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: 53792

Question Stats:
61% (00:45) correct 39% (00:26) wrong based on 233 sessions
HideShow timer Statistics



Math Expert
Joined: 02 Sep 2009
Posts: 53792

Re M2306
[#permalink]
Show Tags
16 Sep 2014, 01:18



Intern
Joined: 21 May 2013
Posts: 8

Re: M2306
[#permalink]
Show Tags
07 Nov 2014, 23:21
Bunuel wrote: Official Solution:
What is the maximum number of 4x4x4 cubes that can fit in a rectangular box measuring 10x12x16 ?
A. 12 B. 18 C. 20 D. 24 E. 30
The 12x16 floor can be covered with 12 cubes. Another 12 cubes will form the second layer. The height of this construction will be 8; the box won't accommodate any more cubes.
Answer: D Hi Bunuel, Thanks for your explanation. I am having trouble understanding this one. Is your method based off of logic, or is there an equation behind it? Thanks!



Math Expert
Joined: 02 Sep 2009
Posts: 53792

Re: M2306
[#permalink]
Show Tags
09 Nov 2014, 06:16



Intern
Joined: 17 Aug 2014
Posts: 1

Re: M2306
[#permalink]
Show Tags
26 Nov 2014, 17:12
Hello,
I am not sure I understand the answer.
I calculate the volume of both solids, then divide the rectangule's by the cube's. Why is this approach wrong?
Thanks !



Math Expert
Joined: 02 Sep 2009
Posts: 53792

Re: M2306
[#permalink]
Show Tags
27 Nov 2014, 03:31



Intern
Joined: 16 May 2014
Posts: 1

Re: M2306
[#permalink]
Show Tags
05 Dec 2014, 09:45
I may be off base but could the way I found the answer was 4/10 =2.5 boxes rounded down to 2 , 4/12 = 3, 4/16= 4..... 2x3x4= 24 ..... I may have gotten lucky based on the numbers. Please tell me if my theory is flawed.



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

Bunuel wrote: Official Solution:
What is the maximum number of 4x4x4 cubes that can fit in a rectangular box measuring 10x12x16 ?
A. 12 B. 18 C. 20 D. 24 E. 30
The 12x16 floor can be covered with 12 cubes. Another 12 cubes will form the second layer. The height of this construction will be 8; the box won't accommodate any more cubes.
Answer: D How do we know that that the floor is 10x16 and it is not 12x16? I am asking because since we are not told which value corresponds to l,w,h, then I would think that we need to use the volume, which does not require you to know which of the values is l,w or h. In this sense, why isn't it volume of rectangular box 10x12x16 = 1920 divided by surface area of the cube 6*16= 96, which gives 20? At first I thought of using the volume for the cube as well, but what we need to know is its outside area, right? So, the space it would assume inside the box. Now, what I am not sure about is whether we also need to match each of the l,w,h of the square with those of the box. In this case though, shouldn't we be told specifically which value corresponds to l,w,h?



Math Expert
Joined: 02 Sep 2009
Posts: 53792

Re: M2306
[#permalink]
Show Tags
21 Jan 2015, 05:32
pacifist85 wrote: Bunuel wrote: Official Solution:
What is the maximum number of 4x4x4 cubes that can fit in a rectangular box measuring 10x12x16 ?
A. 12 B. 18 C. 20 D. 24 E. 30
The 12x16 floor can be covered with 12 cubes. Another 12 cubes will form the second layer. The height of this construction will be 8; the box won't accommodate any more cubes.
Answer: D How do we know that that the floor is 10x16 and it is not 12x16? I am asking because since we are not told which value corresponds to l,w,h, then I would think that we need to use the volume, which does not require you to know which of the values is l,w or h. In this sense, why isn't it volume of rectangular box 10x12x16 = 1920 divided by surface area of the cube 6*16= 96, which gives 20? At first I thought of using the volume for the cube as well, but what we need to know is its outside area, right? So, the space it would assume inside the box. Now, what I am not sure about is whether we also need to match each of the l,w,h of the square with those of the box. In this case though, shouldn't we be told specifically which value corresponds to l,w,h? Positioning of the box is not important. This is fairly simple problem from everyday life. You have 10x12x16 box and you want to know the maximum number of 4x4x4 cubes that can fit in it. No matter what dimensions the floor has the answer would be the same.
_________________
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



Intern
Joined: 11 Nov 2014
Posts: 34
Concentration: Marketing, Finance
WE: Programming (Computer Software)

As you see in the image I attached. total 6 cubes (4*4*4 size) can get fit at level 1. For H = 16 , there will be 4 level. isn't it? so total cubes that can fit in the rectangular box will be 6 x 4 = 24. I hope this helps.
>> !!!
You do not have the required permissions to view the files attached to this post.



