Zeno's Unfinished Furniture sells exactly five types of furniture-foo

Question

Zeno's Unfinished Furniture sells exactly five types of furniture-footstools, hutches, sideboards, tables, and vanities. Irene buys just four items, each of a different type, and each made entirely of one kind of wood-maple, oak, pine, or rosewood. The following conditions govern Irene's purchases:

Any vanity she buys is maple.
Any rosewood item she buys is a sideboard.
If she buys a vanity, she does not buy a footstool.
If lrene buys a footstool, she also buys a table made of the same wood.
Irene does not buy an oak table.
Exactly two of the items she buys are made of the same kind of wood as each other.

Which one of the following CANNOT be the two items Irene buys that are made of the same wood as each other?

(A) footstool, hutch
(B) hutch, sideboard
(C) hutch, table
(D) sideboard, vanity
(E) table, vanity

Nidzo · Answer

Looking at the rules, the only rule which tells us which two items she CAN buy in the same colour is the rule that states, "If lrene buys a footstool, she also buys a table made of the same wood."

Looking at the answer choices that include footstool, the only one is choice (A). Excpet in (A), she would be buying a footstool and a hutch in the same colour which goes against the above mentioned rule. Therefore it is impossible for her to buy a footstool and a hutch in the same colour.

ANSWER A

MBAchild · Answer

Easily D, as Vanity and Sideboard are of different materials (given).

8Harshitsharma · Answer

Choice D is incorrect because Zeno can buy a maple sideboard and a maple vanity.

Choice A is correct.

There can be only two combinations of items that she can get since vanity and footstool can't be together.

1. f, h, s, t
2. v, h, s, t

In combo 1, we know f and t have the same wood - so according to my understanding we are given that only two items have the same wood. So if choice A is taken to be wrong, then f and h can have same wood, making the total of 3 items with the same wood.

For Choice B, however, shouldn't we also reject the hutch and sideboard having the same wood as there would be two pairs of items with the same wood then? This makes me doubt how choice B can be rejected!

egmat · Answer

Hi  8Harshitsharma  &  AdityaRathore

Happy to discuss.

Furniture: F, H, S, T, V
Wood: M, O, P, R

1. Any vanity she buys is maple. 
 
 This means that if Irene buys a vanity, it will be maple wood. But this does NOTmean that a Vanity is the only Maple item she buys. Should could buy something else made of Maple as well.

2. Any rosewood item she buys is a sideboard. 
 
 This means that if Irene buys a Rosewood item, it has to be a sideboard. But this does NOT mean that if she buys a Sideboard it has to be Rosewood. She could buy a Sideoard made of some OTHER wood as well. There is no guarantee that she has to buy a Rosewood Sideboard.

3. If she buys a vanity, she does not buy a footstool. 
This means there are only two combinations of items Irene can purchase: 
 
 F, H, S, & T 
 H, S, T, & V

4. If lrene buys a footstool, she also buys a table made of the same wood. 
 
 This means that in Combination 1 above, F & T are made of the same wood.

5. Irene does not buy an oak table. 
 
 This does NOT mean that Irene does not buy a table. It only means that the table she buys is not made of Oak. It could be made of M, P, or R.

6. Exactly two of the items she buys are made of the same kind of wood as each other.  
 
 This means that only 2 of the 4 items she buys are of the same wood, not more.  
 
 
 Combination 1: F, H, S, & T 
As per rules 4 and 6, F and T have to be of the same wood. From this we can infer:
 
 F & H cannot be of the same wood. 
 F & S cannot be of the same wood. 
 We cannot say the same about T & H, or T & S because we still need to consider Combination 2.

Combination 2: H, S, T, & V
 
 As per rules 1 and 2, V and S can be of the same material. 
 As per rule 5, she could buy a table made of M, P, or R. So, V and T could be of the same wood (M). S and T could also be of the same wood (R, M, or P). 
 None of the rules tell us anthing about H. So, even H could be of any of the 4 types of wood (M, O, P, or R).

This means that as per Combination 2, any two items could be of the same wood and the others would not. So, we cannot say anything for sure in the situation of combination 2. 
This leaves us with Combination 1 as the deciding factor. So, as per our  Pre-thinking , we're left with two potential answers:
 
 F & H cannot be of the same wood. 
 F & S cannot be of the same wood.

Therefore,  the answer has to be A.

Hope this helps.
Happy learning!

