Mar 23 07:00 AM PDT  09:00 AM PDT Christina scored 760 by having clear (ability) milestones and a trackable plan to achieve the same. Attend this webinar to learn how to build trackable milestones that leverage your strengths to help you get to your target GMAT score. Mar 27 03:00 PM PDT  04:00 PM PDT Join a free live webinar and learn the winning strategy for a 700+ score on GMAT & the perfect application. Save your spot today! Wednesday, March 27th at 3 pm PST Mar 29 10:00 PM PDT  11:00 PM PDT Right now, their GMAT prep, GRE prep, and MBA admissions consulting services are up to $1,100 off. GMAT (Save up to $261): SPRINGEXTRAGMAT GRE Prep (Save up to $149): SPRINGEXTRAGRE MBA (Save up to $1,240): SPRINGEXTRAMBA Mar 30 07:00 AM PDT  09:00 AM PDT Attend this webinar and master GMAT SC in 10 days by learning how meaning and logic can help you tackle 700+ level SC questions with ease.
Author 
Message 
TAGS:

Hide Tags

Math Expert
Joined: 02 Sep 2009
Posts: 53795

A rectangular wooden dowel measures 4 inches by 1 inch by 1 inch. If
[#permalink]
Show Tags
17 Jun 2015, 05:55
Question Stats:
54% (02:58) correct 46% (02:39) wrong based on 212 sessions
HideShow timer Statistics




CEO
Status: GMATINSIGHT Tutor
Joined: 08 Jul 2010
Posts: 2844
Location: India
GMAT: INSIGHT
WE: Education (Education)

Re: A rectangular wooden dowel measures 4 inches by 1 inch by 1 inch. If
[#permalink]
Show Tags
17 Jun 2015, 06:22
Bunuel wrote: A rectangular wooden dowel measures 4 inches by 1 inch by 1 inch. If the dowel is painted on all surfaces and then cut into 1/2 inch cubes, what fraction of the resulting cube faces are painted?
(A) 1/3 (B) 3/8 (C) 7/16 (D) 1/2 (E) 9/16
Kudos for a correct solution. Number of pieces in which First Side of Box of Dimension 4 will be cut in cubes of Dimension (1/2)inch = 4/(1/2) = 8 Number of pieces in which Second Side of Box of Dimension 1 will be cut in cubes of Dimension (1/2)inch = 1/(1/2) = 2 Number of pieces in which Third Side of Box of Dimension 1 will be cut in cubes of Dimension (1/2)inch = 1/(1/2) = 2 i.e. Total Number of smaller cubes of Dimension (1/2 each) = 8 x 2 x 2 = 32 METHOD2Total painted Area = Total Surface Area of Bigger Box = 2 (lb+bh+lh) = 2(4x1 + 1x1 + 4x1) = 18 Total Surface Area of all the smaller cubes = No. of Smaller Cubes x Surface Area of Each Cube Please Note: Surface Area of Each Cube = \(6a^2\) where \(a\) is the each dimension of Cubei.e. Total Surface Area of all the smaller cubes = \(32 * [6x(1/2)^2]\) = 48 Painted faces as fraction of total faces = Painted Area / Total area of smaller Cubes = 18/48 = 3/8 Answer: Option
_________________
Prosper!!! GMATinsight Bhoopendra Singh and Dr.Sushma Jha email: info@GMATinsight.com I Call us : +919999687183 / 9891333772 Online OneonOne Skype based classes and Classroom Coaching in South and West Delhi http://www.GMATinsight.com/testimonials.html
ACCESS FREE GMAT TESTS HERE:22 ONLINE FREE (FULL LENGTH) GMAT CAT (PRACTICE TESTS) LINK COLLECTION




CEO
Status: GMATINSIGHT Tutor
Joined: 08 Jul 2010
Posts: 2844
Location: India
GMAT: INSIGHT
WE: Education (Education)

