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Missing digit(s) making a number divisible by 3 or 9 (digit-sum rule)

This type of question, asked 4 times: CDS 2 2018, CDS 2 2019, CDS 2 2020, CDS 2 2024. All 4 questions below, oldest first.

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  1. Question 1

    CDS 2 2018

    5
    A five-digit number XY235 is divisible by 3 where X and Y are digits satisfying X+Y≤5X + Y \le 5. What is the number of possible pairs of values of (X, Y) ?

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  2. Question 2

    CDS 2 2019

    3
    How many pairs (A, B) are possible in the number 479865AB if the number is divisible by 9 and it is given that the last digit of the number is odd ?

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  3. Question 3

    CDS 2 2020

    6
    If the number 23P62971335 is divisible by the smallest odd composite number, then what is the value of P ?

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  4. Question 4

    CDS 2 2024

    28
    Let N=12345678ABN = 12345678AB be a 10-digit number, where AA, BB are digits. If NN is divisible by 9, then which of the following statements is/are correct ? I. (A+B)(A + B) is divisible by 9 II. If AA is odd, then BB is odd Select the answer using the code given below :

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