-Abhishek

8Harshitsharma · Answer

Still unanswered, why haven't you considered choice B) hutch and sideboard. That is where I don't agree. It is given EXACTLY two of 4 items are made of the same wood, so if you take hutch and sideboard to be same then according to the first combination that I stated f, h, s, t - f & t as well as h & s will be made of the same wood. This ALSO violates the given condition. Don't you think?

egmat · Answer

8Harshitsharma

That's the thing - you cannot take H and S to be the same as per Combination 1. In Combination 1, as per the stated rules, only F and T will be made of the same wood. That automatically eliminates "H and S being of the same wood" from the equation.

Note: You mustn't violate the stated rules.

Hope this helps.

-Abhishek

8Harshitsharma · Answer

Well, that is what I am also trying to say.

The question stem asks that which of the following CAN NOT be the two items that are made of the same type of wood.

And you agree that H and S cannot be the same because it violates the final condition, right? Hence, choice B is also a correct answer choice because it violates the conditions, same as choice A.

Nidzo · Answer

Hi @ 8Harshitsharma I'm not entirely sure what you are asking, but I am going to back solve it here to demonstrate that she can buy a hutch and sideboard in the same type of wood. Hopefully this helps you

Items: footstool, hutch, sideboard, table and vanity Wood: maple, oak, pine, or rosewood Once something has been assigned I will change the colour of the item to red. Let's put a hutch and sideboard down: The only rule applicable here is, a ny rosewood item she buys is a sideboard. So let them both be rosewood. Hutch - Rosewood Sideboard - Rosewood Items: footstool, hutch , sideboard , table and vanity Wood: maple, oak, pine, or rosewood As we have assigned two of the same kinds of wood then this rule comes into play, if lrene buys a footstool, she also buys a table made of the same wood . This means that she cannot have both a table and footstool in this group. As she cannot have both, we need to eliminate one. A rule which easily helps eliminate one is the following, if she buys a vanity, she does not buy a footstool . So let's have her buy both a vanity and table. Hutch - Rosewood Sideboard - Rosewood Vanity - ? Table - ? From the woods left we have maple, oak, pine, to assign. One rule states that, any vanity she buys is maple , another states, Irene does not buy an oak table . This means that the vanity has to be maple and the table must be pine. Hutch - Rosewood Sideboard - Rosewood Vanity - Maple Table - Pine

samarpan.g28 · Answer

Very easy. We know that Irene is purchasing two pieces of furniture that are made of the same wood. It is already given that "If lrene buys a footstool, she also buys a table made of the same wood." in the fourth point. Now looking at option (A), if Irene is buying a footstool then she has to buy a table, she cannot get a hutch. So, the footstool and hutch cannot be the two items that she buys. Option (A) is correct.

egmat · Answer

8Harshitsharma

What I said in my previous response was just in response to your query about Combination 1. But what about Combination 2? Why are you ignoring combination 2? Either of the two combinations is possible. In combination 2, H and S can be of the same wood. So, since we don't know which of the two combinations will play out, we can only proceed with what we're certain. And we cannot be certain that H and S will definitely be different, because in C2 they aren't.

If you still don't follow, please go back to the beginning and read my responses over again, from the top.

I'm confident you'll get it!

Hope this helps.
Happy learning!

-Abhishek

Raman109 · Answer

Zeno's Unfinished Furniture sells exactly five types of furniture-footstools, hutches, sideboards, tables, and vanities. Irene buys just four items, each of a different type, and each made entirely of one kind of wood-maple, oak, pine, or rosewood. The following conditions govern Irene's purchases:

Any vanity she buys is maple.
Any rosewood item she buys is a sideboard.
If she buys a vanity, she does not buy a footstool.
If lrene buys a footstool, she also buys a table made of the same wood.
Irene does not buy an oak table.
Exactly two of the items she buys are made of the same kind of wood as each other.

Which one of the following CANNOT be the two items Irene buys that are made of the same wood as each other?

(A) footstool, hutch - Using condition 3, "If Lrene buys a footstool, she also buys a table made of the same wood," we are sure that this condition is not possible as the Footstool and table go together and of course, that'll not be oak. But if "footstool, hutch" go together and they are of the same wood, then "table" has to be the same as "footstool," leading to 3 items of the same wood, which contradicts condition 6. Ok
(B) hutch, sideboard - No
(C) hutch, table - no
(D) sideboard, vanity - no
(E) table, vanity - No

Zeno's Unfinished Furniture sells exactly five types of furniture-foo

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­Zeno's Unfinished Furniture sells exactly five types of furniture-foo

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Zeno's Unfinished Furniture sells exactly five types of furniture-foo