Re: A rectangular wooden dowel measures 4 inches by 1 inch by 1 inch. If
[#permalink]
Show Tags
17 Jun 2015, 06:21
Bunuel wrote: A rectangular wooden dowel measures 4 inches by 1 inch by 1 inch. If the dowel is painted on all surfaces and then cut into 1/2 inch cubes, what fraction of the resulting cube faces are painted?
(A) 1/3 (B) 3/8 (C) 7/16 (D) 1/2 (E) 9/16
Kudos for a correct solution. Number of pieces in which First Side of Box of Dimension 4 will be cut in cubes of Dimension (1/2)inch = 4/(1/2) = 8 Number of pieces in which Second Side of Box of Dimension 1 will be cut in cubes of Dimension (1/2)inch = 1/(1/2) = 2 Number of pieces in which Third Side of Box of Dimension 1 will be cut in cubes of Dimension (1/2)inch = 1/(1/2) = 2 i.e. Total Number of smaller cubes of Dimension (1/2 each) = 8 x 2 x 2 = 32 METHOD1Total Cubes painted on 3 faces = Cubes available on the vertices of Box = No. of Vertics of Box = 8 Total Cubes painted on 2 faces = Cubes available on the edges of Box x 4 = 6 x 4 = 24 Total Cubes painted on 1 faces = Cubes available on the Faces but not on the edges of Vertices Total Cubes painted on 0 faces = Cubes NOT available on anyone of the Faces i.e. Total Painted faces = (8*3) + (24*2) + 0 + 0 = 72 Total faces = No. of Cubes x Faces on each cube = 32x6 = 192 Fraction = 72/192 = 3/8 Answer: Option
_________________
Prosper!!! GMATinsight Bhoopendra Singh and Dr.Sushma Jha email: info@GMATinsight.com I Call us : +919999687183 / 9891333772 Online OneonOne Skype based classes and Classroom Coaching in South and West Delhi http://www.GMATinsight.com/testimonials.html
ACCESS FREE GMAT TESTS HERE:22 ONLINE FREE (FULL LENGTH) GMAT CAT (PRACTICE TESTS) LINK COLLECTION



Math Expert
Joined: 02 Aug 2009
Posts: 7434

Re: A rectangular wooden dowel measures 4 inches by 1 inch by 1 inch. If
[#permalink]
Show Tags
17 Jun 2015, 06:45
Bunuel wrote: A rectangular wooden dowel measures 4 inches by 1 inch by 1 inch. If the dowel is painted on all surfaces and then cut into 1/2 inch cubes, what fraction of the resulting cube faces are painted?
(A) 1/3 (B) 3/8 (C) 7/16 (D) 1/2 (E) 9/16
Kudos for a correct solution. Hi, we have to find the painted faces and total faces.. 1)painted faces.. we have four faces of size 4*1 sq inches...when cut at 1/2 inches , it will give us 8*2 external (painted) faces.. total faces 8*2*4=64faces remaining two faces of size 1*1sq inches...when cut at 1/2 inches, it will give us 2*2 external (painted) faces.. total faces 2*2*2=8faces total 64+8=72 faces 2) total number of faces: number of cubes=4*1*1/(0.5*0.5*0.5)=8*2*2=32.. each cube has 6 faces.. so total faces=32*6=192 fraction of faces painted=painted faces/total faces=72/192=3/8 ans B
_________________
1) Absolute modulus : http://gmatclub.com/forum/absolutemodulusabetterunderstanding210849.html#p1622372 2)Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html 3) effects of arithmetic operations : https://gmatclub.com/forum/effectsofarithmeticoperationsonfractions269413.html 4) Base while finding % increase and % decrease : https://gmatclub.com/forum/percentageincreasedecreasewhatshouldbethedenominator287528.html
GMAT Expert



Manager
Joined: 26 Dec 2011
Posts: 114

Re: A rectangular wooden dowel measures 4 inches by 1 inch by 1 inch. If
[#permalink]
Show Tags
17 Jun 2015, 07:53
Bunuel wrote: A rectangular wooden dowel measures 4 inches by 1 inch by 1 inch. If the dowel is painted on all surfaces and then cut into 1/2 inch cubes, what fraction of the resulting cube faces are painted?
(A) 1/3 (B) 3/8 (C) 7/16 (D) 1/2 (E) 9/16
Kudos for a correct solution. Solution  Total area of the Wooden dowel(Painted) = 2*(4*1+1*4+1*1) = 18 inch^2 No of cubes after cut into 1/2 inch = (4*1*1)/(1/2) = 32 Area of 1/2 inch cube = 6*(1/2)*(1/2) = 3/2 inch^2 Total area of all the 1/2 inch cubes = 32*(3/2) = 48 inch^2* Fraction of the resulting cube faces are painted = 18/48 = 3/8. ANS B. Thanks Kudos Please.
_________________
Thanks, Kudos Please



Intern
Joined: 29 Mar 2015
Posts: 44
Location: United States

Re: A rectangular wooden dowel measures 4 inches by 1 inch by 1 inch. If
[#permalink]
Show Tags
19 Jun 2015, 00:45
Bunuel wrote: A rectangular wooden dowel measures 4 inches by 1 inch by 1 inch. If the dowel is painted on all surfaces and then cut into 1/2 inch cubes, what fraction of the resulting cube faces are painted?
(A) 1/3 (B) 3/8 (C) 7/16 (D) 1/2 (E) 9/16
Kudos for a correct solution. The surface area of the wooden dowel is the area of each of the 6 faces. There is are four 4x1 faces and two 1x1 faces, for a total of 4*4+2=18 square inches that are painted. If it is cut into 1/2 inch cubes, then that means that it will be cut into 8x2x2 1/2 inch cubes. The surface area of each of these cubes is 6*1/2*1/2=6/4=1.5 square inches. There are a total of 8x2x2=32 cubes, so the total surface area is 32*1.5=32+16=48 square inches. 18/48 square inches are painted. 18/48=3/8 so answer is B.



Senior Manager
Status: Math is psychological
Joined: 07 Apr 2014
Posts: 414
Location: Netherlands
GMAT Date: 02112015
WE: Psychology and Counseling (Other)

Re: A rectangular wooden dowel measures 4 inches by 1 inch by 1 inch. If
[#permalink]
Show Tags
19 Jun 2015, 01:14
Hello,
I am a little bit confused here. Are we looking for the fraction of the resulting, painted surface areas, or for the fraction of the number of resulting faces that are painted?
So, the ratio of "total inches of resulting painted surface areas"/"total inches of surface areas" or for the ratio of "total number of resulting faces that are painted"/"total number of resulting faces"?



Math Expert
Joined: 02 Aug 2009
Posts: 7434

Re: A rectangular wooden dowel measures 4 inches by 1 inch by 1 inch. If
[#permalink]
Show Tags
19 Jun 2015, 01:36
pacifist85 wrote: Hello,
I am a little bit confused here. Are we looking for the fraction of the resulting, painted surface areas, or for the fraction of the number of resulting faces that are painted?
So, the ratio of "total inches of resulting painted surface areas"/"total inches of surface areas" or for the ratio of "total number of resulting faces that are painted"/"total number of resulting faces"? Hi, we are looking for the faces and that is mentioned in the Q.. A rectangular wooden dowel measures 4 inches by 1 inch by 1 inch. If the dowel is painted on all surfaces and then cut into 1/2 inch cubes, what fraction of the resulting cube faces are painted so the coloured portion in your query is the ratio you have to find
_________________
1) Absolute modulus : http://gmatclub.com/forum/absolutemodulusabetterunderstanding210849.html#p1622372 2)Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html 3) effects of arithmetic operations : https://gmatclub.com/forum/effectsofarithmeticoperationsonfractions269413.html 4) Base while finding % increase and % decrease : https://gmatclub.com/forum/percentageincreasedecreasewhatshouldbethedenominator287528.html
GMAT Expert



