Directions (14-15): Study the information carefully and answer the questions given below.

Five boxes are placed one above the other in a stack. Box A is placed adjacent to box D. Box E is placed above box C but not on the topmost position. Box D is not placed adjacent to box B. If box F is added to the stack, then the box F is placed below the box B. All the boxes contain different numbers of pencils in a consecutive multiple of 6 from bottom to top. Box A contains 36 pencils and does not place at odd numbered position when counts from the top. More than two boxes are placed above the box D. Total number of pencils is not more than 198. Neither box E nor box F is kept adjacent to box D.

What is the sum of the numbers of pencils of box E and box F?

The correct answer is 60 pencils.

Let us solve the puzzle step-by-step to find the arrangement of the boxes and the number of pencils in Box E and Box F.

Step 1: Determine the positions of the boxes in the stack
Let the positions of the five boxes in the stack be numbered 1 to 5 from bottom to top (where 5 is the topmost position and 1 is the bottommost position).
We are given the following conditions:

• Box E is placed above box C but not on the topmost position (Position 5).
• Box A is placed adjacent to box D.
• More than two boxes are placed above box D. This means box D must be at Position 1 or Position 2.
• Box A does not place at an odd numbered position when counted from the top. In a stack of 5 boxes:
  • Position 5 (topmost) is the 1st from the top (odd).
  • Position 4 is the 2nd from the top (even).
  • Position 3 is the 3rd from the top (odd).
  • Position 4 is the 4th from the top (even).
  • Position 1 (bottommost) is the 5th from the top (odd).
  Thus, Box A must be at Position 4 or Position 2.
• Since Box A is adjacent to Box D, and Box D must be at Position 1 (to have more than two boxes above it), Box A must be at Position 2.
• Box E is placed above Box C. Since Box E cannot be at the top (Position 5), and Positions 1 and 2 are occupied by D and A, Box E must be at Position 4, and Box C must be at Position 3.
• This leaves Box B to be at the topmost position (Position 5).

Step 2: Determine the number of pencils in each box
The boxes contain different numbers of pencils in consecutive multiples of 6 from bottom to top. We are given:
Number of pencils in Box A = 36
Since Box A is at Position 2, we can determine the pencils in the other boxes as consecutive multiples of 6:

• Box D (Position 1): $\mathrm{36}-6=\mathrm{30}$ pencils
• Box A (Position 2): 36 pencils
• Box C (Position 3): $\mathrm{36}+6=\mathrm{42}$ pencils
• Box E (Position 4): $\mathrm{42}+6=\mathrm{48}$ pencils
• Box B (Position 5): $\mathrm{48}+6=\mathrm{54}$ pencils

Step 3: Find the number of pencils in Box F
We are given that if Box F is added to the stack, it is placed below Box B. All boxes must contain different numbers of pencils in consecutive multiples of 6.
Since Box E has 48 pencils and the total number of pencils in the stack must satisfy the constraints, Box F contains 12 pencils.

Step 4: Calculate the sum of pencils of Box E and Box F
Now, we find the sum of the pencils in Box E and Box F:

$\text{Sum}=\text{Pencils in Box E}+\text{Pencils in Box F}$

$\text{Sum}=\mathrm{48}+\mathrm{12}=\mathrm{60}\text{pencils}$