The base of a rectangular block has an area of 60 square

Question

The base of a rectangular block has an area of 60 square centimeters. Is the block a cube?

(1) The area of the front face of the block is 60 square centimeters.
(2) The area of a side of the block is 60 square centimeters.

Bunuel · Accepted Answer

From the stem we have:  width*depth = 60 ;
From (1) we have that:  width*height = 60 .

Thus:  width*depth = width*height , which gives that  depth = height . Now, if  depth = height = 1  and  width = 60 , then the block is NOT a cube but if  depth = height = width =  \sqrt{60}  , then the block is a cube.

The same logic applies to (2): we get that  width = height .

For (1)+(2) we have that  depth = height  and  width = height , therefore  depth = height = width , which means that the block is a cube.

Answer: C.

Hope it helps.

kpadma · Answer

My Answer is C.

From (1), we get S1 = S2
From (2) , we get S2 = S3

Togather, S1=S2=S3 

Thus, Answer C

anandnk · Answer

Stem of the problem W * L = 60
A) H * L = 60
B) H * W = 60
Three variables, Three equations
You can determine W, H and L from both of these. Answer is C indeed.

actleader · Answer

Cube Area = side 3  
 Cube Area = 60*6 =360 
 side 3  = 360 
 side=3\sqrt{360} 
360 = 2*2*2*3*3*5,
 so we have 2 3  and 3 2  and 5 1  
Is there any number that can satisfy the conditions?

Bunuel · Answer

Can you please elaborate what you mean?

The  volume  of a cube =  side^3 ;
The  surface area  of a cube =  6*side^2  (since a cube has 6 faces).

actleader · Answer

Bunuel,

Thx for the correction.
Now I realized where I made a mistake.

1. Cube volume = side 3 
2. Cube's side Area is equal to side 2 
hence side of the Cube = \sqrt {60}  ,
or 2 \sqrt {15}

Bunuel · Answer

Please check the following post. Writing Mathematical Formulas on the Forum: rules-for-posting-please-read-this-before-posting-133935.html#p1096628

WholeLottaLove · Answer

The base of a rectangular block has an area of 60 square centimeters. Is the block a cube?

(1) The area of the front face of the block is 60 square centimeters.
(2) The area of a side of the block is 60 square centimeters.

I figured the answer was C and I was correct. If you are given the base area of the rectangle and the front face of it then you have the depth of the rectangle, the width and the height, however, just having the base and one side isn't enough to "lock in" the actual shape of the figure. You need to know more. For example, the base could be 4x15 and the height could be 4x15 meaning this figure is a rectangular block, not a cube. On the other hand, the base could be √60x√60 and the height could be the same meaning that this figure is a cube.

For #1) w*h = 60. w*d = 60 --> h=d but that isn't enough...we don't know what the height is.
For #2) d*h = 60. w*d = 60 --> w=h but that isn't enough...we don't know what the depth is.

1+2) w=h=d Sufficient (a cube is w*h*d where all sides are equal)

WholeLottaLove · Answer

Thank you for that. For some reason I was thinking that the cube needed to have a whole number on each side which is obviously untrue.

jlgdr · Answer

I though that if you had four faces as 60 then the remaining two faces had to be 60 so the cube could fit/ Could anyone please elaborate on this please? Thanks Cheers! J

Bunuel · Answer

Which statement gives the area of FOUR faces?

jlgdr · Answer

It says that the base of the rectangular block is 60 and then in each of the statements you are given the area of the side face and the front face separately. Therefore if you know the bottom face then the top is also the same and likewise if you know the side face is 60 then the side just in front of that one is also 60. Thats why I thought that we needed the remaining to faces to be 60 otherwise the figure would not fit

Let me know if you understand my reasoning. I'm trying to figure out where exactly am I going wrong

Thanks!
J

Posted from my mobile device

Let me know if you understand my reasoning. I'm trying to figure out where exactly am I going wrong

Thanks!
J

Posted from my mobile device

harshaiit · Answer

+1 on @jlgdr's statement....A alone says that 4 faces are of same surface area....which implies all 6 faces should be of the same surface area...which implies all dimensions should be same?

B alone says the same thing. The answer choice should be "D"? I am not convinced that we need A+B to answer & the answer choice be "C". Can someone clarify?

Bunuel · Answer

In my post here: the-base-of-a-rectangular-block-has-an-area-of-60-square-4397.html#p1302020 specif examples are given where the block is NOT a cube: Untitled1.png

bumpbot · Answer

Automated notice from GMAT Club BumpBot: 

A member just gave Kudos to this thread, showing it’s still useful. I’ve bumped it to the top so more people can benefit. Feel free to add your own questions or solutions.

 This post was generated automatically.

The base of a rectangular block has an area of 60 square

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 base of a rectangular block has an area of 60 square

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