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

Bunuel wrote: Official Solution:
What is the maximum number of 4x4x4 cubes that can fit in a rectangular box measuring 10x12x16 ?
A. 12 B. 18 C. 20 D. 24 E. 30
The 12x16 floor can be covered with 12 cubes. Another 12 cubes will form the second layer. The height of this construction will be 8; the box won't accommodate any more cubes.
Answer: D One question, cannot the floor also be 10*16? Because this would mean that the first layer would fit 160/16 = 10 cubes, up to the second layer 20, and up to the third layer 30. The height of this construction would be the side of the cube times the number of the layers, so 3*4 = 12. In this case then the solid can fit 30 cubes measuring 4*4*4...or not...? OK I just realised my mistake. When I take two sides, one of them being 10, this leaves out 2, because the same side of the cube would be 4. So, it would fit 2 cubes and a half. So, I missed the amount of space each side occupies.



Intern
Joined: 02 Aug 2014
Posts: 4

Re M2306
[#permalink]
Show Tags
15 Aug 2015, 02:39
I think this is a highquality question and the explanation isn't clear enough, please elaborate. why shouldnt i use the area formulae as in 10*12*16/64



Math Expert
Joined: 02 Sep 2009
Posts: 53792

Re: M2306
[#permalink]
Show Tags
17 Aug 2015, 04:04



Manager
Joined: 19 Dec 2015
Posts: 111
Location: United States
GPA: 3.8
WE: Information Technology (Computer Software)

Re: M2306
[#permalink]
Show Tags
15 Feb 2016, 15:08
Alternate approach to this question :
Find the highest multiple less or equal to the edges of the cuboid. You have a cube with an edge of 4, to be fit in 10X12X16. So that would be 08*12*16 cube space that can be occupied. Now find the cubes > 2*3*4 = 24.



Intern
Joined: 03 Feb 2018
Posts: 1

Re: M2306
[#permalink]
Show Tags
21 Feb 2018, 09:59
Cube size is=4x4x4 Rectangular box size=10x12x16 We have to find no of cubes in rectangular box.
Available size for cubes to put in rectangular box=8x12x16 Because we can put 2 cubes in 10th side, 3 cubes in 12th side and 4 cubes in 16th side.
So, 8x12x16/4x4x4 = 1536/64 = 24
Answer=D



Intern
Joined: 11 Aug 2013
Posts: 8
Location: India
GPA: 3.2

Re: M2306
[#permalink]
Show Tags
17 Sep 2018, 07:50
Bunuel wrote: What is the maximum number of 4x4x4 cubes that can fit in a rectangular box measuring 10x12x16 ?
A. 12 B. 18 C. 20 D. 24 E. 30 buneul if the question was to number of 5*5*5 cubes then it is 12...am i right ?? 10*12*16 can take only 10*10*15 /5*5*5 =12? thanks



Math Expert
Joined: 02 Sep 2009
Posts: 53792

Re: M2306
[#permalink]
Show Tags
17 Sep 2018, 07:53



Intern
Joined: 25 Jun 2017
Posts: 1

Re M2306
[#permalink]
Show Tags
16 Nov 2018, 11:17
I think this is a highquality question and the explanation isn't clear enough, please elaborate. Please elaborate.



Intern
Joined: 27 Sep 2017
Posts: 1

Re M2306
[#permalink]
Show Tags
07 Jan 2019, 08:44
I think this is a poorquality question and the explanation isn't clear enough, please elaborate. Hi,
I couldn't understand the explanation, can someone please explain it using the diagram.
Thanks



Math Expert
Joined: 02 Sep 2009
Posts: 53792

Re: M2306
[#permalink]
Show Tags
07 Jan 2019, 08:57










