Let \( n \) be any natural number such that \( 5^{n-1} < 3^{n+1} \). The least integer value of \( m \) that satisfies \( 3^{n+1} < 2^{n+m} \) for all such \( n \) is?
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Vedic Tables G Strategy CAT 2023 Slot 3
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Question 1 of 4
The population of a town in 2020 was 100,000. The population decreased by \( y\% \) from 2020 to 2021, and increased by \( x\% \) from 2021 to 2022. If the population in 2022 was greater than in 2020 and \( x - y = 10 \), what was the lowest possible population in 2021?
Two collectors A and B collect coins weekly in the ratio 3:4. If A collects a multiple of 7 in 5 weeks and B collects a multiple of 24 in 3 weeks, what is the minimum number of coins collected by A in one week?
Let \( a_n = 46 + 8n \) and \( b_n = 98 + 4n \) be two sequences. Find the sum of all terms common to both sequences.