It is currently 19 Oct 2017, 15:20

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
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

Events & Promotions

Events & Promotions in June
Open Detailed Calendar

The dimensions of a rectangular solid are 4 inches, 5 inches

 new topic post reply Question banks Downloads My Bookmarks Reviews Important topics
Author Message
TAGS:

Hide Tags

Manager
Joined: 12 Dec 2012
Posts: 226

Kudos [?]: 98 [0], given: 181

Concentration: Leadership, Marketing
GMAT 1: 540 Q36 V28
GMAT 2: 550 Q39 V27
GMAT 3: 620 Q42 V33
GPA: 2.82
WE: Human Resources (Health Care)
The dimensions of a rectangular solid are 4 inches, 5 inches [#permalink]

Show Tags

29 Mar 2013, 14:48
3
This post was
BOOKMARKED
00:00

Difficulty:

25% (medium)

Question Stats:

73% (01:22) correct 27% (01:23) wrong based on 151 sessions

HideShow timer Statistics

The dimensions of a rectangular solid are 4 inches, 5 inches, and 8 inches. If a cube, a side of which is equal to one of the dimensions of the rectangular solid, is placed entirely within the rectangular solid, what the ratio of the volume of the cube to the volume within the rectangular solid that is not occupied by the cube?
(A) 2:3
(B) 2:5
(C) 5:16
(D) 25:7
(E) 32:25

The question is today's question by Jeff Sackmann . In his answer he mentioned:

"Since the cube shares one of the dimensions of the rectangular solid, it must have a side of 4, 5, or 8. However, if its side is 5 or 8, it won't fit entirely within the solid."

Why ? could any body please clarify this statement further ? Thanks in advance
[Reveal] Spoiler: OA

_________________

My RC Recipe
http://gmatclub.com/forum/the-rc-recipe-149577.html

My Problem Takeaway Template
http://gmatclub.com/forum/the-simplest-problem-takeaway-template-150646.html

Kudos [?]: 98 [0], given: 181

Intern
Joined: 18 Nov 2011
Posts: 36

Kudos [?]: 15 [0], given: 0

Concentration: Strategy, Marketing
GMAT Date: 06-18-2013
GPA: 3.98
Re: The dimensions of a rectangular solid are 4 inches, 5 inches [#permalink]

Show Tags

29 Mar 2013, 15:28
TheNona wrote:
The dimensions of a rectangular solid are 4 inches, 5 inches, and 8 inches. If a cube, a side of which is equal to one of the dimensions of the rectangular solid, is placed entirely within the rectangular solid, what the ratio of the volume of the cube to the volume within the rectangular solid that is not occupied by the cube?
(A) 2:3
(B) 2:5
(C) 5:16
(D) 25:7
(E) 32:25

The question is today's question by Jeff Sackmann . In his answer he mentioned:

"Since the cube shares one of the dimensions of the rectangular solid, it must have a side of 4, 5, or 8. However, if its side is 5 or 8, it won't fit entirely within the solid."

Why ? could any body please clarify this statement further ? Thanks in advance

Volume of rectangular solid =$$4*5*8 = 160$$

Volume of cube = $$4*4*4 = 64$$ (it must be 4, becuase if it is 5 or 8 the cube will be longer than the shortest side of the rectangular solid ($$4$$) and therefore not fit in the box. Remember, a cube is the same dimension on each of the three sides)

Area not occupied by cube = $$160 - 64 = 96$$

Ratio is $$64:96 = 2:3$$

Answer is A

Kudos [?]: 15 [0], given: 0

VP
Status: Far, far away!
Joined: 02 Sep 2012
Posts: 1120

Kudos [?]: 2327 [0], given: 219

Location: Italy
Concentration: Finance, Entrepreneurship
GPA: 3.8
Re: The dimensions of a rectangular solid are 4 inches, 5 inches [#permalink]

Show Tags

29 Mar 2013, 15:36
TheNona wrote:
The dimensions of a rectangular solid are 4 inches, 5 inches, and 8 inches. If a cube, a side of which is equal to one of the dimensions of the rectangular solid, is placed entirely within the rectangular solid, what the ratio of the volume of the cube to the volume within the rectangular solid that is not occupied by the cube?
(A) 2:3
(B) 2:5
(C) 5:16
(D) 25:7
(E) 32:25

The question is today's question by Jeff Sackmann . In his answer he mentioned:

"Since the cube shares one of the dimensions of the rectangular solid, it must have a side of 4, 5, or 8. However, if its side is 5 or 8, it won't fit entirely within the solid."

