Number Systems, Digit Problems and Divisibility Previous Year Questions (PYQs) for GATE DA: 2+ Solved Questions with Step-by-Step Solutions

    Solve 2+ Number Systems, Digit Problems and Divisibility previous year questions for GATE DA with answers and detailed solutions. Free sample questions below.

    Fundamental Rules of Number Formation

    Fundamental Rules of Number Formation

    When forming an -digit number, the most significant digit (the leading digit) can never be .

    Basic Counting Rules

    1. Leading Zero Constraint: For an -digit number, the first position has restricted choices. If forming a number from a set containing , the first position cannot be .
    2. Repetition Allowed: If digits can be repeated, each subsequent position has the full set of available choices.
    3. Repetition Not Allowed: If digits cannot be repeated, each subsequent position has one fewer choice than the previous.

    Example

    Form a 3-digit number from the set without repetition.

    • Hundreds place: choices (cannot be ).
    • Tens place: choices (includes , but one non-zero digit is used).
    • Units place: choices.

    Total numbers = .

    Applying Divisibility Rules to Formed Numbers

    Applying Divisibility Rules

    Fix the digits that satisfy the divisibility rule first, then fill the remaining positions.

    Div by 2
    Unit:
    Div by 4
    Last 2 digits
    Div by 5
    Unit: or

    Worked Example

    How many 4-digit numbers from without repetition are divisible by ?

    Step 1 Fix unit digit: ( choice).
    Step 2 Thousands place: choices.
    Step 3 Hundreds place: choices.
    Step 4 Tens place: choices.

    Total =

    Number Systems, Digit Problems and Divisibility: Solved Questions with Step-by-Step Explanations (2 Problems)

    Question 1 · Quantitative Aptitude MCQ

    The product of the digits of a three-digit number is 70. The sum of the digits of this three-digit number is _____

    1. A.

      12

    2. B.

      14

    3. C.

      16

    4. D.

      18

    Question 2 · Quantitative Aptitude MCQ
    and are distinct single-digit whole numbers taking values from 0 to 9.
    is a two-digit number with being in the units place and in the tens place. Similarly, is a two-digit number.
    It is known that and are consecutive numbers and

    with being a three-digit number.
    The value of is __________
    1. A.

      4

    2. B.

      5

    3. C.

      6

    4. D.

      7

    More previous year questions (pyqs) in this unit

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    Number Systems, Digit Problems and Divisibility Previous Year Questions (PYQs) for GATE DA: 2+ Solved Questions with Step-by-Step Solutions

    Solve 2+ Number Systems, Digit Problems and Divisibility previous year questions for GATE DA with answers and detailed solutions. Free sample questions below.

    A question from this chapter

    Question 1

    The product of the digits of a three-digit number is 70. The sum of the digits of this three-digit number is _____

    Question 2
    and are distinct single-digit whole numbers taking values from 0 to 9.
    is a two-digit number with being in the units place and in the tens place. Similarly, is a two-digit number.
    It is known that and are consecutive numbers and

    with being a three-digit number.
    The value of is __________
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