Question Details

Six boxes - A, B, C, D, E and F are placed one above another. These boxes are of different types – Jute, Steel, Iron, Wood, Leather, Brass. All the information is not necessarily in the same order.

Box D is placed three places above leather box. Same number of boxes are placed above box D and below steel box. Box B is placed just below box F and juts above wood box. Box A is placed two places below iron box. More than one box is placed below box C which is placed below brass box.

Which of the following statement is incorrect?

Options

A

Box E is bottommost box

B

Box B is leather box

C

Box D is placed above box F

D

Box A and B are adjacent to each other

E

Box C is brass box

Show Answer

Correct Answer :

Option E

Box C is brass box

Solution :

The correct statement that is incorrect (i.e. false) is Box C is brass box.


Step-by-Step Explanation:


Let us determine the exact arrangement of the 6 boxes (numbered 6 at the top to 1 at the bottom) and their respective material types based on the given clues:


1. Clue 1: "Box D is placed three places above leather box."
This means Box D is at a position such that if Leather box is at position k, Box D is at position k+3 (i.e., there are two boxes between Box D and the Leather box).


2. Clue 2: "Same number of boxes are placed above box D and below steel box."
If Box D is at position 6, Steel box is at position 1.
If Box D is at position 5, Steel box is at position 2.
If Box D is at position 4, Steel box is at position 3.


3. Clue 3: "Box B is placed just below box F and just above wood box."
This gives a consecutive block of three boxes from top to bottom: F, B, Wood box.


4. Clue 4: "Box A is placed two places below iron box."
This means Iron box is 2 places above Box A (i.e., Iron box, then one box, then Box A).


5. Clue 5: "More than one box is placed below box C which is placed below brass box."
Since more than one box is placed below Box C, Box C cannot be at position 1 or position 2. So Box C must be at position 3 or higher, but below the Brass box.


Deducing the Box Positions:

Let's test the positions for Box D:

Case A: If Box D is at position 6 (topmost):
- Leather box is 3 places below, so Leather box is at position 3.
- Steel box is at position 1 (bottommost, since 0 boxes are above D, so 0 boxes below Steel).
- Now we need to place the block F - B - Wood.
- If F is at position 5, B is at 4, Wood is at 3. But position 3 is already Leather box! Contradiction.
- If F is at position 4, B is at 3 (Leather), Wood is at 2. Then Box A must be placed. But Box A is 2 places below Iron. The remaining positions for boxes are 5, 2, 1. If A is at 2 or 1, Iron could be at 4 (Box F) or 3 (Box B). Let's check:
- If Box C is placed, since C is below Brass and >1 box is below C, Box C must be at position 3 or 4. But positions 6 (D), 4 (F), 3 (B), 2 (Wood), 1 (Steel) leaves 5 for C. Position 5 has 4 boxes below it, which satisfies >1 box below C.
- Let's check the remaining clues: F (pos 4), B (pos 3), Wood (pos 2). Box A is 2 places below Iron box. The available boxes for A and E are pos 5 and 1 or 2. If A is at pos 1, Iron is at pos 3 (B is Iron). But B is Leather! Contradiction.


Case B: If Box D is at position 5:
- Leather box is at position 2.
- Steel box is at position 2 (since 1 box is above D, 1 box is below Steel). But position 2 is already Leather box! Contradiction (a box cannot be both Leather and Steel).


Case C: If Box D is at position 4:
- Leather box is 3 places below D, so Leather box is at position 1.
- 2 boxes are above D, so 2 boxes are below Steel box. Thus, Steel box is at position 3.
- Now place block F - B - Wood:
- Since positions 4, 3, 1 are taken by D, Steel (pos 3), Leather (pos 1), the remaining continuous 3 spots for F - B - Wood must be positions 6, 5, 4? No, pos 4 is D.
- What about positions 6, 5, 4? Position 4 is D, so that doesn't work.
- What if F is at position 6, B is at position 5, and Wood box is at position 4 (Box D)? That works perfectly!
- Position 6: Box F
- Position 5: Box B
- Position 4: Box D (Wood box)
- Position 3: Steel box
- Position 2: ?
- Position 1: Leather box


Let's complete Case C:
- Positions 3 and 2 are left for Box A and Box C, or Box E.
- Clue 4: Box A is two places below Iron box.
- If Box A is at position 3, then Iron box must be at position 5 (Box B).
- If Box A is at position 2, then Iron box must be at position 4 (Box D). But Box D is Wood box! So Box A cannot be at position 2.
- Therefore, Box A is at position 3 (Steel box), and Box B (position 5) is the Iron box.
- Now positions left for boxes C and E are 2 and 1.
- Clue 5: "More than one box is placed below box C which is placed below brass box."
- If Box C is at position 2, there is only 1 box below it (position 1). But the clue says "More than one box is placed below box C".
- Wait, let's re-verify position options for C. Could Box C be at position 4? No, position 4 is D. Position 5 is B. Position 6 is F.
- What if Box C is at position 6 (Brass box above it? No, nothing above 6).


