CAT Averages Bible Top 10 Must Solve Averages Questions covering 90% of Syllabus – Page 5
All 10 Averages questions from CAT papers. Tap Show answer, or open the detailed solution (free login). Page 5 of 5.
Refer to the passage above ↑
In an examination, the average marks of students in sections A and B are 32 and 60, respectively. The number of students in section A is 10 less than that in section B. If the average marks of all the students across both the sections combined is an integer, then the difference between the maximum and minimum possible number of students in section A is
Answer: 63
Solution — first steps
Step 1. Let section A count a>0, section B count a+10.
Step 2. Combined average=(32a+60(a+10))/(2a+10)=46+70/(a+5).
Step 2. Combined average=(32a+60(a+10))/(2a+10)=46+70/(a+5).
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Refer to the passage above ↑
Consider six distinct natural numbers such that the average of the two smallest numbers is 14, and the average of the two largest numbers is 28. Then, the maximum possible value of the average of these six numbers is
Answer: D. 22.5
Solution — first steps
Step 1. Order numbers a<b<c<d<e<f. Given a+b = 28 and e+f(56).
Step 2. As e<f and integers, e≤27.
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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.