It is currently 17 Oct 2017, 21:00

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

Events & Promotions

Events & Promotions in June
Open Detailed Calendar

In the 7-inch square above, another square is inscribed. What fraction

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

Hide Tags

1 KUDOS received
Intern
Intern
avatar
Joined: 08 May 2014
Posts: 8

Kudos [?]: 40 [1], given: 1

In the 7-inch square above, another square is inscribed. What fraction [#permalink]

Show Tags

New post 24 Nov 2014, 22:42
1
This post received
KUDOS
8
This post was
BOOKMARKED
00:00
A
B
C
D
E

Difficulty:

  25% (medium)

Question Stats:

68% (01:03) correct 32% (02:05) wrong based on 253 sessions

HideShow timer Statistics

In the 7-inch square above, another square is inscribed. What fraction of the larger square is shaded?( picture is on the attachment)

(A) 3/12
(B) 24/49
(C) 1/2
(D) 25/49
(E) 7/12

my ans is c but OA is b, what wil be right one?
[Reveal] Spoiler: OA

Attachments

1.jpg
1.jpg [ 21.29 KiB | Viewed 3189 times ]

Kudos [?]: 40 [1], given: 1

1 KUDOS received
Senior Manager
Senior Manager
User avatar
Joined: 13 Jun 2013
Posts: 278

Kudos [?]: 467 [1], given: 13

Premium Member
Re: In the 7-inch square above, another square is inscribed. What fraction [#permalink]

Show Tags

New post 25 Nov 2014, 03:05
1
This post received
KUDOS
anik89 wrote:
In the 7-inch square above, another square is inscribed. What fraction of the larger square is shaded?( picture is on the attachment)

(A) 3/12
(B) 24/49
(C) 1/2
(D) 25/49
(E) 7/12

my ans is c but OA is b, what wil be right one?


each shaded represents a right angle triangle with 3,4 as its perpendicular sides. area of one of these right angle triangle = \(\frac{3.4}{2}\) \(= 6\)

thus total area of the shaded region \(= 4.6 =24\)

and the required fraction = (area of shaded region)/(area of the larger square) = \(\frac {24}{7^2}\) \(= 24/49\)

Kudos [?]: 467 [1], given: 13

Manager
Manager
User avatar
Joined: 21 Jul 2014
Posts: 127

Kudos [?]: 162 [0], given: 12

GMAT ToolKit User
Re: In the 7-inch square above, another square is inscribed. What fraction [#permalink]

Show Tags

New post 25 Nov 2014, 08:47
anik89 wrote:
In the 7-inch square above, another square is inscribed. What fraction of the larger square is shaded?( picture is on the attachment)

(A) 3/12
(B) 24/49
(C) 1/2
(D) 25/49
(E) 7/12

my ans is c but OA is b, what wil be right one?


Another way to do this problem is to notice that these side lengths are going to give us a special right triangle of 3-4-5. Since we know both the outer and inner objects are squares, we know that the side ratios are going to be the same on all sides. This means all of those outer triangles will be 3-4-5 right triangles.

Since this is the case, we know the inner square is a 5x5, with area of 25 square units. Taking the side length of the outer square, we know it is 7x7 or 49 square units. This means the inner square is 25/49 the size of the outer square. Subtracting 25 from 49 gives us the ratio of the shaded region, 24/49.

So the answer is B.

Kudos [?]: 162 [0], given: 12

2 KUDOS received
SVP
SVP
User avatar
Status: The Best Or Nothing
Joined: 27 Dec 2012
Posts: 1853

Kudos [?]: 2616 [2], given: 193

Location: India
Concentration: General Management, Technology
WE: Information Technology (Computer Software)
Re: In the 7-inch square above, another square is inscribed. What fraction [#permalink]

Show Tags

New post 25 Nov 2014, 19:04
2
This post received
KUDOS
Answer = (B) \(\frac{24}{49}\)

There are 4 triangles with base, height = 4, 3

Total shaded region area \(= 4 * \frac{1}{2} * 4 * 3 = 24\)

Square area \(= 7^2 = 49\)

Fraction \(= \frac{24}{49}\)
_________________

Kindly press "+1 Kudos" to appreciate :)

Kudos [?]: 2616 [2], given: 193

SVP
SVP
User avatar
Status: The Best Or Nothing
Joined: 27 Dec 2012
Posts: 1853

Kudos [?]: 2616 [0], given: 193

Location: India
Concentration: General Management, Technology
WE: Information Technology (Computer Software)
Re: In the 7-inch square above, another square is inscribed. What fraction [#permalink]

Show Tags

New post 25 Nov 2014, 19:11
anik89 wrote:
In the 7-inch square above, another square is inscribed. What fraction of the larger square is shaded?( picture is on the attachment)

(A) 3/12
(B) 24/49
(C) 1/2
(D) 25/49
(E) 7/12

my ans is c but OA is b, what wil be right one?


