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Question of the week - 46(A pastry is in the shape of a cube, .....)

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Question of the week - 46(A pastry is in the shape of a cube, .....)  [#permalink]

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e-GMAT Question of the Week - 46

A hollow box is in the shape of a cube, that has a side length of 2 metres. If a portion of it is cut along three adjacent face diagonals of the cube, then what is the total surface area of remaining larger piece of the box?

    A. 4
    B. 6
    C. 16
    D. 18
    E. 24

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Originally posted by EgmatQuantExpert on 28 Jun 2019, 03:33.
Last edited by EgmatQuantExpert on 30 Jun 2019, 18:17, edited 2 times in total.
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Re: Question of the week - 46(A pastry is in the shape of a cube, .....)  [#permalink]

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New post Updated on: 29 Jun 2019, 03:28
giving a try
visualize that the cut of the cake along three sides is done on one of the faces along the digaonal

TSA; 6*s^2 ; 24
and digaonal ; 2√2
along the diagonal cake is cut gives us three ∆ ; area;; 1/2 * 2*2 ; 2 *3 ; 6
left area l 24-6 = 18
IMO D


EgmatQuantExpert wrote:
e-GMAT Question of the Week - 46

A pastry is in the shape of a cube, that has a side length of 2 metres. If a portion of it is cut along three adjacent face diagonals of the cube, then what is the area of remaining larger piece of the pastry?

    A. 4
    B. 6
    C. 16
    D. 18
    E. 24

Image

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Originally posted by Archit3110 on 28 Jun 2019, 10:50.
Last edited by Archit3110 on 29 Jun 2019, 03:28, edited 1 time in total.
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Re: Question of the week - 46(A pastry is in the shape of a cube, .....)  [#permalink]

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New post Updated on: 29 Jun 2019, 19:12
We will get smaller piece, a tetrahedron having 3 faces as right angle isosceles triangles whose equal sides are 2 cm, and fourth face is equilateral triangle having side \(2\sqrt{2}\).
We can't find the area of a 3-D figure. It should be either volume, curved surface area or total surface area.



EgmatQuantExpert wrote:
e-GMAT Question of the Week - 46

A pastry is in the shape of a cube, that has a side length of 2 metres. If a portion of it is cut along three adjacent face diagonals of the cube, then what is the area of remaining larger piece of the pastry?

    A. 4
    B. 6
    C. 16
    D. 18
    E. 24

Image

Originally posted by nick1816 on 28 Jun 2019, 23:57.
Last edited by nick1816 on 29 Jun 2019, 19:12, edited 1 time in total.
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Re: Question of the week - 46(A pastry is in the shape of a cube, .....)  [#permalink]

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New post 29 Jun 2019, 00:31
Archit3110 wrote:
giving a try
visualize that the cut of the cake along three sides is done on one of the faces along the digaonal

area = 2^3 ; 8
and digaonal ; 2√2
let three pieces be cut such that each has length ; √2 so we get two ∆ √2:√2:2
area of ∆ ; 1/2 * √2*√2 ; 1 since two ∆ are there so 1*2 ; 2
left area of pastry cube; 8-2 ; 6
IMO B


EgmatQuantExpert wrote:
e-GMAT Question of the Week - 46

A pastry is in the shape of a cube, that has a side length of 2 metres. If a portion of it is cut along three adjacent face diagonals of the cube, then what is the area of remaining larger piece of the pastry?

    A. 4
    B. 6
    C. 16
    D. 18
    E. 24

Image


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Re: Question of the week - 46(A pastry is in the shape of a cube, .....)  [#permalink]

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New post 29 Jun 2019, 03:25
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EgmatQuantExpert wrote:
e-GMAT Question of the Week - 46

A pastry is in the shape of a cube, that has a side length of 2 metres. If a portion of it is cut along three adjacent face diagonals of the cube, then what is the area of remaining larger piece of the pastry?

