Author 
Message 
TAGS:

Hide Tags

Senior Manager
Joined: 06 Jan 2015
Posts: 340
Location: India
Concentration: Operations, Finance
GPA: 3.35
WE: Information Technology (Computer Software)

The figure above shows a side view of the insert and the four componen [#permalink]
Show Tags
30 Jul 2016, 06:16
5
This post was BOOKMARKED
Question Stats:
67% (01:50) correct 33% (01:58) wrong based on 132 sessions
HideShow timer Statistics
The figure above shows a side view of the insert and the four components of a box designed to package four lightbulbs. The package is a rectangular box, whose base is a square with a side of 8 inches and whose height is 12 inches. A single rectangular insert is folded twice to form two identical diagonal planes, one at each end, and a horizontal plane in the middle, so that the box is divided into four identical compartments. What is the area of the insert in square inches? A) 192 B) 224 C) \(64+4\sqrt{52}\) D) \(64+96\sqrt{2}\) E) \(64+128\sqrt{2}\) Attachment:
Figure.jpg [ 4.78 KiB  Viewed 2961 times ]
Official Answer and Stats are available only to registered users. Register/ Login.
_________________
आत्मनॊ मोक्षार्थम् जगद्धिताय च
Resource: GMATPrep RCs With Solution
Last edited by Bunuel on 30 Jul 2016, 07:14, edited 1 time in total.
Edited the question.



EMPOWERgmat Instructor
Status: GMAT Assassin/CoFounder
Affiliations: EMPOWERgmat
Joined: 19 Dec 2014
Posts: 11292
Location: United States (CA)
GRE 1: 340 Q170 V170

Re: The figure above shows a side view of the insert and the four componen [#permalink]
Show Tags
30 Jul 2016, 13:19
Hi NandishSS, While this question looks complex, it's actually built around some fairly simple Geometry. It might help to break this calculation down into 'pieces' and think about the rules involved in this 3dimensional shape. To start, the 'insert' is a rectangle that's been folded in 2 spots. By definition, it has a length and a width; once we figure out those two dimensions, we can figure out its area. We're meant to assume that the insert 'touches' the sides, so the width of the insert has to match the width of the box. Since the base of the box is an 8inch square, the width of the insert is also 8 inches. Next, we'll work on the 'middle' horizontal piece (it's the easiest part)  since it's horizontal, then it has the same length as the box (which is also 8 inches). Thus, that 'middle piece' is an 8x8 square = 64 in^2 The two diagonal pieces are the same length, so once we figure out one, we can double it and get the total area of those 2 'pieces.' You should notice how a bunch of right triangles are formed. The base of each of those triangles is 8 and the height is 6. This is a classic 3/4/5 right triangle that's been doubled to become a 6/8/10. Thus, the two diagonal pieces are 8x10 rectangles = 80 in^2 each. 64+80+80 = 224 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!***********************



Senior Manager
Joined: 06 Jan 2015
Posts: 340
Location: India
Concentration: Operations, Finance
GPA: 3.35
WE: Information Technology (Computer Software)

Re: The figure above shows a side view of the insert and the four componen [#permalink]
Show Tags
24 Aug 2016, 08:38
NandishSS wrote: The figure above shows a side view of the insert and the four components of a box designed to package four lightbulbs. The package is a rectangular box, whose base is a square with a side of 8 inches and whose height is 12 inches. A single rectangular insert is folded twice to form two identical diagonal planes, one at each end, and a horizontal plane in the middle, so that the box is divided into four identical compartments. What is the area of the insert in square inches? A) 192 B) 224 C) \(64+4\sqrt{52}\) D) \(64+96\sqrt{2}\) E) \(64+128\sqrt{2}\) VeritasPrepKarishma, Abhishek009, Engr2012, Skywalker18, Bunuel Any other method to approach this problem
_________________
आत्मनॊ मोक्षार्थम् जगद्धिताय च
Resource: GMATPrep RCs With Solution



Current Student
Joined: 08 Jan 2015
Posts: 86

Re: The figure above shows a side view of the insert and the four componen [#permalink]
Show Tags
04 Sep 2016, 05:15
NandishSS wrote: NandishSS wrote: The figure above shows a side view of the insert and the four components of a box designed to package four lightbulbs. The package is a rectangular box, whose base is a square with a side of 8 inches and whose height is 12 inches. A single rectangular insert is folded twice to form two identical diagonal planes, one at each end, and a horizontal plane in the middle, so that the box is divided into four identical compartments. What is the area of the insert in square inches? A) 192 B) 224 C) \(64+4\sqrt{52}\) D) \(64+96\sqrt{2}\) E) \(64+128\sqrt{2}\) VeritasPrepKarishma, Abhishek009, Engr2012, Skywalker18, Bunuel Any other method to approach this problem The solution above is pretty straightforward.



