Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized for You

we will pick new questions that match your level based on your Timer History

Track Your Progress

every week, we’ll send you an estimated GMAT score based on your performance

Practice Pays

we will pick new questions that match your level based on your Timer History

Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.

Thank you for using the timer!
We noticed you are actually not timing your practice. Click the START button first next time you use the timer.
There are many benefits to timing your practice, including:

A cube of side 5cm is painted on all of its sides. If it is [#permalink]
01 Aug 2011, 07:23

2

This post was BOOKMARKED

00:00

A

B

C

D

E

Difficulty:

45% (medium)

Question Stats:

59% (26:42) correct
41% (01:11) wrong based on 66 sessions

A cube of side 5cm is painted on all of its sides. If it is sliced into 1 cubic cm cubes, how many 1 cubic cm cubes will have exactly one of their sides painted?

Re: 3-D Cube Question [#permalink]
01 Aug 2011, 07:30

1

This post received KUDOS

The answer is 'D'.

A 5 cm^3 cube divided in 1cm^3 cubes = 125 cubes in total. A cube has 6 faces. On each face, all the cubes surrounding the boundary will have more than 1 side painted, which makes total of 5+5+3+3 = 16 cubes.

So we are left with 25-16 = 9 cubes on each face (which has only 1 side painted) totaling to 9*6=54 cubes.

Re: 3-D Cube Question [#permalink]
01 Aug 2011, 08:16

4

This post received KUDOS

I think the quickest way is to imagine in your mind 1 side of the cube. Understand that the border cubes will have more than one side painted, so the ones with only one side are the ones in the middle, in this case 3x3=9. Then multiply that by 6 sides. If you will make a diagram, make only one side and then multiply by 6. Don't waste the little precious time that you have. See the picture below to understand it better. The green squares have adjacent surfaces painted. Only the blue ones have 1 side only painted.

Re: 3-D Cube Question [#permalink]
01 Aug 2011, 12:50

the smaller cubes which will share an edge will have more than 2 faces painted.. so only the center cubes will have to be considered.. so .. 3*3 on each face.. 6 faces = 54

A 5 cm^3 cube divided in 1cm^3 cubes = 125 cubes in total. A cube has 6 faces. On each face, all the cubes surrounding the boundary will have more than 1 side painted, which makes total of 5+5+3+3 = 16 cubes.

So we are left with 25-16 = 9 cubes on each face (which has only 1 side painted) totaling to 9*6=54 cubes.

Hi.. is there any formula to calculate total number of cubes after division. Let say a 6cm cube is divided into 2cm cubes ?

Re: 3-D Cube Question [#permalink]
21 Feb 2013, 04:41

Expert's post

cano wrote:

I think the quickest way is to imagine in your mind 1 side of the cube. Understand that the border cubes will have more than one side painted, so the ones with only one side are the ones in the middle, in this case 3x3=9. Then multiply that by 6 sides. If you will make a diagram, make only one side and then multiply by 6. Don't waste the little precious time that you have. See the picture below to understand it better. The green squares have adjacent surfaces painted. Only the blue ones have 1 side only painted.

For those who have a problem in visualising they can atleast come to a conlusion that such cubes will be present on all the six sides. Now, whatever be this number(9 in this case), the answer will be a multiple of 6. Thus, just choose an option which is a multiple of 6. However, GMAT can give 2 options where in more than 1 option is a multiple of 6. In this question, luckily we have only one such option.

Hey everyone, today’s post focuses on the interview process. As I get ready for interviews at Kellogg and Tuck (and TheEngineerMBA ramps up for his HBS... ...

I got invited to interview at Sloan! The date is October 31st. So, with my Kellogg interview scheduled for this Wednesday morning, and my MIT Sloan interview scheduled...