Let \( a \) and \( b \) be two sequences such that \( a_n = 13 + 6(n-1) \) and \( b_n = 15 + 7(n-1) \) for all natural numbers \( n \). Then, the largest three-digit integer that is common to both these sequences is:
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Breakup G Strategy CAT 2023 Slot 3
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Question 1 of 5
A container has 40 liters of milk. Then, 4 liters are removed from the container and replaced with 4 liters of water. This process is repeated until the volume of milk becomes less than that of water. The smallest number of times this process is repeated to achieve this is:
If a person D joins a group of three people, the average weight of the group reduces by \( x \) kg. If another person E joins instead of D, the average increases by \( 2x \) kg. If E’s weight is 12 kg more than D’s, then the value of \( x \) is:
In a fruit market, there are initially 40% mangoes, 30% bananas, and 30% apples. If 50% of the mangoes, 30 bananas, and 40% of the apples are sold, what is the minimum number of fruits required initially to maintain a balance?
Let \( a_1, a_2, a_3, \ldots \) 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: