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Dice Test - 9

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Dice Test - 9
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Weekly Quiz Competition
  • Question 1
    1 / -0
    Two orientations of a die are shown below. When number 2 is on the top, then which number is at the bottom?

    Solution
    From figures (i) and (ii), we conclude that numbers 1, 5, 6 and 3 appear adjacent to number 2. Therefore, number 2 must appear opposite to number 4. Thus, if number 2 is on the top, then number 4 is at the bottom.
  • Question 2
    1 / -0
    Directions: The question is based on the following figures of the same dice.



    Symbol that appears at the bottom in figure (ii) is
    Solution
  • Question 3
    1 / -0
    Directions: The question is based on the following figures of the same dice.



    Which of the following symbols appears on the opposite surface of = symbol?
    Solution
    Correct Answer:
    Because that's the correct orientation.
  • Question 4
    1 / -0
    Directions: The question is based on the following figures of the same dice.



    Which of the following symbol appears opposite to the face with triangle on it?
  • Question 5
    1 / -0
    Two orientations of a block are shown below:



    When six is at the bottom, which number will be at the top?
    Solution
    From figures (i) and (ii), we conclude that the numbers 1, 2, 3 and 4 appear adjacent to 6. Thus, the number 5 will appear opposite 6. Therefore, when 6 is at the bottom, then 5 will be at the top.
  • Question 6
    1 / -0
    A cubical block with designs on the faces is presented as shown in following figures. Find the design on the surface marked with (?).

    Solution
    The orientation of the figure I and figure IV is same. Therefore, option 2 is correct option.
  • Question 7
    1 / -0
    In the given dice, a, b, c and d are written on the adjacent faces in a clockwise order, and e and f at the top and the bottom, respectively. When c is at the top, what will be at the bottom?

    Solution
    Clearly, the six faces of the dice are labelled as shown:
    Face I a, Face II b, Face III c, Face IV d, Face V e, Face VI f
    Therefore, 'a' appears opposite 'c'.
    Hence, when 'c' is at the top, then 'a' will be at the bottom.
  • Question 8
    1 / -0

    Directions For Questions

    Directions: Six dice are shown in the following figure, the upper faces of each dice having been erased. The number of dots on each surface of every dice has been arranged in such a way that the sum of the number of dots on the opposite faces is 7.

    ...view full instructions

    If the dice (i), (ii), (iii) have even number of dots on their bottom faces, then what would be the total number of dots on the top faces?
    Solution
    According to the given figures,
    Top face in (i) dice contain 3 dots;
    Top face in (ii) dice contain 1 dots;
    Top face in (iii) dice contain 3 dots;
    Therefore,
    Total dots = 3 + 1 + 3 = 7
    Correct Answer: 7
  • Question 9
    1 / -0

    Directions For Questions

    Directions: Six dice are shown in the following figure, the upper faces of each dice having been erased. The number of dots on each surface of every dice has been arranged in such a way that the sum of the number of dots on the opposite faces is 7.

    ...view full instructions

    If dice (i), (ii), (iii) have even number of dots on their bottom faces and the dice (iv), (v), (vi) have odd number of dots on their top faces, then what would be the difference in the total number of top face dots between these two sets?
    Solution
    According to the given figures,
    Bottom face of dice (i) contains 4 dots and top face in (i) dice contain 3 dots.
    Bottom face of dice (ii) contains 6 dots and top face in (ii) dice contain 1 dots.
    Bottom face of dice (iii) contains 4 dots top face in (iii) dice contain 3 dots.
    Therefore, Total top face dots = 3 + 1 + 3 = 7
    Top face of dice (iv) contains 1 dot and bottom face in (iv) dice contain 6 dots.
    Top face of dice (v) contains 3 dots and bottom face in (v) dice contain 4 dots.
    Top face of dice (vi) contains 1 dot and bottom face in (vi) dice contain 6 dots.
    Therefore, total top face dots = 1 + 3 + 1 = 5
    Required difference = 7 - 5 = 2

  • Question 10
    1 / -0

    Directions For Questions

    Directions: Six dice are shown in the following figure, the upper faces of each dice having been erased. The number of dots on each surface of every dice has been arranged in such a way that the sum of the number of dots on the opposite faces is 7.

    ...view full instructions

    If odd numbered dice have odd number of dots on their bottom faces, then what would be the total number of dots on the top faces of these dices?
    Solution
    According to the given figures,
    Bottom face in (i) dice contain 3 dots;
    Bottom face in (iii) dice contain 3 dots;
    Bottom face in (v) dice contain 3 dots;
    Therefore,
    Total dots on top faces of dice (i), (iii) and (v) = 4 + 4 + 4 = 12
  • Question 11
    1 / -0

    Directions For Questions

    Directions: Six dice are shown in the following figure, the upper faces of each dice having been erased. The number of dots on each surface of every dice has been arranged in such a way that the sum of the number of dots on the opposite faces is 7.

    ...view full instructions

    If even numbered die has even number of dots on their top faces, what would be the total number of dots on the top faces of these dices?
    Solution
    According to the given figures,
    Top face in (i) dice contain 6 dots;
    Top face in (ii) dice contain 6 dots;
    Top face in (iii) dice contain 6 dots;
    Therefore,
    Total dots = 6 + 6 + 6 = 18
    Correct Answer: 18
  • Question 12
    1 / -0
    Each of the six faces of a cube is numbered by one of the six digits from 1 to 6. The cube is shown in four different orientations in the figures: (i), (ii), (iii) and (iv).



    Which of the following statements are true?

    I. Figures (ii) and (iii) are sufficient to know which face is opposite to the face numbered 6.
    II. Figures (ii) and (iii) are sufficient to know which face is opposite to the face numbered 4.
    III. Figures (i) and (iv) are sufficient to know which face is opposite to the face numbered 3.
    Solution
    All statements I, II and III are true as with the help of figures (ii) and (iii) we can find the face opposite to face numbered 6 and with (ii) and (iii) we can find the face opposite to face numbered 4. With the help of figures (i) and (iv) we can find the face opposite to face numbered 3.
  • Question 13
    1 / -0
    Directions: Six faces of a cube have been marked with numbers 1, 2, 3, 4, 5 and 6. The surfaces of the cube have been unfolded and this unfolded position of the cube has been shown in four different figures (1), (2), (3) and (4). Choose the figure that will be formed when the cube is unfolded.

    Solution
    From the given figure, we found that 2 is adjacent to 1, 3, 4 and 6. So, 2 cannot be opposite to any of 1, 3, 4 and 6.
    Therefore, option 3 is correct because 1 is opposite to 6, 3 is opposite to 4, and 2 is opposite to 5. So, these cannot be adjacent or written together.
  • Question 14
    1 / -0
    Directions: The question is based on a dice having faces numbered from 1 to 6 in different ways as indicated:

    If 1 is adjacent to 2, 4 and 6, then which of the following statements is necessarily true?
    Solution
    If 1 is adjacent to 2, 4 and 6, then either 3 or 5 lies opposite to 1. So, the numbers 3 and 5 cannot lie opposite to each other. Hence, 3 is adjacent to 5 (necessarily).
  • Question 15
    1 / -0
    Directions: The question is based on a dice having faces numbered from 1 to 6 in different ways as indicated:

    If 1 is opposite to 5 and 2 is opposite to 3, which of the following statements is necessarily true?
    Solution
    If 1 is opposite to 5 and 2 is opposite to 3, then 4 definitely lies opposite to 6. Therefore, 2 cannot lie opposite to any of the two numbers: 4 or 6. Hence, 2 necessarily lies adjacent to both 4 and 6.
  • Question 16
    1 / -0
    Directions: The question is based on a dice numbered 1 to 6 in different ways as indicated:

    If 1 is adjacent to 2, 3 and 5, then which of the following statements is necessarily true?
    Solution
    If 1 is adjacent to 2, 3, and 5, then either 4 or 6 lies opposite to 1. So, the numbers 4 and 6 cannot lie opposite to each other. Hence, 4 necessarily lies adjacent to 6.
  • Question 17
    1 / -0
    Directions: The question is based on a dice numbered 1 to 6 in different ways as indicated:

