CAT Averages Bible Top 10 Must Solve Averages Questions covering 90% of Syllabus – Page 2
All 10 Averages questions from CAT papers. Tap Show answer, or open the detailed solution (free login). Page 2 of 5.
There are three persons \(\mathrm{A}, \mathrm{B}\) and \(\mathrm{C}\) in a room. If a person \(\mathrm{D}\) joins the room, the average weight of the persons in the room reduces by \(x \mathrm{~kg}\). Instead of \(\mathrm{D}\), if person \(\mathrm{E}\) joins the room, the average weight of the persons in the room increases by \(2 x \mathrm{~kg}\). If the weight of \(\mathrm{E}\) is \(12 \mathrm{~kg}\) more than that of \(\mathrm{D}\), then the value of \(x\) is
Answer: 1
Solution — first steps
Step 1. Let the original total weight of A,B,C be S.
Step 2. With D, average falls by x: (S+D)/4=S/3−x.
Step 2. With D, average falls by x: (S+D)/4=S/3−x.
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Last day solving checklist
- Name the unknown. Include its unit and state whether it is a count, amount, rate or parameter.
- Form the relationships. Translate each given condition into an equation or restriction.
- Choose the method. Use the formula, substitution, elimination, a sign chart or a bound appropriate to this concept.
- Check restrictions. Check integer counts, signs, nonzero denominators, domains and all original conditions.
- Verify the answer. Substitute into the original question; for an extreme, show a feasible example reaches it.
All 13 repeating CAT PYQs and how much each adds
| CAT PYQ | Repeating CAT PYQ | Questions | Representative | Cumulative questions | Cumulative share |
|---|---|---|---|---|---|
| 1 | Weighted subgroup payroll or marks averages | 4 | CAT 2023 S1 Q10 | 4 | 16.67% |
| 2 | Add a person or compare alternative final averages | 3 | CAT 2021 S2 Q14 | 7 | 29.17% |
| 3 | Maximise or minimise distinct scores with a fixed total | 3 | CAT 2021 S3 Q7 | 10 | 41.67% |
| 4 | Recover entries from overlapping or prefix totals | 2 | CAT 2024 S1 Q11 | 12 | 50.00% |
| 5 | Change an entry and track the total difference | 2 | CAT 2022 S2 Q8 | 14 | 58.33% |
| 6 | Whole number averages impose divisibility | 2 | CAT 2022 S1 Q7 | 16 | 66.67% |
| 7 | Weighted unit cost from total spending and quantity | 2 | CAT 2021 S1 Q7 | 18 | 75.00% |
| 8 | Fixed cost divided by changing headcount | 1 | CAT 2021 S3 Q8 | 19 | 79.17% |
| 9 | Unknown group counts produce rational average equations | 1 | CAT 2021 S1 Q16 | 20 | 83.33% |
| 10 | Savings target average converted to an annual total | 1 | CAT 2022 S2 Q5 | 21 | 87.50% |
| 11 | Permutation symmetry gives an equal positional contribution | 1 | CAT 2022 S3 Q8 | 22 | 91.67% |
| 12 | Mean of AP terms equals the endpoint mean | 1 | CAT 2022 S3 Q17 | 23 | 95.83% |
| 13 | An arithmetic mean fixes a middle salary | 1 | CAT 2023 S1 Q12 | 24 | 100% |
Based on CAT Actual Quant Papers.