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

Question

https://gmatclub.com/forum/download/file.php?id=47618 The figure above shows a piece of cheese with a corner cut off to expose plane surface ABC. What is the area of surface ABC ? (1) AD = 10 centimeters (2) The shape of the cheese was a cube before the corner was cut off. DS80602.01 Quantitative Review 2020 NEW QUESTION 2019-04-26_1844.png

DavidTutorexamPAL · Answer

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

Archit3110 · Answer

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

EgmatQuantExpert · Answer

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.

https://e-gmat.com/blogs/wp-content/uploads/2016/12/Geometry-Ability-Quiz-4-e1480581478957.png

menonpriyanka92 · 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?

Karmesh · Answer

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.

chenjk · Answer

How can we assume ABC are vertices?

Karmesh · Answer

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

MHIKER · Answer

(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

Marcost · Answer

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

Chitra657 · Answer

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

Bunuel · Answer

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

Does this make sense?

Chitra657 · Answer

OH RIGHT! Totally missed that. Thanks a lot!

woohoo921 · Answer

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

bumpbot · Answer

Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.

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

Prep Toolkit

Top 5 GMAT Debrief Videos

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards

GMAT Data Sufficiency (DS) Questions

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

Prep Toolkit

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards