Directions (33-37): Read the given information carefully and answer the questions based on it:
Some boxes are placed one above other in three stacks C, K and T (west to east in same order). None of the stack contains more than six boxes. Two boxes are placed below box D. Box Y is not in the same stack of box D. Box W is in the west of box Y but not in stack K. Box L is placed three places above box W. Same number of boxes are placed above and below box D and box L respectively. Total number of boxes in the stack in which box R is placed is half the number of boxes placed in the stack in which box G is placed. Only box J is placed just above box R. Box U is in immediate north-east of box F which is in the west of box J. Number of boxes in stack C is equal to the number of boxes placed between box G and box S.
The boxes in each stack contains some number of pencils. The number of pencils is the consecutive multiple of 5, 6 and 7 from bottom to top. Now, some new boxes are entered in these stacks. Box M is in the south-west of box P and contains 21 pencils. The number of pencils in topmost box of stack C is of the number of pencils in lowermost box of stack T. Box A is not adjacent to box G but its number of pencils is one less than the total number of boxes in all the stack together.
Which of the following statement is true?
Correct Answer :
No box is placed in east of box P
Solution :
1. Analyzing the Stacks and Box Positions:
The three stacks are arranged from west to east as C, K, and T. Each stack contains at most 6 boxes.
Let us represent the positions using coordinates (Stack, Height), where the height starts from 1 at the bottom.
2. Determining Positions of W and L:
- We are given that Box W is in the west of box Y but not in stack K. Since Stack C is the only stack to the west of K, Box W must be in Stack C.
- Box L is placed three places above box W. In Stack C, if W is at level , then L is at level .
- Two boxes are placed below box D, which means D is at level 3 in its stack.
- Same number of boxes are placed above D and below L respectively. Since there are at most 6 boxes in a stack:
If W is at level 1, then L is at level 4. The number of boxes below L is 3.
This means the number of boxes above D is 3. Since D is at level 3 (having 2 boxes below it), the stack containing D has a total height of:
This is consistent with the rules. If W were at level 2 or higher, the height of D's stack would exceed the limit of 6 boxes. Therefore, W is at level 1 and L is at level 4 of Stack C.
3. Determining Stack Heights:
- Total number of boxes in the stack of R is half of those in the stack of G.
- Only box J is placed just above box R. This means J is the topmost box in R's stack.
- Box U is in the immediate north-east of box F, which is in the west of box J. Since F is west of J, F and J are at the same level. Since U is in the immediate north-east of F, U must be one level higher than F and in the stack immediately to the east of F.
Through these conditions, we find that:
- The height of Stack T (containing R and J) is 3.
- The height of Stack K is 6.
- The height of Stack C is 4.
4. Positioning Box P:
Based on the placement rules and the introduction of new boxes:
- Box M is in the south-west of Box P.
- For Box M to be in the south-west of P, P must be located in a stack to the east of M.
- Since Stack T is the easternmost stack, Box P is placed in Stack T.
- Because Stack T is the easternmost stack (C, K, T from west to east), there is no stack to the east of T. Therefore, no box is placed in the east of box P.
Thus, the statement "No box is placed in east of box P" is indeed the correct statement.
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