    A. 4
    B. 6
    C. 16
    D. 18
    E. 24

[url=https://e-gmat.com/quant-workshop-free-session/?
utm_source=GC&utm_medium=questions_q&utm_campaign=free_session&utm_content=quant_workshop&utm_term=GCquestions_q_fs_qow_qw]Image[/url]


Total surface area of original cube = 6 * 4 = 24 sq m
Cut area = 3 * 1/2 *(2*2) = 6 sq m
Since there are 3 right angled triangles of base 2 & height 2 m cut from the original cube
Thus remaining area = 24 - 6 = 18 sq m

Alternatively remaining area = 3 * (2*2) + 3 * 1/2 (2*2) = 18 sq m
since there are 3 sides 0f 2*2 sq m = 12 sq m
and there are 3 right angles triangles of are = 3 * 1/2 (2*2) = 6 sq m

The solutions do not include area of equilateral triangle generated as a result of the cut = 2\(\sqrt{3}\).
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Re: Question of the week - 46(A pastry is in the shape of a cube, .....)  [#permalink]

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New post 29 Jun 2019, 03:36
Kinshook wrote:
EgmatQuantExpert wrote:
e-GMAT Question of the Week - 46

A pastry is in the shape of a cube, that has a side length of 2 metres. If a portion of it is cut along three adjacent face diagonals of the cube, then what is the area of remaining larger piece of the pastry?

    A. 4
    B. 6
    C. 16
    D. 18
    E. 24

[url=https://e-gmat.com/quant-workshop-free-session/?
utm_source=GC&utm_medium=questions_q&utm_campaign=free_session&utm_content=quant_workshop&utm_term=GCquestions_q_fs_qow_qw]Image[/url]


Total surface area of original cube = 6 * 4 = 24 sq m
Cut area = 3 * 1/2 *(2*2) = 6 sq m
Since there are 3 right angled triangles of base 2 & height 2 m cut from the original cube
Thus remaining area = 24 - 6 = 18 sq m

Alternatively remaining area = 3 * (2*2) + 3 * 1/2 (2*2) = 18 sq m
since there are 3 sides 0f 2*2 sq m = 12 sq m
and there are 3 right angles triangles of are = 3 * 1/2 (2*2) = 6 sq m

The solutions do not include area of equilateral triangle generated as a result of the cut = 2\(\sqrt{3}\).


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Question of the week - 46(A pastry is in the shape of a cube, .....)  [#permalink]

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New post Updated on: 30 Jun 2019, 18:21
nick1816 wrote:
We will get smaller piece, a tetrahedron having 3 faces as right angle isosceles triangles whose equal sides are 2 cm, and fourth face is equilateral triangle having side \(2\sqrt{2}\).
We can't find the area of a 3-D figure. It should be either volume, curved surface area or total surface area.


Hi @nikh1816,

When we say area, it implicitly means TSA. Anyway, we have edited the question to remove all the ambiguity.

Thanks & Regards,
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Originally posted by EgmatQuantExpert on 30 Jun 2019, 07:49.
Last edited by EgmatQuantExpert on 30 Jun 2019, 18:21, edited 1 time in total.
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Re: Question of the week - 46(A pastry is in the shape of a cube, .....)  [#permalink]

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New post 30 Jun 2019, 07:52
EgmatQuantExpert wrote:
nick1816 wrote:
We will get smaller piece, a tetrahedron having 3 faces as right angle isosceles triangles whose equal sides are 2 cm, and fourth face is equilateral triangle having side \(2\sqrt{2}\).
We can't find the area of a 3-D figure. It should be either volume, curved surface area or total surface area.


Hi @nikh1816,

When we say area, it implicitly means TSA. Anyway, we have edited the question to remove all the ambiguity.

Thanks & Regards,
Sandeep.


EgmatQuantExpert ; thanks for editing the question .. else considering volume as answer would have been 6 ...
nick1816 :)
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Re: Question of the week - 46(A pastry is in the shape of a cube, .....)  [#permalink]

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New post 30 Jun 2019, 08:13
Thanks for editing. But if we're considering TSA, then we should not exclude the area of the equilateral triangle that's left after we removed the cutting portion. None of the options is correct in that scenario. That's why i was confused. Imo question is poorly written and designed.

Archit3110 wrote:
EgmatQuantExpert wrote:
nick1816 wrote:
We will get smaller piece, a tetrahedron having 3 faces as right angle isosceles triangles whose equal sides are 2 cm, and fourth face is equilateral triangle having side \(2\sqrt{2}\).
We can't find the area of a 3-D figure. It should be either volume, curved surface area or total surface area.


Hi @nikh1816,

When we say area, it implicitly means TSA. Anyway, we have edited the question to remove all the ambiguity.

Thanks & Regards,
Sandeep.


