Direction : Study the following information carefully and answer the questions…
2019
Direction : Study the following information carefully and answer the questions given below:
Thirteen boxes of different colors are placed one above another in alphabetical order either from bottom or from top. Each box contains different number of toffees which is multiple of 13. Maximum toffees in a box is 169.
There are equal number of boxes are placed above as well as below J. Two boxes are placed between box J and the Pink colored box. Five Boxes are placed between Pink and Yellow colored box. Box which have 13 toffees is placed just below Yellow colored box. Black colored box is placed just above Red colored box and just below the box which have 169 toffees. There are as many boxes are placed above Red colored box as below the box which have 13 toffees. White colored box is placed just above the box which have 65 toffees and just below the box which have 104 toffees. There are as many boxes are placed between the boxes which have 13 and 52 toffees as between the boxes which have 52 and 104 toffees. Two boxes are placed between Blue colored box which doesn’t have 13 toffees and Green colored box which is placed just below J.
Which of the following colored box have 52 toffees?
- A.
Red
- B.
Pink
- C.
Blue
- D.
Green
- E.
None of these
Show answer & explanation
Correct answer: D
Concept
In a vertical box-arrangement puzzle, fix the most restrictive clue first, then chain the relative-position clues ("between", "just above/below") off it. The alphabetical-labelling clause only fixes the order of the box LABELS (A onward) along the stack; the colours and toffee counts asked about are pinned entirely by the relational clues, so we solve those directly. "Equal number above and below" a box forces that box to the exact middle of the stack; with 13 positions the middle is the 7th from the bottom. Each later clue then locks one more box relative to an already-placed one, until every position is determined.
Application — fixing the frame
Number the positions 1 (bottom) to 13 (top). "Equal boxes above and below J" puts J at the centre: 6 boxes above and 6 below, so J is at position 7.
"Green is just below J" places Green at position 6.
"Two boxes between J and Pink" and "five boxes between Pink and Yellow" can only be satisfied with Pink at 10 and Yellow at 4.
"The box with 13 toffees is just below Yellow" gives 13 toffees at position 3.
"Black just above Red, and just below the 169-toffee box", together with "boxes above Red equal boxes below the 13-toffee box", forces Red 11, Black 12, 169 toffees at 13.
The White/65/104 chain ("White just above the 65-box and just below the 104-box") gives a rigid 3-block 65–White–104. With Pink, Yellow, Red, Black and the 169/13 boxes placed, this block can still sit in more than one gap, so it is not yet uniquely fixed — we carry the candidate 65 at 7, White at 8, 104 at 9 and confirm it in the next step, where the toffee-spacing and Blue clues rule out every other placement.
Finally, apply the two remaining counting clues together: "equal boxes between (13 & 52) and between (52 & 104)" and "two boxes between Blue and Green, with Blue not holding 13 toffees". With 13 at 3 and 104 at 9, the only value of 52's position that keeps both gaps equal is the midpoint, fixing 52 toffees at position 6 and Blue at position 9.
Final arrangement (top to bottom)
Position | Color | Toffees |
|---|---|---|
13 (top) | — | 169 |
12 | Black | — |
11 | Red | — |
10 | Pink | — |
9 | Blue | 104 |
8 | White | — |
7 (J) | — | 65 |
6 | Green | 52 |
5 | — | — |
4 | Yellow | — |
3 | — | 13 |
2 | — | — |
1 (bottom) | — | — |
Cross-check
Position 6 carries 52 toffees, and the box at position 6 is Green, so the Green box holds 52 toffees. This is consistent with every clue: the gap between the 13- and 52-toffee boxes (positions 3 and 6) is 2 boxes, equal to the gap between the 52- and 104-toffee boxes (positions 6 and 9). Hence the box with 52 toffees is Green.