Chapter 4 · Topic 4.3 · Prelims + Mains3 of 3
Decision Making & Problem Solving: Problem-solving approach: rules, cases and what is
Key points
- Problem solving by cases.
8 PYQs 2014–2026
Prelims box: facts and traps
| Step | What to do |
|---|---|
| 1 | Write each rule in short form |
| 2 | List the cases the question names |
| 3 | For each option, test it in every case |
| 4 | Keep only the option true in all cases. |
- CSAT 2012, Q63: Consider the following statements: Prelims 2012 Electric machines are cheap to maintain and cause no pollution: two advantages, so they are preferable to use (d).
- CSAT 2012, Q40: Only six roads A, B, C, P, Q and R connect a military camp to the rest of the country.
- Trap: The other options give exact numbers that the rules never fix.
- Trap (UPSC Prelims 2012): “All machines consume energy” is incorrect. “Electricity provides energy” is incorrect. “Electrically operated machines are cheap to maintain” is incorrect. “Electrically operated machines do not cause pollution” is incorrect.
Problem-solving approach: rules, cases and what is
certain Problem-solving questions give a few rules and ask what is certain. Method: list the rules, take each case (normal, storm, flood), and keep only what is true in every case.
CSAT 2012, Q40: Only six roads A, B, C, P, Q and R connect a military camp to the rest of the country. Only one out of A, P and R is open at any one time. If B is closed so is Q. Only one of A and B is open during storms. P is closed during floods. In the context, which one of the following statements is correct? Prelims 2012 During storms exactly one of A and B is open, so at least one road is open: (b). The other options give exact numbers that the rules never fix. Answer (b).
Only six roads A, B, C, P, Q and R connect a military camp to the rest of the country. Only one out of A, P and R is open at any one time. If B is closed so is Q. Only one of A and B is open during storms. P is closed during floods. In the context, which one of the following statements is correct?
- Under normal conditions only three roads are open.
- During storms at least one road is open.
- During floods only three roads are open.
- During calamities all roads are closed.
Show answer
Answer: (b) · UPSC official key
CSAT 2012, Q63: Consider the following statements: Prelims 2012 Electric machines are cheap to maintain and cause no pollution: two advantages, so they are preferable to use (d). Nothing says how many machines are electric, or that electricity is the only energy. Answer (d).
Consider the following statements: 1. All machines consume energy. 2. Electricity provides energy. 3. Electrically operated machines are cheap to maintain. 4. Electrically operated machines do not cause pollution. Which one of the following inferences can be drawn from the above statements?
- All machines are run by electric energy.
- There is no form of energy other than electricity.
- Most machines are operated on electric energy.
- Electrically operated machines are preferable to use.
Show answer
Answer: (d) · UPSC official key
| Step | What to do |
|---|---|
| 1 | Write each rule in short form |
| 2 | List the cases the question names |
| 3 | For each option, test it in every case |
| 4 | Keep only the option true in all cases |
Battle IAS teaching summary.
Mains box: analysis and answer points
- certain Problem-solving questions give a few rules and ask what is certain.
- Method: list the rules, take each case (normal, storm, flood), and keep only what is true in every case.
- Likely next angle: Certain only
Practice
Prelims PYQs on this topic (8)
What is the least four-digit number when divided by 3, 4, 5 and 6 leaves a remainder 2 in each case?
Answer (b) & explanation
The least such number is 1022 (b). Step 1: a number leaving remainder 2 when divided by 3, 4, 5 and 6 has the form LCM × k + 2. LCM(3, 4, 5, 6) = 60. Step 2: the smallest four-digit multiple of 60: 60 × 17 = 1020. Step 3: add 2: 1022. Option (a), 1012, is 60 × 16·8 + 2, not valid. Option (c), 1122 = 60 × 18·67 + 2, fails. Option (d) also fails.
Tip: same remainder for all divisors → number = LCM × k + remainder. Find the LCM, then the first suitable multiple.
Answer as per the official UPSC answer key.
In the context of food and nutritional security of India, enhancing the 'Seed Replacement Rates' of various crops helps in achieving the food production targets of the future. But what is/are the constraint/constraints in its wider/greater implementation?
- 1. There is no National Seeds Policy in place.
- 2. There is no participation of private sector seed companies in the supply of quality seeds of vegetables and planting materials of horticultural crops.
- 3. There is a demand-supply gap regarding quality seeds in case of low value and high volume crops.
Select the correct answer using the code given below.