Why ? could any body please clarify this statement further ? Thanks in advance

If the cube has a length of 4, it will fit in a 4x5x8 cube; because the length of the cube is equal to the shortest side of the solid.
Even if our cube has a length of 4,1 it will not fit in such rectangular solid: in the faces 5x8 or 8x5 fits, but in a face 4x8 or 4x5 does not ( the cube s side is longer than 4, so 0,1 will be outside of the face, and so outside of the solid)

Hope it is clear
_________________

It is beyond a doubt that all our knowledge that begins with experience.

Kant , Critique of Pure Reason

Tips and tricks: Inequalities , Mixture | Review: MGMAT workshop
Strategy: SmartGMAT v1.0 | Questions: Verbal challenge SC I-II- CR New SC set out !! , My Quant

Rules for Posting in the Verbal Forum - Rules for Posting in the Quant Forum[/size][/color][/b]

Kudos [?]: 2327 [0], given: 219

Manager
Joined: 12 Dec 2012
Posts: 226

Kudos [?]: 98 [0], given: 181

Concentration: Leadership, Marketing
GMAT 1: 540 Q36 V28
GMAT 2: 550 Q39 V27
GMAT 3: 620 Q42 V33
GPA: 2.82
WE: Human Resources (Health Care)
Re: The dimensions of a rectangular solid are 4 inches, 5 inches [#permalink]

Show Tags

29 Mar 2013, 15:37
hitman5532 wrote:
(it must be 4, becuase if it is 5 or 8 the cube will be longer than the shortest side of the rectangular solid ($$4$$) and therefore not fit in the box. Remember, a cube is the same dimension on each of the three sides)

This is exactly the part I do not understand ... why it cannot be longer than the shorter side of the solid ? still cannot imagine
_________________

My RC Recipe
http://gmatclub.com/forum/the-rc-recipe-149577.html

My Problem Takeaway Template
http://gmatclub.com/forum/the-simplest-problem-takeaway-template-150646.html

Kudos [?]: 98 [0], given: 181

Manager
Joined: 12 Dec 2012
Posts: 226

Kudos [?]: 98 [0], given: 181

Concentration: Leadership, Marketing
GMAT 1: 540 Q36 V28
GMAT 2: 550 Q39 V27
GMAT 3: 620 Q42 V33
GPA: 2.82
WE: Human Resources (Health Care)
Re: The dimensions of a rectangular solid are 4 inches, 5 inches [#permalink]

Show Tags

29 Mar 2013, 15:41
Zarrolou wrote:
TheNona wrote:
The dimensions of a rectangular solid are 4 inches, 5 inches, and 8 inches. If a cube, a side of which is equal to one of the dimensions of the rectangular solid, is placed entirely within the rectangular solid, what the ratio of the volume of the cube to the volume within the rectangular solid that is not occupied by the cube?
(A) 2:3
(B) 2:5
(C) 5:16
(D) 25:7
(E) 32:25

The question is today's question by Jeff Sackmann . In his answer he mentioned:

"Since the cube shares one of the dimensions of the rectangular solid, it must have a side of 4, 5, or 8. However, if its side is 5 or 8, it won't fit entirely within the solid."

Why ? could any body please clarify this statement further ? Thanks in advance

If the cube has a length of 4, it will fit in a 4x5x8 cube; because the length of the cube is equal to the shortest side of the solid.
Even if our cube has a length of 4,1 it will not fit in such rectangular solid: in the faces 5x8 or 8x5 fits, but in a face 4x8 or 4x5 does not ( the cube s side is longer than 4, so 0,1 will be outside of the face, and so outside of the solid)

Hope it is clear

thanks for the kind care but I would appreciate if you clarify more , please
_________________

My RC Recipe
http://gmatclub.com/forum/the-rc-recipe-149577.html

My Problem Takeaway Template
http://gmatclub.com/forum/the-simplest-problem-takeaway-template-150646.html

Kudos [?]: 98 [0], given: 181

VP
Status: Far, far away!
Joined: 02 Sep 2012
Posts: 1120

Kudos [?]: 2327 [1], given: 219

Location: Italy
Concentration: Finance, Entrepreneurship
GPA: 3.8
Re: The dimensions of a rectangular solid are 4 inches, 5 inches [#permalink]

Show Tags

29 Mar 2013, 15:58
1
This post received
KUDOS
We have a rectangular solid and a cube, the first has three different values for each side, the second has the same value of each side.
rectangular: 4,5,8 ( as in our case)
cube: x,x,x
Imagine now this rectangular solid, how would you "cut" it in order to obtain a cube? Or even better: what is the biggest cube you can obtain from it?
From the rectangular (4,5,8) you could extract a cube 1x1x1, but this isn't clearly the biggest possible, try now with a 2x2x2 and so on...
you'll reach 4x4x4 and this is our biggest value. Why? Because if you try to "cut" a 4,1x4,1x4,1 cube from a rectangular 4x5x8, how can you obtain a 4,1 side (for the cube) from a side of 4? it's impossible!
From 8 you can cut a side of 4,1; from 5 you can cut a side of 4,1; but you cannot do it from a side of 4!
That's why in this problem the cube must have a side of 4.