As far as your calculation is concerned, answer would be C (1/2) when the small square is inscribed at mid points of the 7 inch square (per diagram below)

Attachment:
sq.png
sq.png [ 3.55 KiB | Viewed 3039 times ]

_________________

Kindly press "+1 Kudos" to appreciate :)

Kudos [?]: 2616 [0], given: 193

GMAT Club Legend
GMAT Club Legend
User avatar
Joined: 09 Sep 2013
Posts: 16762

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

Premium Member
Re: In the 7-inch square above, another square is inscribed. What fraction [#permalink]

Show Tags

New post 19 Jan 2016, 02:56
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.
_________________

GMAT Books | GMAT Club Tests | Best Prices on GMAT Courses | GMAT Mobile App | Math Resources | Verbal Resources

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

Expert Post
EMPOWERgmat Instructor
User avatar
P
Status: GMAT Assassin/Co-Founder
Affiliations: EMPOWERgmat
Joined: 19 Dec 2014
Posts: 9968

Kudos [?]: 3403 [0], given: 172

Location: United States (CA)
GMAT 1: 800 Q51 V49
GRE 1: 340 Q170 V170
Re: In the 7-inch square above, another square is inscribed. What fraction [#permalink]

Show Tags

New post 21 Jan 2016, 16:19
Hi All,

The error that was made by the original poster was in assuming that the answer to THIS prompt is the same as the answer to a slightly different version of this prompt. IF the interior square had its corners at the exact midpoint of each of the 4 sides of the larger square, THEN exactly HALF of the larger square would be shaded. Since that's NOT the case in this prompt (the 4 corners are NOT at the exact midpoints), then the shaded area will be LESS than half.

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

Co-Founder & 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!***********************

Kudos [?]: 3403 [0], given: 172

Director
Director
User avatar
Joined: 04 Jun 2016
Posts: 647

Kudos [?]: 365 [0], given: 36

GMAT 1: 750 Q49 V43
In the 7-inch square above, another square is inscribed. What fraction [#permalink]

Show Tags

New post 31 Jul 2016, 21:29
anik89 wrote:
In the 7-inch square above, another square is inscribed. What fraction of the larger square is shaded?( picture is on the attachment)

(A) 3/12
(B) 24/49
(C) 1/2
(D) 25/49
(E) 7/12

my ans is c but OA is b, what wil be right one?


Outer square area = \(7^2 = 49\)

Inner square area = \(\frac{Diagonal^2}{2}\)= \(\frac{7^2}{2} = \frac{49}{2}\)

Total area = 49
Unshaded area (inner square) is 49/2 which is half of 49
so obviously the remaining shaded area will also be half of the total area =49/2
Shaded area = 1/2
Unshaded area = 1/2

Remember the question is asking for "What fraction of "
ANSWER is C
_________________

Posting an answer without an explanation is "GOD COMPLEX". The world doesn't need any more gods. Please explain you answers properly.
FINAL GOODBYE :- 17th SEPTEMBER 2016. .. 16 March 2017 - I am back but for all purposes please consider me semi-retired.

Kudos [?]: 365 [0], given: 36

Expert Post
Top Contributor
2 KUDOS received
SVP
SVP
User avatar
G
Joined: 12 Sep 2015
Posts: 1794

Kudos [?]: 2446 [2], given: 356

Location: Canada
Re: In the 7-inch square above, another square is inscribed. What fraction [#permalink]

Show Tags

New post 08 Sep 2017, 13:20
2
This post received
KUDOS
Expert's post
Top Contributor
anik89 wrote:
In the 7-inch square above, another square is inscribed. What fraction of the larger square is shaded?( picture is on the attachment)

(A) 3/12
(B) 24/49
(C) 1/2
(D) 25/49
(E) 7/12


The first thing we need to recognize is that the 4 SHADED triangles are identical. Here's why:

If we focus on one triangle and let x and y represent the 2 angles that are not 90 degrees, we get the following:
Image
From this, we can see that x + y + 90° = 180°

So, when we examine another right triangle (this time in green)....
Image
...we can see that the angle represented by ? must be equal to x, since we already know that x + y + 90° = 180°

So, we'll add that information to the diagram...
Image

Using similar logic, we can see that the 3rd angle in the green triangle must be equal to y, since we know that x + y + 90° = 180°
Image

Using the exact same process, we can show that all 4 shaded triangles have the same 3 angles: x, y and 90°
We're told that the white quadrilateral in the middle of the diagram is a SQUARE, so we can see that the hypotenuse in each of the SHADED triangles has the same length.
This means that all 4 SHADED triangles are identical....
Image

So, the area of each SHADED triangle = (base)(height)/2 = (4)(3)/2 =12/2 = 6
So, the TOTAL area of all 4 SHADED triangles = (4)(6) = 24

The area of the LARGER square = (7)(7) = 49

So, 24/49 of the larger square is shaded

Answer:
[Reveal] Spoiler:
B


Cheers,
Brent
_________________

Brent Hanneson – Founder of gmatprepnow.com

Image

Kudos [?]: 2446 [2], given: 356

Re: In the 7-inch square above, another square is inscribed. What fraction   [#permalink] 08 Sep 2017, 13:20
Display posts from previous: Sort by

In the 7-inch square above, another square is inscribed. What fraction

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


GMAT Club MBA Forum Home| About| Terms and Conditions| GMAT Club Rules| Contact| Sitemap

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®.