Answer (b) & explanation
The seed replacement rate is the share of area sown with fresh certified seed instead of farm-saved seed. Statement 1 is wrong because India has had a National Seeds Policy since 2002. Statement 2 is wrong because private firms dominate vegetable and horticulture seed. The real gap lies in low-value, high-volume crops such as wheat, paddy and pulses, where private firms see little profit (3 correct). So the answer is (b).
Public bodies like the National Seeds Corporation and State seed corporations fill this gap. Notice how better seed is the cheapest input for higher yields.
Answer as per the official UPSC answer key.
A toy T jumps forward or backward. In each forward jump, it moves 5' forward whereas in each backward jump, it moves 2' backward. If in 31 jumps, T moves exactly 15' forward, then what is the difference of the number of forward and backward jumps?
Answer (d) & explanation
The difference is 9 jumps (d). Step 1: let f be forward jumps and b backward jumps. Total jumps: f + b = 31. Net movement: 5f − 2b = 15. Step 2: put b = 31 − f: 5f − 2(31 − f) = 15, so 5f − 62 + 2f = 15, giving 7f = 77 and f = 11. Then b = 20. Step 3: difference = 20 − 11 = 9. Check: 5 × 11 − 2 × 20 = 55 − 40 = 15 ✓. Options (a), (b) and (c) fail.
Tip: two unknowns need two equations: one for the count and one for the total effect. Always check your answer in both.
Answer as per the official UPSC answer key.
What is the minimum number of times one needs to measure to get 298 litres of water from a tank, if the measuring cylinders have capacities 1 litre, 6 litres, 25 litres and 100 litres?
Answer (b) & explanation
The minimum is 5 measures (b). Step 1: adding only, the best is 2 × 100 + 2 × 25 + 8 × 6 = 298, which needs 12 measures. That is not an option, so think about taking water out too. Step 2: 298 = 3 × 100 − 2 × 1. Pour in 100 litres three times, then remove 1 litre twice: 5 measures. Step 3: could 4 work? 3 × 100 leaves 2 litres to remove, and no single cylinder holds 2 litres, so 4 is impossible. Options (a), (c) and (d) fail.
Tip: when adding gives too many steps, try overshooting and subtracting. Measuring questions often allow both pouring in and taking out.
Answer as per the official UPSC answer key.
There are four types of weights, namely 1 kg, 2 kg, 5 kg and 10 kg. What is the maximum number of different ways one can measure 20 kg, if at least eight but not more than eleven weights of 1 kg are to be used while measuring?
Answer (b) & explanation
There are 8 ways (b). Step 1: with eight 1 kg weights, we need 12 kg from 2, 5 and 10 kg weights (no more 1s): 10 + 2, 5 + 5 + 2, and six 2s: 3 ways. Step 2: with nine 1 kg, we need 11 kg: only 5 + 2 + 2 + 2: 1 way. Step 3: with ten 1 kg, we need 10 kg: 10, 5 + 5, five 2s: 3 ways. With eleven 1 kg, we need 9 kg: 5 + 2 + 2: 1 way. Total = 3 + 1 + 3 + 1 = 8. Options (a), (c) and (d) miscount.
Tip: fix one variable at a time and count the rest. Here, fixing the number of 1 kg weights keeps the cases clean.
an odd remainder needs exactly one 5 (two or more would be too much or leave an odd gap).
Fell for this one? Most aspirants do. The PYQ Book puts every UPSC trap side by side, so the pattern finally clicks. Try the free sample
Answer as per the official UPSC answer key.
Suppose x, y and z are variables taking positive real numbers as their possible values. It is given that y is directly proportional to x2 and x is inversely proportional to z. For z = 7/25, the values of x and y are 5 and 50, respectively. If y = 98, what is z equal to?
Answer (b) & explanation
z equals 1/5 (b). Step 1: y is directly proportional to x², so y = k × x². With x = 5 and y = 50: 50 = k × 25, so k = 2. Step 2: y = 98 means 2x² = 98, so x² = 49 and x = 7. Step 3: x is inversely proportional to z, so x × z stays the same. At the start: 5 × 7/25 = 7/5. Now 7 × z = 7/5, so z = 1/5. Options (a), (c) and (d) fail.
Tip: "directly proportional" means the ratio stays fixed; "inversely proportional" means the product stays fixed. Find the constant first, then use it.
Answer as per the official UPSC answer key.
Write an answer
In 150 words, explain the significance of Decision Making & Problem Solving with one recent example.
Flashcards (3)
Problem-solving method?
Rules in short form, test every case, keep what is always true.
Roads during storms (2012 Q40)?
At least one road is open.
Electric machines cheap and clean (2012
Q63) imply? They are preferable to use.
Next chapter · 5. General Mental Ability →General Mental Ability: Clocks and calendars