EgmatQuantExpert ; thanks for editing the question .. else considering volume as answer would have been 6 ...
nick1816 :)
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Question of the week - 46(A pastry is in the shape of a cube, .....)  [#permalink]

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New post 30 Jun 2019, 18:21
nick1816 wrote:
Thanks for editing. But if we're considering TSA, then we should not exclude the area of the equilateral triangle that's left after we removed the cutting portion. None of the options is correct in that scenario. That's why i was confused. Imo question is poorly written and designed.


Hi nick1816,

Thanks for pointing out the issue.

Apologies, we have edited the question now.

Thanks & Regards,
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Re: Question of the week - 46(A pastry is in the shape of a cube, .....)  [#permalink]

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New post 02 Jul 2019, 03:25
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The question is still incorrect EgmatQuantExpert

Because the box is hollow, on cutting it along the given dimensions, the inside portion will get exposed and thus will increase the area. In fact, whatever is the surface area of the outside portion, the same area would be inside after cutting the hollow box.

Still, the question is wrong. Please check

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Re: Question of the week - 46(A pastry is in the shape of a cube, .....)  [#permalink]

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New post 02 Jul 2019, 05:37
Archit3110 wrote:
giving a try
visualize that the cut of the cake along three sides is done on one of the faces along the digaonal

TSA; 6*s^2 ; 24
and digaonal ; 2√2
along the diagonal cake is cut gives us three ∆ ; area;; 1/2 * 2*2 ; 2 *3 ; 6
left area l 24-6 = 18
IMO D


EgmatQuantExpert wrote:
e-GMAT Question of the Week - 46

A pastry is in the shape of a cube, that has a side length of 2 metres. If a portion of it is cut along three adjacent face diagonals of the cube, then what is the area of remaining larger piece of the pastry?

    A. 4
    B. 6
    C. 16
    D. 18
    E. 24

Image


Hi Archit3110. Thanks for the solution. Could you please explain to me why it would be 3 triangles and not 4? what about the base of the shape is that not the 4th side. I followed the same method but when I tried to visualize the shape, to me the it seemed that the shape would have four faces. What am I missing?

Thanks in advance!
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Re: Question of the week - 46(A pastry is in the shape of a cube, .....)  [#permalink]

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New post 04 Jul 2019, 05:37

Solution


Given:
    • A hollow box is in the shape of a cube that has a side length of 2 meters
    • A portion of it is cut along three adjacent face diagonals of the cube

To find:
    • The total surface area of remaining larger piece of the box

Approach and Working out:
    • A hollow box has all sides closed, and the total surface = 6 * area of a face.

Now, let us try to visualize the hollow box after it is cut along three adjacent face diagonals of the cube.

Image Image Image

    • From the third figure, we can see that the total surface area of the larger piece = \(3 * area of a face + 3 * \frac{area of a face}{2}\)

Note: we should not consider the area of the triangle in total surface area, since the box is hollow.
    • Area of a face = \((side length)^2 = 2^2 = 4\)
    • Therefore, the total surface area of the larger piece = \(3 * 4 + 3 * \frac{4}{2} = 12 + 6 = 18\) sq. meters

Hence, the correct answer is Option D.

Answer: D

Image

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Re: Question of the week - 46(A pastry is in the shape of a cube, .....)  [#permalink]

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New post 05 Aug 2019, 18:02
EgmatQuantExpert wrote:

Solution


Given:
    • A hollow box is in the shape of a cube that has a side length of 2 meters
    • A portion of it is cut along three adjacent face diagonals of the cube

To find:
    • The total surface area of remaining larger piece of the box

Approach and Working out:
    • A hollow box has all sides closed, and the total surface = 6 * area of a face.

Now, let us try to visualize the hollow box after it is cut along three adjacent face diagonals of the cube.

Image Image Image

    • From the third figure, we can see that the total surface area of the larger piece = \(3 * area of a face + 3 * \frac{area of a face}{2}\)

Note: we should not consider the area of the triangle in total surface area, since the box is hollow.
    • Area of a face = \((side length)^2 = 2^2 = 4\)
    • Therefore, the total surface area of the larger piece = \(3 * 4 + 3 * \frac{4}{2} = 12 + 6 = 18\) sq. meters

Hence, the correct answer is Option D.

Answer: D

Image



This problem is so easy yet so difficult.

errr. Let me re-phrase my sentence :-D

This problem is so difficult if you cannot visualize the diagram, and so easy when you are able to visualize (or draw) it correctly. Thank you so much for the diagram EgmatQuantExpert :angel: :please
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Re: Question of the week - 46(A pastry is in the shape of a cube, .....)   [#permalink] 05 Aug 2019, 18:02
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