Let's re-evaluate position 6 for Box D:
- D at position 5: Leather at 2, Steel at 2 (conflict).
- D at position 4: 2 boxes above D (positions 5, 6). 2 boxes below Steel => Steel is at position 3.
- Leather is at position 1 (3 places below D).
- Block F - B - Wood: F=6, B=5, Wood=4 (D).
- Box A is 2 places below Iron: Iron=5 (B), A=3 (Steel).
- Remaining box positions: 2 and 1.
- Remaining boxes: C and E.
- If C is at position 2: boxes below C = 1 (which is NOT more than 1).
- What if F=5, B=4... no D is at 4.
- Let's check D at position 6:
- 0 boxes above D => 0 boxes below Steel => Steel at position 1.
- Leather is 3 places below D => Leather at position 3.
- Block F - B - Wood:
- If F=5, B=4, Wood=3 (Leather? Leather is a type, so Box B at 4 is above Wood box at 3 (Leather)). This works! Box at position 3 is Leather and Wood? No, each box is of ONE type.
- Ah! "just below box F and just above wood box". So Box B is at 4, Wood box is at 3. But position 3 is Leather! A box cannot be both Wood and Leather. So F cannot be 5.
- Wait! What if Leather is at position 3, and block F - B - Wood is at positions 4 - 3 - 2? That means F=4, B=3 (Leather box), Wood=2.
- Pos 6: Box D
- Pos 5: ?
- Pos 4: Box F
- Pos 3: Box B (Leather)
- Pos 2: Wood box
- Pos 1: Steel box
- Let's check Box A (2 places below Iron):
- If A is at pos 2, Iron is pos 4 (Box F).
- If A is at pos 1 (Steel), Iron is pos 3 (Box B).
- If A is at pos 5, Iron cannot be 7.
- Let's check Box C ("More than one box is placed below box C which is placed below brass box"):
- C must have >1 box below it, so C can be at pos 5 or pos 4.
- If C is at pos 5: boxes below C = 4 (>1). C is below Brass box, so Box D (pos 6) must be Brass box!
- If C is at pos 5, then Box A must be at pos 2 (Wood box) or pos 1 (Steel box).
- Since C is at pos 5, remaining spots for A and E are 2 and 1.
- If Box A is at pos 2, Iron box is pos 4 (Box F).
- Then Box E is at pos 1 (Steel box).
- Let's check all conditions for this complete arrangement:
- Pos 6: Box D (Brass)
- Pos 5: Box C (Jute/Iron)
- Pos 4: Box F (Iron)
- Pos 3: Box B (Leather)
- Pos 2: Box A (Wood)
- Pos 1: Box E (Steel)


Verification of the Final Arrangement:

1. Box D (pos 6) is 3 places above Leather box (pos 3, Box B). (Correct)
2. Same number of boxes above D (0) and below Steel box (0 below pos 1, Box E). (Correct)
3. Box B (pos 3) is just below Box F (pos 4) and just above Wood box (pos 2, Box A). (Correct)
4. Box A (pos 2) is 2 places below Iron box (pos 4, Box F). (Correct)
5. Box C (pos 5) has 4 boxes below it (>1 box) and is below Brass box (pos 6, Box D). (Correct)
6. Remaining material for Box C is Jute.


Checking the Options:

1. Box E is bottommost box: True (Box E is at position 1).
2. Box B is leather box: True (Box B is at position 3, Leather).
3. Box D is placed above box F: True (Box D is at position 6, Box F is at position 4).
4. Box A and B are adjacent to each other: True (Box B is at position 3, Box A is at position 2).
5. Box C is brass box: INCORRECT / FALSE (Box C is Jute box, while Box D is Brass box).


Therefore, the incorrect statement is Box C is brass box.

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