Math Expert
Joined: 02 Sep 2009
Posts: 53795

Re: A rectangular wooden dowel measures 4 inches by 1 inch by 1 inch. If
[#permalink]
Show Tags
22 Jun 2015, 07:18
Bunuel wrote: A rectangular wooden dowel measures 4 inches by 1 inch by 1 inch. If the dowel is painted on all surfaces and then cut into 1/2 inch cubes, what fraction of the resulting cube faces are painted?
(A) 1/3 (B) 3/8 (C) 7/16 (D) 1/2 (E) 9/16
Kudos for a correct solution. MANHATTAN GMAT OFFICIAL SOLUTION:If you draw a picture, this problem becomes a matter of counting: Total Cubes = (4 inches × 2 cubes per inch) × (1 × 2) × (1 × 2) = 32 cubes Total Cube Faces = 32 cubes × 6 faces per cube = 192 faces total We now consider the faces that were painted on the front and back of the dowel, the top and bottom of the dowel, and the ends of the dowel. In the diagram above, we can see 16 faces on the front, 16 faces on the top, and 4 faces on the end shown. Of course, there are other sides: the back, the bottom, and the other end. The fraction of faces that are painted = 72/192 = 24(3)/24(8) = 3/8. The correct answer is B.Notice that there is no shortcut to solving this kind of problem, so don't waste time looking for one—just draw the diagram and count. !

Even if you can easily picture 3D shapes and objects in your head, it is still better to draw a picture on your scrapboard. Wrong answer choices are often those you might get by losing track of your progress as you process the object in your mind. 
This kind of process can also help you with questions that deal with the relative size of different objects. Attachment:
20150622_1814.png [ 38.37 KiB  Viewed 3417 times ]
Attachment:
20150622_1815.png [ 29.26 KiB  Viewed 3398 times ]
_________________
New to the Math Forum? Please read this: Ultimate GMAT Quantitative Megathread  All You Need for Quant  PLEASE READ AND FOLLOW: 12 Rules for Posting!!! Resources: GMAT Math Book  Triangles  Polygons  Coordinate Geometry  Factorials  Circles  Number Theory  Remainders; 8. Overlapping Sets  PDF of Math Book; 10. Remainders  GMAT Prep Software Analysis  SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS)  Tricky questions from previous years.
Collection of Questions: PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.
What are GMAT Club Tests? Extrahard Quant Tests with Brilliant Analytics



Manager
Joined: 01 Sep 2016
Posts: 193

A rectangular wooden dowel measures 4 inches by 1 inch by 1 inch. If
[#permalink]
Show Tags
17 Aug 2017, 15:53
Hey Experts Bunuel mikemcgarry  Can you please validate my approach below. I used the volume method to find the number of cubes that would be contained in the cuboid instead of the counting technique. Is it alright to use this method? Are there any caveats to consider. For example the volume approach often does not take into account the exact cuts and specifics of a figure. This approach might be working in this question, but does it work well with other scenarios as well? BEFORE the cuts There are 6 faces to the dowel, and each face is a rectangle. 4 of the faces have dimensions 4 by 1. So, the area of each rectangle = (4)(1) = 4 So, the total area of those 4 rectangles = (4)(4) = 16 The remaining 2 faces have dimensions 1 by 1. So, the area of each rectangle (square) = (1)(1) = 1 So, the total area of those 2 rectangles = (2)(1) = 2 So, BEFORE the cuts, the TOTAL surface area of the dowel = 16 + 2 = 18 In other words, there are 18 square inches of paint. AFTER the cuts Each cube has dimensions 1/2 by 1/2 by 1/2 So, the VOLUME of each cube = (1/2)(1/2)(1/2) = 1/8 BEFORE the cut, the VOLUME of the dowel = (4)(1)(1) = 4 So, the NUMBER of cubes = 4/(1/8) = 32 So, after the cuts, there are 32 mini cubes Each individual minicube has 6 sides, and each side is a 1/2 by 1/2 square. So, the area of ONE square = (1/2)(1/2) = 1/4 So, the total surface area of one mini cube = (6)(1/4) = 6/4 = 3/2 So, the TOTAL surface are of all 32 mini cubes = (32)(3/2) = 48 square inches So, the 32 mini cubes have a TOTAL surface are of 48 square inches, and 18 square inches are painted. So, the correct answer is 18/48
_________________
we shall fight on the beaches, we shall fight on the landing grounds, we shall fight in the fields and in the streets, we shall fight in the hills; we shall never surrender!



