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Remainders of two numbers known: remainder of their sum or difference

This type of question, asked 2 times: CDS 2 2022, CDS 1 2025. All 2 questions below, oldest first.

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  1. Question 1

    CDS 2 2022

    19
    There are two natural numbers x and y, where x>yx > y. When x is divided by 6, it leaves the remainder 2 and; when y is divided by 6, it leaves the remainder 3. What is the remainder when (x−y)(x - y) is divided by 6 ?

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  2. Question 2

    CDS 1 2025

    43
    There are two natural numbers m and n (m>n)(m > n). When m is divided by 12, it leaves a remainder 4. When n is divided by 12, it leaves a remainder 6. Which of the following statements is/are correct ? I. The remainder when (m+n)(m + n) is divided by 12 is 10. II. The remainder when (m−n)(m - n) is divided by 12 is 10. Select the correct answer using the code given below :

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