Senior Manager
Joined: 03 Apr 2013
Posts: 291
Location: India
Concentration: Marketing, Finance
GPA: 3

Re: The figure above shows a side view of the insert and the four componen [#permalink]
Show Tags
13 Nov 2017, 03:00
EMPOWERgmatRichC wrote: Hi NandishSS, While this question looks complex, it's actually built around some fairly simple Geometry. It might help to break this calculation down into 'pieces' and think about the rules involved in this 3dimensional shape. To start, the 'insert' is a rectangle that's been folded in 2 spots. By definition, it has a length and a width; once we figure out those two dimensions, we can figure out its area. We're meant to assume that the insert 'touches' the sides, so the width of the insert has to match the width of the box. Since the base of the box is an 8inch square, the width of the insert is also 8 inches. Next, we'll work on the 'middle' horizontal piece (it's the easiest part)  since it's horizontal, then it has the same length as the box (which is also 8 inches). Thus, that 'middle piece' is an 8x8 square = 64 in^2 The two diagonal pieces are the same length, so once we figure out one, we can double it and get the total area of those 2 'pieces.' You should notice how a bunch of right triangles are formed. The base of each of those triangles is 8 and the height is 6. This is a classic 3/4/5 right triangle that's been doubled to become a 6/8/10. Thus, the two diagonal pieces are 8x10 rectangles = 80 in^2 each. 64+80+80 = 224 Final Answer: GMAT assassins aren't born, they're made, Rich Hi. Please help, I don't even understand the language of the question. Please break the question down as I cant connect the language to the given diagram.
_________________
Spread some love..Like = +1 Kudos



Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
Posts: 7996
Location: Pune, India

Re: The figure above shows a side view of the insert and the four componen [#permalink]
Show Tags
13 Nov 2017, 04:47
NandishSS wrote: The figure above shows a side view of the insert and the four components of a box designed to package four lightbulbs. The package is a rectangular box, whose base is a square with a side of 8 inches and whose height is 12 inches. A single rectangular insert is folded twice to form two identical diagonal planes, one at each end, and a horizontal plane in the middle, so that the box is divided into four identical compartments. What is the area of the insert in square inches? A) 192 B) 224 C) \(64+4\sqrt{52}\) D) \(64+96\sqrt{2}\) E) \(64+128\sqrt{2}\) Too much of confusing explanation is given in the question which makes me think that the diagram tells it all. That is pretty much what the first sentence of the question says too. We see the 8 x 12 rectangular box as shown in the figure. A single rectangular insert is folded twice to make four identical compartments. We see in the figure that we have 4 identical right triangular compartments. So the insert is just the lightening shape shown in the figure. We need its area. It is actually a rectangle which is folded into this shape. If we open it up, we will get a rectangle and its area will be the total height * Width (which is 8 since the box has a square base of side 8) Now all we need is the height. Since the compartments are equal, height of each compartment is 6. So each diagonal in the figure is 10 (using multiple of pythagorean triplet 345). Total height of the rectangular insert = 10 + 8 + 10 = 28 Its area = 28*8 = 224
_________________
Karishma Veritas Prep  GMAT Instructor My Blog
Get started with Veritas Prep GMAT On Demand for $199
Veritas Prep Reviews



Intern
Joined: 06 Oct 2017
Posts: 10

Re: The figure above shows a side view of the insert and the four componen [#permalink]
Show Tags
13 Nov 2017, 19:35
NandishSS wrote: The figure above shows a side view of the insert and the four components of a box designed to package four lightbulbs. The package is a rectangular box, whose base is a square with a side of 8 inches and whose height is 12 inches. A single rectangular insert is folded twice to form two identical diagonal planes, one at each end, and a horizontal plane in the middle, so that the box is divided into four identical compartments. What is the area of the insert in square inches? A) 192 B) 224 C) \(64+4\sqrt{52}\) D) \(64+96\sqrt{2}\) E) \(64+128\sqrt{2}\) I'm surprised this is an official GMAT question, it's pretty badly worded. I took me a good 10 minutes to understand that we're dealing with a 3D shape, and that the base (not shown) is 8x8...




Re: The figure above shows a side view of the insert and the four componen
[#permalink]
13 Nov 2017, 19:35






