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Remainders each short of the divisor by the same amount: N = k x LCM - d

This type of question, asked 2 times: CDS 2 2016, CDS 2 2024. All 2 questions below, oldest first.

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  1. Question 1

    CDS 2 2016

    6
    AA is a set of positive integers such that when divided by 2, 3, 4, 5 and 6 leaves the remainder 1, 2, 3, 4 and 5 respectively. How many integers between 0 and 100 belong to the set AA ?

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  2. Question 2

    CDS 2 2024

    3
    Let NN be a 5-digit number. When NN is divided by 6, 12, 15, 24 it leaves respectively 2, 8, 11, 20 as remainders. What is the greatest value of NN ?

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