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Difference of a 3-digit number and its digit swap: 99(X - Z) or 90(X - Y)

This type of question, asked 3 times: CDS 2 2024, CDS 2 2025, CDS 1 2026. All 3 questions below, oldest first.

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  1. Question 1

    CDS 2 2024

    89
    XYZXYZ is a 3-digit number, where XX, YY, ZZ are distinct non-zero digits. The difference between the two 3-digit numbers XYZXYZ and YXZYXZ is 90. How many possible values exist for the sum (X+Y)(X + Y) ?

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  2. Question 2

    CDS 2 2025

    19
    Let XYZXYZ be a 3-digit number. Let DD be the difference between XYZXYZ and ZYXZYX. What is the remainder when DD is divided by 99?

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  3. Question 3

    CDS 1 2026

    80
    A Question is given followed by two Statements I and II. Consider the Question and the Statements and mark the correct option. Question : Let XYZ be a 3-digit number and the difference between XYZ and ZYX is equal to PQR. Is (P+R)(P + R) equal to Q ? Statement-I : P=3P = 3 Statement-II : R=6R = 6 Which one of the following is correct in respect of the above Question and the Statements ?

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