3. C) 0
  4. D) 200
Correct Answer
D) 200
Step-by-step solution
📌 Core Concept
The trade balance of ROW is its exports minus its imports. Exports to ROW from ROW itself cancel, because they appear on both sides.
🔢 Step-by-Step Solution
1
ROW's total exports are 2100. Of this, 1008 goes to ROW itself, so exports to the three named countries total 1092.
2
Imports from P: P sends 200 to ROW.
3
Imports from C: C sends 4% of 800, which is 32.
4
Imports from X: X's exports are 1100, and 40% (440) goes to P. X cannot export to C because P is C's only supplier. So the remaining 660 goes to ROW.
5
ROW's imports from outside are 200+32+660=892200+32+660=892, plus 1008 from itself, for a total of 1900.
6
Trade balance =2100−1900=200=2100-1900=200.
Why Not the Others
A (100) and B (-200) do not match the totals of 2100 exports and 1900 imports.
C (0) would need imports of 2100, but they are 1900.
Correct Answer: D

Q5. Math Puzzles

MCQ · +3 / −1
Which among the countries P, X, and C has/have the least total trade?
  1. A) Only X
  2. B) Only P
  3. C) Both X and C
  4. D) Only C
Correct Answer
C) Both X and C
Step-by-step solution
📌 Core Concept
Total trade is exports plus imports. Compute it for each of P, X and C and compare.
🔢 Step-by-Step Solution
1
P: exports and imports are both 2000, since its balance is 0%. Total trade is 4000.
2
X: exports are 1100 and imports are 900, from the balance condition, so total trade is 2000. Check: 1100−9002000=10%\frac{1100-900}{2000}=10\%.
3
C: exports are 800 and imports are 1200 (all from P). Total trade is 2000. Check: 800−12002000=−20%\frac{800-1200}{2000}=-20\%.
4
X and C tie at 2000, and both are below P's 4000.
Why Not the Others
A (Only X) and D (Only C) each ignore the other country, which has the same total.
B (Only P) is wrong because P has the largest total trade, not the least.
Correct Answer: C
Timed Practice

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CAT 2025 Slot 3 DILR at a Glance

Sets in this section5
Questions in this section22
Section time40 minutes
Convenor IIMIIM Kozhikode

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