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    There are six toys arranged one above the other in form of a stack, the lowermost is numbered 1 and the toy above it as 2 and so on. Each toy is of a
    Question

    There are six toys arranged one above the other in form of a stack, the lowermost is numbered 1 and the toy above it as 2 and so on. Each toy is of a different colour Purple, Pink, White, Yellow, Red and Grey. Purple toy is at the even position but not at the top. Red toy is not adjacent to white or yellow toy. Grey toy is at the 5th position. There are two toys between pink and white toy where pink toy is above the white one. White toy is not at the bottommost position. Which toy among the following options is at an odd position?

    A.

    White toy

    B.

    Pink toy

    C.

    Yellow toy

    D.

    Purple toy

    Correct option is A

    SOLUTION:
    Information Provided:
    1. Purple toy is at an even position but not at the top.
    2. Red toy is not adjacent to the white or yellow toy.
    3. Grey toy is at the 5th position.
    4. There are two toys between the pink and white toy, and the pink toy is above the white one.
    5. White toy is not at the bottommost position.
    Step-by-Step Arrangement:
    · Grey toy is in the 5th position (this is fixed).
    · Purple toy must be at an even position, and it's not at the top. The even positions are 2, 4, and 6. Since it's not at the top (6th position), it must be either in the 2nd or 4th position.
    · Pink toy is above the white toy, and there are two toys between them. This means if Pink is at position xxx, then White is at position x−3x-3x−3. For example, if Pink is at the 4th position, White must be at the 1st position.
    · White toy is not at the bottom (1st position), so Pink cannot be at the 4th position. Therefore, Pink must be at the 6th position, and White at the 3rd position.
    · Red toy cannot be adjacent to White or Yellow. So, Red cannot be in the 2nd or 4th position (which are adjacent to White in the 3rd position and Yellow, yet to be placed). Therefore, Red toy must be at the 1st position.
    · Yellow toy is the only toy left, and it must be at the 4th position.
    Final Arrangement:
    1. Red toy (Position 1)
    2. Purple toy (Position 2)
    3. White toy (Position 3)
    4. Yellow toy (Position 4)
    5. Grey toy (Position 5)
    6. Pink toy (Position 6)

    Odd Positions:
    · The odd positions are 1, 3, and 5.
    · Toys at odd positions: Red (1st), White (3rd), and Grey (5th).
    Correct Answer:
    (a) White toy is at an odd position (3rd position).

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