CAT Inequalities Bible Top 10 Must Solve Inequalities Questions covering 80% of Syllabus – Page 8
All 38 Inequalities questions from CAT papers. Tap Show answer, or open the detailed solution (free login). Page 8 of 11.
Refer to the passage above ↑
In an examination, there were 75 questions. 3 marks were awarded for each correct answer, 1 mark was deducted for each wrong answer and 1 mark was awarded for each unattempted question. Rayan scored a total of 97 marks in the examination. If the number of unattempted questions was higher than the number of attempted questions, then the maximum number of correct answers that Rayan could have given in the examination is
Answer: 24
Solution — first steps
Step 1. Let correct c, wrong w, unattempted u. Then c+w+u = 75 and 3c−w+u = 97.
Step 2. Subtract to obtain c−w = 11, hence w=c−11 and u = 86−2c.
Step 2. Subtract to obtain c−w = 11, hence w=c−11 and u = 86−2c.
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Refer to the passage above ↑
Five students, including Amit, appear for an examination in which possible marks are integers between 0 and 50, both inclusive. The average marks for all the students is 38 and exactly three students got more than 32. If no two students got the same marks and Amit got the least marks among the five students, then the difference between the highest and lowest possible marks of Amit is
Answer: D. 20
Solution — first steps
Step 1. Total marks 190. To minimize Amit, maximize the other four as 50, 49, 48, 32.
Step 2. This gives minimum 11 and meets exactly three scores above 32.
Step 2. This gives minimum 11 and meets exactly three scores above 32.
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Refer to the passage above ↑
The number of distinct integer values of n satisfying (4 − log2 n) / (3 − log4 n) < 0 is
Answer: 47
Solution — first steps
Step 1. Put t=log 2 n, so log 4 n=t/2 and n>0.
Step 2. The rational expression is(4−t)/(3−t/2).
Step 2. The rational expression is(4−t)/(3−t/2).
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Refer to the passage above ↑
If a and b are non-negative real numbers such that a+ 2b = 6, then the average of the maximum and minimum possible values of (a+ b) is
Answer: D. 4.5
Solution — first steps
Step 1. From a+2b6 and nonnegativity, 0≤b≤3.
Step 2. Target a+b=6−b ranges from 3 to 6.
Step 2. Target a+b=6−b ranges from 3 to 6.
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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 21 repeating CAT PYQs and how much each adds
| CAT PYQ | Repeating CAT PYQ | Questions | Representative | Cumulative questions | Cumulative share |
|---|---|---|---|---|---|
| 1 | Exponential bounds and smallest integer periods | 7 | CAT 2021 S2 Q15 | 7 | 12.73% |
| 2 | Discriminant bounds for real roots or ranges | 6 | CAT 2022 S1 Q5 | 13 | 23.64% |
| 3 | Linear allocation bounds with nonnegative counts | 6 | CAT 2022 S1 Q8 | 19 | 34.55% |
| 4 | Absolute value intervals and sign cases | 5 | CAT 2021 S1 Q2 | 24 | 43.64% |
| 5 | Ordered values and average bounds | 5 | CAT 2022 S2 Q8 | 29 | 52.73% |
| 6 | Logarithmic bounds and monotonicity | 4 | CAT 2024 S2 Q9 | 33 | 60.00% |
| 7 | Rational sign charts and excluded poles | 3 | CAT 2021 S1 Q1 | 36 | 65.45% |
| 8 | Set overlap bounds and feasible endpoints | 3 | CAT 2022 S1 Q17 | 39 | 70.91% |
| 9 | Finite integer enumeration within bounds | 3 | CAT 2025 S1 Q17 | 42 | 76.36% |
| 10 | Floor intervals and endpoint inclusion | 2 | CAT 2022 S1 Q12 | 44 | 80.00% |
| 11 | Factorial size bounds | 1 | CAT 2022 S2 Q13 | 45 | 81.82% |
| 12 | Bounds on eligible AP terms | 1 | CAT 2022 S3 Q17 | 46 | 83.64% |
| 13 | Remainders with an upper population bound | 1 | CAT 2022 S3 Q19 | 47 | 85.45% |
| 14 | Polygon side inequality | 1 | CAT 2022 S3 Q22 | 48 | 87.27% |
| 15 | Speed bound with a palindrome restriction | 1 | CAT 2023 S1 Q8 | 49 | 89.09% |
| 16 | Translate time bounds to work rate bounds | 1 | CAT 2023 S3 Q8 | 50 | 90.91% |
| 17 | Quadratic percentage growth inequality | 1 | CAT 2023 S3 Q10 | 51 | 92.73% |
| 18 | Geometric regions defined by inequalities | 1 | CAT 2024 S1 Q4 | 52 | 94.55% |
| 19 | Square bound with an equality condition | 1 | CAT 2024 S1 Q8 | 53 | 96.36% |
| 20 | Compare quadratic extrema | 1 | CAT 2025 S1 Q8 | 54 | 98.18% |
| 21 | Range by completing the square and reciprocal bounds | 1 | CAT 2021 S2 Q13 | 55 | 100% |
Based on CAT Actual Quant Papers.