Last visit was: 06 Dec 2024, 00:38 It is currently 06 Dec 2024, 00:38
Close
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
Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.
Close
Request Expert Reply
Confirm Cancel
User avatar
NandishSS
Joined: 06 Jan 2015
Last visit: 28 Jan 2021
Posts: 723
Own Kudos:
1,629
 [79]
Given Kudos: 579
Location: India
Concentration: Operations, Finance
GPA: 3.35
WE:Information Technology (Computer Software)
Posts: 723
Kudos: 1,629
 [79]
1
Kudos
Add Kudos
77
Bookmarks
Bookmark this Post
Most Helpful Reply
User avatar
KarishmaB
Joined: 16 Oct 2010
Last visit: 05 Dec 2024
Posts: 15,532
Own Kudos:
70,051
 [15]
Given Kudos: 449
Location: Pune, India
Expert reply
Active GMAT Club Expert! Tag them with @ followed by their username for a faster response.
Posts: 15,532
Kudos: 70,051
 [15]
11
Kudos
Add Kudos
4
Bookmarks
Bookmark this Post
User avatar
CrackverbalGMAT
User avatar
GMAT Club Legend
Joined: 03 Oct 2013
Last visit: 05 Dec 2024
Posts: 4,879
Own Kudos:
8,121
 [10]
Given Kudos: 224
Affiliations: CrackVerbal
Location: India
Posts: 4,879
Kudos: 8,121
 [10]
9
Kudos
Add Kudos
1
Bookmarks
Bookmark this Post
General Discussion
User avatar
EMPOWERgmatRichC
User avatar
GMAT Club Legend
Joined: 19 Dec 2014
Last visit: 31 Dec 2023
Posts: 21,808
Own Kudos:
12,039
 [8]
Given Kudos: 450
Status:GMAT Assassin/Co-Founder
Affiliations: EMPOWERgmat
Location: United States (CA)
GMAT 1: 800 Q51 V49
GRE 1: Q170 V170
Expert reply
GMAT 1: 800 Q51 V49
GRE 1: Q170 V170
Posts: 21,808
Kudos: 12,039
 [8]
5
Kudos
Add Kudos
3
Bookmarks
Bookmark this Post
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 3-dimensional 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 8-inch 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
User avatar
pthet9801
Joined: 18 Aug 2020
Last visit: 03 May 2022
Posts: 2
Own Kudos:
Given Kudos: 2
Concentration: Finance, Other
GMAT 1: 680 Q44 V39
GPA: 3.78
WE:Engineering (Energy)
GMAT 1: 680 Q44 V39
Posts: 2
Kudos: 1
Kudos
Add Kudos
Bookmarks
Bookmark this Post
I'm having trouble understanding why the area of the rectangular box wouldn't be: (10+8+6)*8? Isn't the right side of the triangle 6 in.? I'm missing where the other 10 in. comes from.
User avatar
EMPOWERgmatRichC
User avatar
GMAT Club Legend
Joined: 19 Dec 2014
Last visit: 31 Dec 2023
Posts: 21,808
Own Kudos:
12,039
 [2]
Given Kudos: 450
Status:GMAT Assassin/Co-Founder
Affiliations: EMPOWERgmat
Location: United States (CA)
GMAT 1: 800 Q51 V49
GRE 1: Q170 V170
Expert reply
GMAT 1: 800 Q51 V49
GRE 1: Q170 V170
Posts: 21,808
Kudos: 12,039
 [2]
2
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Hi pthet9801,

I assume that you're actually talking about the INSERT and not the BOX (since we're told the dimensions of the box - it's 8x8x12).

The insert can be broken down into 3 pieces: the two 'diagonal' sections and the middle 'horizontal' section. Since we're meant to assume that the insert 'touches' the sides, the width of the insert has to match the width of the box. The base of the box is an 8-inch square, so the width and length of the middle section is also 8x8 inches = 64 square inches.

The two diagonal pieces are the same length. You should notice how a bunch of right triangles are formed by those two pieces. The base of each of those triangles is 8 and since each 'pair' of triangles is HALF the height (re: half of 12 inches), the height of each triangle is 6 inches. This is a classic 3/4/5 right triangle that's been doubled to become a 6/8/10. Thus, the two diagonal pieces have a width of 8 inches and a length of 10 inches = 80 square inches each.

If you wanted to form a calculation in the way that you did in your post, then it would be (8+10+10)(8).

GMAT assassins aren't born, they're made,
Rich
User avatar
chetan2u
User avatar
RC & DI Moderator
Joined: 02 Aug 2009
Last visit: 21 Nov 2024
Posts: 11,445
Own Kudos:
37,849
 [1]
Given Kudos: 333
Status:Math and DI Expert
Products:
Expert reply
Posts: 11,445
Kudos: 37,849
 [1]
1
Kudos
Add Kudos
Bookmarks
Bookmark this Post
NandishSS

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:
The attachment Figure.jpg is no longer available


CrackverbalGMAT is absolutely correct with the sketch.

I will add on to it a bit

INSERT is the cardboard which is placed inside ( Red in colour ).
Partitions are equal so ABCD gives us the length of the partition as the entire INSERT is made by folding the rectagular cardboard at two places - B and C.

AB=CD= hypotenuse with other two sides 6 and 8, so both are 10.

Thus the insert becomes a rectangular piece with sides 8 and 10+8+10 as shown in the third sketch.
Area = 8*28 = 224

B
Attachments

UntitledA.png
UntitledA.png [ 35.23 KiB | Viewed 8095 times ]

Moderator:
Math Expert
97567 posts