So if you want to obtain a cube from a rectangular solid, the max value the side of the cube can have is the min value of the side of the rectangular.
_________________

It is beyond a doubt that all our knowledge that begins with experience.

Kant , Critique of Pure Reason

Tips and tricks: Inequalities , Mixture | Review: MGMAT workshop
Strategy: SmartGMAT v1.0 | Questions: Verbal challenge SC I-II- CR New SC set out !! , My Quant

Rules for Posting in the Verbal Forum - Rules for Posting in the Quant Forum[/size][/color][/b]

Kudos [?]: 2327 [1], given: 219

Intern
Joined: 18 Nov 2011
Posts: 36

Kudos [?]: 15 [1], given: 0

Concentration: Strategy, Marketing
GMAT Date: 06-18-2013
GPA: 3.98
Re: The dimensions of a rectangular solid are 4 inches, 5 inches [#permalink]

Show Tags

29 Mar 2013, 16:19
1
This post received
KUDOS
TheNona wrote:
hitman5532 wrote:
(it must be 4, becuase if it is 5 or 8 the cube will be longer than the shortest side of the rectangular solid ($$4$$) and therefore not fit in the box. Remember, a cube is the same dimension on each of the three sides)

This is exactly the part I do not understand ... why it cannot be longer than the shorter side of the solid ? still cannot imagine

If i told you to put a 12 inch tall product in a shipping box which is only 4" x 4" x 4", would it fit? No.

Why?

Because 12" is greater than 4" and therefore you could not close the box to ship the item, right?

This follows the same idea. If the smallest side of an item is larger than the smallest side of a box within which it is to fit, you could not close to box. With a cube, all three sides are the same size.

If you are still struggling with this, I suggest drawing or constructing two box of the given measurements in the problem and to a look at what is occuring

Kudos [?]: 15 [1], given: 0

Intern
Joined: 18 Nov 2011
Posts: 36

Kudos [?]: 15 [1], given: 0

Concentration: Strategy, Marketing
GMAT Date: 06-18-2013
GPA: 3.98
Re: The dimensions of a rectangular solid are 4 inches, 5 inches [#permalink]

Show Tags

29 Mar 2013, 16:51
1
This post received
KUDOS
CHeck the picture below. Do you see how a 4" cube fills the height? if it is any larger than a 4" cube, it will protrude out of the rectangular solid
Attachments

box.jpg [ 62.15 KiB | Viewed 2597 times ]

Kudos [?]: 15 [1], given: 0

Director
Status: 1,750 Q's attempted and counting
Affiliations: University of Florida
Joined: 09 Jul 2013
Posts: 514

Kudos [?]: 987 [0], given: 630

Location: United States (FL)
Schools: UFL (A)
GMAT 1: 600 Q45 V29
GMAT 2: 590 Q35 V35
GMAT 3: 570 Q42 V28
GMAT 4: 610 Q44 V30
GPA: 3.45
WE: Accounting (Accounting)
Re: The dimensions of a rectangular solid are 4 inches, 5 inches [#permalink]

Show Tags

24 Oct 2013, 09:33
Here's the full Official Explanation is case anyone was interested.

Answer: A Since the cube shares one of the dimensions of the rectangular solid, it must have a side of 4, 5, or 8. However, if its side is 5 or 8, it won't fit entirely within the solid. Since one of the lengths of the solid is 4, all of the lengths of the cube must be 4 or shorter. Thus the side of the cube is 4, and the volume of the cube is 4^3 = 64.

The volume of the solid is the product of the dimensions: (4)(5)(8) = 160. We're looking for the ratio of the volume of the cube (64) to the volume of the solid that is not occupied by the cube-- that is, 160 - 64 = 96. The ratio of 64 to 96 can be simplied by dividing both terms by 32. The result is 2 to 3, choice (A).

Hope it helps.

Kudos [?]: 987 [0], given: 630

GMAT Club Legend
Joined: 09 Sep 2013
Posts: 16651

Kudos [?]: 273 [0], given: 0

Re: The dimensions of a rectangular solid are 4 inches, 5 inches [#permalink]

Show Tags

01 Jul 2015, 09:10
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________

Kudos [?]: 273 [0], given: 0

Re: The dimensions of a rectangular solid are 4 inches, 5 inches   [#permalink] 01 Jul 2015, 09:10
Display posts from previous: Sort by

The dimensions of a rectangular solid are 4 inches, 5 inches

 new topic post reply Question banks Downloads My Bookmarks Reviews Important topics

 Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne Kindly note that the GMAT® test is a registered trademark of the Graduate Management Admission Council®, and this site has neither been reviewed nor endorsed by GMAC®.