The figure above shows a piece of cheese with a corner cut off to expo

The Logical approach to this question is quite simple: we must have at least one number to find the area of the triangle, and thus we need statement (1), but it is not sufficient on its own. In statement two were told that the triangle is an equilateral triangle, since a cube is symmetrical. We only need one side of an equilateral triangle in order to find its area, and thus both statements together are required, and the correct answer is (C).
The Precise approach would use congruence of triangles and the formula for the area of equilateral triangle, but, as in most DS questions, that would be longer and redundant as we're not asked what the area IS, but rather whether there's enough information to solve the question.

Posted from my mobile device

trap question
#1
AD=10 cm
we dont know cheese is a cube/or any other plygon shape
#2
cube given dimensions missing
from 1 & 2
10√2 is each side and area ; √3/4 * 200 ; 50 √3
IMO C

Solution

Steps 1 & 2: Understand Question and Draw Inferences
In this question, we are given:

• A figure having a piece of cheese from which a corner has been cut off.
• The removed corner exposes the plane surface ABC.

We need to determine:

• The area of the surface ABC.

The surface ABC is in the shape of a triangle.

• Therefore, to find the area of ABC, we either need the length of all the 3 sides or length of 2 sides and angle between them.

With this understanding, let us now analyse the individual statements.

Step 3: Analyse Statement 1
“AD = 10 centimetres”

From this statement, we cannot determine any information about the length of sides of the triangle.
Hence, statement 1 is not sufficient to answer the question.

Step 4: Analyse Statement 2
“The shape of the cheese was a cube before the corner was cut off”

• From this statement, we can say that length of sides of the triangle are the face diagonals of the cube.
• And, all the diagonals will be of the equal length
Hence, ABC is an equilateral triangle.

However, we cannot determine any information about the length of sides of the triangle.
Hence, statement 2 is not sufficient to answer the question.

Step 5: Combine Both Statements Together (If Needed)
From Statement 1:

• AD = 10 cm

From Statement 2:

• The length of sides of the triangle are the face diagonals of the cube.
• ABC is an equilateral triangle.

Combining both the statements:

• Side of the cube = 10 cm
• Length of face diagonal of the cube = √(〖10〗^2+〖10〗^2 ) = 10√2 cm.

Now, we know the length of the side of the equilateral triangle. We can easily find the area of the surface ABC.
Since we could find the answer by combining both the statements, option C is the correct answer.


_________________

Hi! Nowhere is it mentioned if its a cube or a rectangular solid...how is it safe to assume that the figure above is a cube?

You are right the question stem does not say the figure is a cube and that is why we are not assuming it to be a cube.
If it were given that the figure is a cube then statement 1 alone would have been sufficient.
BUT,
Read statement 2 it says "The shape of the cheese was a cube before the corner was cut off."
This statement tells us that it is a cube, so we are not assuming anything now. However, this statement does not give us any value, making it INSUFF.

When combined, they yield the answer.

How can we assume ABC are vertices?

We are not assuming anything. It is literally given in the figure.

(1) We don't know about the nature of the shape; Insufficient.

(2) We don't the size of any sides of the cube. Insufficient.

Considering Both:
The surface an equilateral triangle with the corners of the cube. Corner of a cube\(=\sqrt{S}\) Sufficient.

The answer is \(C\)

Hi, would anyone explain why the second graph (shown below) is not possible considering the information given?

If we consider the second graph possible, then the area of the shaded region can't be determined. Since it is not mention that AD or BE are vertical lines, I think that the second graph is possible.

Initial cheese keeps the form of a cube, what i'm changing is the axis AB since I don't find any restriction to do so.

Bunuel , DavidTutorexamPAL , EgmatQuantExpert chetan2u , Sajjad1994

Silly Question, but I havent understood how is it implied that the triangle is an equilateral triangle, based on the fact that the the cheese is a cube.

Could you pls explain? Bunuel VeritasKarishma

AB, BC and AC are diagonals of three equal faces (squares), so AB = BC = AC.

Does this make sense?
_________________

OH RIGHT! Totally missed that. Thanks a lot!

Unfortunately, I still do not get this. Can't they still be diagonals of the equal faces and let's say the cut takes more out of one side of the triangle than the others? egmat