The number of positive integers less than 1000, having exactly two distinct prime factors, is:
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Visual POE 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 is greater than the population in 2020 and \( x - y = 10 \), what is the smallest possible population in 2021?
Anil mixes cocoa with sugar in the ratio 3 : 2 to prepare mixture A, and coffee with sugar in the ratio 7 : 3 to prepare mixture B. He combines mixtures A and B in the ratio 2 : 3 to make a new mixture C. If he mixes C with an equal amount of milk to make a drink, then the percentage of sugar in this drink will be:
Let both the sequences \(a_1, a_2, a_3, \ldots\) and \(b_1, b_2, b_3, \ldots\) be arithmetic progressions such that their common differences are prime numbers. If \( a_4 = b_4 \), \( a_7 = b_7 \), and \( b_1 = 0 \), then \( a_1 \) is equal to: