Reasoning: Puzzles and Arrangements Set 63 (for PO Mains)

Directions (1 – 5): Answer the questions on the basis of the information given below.

There are 8 boxes which are placed one above the other. Their outer surface is colored with different colors namely – green, blue, red, white, orange, yellow, pink and black in any order. They contain some number of balls (all different in number). The balls are also colored with different colors namely – red, black, brown, purple, violet, grey, maroon and orange. A box cannot contain same colored balls, like red colored box cannot contain red colored balls, and so on. There is a total of 76 balls in all the eight boxes. 

Two boxes are placed between green colored box and box having 8 balls. Green colored box is above the box having 8 balls. The box having brown colored balls and having 8 balls are placed together. Maroon colored balls are 7 in number. Three boxes are placed between green colored box and box having maroon colored balls. There are at least 2 boxes above green colored box. Same number of boxes are placed below white colored box as above the box having red colored balls. White colored box does not contain 7 balls. Two boxes are placed between red colored box and box containing red balls. Red colored box contains 3 balls more than green colored box and is placed somewhere above green colored box. Highest number of balls among all boxes are placed in pink colored box. No box contains more than 15 balls. Orange colored box is placed just above pink colored box. Box containing orange colored balls is placed somewhere below box containing red colored balls, but not at the lowest place. Yellow colored box contains 11 balls, which is also equal to the total number of balls in black colored box and box containing black balls. There are two boxes placed between box containing 6 and 11 balls. No box contains 5 balls. Yellow colored box is placed somewhere below green colored box. The box in which violet colored balls are there is placed just above box containing 12 balls. Grey colored balls are not 12 in number.

1. Pink colored box  how many balls?
   A) 12
   B) 14
   C) 15
   D) 13
   E) Cannot be determined
   
   View Answer

   Option DC
   Arrangement:
   Two boxes are placed between green colored box and box having 8 balls. Green colored box is above the box having 8 balls. The box having brown colored balls and having 8 balls are placed together. Maroon colored balls are 7 in number. Three boxes are placed between green colored box and box having maroon colored balls. There are at least 2 boxes above green colored box.
   Gives (top to bottom)::
   
   Now – Same number of boxes are placed below white colored box as above the box having red colored balls. White colored box does not contain 7 balls. Two boxes are placed between red colored box and box containing red balls.  Red colored box contains 3 balls more than green colored box and is placed somewhere above green colored box. So now respective arrangements become::
   
   Now – Highest number of balls among all boxes are placed in pink colored box. No box contains more than 15 balls. Orange colored box is placed just above pink colored box.
   Pink colored balls are highest in number and there are total 76 balls in all boxes, so pink colored box cannot contain 7 or 8 balls, because 7 or 8 cannot be highest number of balls. Also each box has different number of balls. So now only arrangement is
   
   Box containing orange colored balls is placed somewhere below box containing red colored balls, but not at the lowest place.
   So 1st arrangement gets cancelled, because orange colored balls cannot be at lowest place and also cannot be in orange colored box.
   Now: Yellow colored box contains 11 balls, which is also equal to the total number of balls in black colored box and box containing black balls. There are two boxes placed between box containing 6 and 11 balls.
   In we use this in 3rd arrangement, 11-yellow will be with brown. So 6 balls in pink colored box. But pink colored box contains  highest number of balls so 6 balls cannot be placed n pink box, so 3rd arrangement also gets cancelled.
   Now proceed with 2nd arrangement. Yellow colored box is placed somewhere below green colored box. So only place between Green and White box. So Red box contains 6 balls. Red contains 3 balls more than green. So green box contains 3 balls. So
   
   Now, total number of balls in black colored box and box containing black balls is 11
   I. If black colored box is placed with 8 balls, black balls will be 3 in number means in green box.
   II. If black colored box is placed below red colored box, then
   (i) if black balls placed at top, then black colored box will contain 5 balls, but given that no box contains 5 balls.
   (ii) if black balls with green box, then black colored box will contain 8 balls, but orange balls are already 8 in number so black box cannot contain 8 balls
   (iii) black balls cannot be placed with pink box, because pink box contains highest no. of balls. 11 cannot be equal to (highest number +..)
   So II part gets cancelled.
   So — black colored box is placed with 8 balls, black balls will be 3 in number means in green box.
   Now – Violet colored box is placed just above box containing 12 balls. Grey colored balls are not 12 in number.
   Next count all balls placed – 6+12+3+11+8+7 = 47, Total = 76, so remaining  = 76 – 47 = 29. 2 boxes are left. Pink contains highest no. No box contains more than 15 balls. So possibility is 14+15= 29
   So final:
   
   
2. How many boxes are placed between yellow and orange colored boxes?
   A) Four
   B) Two
   C) Three
   D) None
   E) One
   
   View Answer

    Option B
   A and E
3. What is the total number of balls in red colored box and box which contains red colored balls?
   A) 14
   B) 10
   C) 16
   D) 19
   E) 17
   
   View Answer

    Option E
   
4. Which colored box contains maroon colored balls?
   A) Pink
   B) Orange
   C) Green
   D) White
   E) Blue
   
   View Answer

    Option B
   
5. Which of the following combination of no. of balls – box color – balls color is correct as per given arrangment?
   A) 6 – Blue – Red
   B) 12 – Green – Purple
   C) 8 – Black – Maroon
   D) 14 – White – Brown
   E) 11 – Yellow – Grey
   
   View Answer

    Option D
   

Directions (6 – 10): Answer the questions on the basis of the information given below.

There are 6 cars – A, B, C, D, E and F which are parked in a straight line. But alternate cars cannot be alphabetically placed, like car A cannot be parked alternate to car B, car B cannot be parked alternate to car A and C, and so on. Distance between each car is a successive multiple of 4.

Distance between cars A and B is 60 m. Car A is parked left of car B. There is 1 car parked between cars A and B. Distance between cars B and E is 84 m. Distance between cars C and F is a multiple of 3. Car F is parked somewhere right of car C.

From a point, Car G moves 16 m east, takes a right turn, moves 12 m and stops at point Z. Point Z is 15 m north of car A.
If Car F goes 7 m in South direction, takes a left turn and moves 16 m, then it turns right and moves 5 m, next takes a left turn again and moves 22 m, then it reaches point X. 

6. How many cars are parked between cars A and D?
   A) One
   B) None
   C) Three
   D) Two
   E) Four
   
   View Answer

   Option D
   Arrangement:
   AB = 60 and successive distance is a multiple of 4
   Only 28 + 32 makes 60 — successive 28, and 32 .
   24 + 36 is also 60, but 24 and 36 are not successive multiples of 4.
   
   
7. What is the distance car B and point X?
   A) 13 m
   B) 2√5 m
   C) 6√2 m
   D) 14 m
   E) 6√5 m
   
   View Answer

    Option E
   √(12² + 6²) = 6√5 m
   
8. Car C will have to move how much to reach to car G?
   A) 15 m north, 38 m east
   B) 24 m east, 17 m north
   C) 44 m east, 15 m north
   D) 17 m north, 38 m east
   E) 17 m north, 44 m east
   
   View Answer

    Option C
   
9. Car D will have to move how much to reach to point X?
   A) 10 m west, 30 m south
   B) 12 m south, 30 m west
   C) 12 m south, 30 m east
   D) 32 m west, 10 m west
   E) 36 m west, 10 m south
   
   View Answer

    Option B
   
10. If car G moves 28 m east, takes a right turn, and stops at point Y after moving 17 m, then car B is in which direction with respect to point Y?
    A) North-west
    B) South-east
    C) Cannot be determined
    D) North-east
    E) South-west
    
    View Answer

     Option D
    

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