    If 1 is opposite to 2 and adjacent to 3 and 4, then which of the following statements is necessarily true?
    Solution
    If 1 is opposite to 2, then 2 cannot lie opposite to any of the numbers 3, 4, 5 or 6. Hence, 2 necessarily lies adjacent to 6.
  • Question 18
    1 / -0
    The following question is based on a dice numbered 1 to 6 in different ways as indicated:

    If 2 is opposite to 3 and adjacent to 4 and 6, then which of the following statements is necessarily true?
    Solution
    If 2 is opposite to 3, then 1 cannot lie opposite to either of the two numbers – 2 or 3. Hence, 1 is necessarily adjacent to both 2 and 3.
  • Question 19
    1 / -0
    Two orientations of a dice are shown below. When there are two dots at the bottom, the number of dots at the top will be

    Solution
    6 is opposite to 1, 5 is opposite to 4 and 2 is opposite to 3.
  • Question 20
    1 / -0
    Directions: The figure X given on the left hand side is folded to form a cube. Choose from the alternatives, A, B, C and D, the cube(s) that is/are similar to the cube formed.

    Solution
    From (X), we conclude that 5 is opposite to 3, 2 is opposite to 4 and 1 is opposite to 6.
    We know that 2 opposite faces cannot be together when net is folded.
    In figure (A), 1 is adjacent to 6; which is not true.
    In figure (B), 3 is adjacent to 5; which is not true.
    In figure (C), 2 is adjacent to 4; which is not true.
    Hence, only figure (D) is similar to figure X.
  • Question 21
    1 / -0
    Directions: The figure (X) given on the left hand side is folded to form a cube. Choose from the alternatives (a), (b), (c) and (d), the cube(s) that is/are similar to the cube formed.

    Solution
    B and D are correct.
    and E are in front of each other.
    B and D are in front of each other.
  • Question 22
    1 / -0
    Directions: The figure (X) given on the left hand side is folded to form a cube. From the given alternatives (A), (B), (C) and (D), the cube(s) that are similar to the cube formed is/are

    Solution
    Figure (A) is not possible because the lined face is opposite the face having '0'. Therefore, they cannot be adjacent to each other.
    Figure (B) is not possible because the blank face is opposite the face having 'x'. Therefore, they cannot be adjacent to each other.
    Figure (C) is not possible because the lined face is opposite the face having '0'. Therefore, they cannot be adjacent to each other.
    Figure (D) can be formed from figure (X). Hence, this is the correct answer.
  • Question 23
    1 / -0
    Directions: The figure X given on the left hand side is folded to form a cube. Choose from the alternatives, A, B, C and D, the cube(s) that is/are similar to the cube formed.

    Solution
    From figure X, we conclude that 1 is opposite to 4, 6 is opposite 2 and 5 is opposite to 3.
    6 is the left of 1,4,5, and 3
    and 2 is the right of 1,4,5, and 3
    In figure (D), 2 is adjacent to 6; which is not possible. Hence, figure (D) is not possible.
    In figure (A), 1, 6 and 5 are adjacent faces of cube, and 6 is left of 5; which is possible.
    In figure (B) 2, 3 and 4 are adjacent faces of cube, but 2 is not right of 3
    In figure (C) 2, 3 and 4 are adjacent faces of cube, also 2 is the right of the 3; which is possible.
  • Question 24
    1 / -0
    Directions: The figure X given on the left hand side is folded to form a cube. Choose from the alternatives, A, B, C and D, the cube(s) that is/are similar to the cube formed.

    Solution
    From figure (X), we conclude that face having + is opposite to the face having =.
    Face having marked line is opposite to the face having square.
    Face having filled dot is opposite to face having x.
    In figure (A), marked face is adjacent to face having + and face having x; which is possible.
    Therefore, option 1 is true.
  • Question 25
    1 / -0
    Two orientations of a dice are shown below. If the face with 1 dot is at the bottom, then how many dots will be at the top of the dice?

    Solution
    From figures (i) and (ii), we conclude that 5, 4, 6 and 2 dots appear adjacent to 3 dots. Therefore, 1 dot must appear opposite to 3 dots. Thus, if the face with 1 dot is at the bottom, then the face with 3 dots will appear at the top.
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