Let a m × b n = 144. Then the largest possible value of n - m is Options: A) 579 B) 580 C) 289 D) 290

A. 579. Solution: We are given a m × b n = 144. We can express 144 as 2 4 × 3 2 .

CAT Integer Solutions Bible Top 10 Must Solve Integer Solutions Questions covering 80% of Syllabus – Page 7

All 64 Integer Solutions questions from CAT papers. Tap Show answer, or open the detailed solution (free login). Page 7 of 14.

CAT 2023 Slot 2 · Quant

Jayant bought a certain number of white shirts at the rate of Rs 1000 per piece and a certain number of blue shirts at the rate of Rs 1125 per piece. For each shirt, he then set a fixed market price which was 25% higher than the average cost of all the shirts. He sold all the shirts at a discount of 10% and made a total profit of Rs 51000. If he bought both colors of shirts, then the maximum possible total number of shirts that he could have bought is

CAT 2023 Slot 2 · Quant

Let a, b, m and n be natural numbers such that a > 1 and b > 1. If a
m
b
n
144
145
, then the largest possible value of n-m is

CAT 2023 Slot 2 · Quant

A container has 40 liters of milk. 4 liters are removed and replaced with 4 liters of water. This process is repeated. The smallest number of times required for milk to be less than water is:

CAT 2023 Slot 2 · Quant

Let a
m
× b
n
= 144. Then the largest possible value of n - m is

CAT 2023 Slot 2 · Quant

Let both series \( a_1, a_2, a_3, \ldots \) and \( b_1, b_2, b_3, \ldots \) be in arithmetic progression with common differences as prime numbers. If a5=b9, a19=b19 and b2=0, , then a11 equals, find \( a_{19} \):

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 18 repeating CAT PYQs and how much each adds

CAT PYQ	Repeating CAT PYQ	Questions	Representative	Cumulative questions	Cumulative share
1	Integer exponent thresholds	8	CAT 2021 S2 Q15	8	10.67%
2	Integer count equations with totals and bounds	8	CAT 2022 S2 Q15	16	21.33%
3	Prime exponent and divisor restrictions	7	CAT 2022 S1 Q4	23	30.67%
4	Ordered scores and counts under average bounds	6	CAT 2021 S3 Q7	29	38.67%
5	Integer roots and quadratic parameter bounds	6	CAT 2022 S1 Q15	35	46.67%
6	Factor pair enumeration with extra bounds	6	CAT 2024 S1 Q2	41	54.67%
7	AP terms intersections and index restrictions	5	CAT 2021 S2 Q10	46	61.33%
8	Integer points under modulus or linear bounds	4	CAT 2021 S1 Q2	50	66.67%
9	Divisibility of averages ratios and remainders	4	CAT 2022 S1 Q7	54	72.00%
10	Floor and logarithm intervals containing integers	4	CAT 2022 S2 Q14	58	77.33%
11	Digit construction and digit bounds	3	CAT 2021 S2 Q12	61	81.33%
12	Integer feasibility of set overlaps	3	CAT 2022 S1 Q17	64	85.33%
13	Whole time periods and work schedules	3	CAT 2022 S2 Q18	67	89.33%
14	Distribution with minimum or even allocations	2	CAT 2021 S2 Q1	69	92.00%
15	Balancing distinct or near equal integers	2	CAT 2023 S2 Q13	71	94.67%
16	Integer bounds from ratios or polygon sides	2	CAT 2022 S1 Q8	73	97.33%
17	Power equals one and exponent parity	1	CAT 2022 S2 Q17	74	98.67%
18	Integer percentage constrained by net growth	1	CAT 2023 S3 Q10	75	100%

Based on CAT Actual Quant Papers.

CAT Integer Solutions Bible Top 10 Must Solve Integer Solutions Questions covering 80% of Syllabus – Page 7

Solution — first steps

Solution — first steps

Solution — first steps

Solution — first steps

Solution — first steps