Magoosh GMAT Instructor
Joined: 28 Dec 2011
Posts: 4486

Re: A rectangular wooden dowel measures 4 inches by 1 inch by 1 inch. If
[#permalink]
Show Tags
17 Aug 2017, 16:43
bkpolymers1617 wrote: Hey Experts Bunuel mikemcgarry  Can you please validate my approach below. I used the volume method to find the number of cubes that would be contained in the cuboid instead of the counting technique. Is it alright to use this method? Are there any caveats to consider. For example the volume approach often does not take into account the exact cuts and specifics of a figure. This approach might be working in this question, but does it work well with other scenarios as well?
BEFORE the cuts There are 6 faces to the dowel, and each face is a rectangle. 4 of the faces have dimensions 4 by 1. So, the area of each rectangle = (4)(1) = 4 So, the total area of those 4 rectangles = (4)(4) = 16 The remaining 2 faces have dimensions 1 by 1. So, the area of each rectangle (square) = (1)(1) = 1 So, the total area of those 2 rectangles = (2)(1) = 2
So, BEFORE the cuts, the TOTAL surface area of the dowel = 16 + 2 = 18 In other words, there are 18 square inches of paint.
AFTER the cuts Each cube has dimensions 1/2 by 1/2 by 1/2 So, the VOLUME of each cube = (1/2)(1/2)(1/2) = 1/8 BEFORE the cut, the VOLUME of the dowel = (4)(1)(1) = 4 So, the NUMBER of cubes = 4/(1/8) = 32 So, after the cuts, there are 32 mini cubes
Each individual minicube has 6 sides, and each side is a 1/2 by 1/2 square. So, the area of ONE square = (1/2)(1/2) = 1/4 So, the total surface area of one mini cube = (6)(1/4) = 6/4 = 3/2 So, the TOTAL surface are of all 32 mini cubes = (32)(3/2) = 48 square inches
So, the 32 mini cubes have a TOTAL surface are of 48 square inches, and 18 square inches are painted.
So, the correct answer is 18/48 Dear bkpolymers1617, I'm happy to respond. :) What you did is fine. I would think that this approach might take slightly longer than the counting method, but whatever makes the most intuitive sense to you is often the easier and faster method. This is a relatively straightforward problem. As you move into harder problems, and you are wondering about the relative strengths of two different approaches, experiment: do them both, and see which one is faster. Ideally, you will find that you are confident in more than one way to solve a number of problems. Does this make sense? Mike :)
_________________
Mike McGarry Magoosh Test Prep
Education is not the filling of a pail, but the lighting of a fire. — William Butler Yeats (1865 – 1939)



EMPOWERgmat Instructor
Status: GMAT Assassin/CoFounder
Affiliations: EMPOWERgmat
Joined: 19 Dec 2014
Posts: 13777
Location: United States (CA)

Re: A rectangular wooden dowel measures 4 inches by 1 inch by 1 inch. If
[#permalink]
Show Tags
12 Jan 2018, 13:07
Hi All, This question can be approached in a couple of different ways (most of which involve lots of math steps). Based on the 'spread' of the answer choices though, you can do a little bit of math and use a bit of logic to get to the correct answer. To start, it would help to physically draw the rectangular solid that is described (including the "cut lines"). Since a (1 in.) x (1 in.) x (1 in.) cube will contain eight 1/2 in. minicubes, the (4 in.) x (1 in.) x (1in.) dowel will end up being cut into 4(8) = 32 minicubes. When the outside of the dowel is painted, you should recognize that each of the smaller cubes will have paint on either 3 faces (the 8 'corner' pieces) or 2 faces (all of the noncorner pieces  24 in total). Put a different way  the 8 corner pieces have HALF of their faces painted and all of the other pieces have a THIRD of their faces painted. This then can be looked at as a Weighted Average. The AVERAGE fractional number of faces painted must be closer to 1/3 than to 1/2. There's only one answer that fits... Final Answer: GMAT assassins aren't born, they're made, Rich
_________________
760+: Learn What GMAT Assassins Do to Score at the Highest Levels Contact Rich at: Rich.C@empowergmat.com
Rich Cohen
CoFounder & GMAT Assassin
Special Offer: Save $75 + GMAT Club Tests Free
Official GMAT Exam Packs + 70 Pt. Improvement Guarantee www.empowergmat.com/
*****Select EMPOWERgmat Courses now include ALL 6 Official GMAC CATs!*****




Re: A rectangular wooden dowel measures 4 inches by 1 inch by 1 inch. If
[#permalink]
12 Jan 2018, 13:07






