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Primes with a sum or difference condition: parity forces one of them to be 2

This type of question, asked 3 times: CDS 2 2019, CDS 2 2025, CDS 1 2026. All 3 questions below, oldest first.

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  1. Question 1

    CDS 2 2019

    14
    The sum of three prime numbers is 100. If one of them exceeds another by 36, then one of the numbers is

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  2. Question 2

    CDS 2 2025

    4
    Let xx and yy be natural numbers, each less than 20, such that xx, yy, x+yx+y and x−yx-y are prime numbers. How many such combinations of (x, y, x+y, x−y)(x,\ y,\ x+y,\ x-y) are possible?

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  3. Question 3

    CDS 1 2026

    77
    A Question is given followed by two Statements I and II. Consider the Question and the Statements and mark the correct option. Question : Is (p2+q2)(p^2 + q^2) always composite number, where p and q are different prime numbers ? Statement-I : (p−q)(p - q) is an odd integer Statement-II : (p+q)(p + q) is an odd integer Which one of the following is correct in respect of the above Question and the Statements ?

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