GMAT Question of the Day - Daily to your Mailbox; hard ones only

 It is currently 20 Jan 2019, 03:21

### GMAT Club Daily Prep

#### 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

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

## Events & Promotions

###### Events & Promotions in January
PrevNext
SuMoTuWeThFrSa
303112345
6789101112
13141516171819
20212223242526
272829303112
Open Detailed Calendar
• ### FREE Quant Workshop by e-GMAT!

January 20, 2019

January 20, 2019

07:00 AM PST

07:00 AM PST

Get personalized insights on how to achieve your Target Quant Score.
• ### GMAT Club Tests are Free & Open for Martin Luther King Jr.'s Birthday!

January 21, 2019

January 21, 2019

10:00 PM PST

11:00 PM PST

Mark your calendars - All GMAT Club Tests are free and open January 21st for celebrate Martin Luther King Jr.'s Birthday.

# The figure above represents a wooden block 3 inches on an edge, all

Author Message
TAGS:

### Hide Tags

Math Expert
Joined: 02 Sep 2009
Posts: 52295
The figure above represents a wooden block 3 inches on an edge, all  [#permalink]

### Show Tags

05 Feb 2018, 08:09
00:00

Difficulty:

15% (low)

Question Stats:

73% (00:52) correct 27% (00:53) wrong based on 44 sessions

### HideShow timer Statistics

The figure above represents a wooden block 3 inches on an edge, all of whose faces are painted black. If the block is cut up along the dotted lines, 27 blocks result, each 1 cubic inch in volume. Of these, how many will have no painted faces?

(A) 1

(B) 3

(C) 4

(D) 5

(E) 7

Attachment:

2018-02-05_2007.png [ 20.87 KiB | Viewed 557 times ]

_________________
Senior SC Moderator
Joined: 22 May 2016
Posts: 2350
The figure above represents a wooden block 3 inches on an edge, all  [#permalink]

### Show Tags

05 Feb 2018, 10:23
Bunuel wrote:

The figure above represents a wooden block 3 inches on an edge, all of whose faces are painted black. If the block is cut up along the dotted lines, 27 blocks result, each 1 cubic inch in volume. Of these, how many will have no painted faces?

(A) 1

(B) 3

(C) 4

(D) 5

(E) 7

Attachment:
2018-02-05_2007.png

Visualize. Only one little cube, in the very center, has no paint.

Each face will have blocks with one, two, or three sides painted.

Imagine levels (top third, bottom third, middle third, 9 cubes in each, 3 by 3) as a "layer":

Top layer, e.g.
MNO
PQR
STU
4 corner cubes (M, O, U, S) have three faces painted
4 edge cubes between corners (P, N, R, T) have two faces painted
1 center cube, Q, has 1 face painted
Total cubes with 1, 2, or 3 faces painted = 9

The bottom layer is the same as the top layer.

9 painted cubes in both the top and bottom layers =
18 cubes painted

Then the middle, another layer with 9 cubes, 3 by 3:

ABC
DEF
GHJ

A, G, J, and C have paint on two sides - 4 more that are painted
B, D, H, and F have paint on one side - 4 more that are painted
E has no paint.

There is only one cube with no paint. It is the little cube, E, at the very center.

18 + 4 + 4 = 26 are painted
There are 27 cubes
(27 Total-26 painted) = 1 not painted

So 1 cube is not painted.

_________________

Never look down on anybody unless you're helping them up.
--Jesse Jackson

The figure above represents a wooden block 3 inches on an edge, all &nbs [#permalink] 05 Feb 2018, 10:23
Display posts from previous: Sort by