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📌 Section 1 is Logical reasoning specially designed for CAT
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SET 1 — 🔍 CAT Level
An agricultural development board is studying the resource requirements of different crops cultivated in a semi-arid region. Five major crops are selected for analysis: Wheat, Rice, Sugarcane, Cotton, and Maize.
The board wants to ensure that the minimum farming requirements of Water, Fertilizer, and Labor Hours are fulfilled for a model agricultural project.
The Minimum Resource Requirement (MRR) for the project is:
Water = 1200 liters
Fertilizer = 90 kg
Labor = 150 hours
The table below shows the resource requirement per acre for each crop.
The additional information is also known:
Each acre contributes a certain percentage of the MRR. For example, one acre of Rice satisfies 25% of the Water requirement.
Further, the number of acres under any crop should be a whole number.
Question 1
The crop(s) that can satisfy at least half of the MRR for all the three resources using not more than three acres of that single crop alone is:
Only Rice and Sugarcane
Only Sugarcane
Only Rice, Sugarcane, and Cotton
Only Cotton
Question 2
If only A acres of Sugarcane and B acres of Rice are included in the agricultural project, what is the minimum value of A + B that will satisfy the MRR of all the three resources?
Question 3
When one acre of each of the five crops is included in the agricultural project, which of the following resources satisfies the least fraction of the MRR?
Fertilizer satisfies 19/20 of the MRR.
Labor satisfies 23/25 of the MRR.
Water satisfies 131/120 of the MRR.
Fertilizer satisfies 8/9 of the MRR.
Question 4
How many crops can satisfy at least 20% of the MRR for at least two resources in one acre?
1
2
3
4
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✅ Answers & Explanations
Final Table
Crop | Water | Fertilizer | Labor |
|---|---|---|---|
Wheat | 180 | 12 | 20 |
Rice | 300 | 18 | 25 |
Sugarcane | 450 | 25 | 40 |
Cotton | 220 | 15 | 35 |
Maize | 160 | 10 | 18 |
Given MRR
Water = 1200 liters
Fertilizer = 90 kg
Labor = 150 hours
Set 1
Q1 Solution
Need at least half of MRR for all 3 resources using not more than 3 acres.
Half MRR:
Water = 600
Fertilizer = 45
Labor = 75
Check crops with 3 acres:
Wheat: 540, 36, 60 → fails
Rice: 900, 54, 75 → satisfies
Sugarcane: 1350, 75, 120 → satisfies
Cotton: 660, 45, 105 → satisfies
Maize: 480, 30, 54 → fails
✅ Answer: 3) Only Rice, Sugarcane, and Cotton
Q2 Solution
Only Sugarcane and Rice are used.
Let Sugarcane = A acres, Rice = B acres.
Requirements:
Water: 450A + 300B ≥ 1200
Fertilizer: 25A + 18B ≥ 90
Labor: 40A + 25B ≥ 150
We need minimum A + B.
Try A + B = 3:
Maximum possible water with 3 acres is 3 acres of Sugarcane:
3 × 450 = 1350, enough water.
But fertilizer = 3 × 25 = 75, not enough.
So 3 acres is not enough.
Try A + B = 4.
A = 4, B = 0:
Water = 1800
Fertilizer = 100
Labor = 160
All three MRRs are satisfied.
✅ Answer: 4
Q3 Solution
One acre of each crop is included.
Total resources:
Water = 180 + 300 + 450 + 220 + 160 = 1310
Fertilizer = 12 + 18 + 25 + 15 + 10 = 80
Labor = 20 + 25 + 40 + 35 + 18 = 138
Now compare with MRR:
Water fraction = 1310/1200 = 131/120
Fertilizer fraction = 80/90 = 8/9
Labor fraction = 138/150 = 23/25
Compare:
8/9 = 0.889
23/25 = 0.92
131/120 = 1.092
Least fraction is Fertilizer = 8/9.
✅ Answer: 4) Fertilizer satisfies 8/9 of the MRR
Q4 Solution
Need crops that satisfy at least 20% of MRR for at least two resources in one acre.
20% of MRR:
Water = 240
Fertilizer = 18
Labor = 30
Check each crop:
Wheat: Water 180 ❌, Fertilizer 12 ❌, Labor 20 ❌ → 0 resources
Rice: Water 300 ✅, Fertilizer 18 ✅, Labor 25 ❌ → 2 resources
Sugarcane: Water 450 ✅, Fertilizer 25 ✅, Labor 40 ✅ → 3 resources
Cotton: Water 220 ❌, Fertilizer 15 ❌, Labor 35 ✅ → 1 resource
Maize: Water 160 ❌, Fertilizer 10 ❌, Labor 18 ❌ → 0 resources
Only Rice and Sugarcane qualify.
✅ Answer: 2) 2
⚡ Brain teasers are not just about getting the right answer — they train you to think differently under pressure.
Stay consistent with your daily practice, challenge your assumptions, and keep sharpening your reasoning skills.
See you in tomorrow’s challenge!