GMAT Question of the Day - Daily to your Mailbox; hard ones only

 It is currently 16 Oct 2019, 02:40 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

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.  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

Math Expert V
Joined: 02 Sep 2009
Posts: 58400
In the 7-inch square above, another square is inscribed. What fraction  [#permalink]

Show Tags 00:00

Difficulty:   25% (medium)

Question Stats: 72% (01:13) correct 28% (01:49) wrong based on 107 sessions

HideShow timer Statistics In the 7-inch square above, another square is inscribed. What fraction of the larger square is shaded?

(A) $$\frac{3}{12}$$

(B) $$\frac{24}{49}$$

(C) $$\frac{1}{2}$$

(D) $$\frac{25}{49}$$

(E) $$\frac{7}{12}$$

Attachment: Capture (2).JPG [ 15.52 KiB | Viewed 1143 times ]

_________________
Math Expert V
Joined: 02 Aug 2009
Posts: 7958
Re: In the 7-inch square above, another square is inscribed. What fraction  [#permalink]

Show Tags

1
Bunuel wrote: In the 7-inch square above, another square is inscribed. What fraction of the larger square is shaded?

(A) $$\frac{3}{12}$$

(B) $$\frac{24}{49}$$

(C) $$\frac{1}{2}$$

(D) $$\frac{25}{49}$$

(E) $$\frac{7}{12}$$

Attachment:
The attachment Capture (2).JPG is no longer available

So every corner makes a right angled triangle with sides 3-4-5...
And hypotenuse of this triangle is the side of inner square, so 5..

Area of shaded region = $$7^2-5^2=49-25=24$$
Total area =7^2=49

Shaded region as a fraction of total =$$\frac{24}{49}$$

B
Attachments PicsArt_10-12-08.32.54.jpg [ 9.91 KiB | Viewed 988 times ]

_________________
Target Test Prep Representative D
Status: Founder & CEO
Affiliations: Target Test Prep
Joined: 14 Oct 2015
Posts: 8069
Location: United States (CA)
Re: In the 7-inch square above, another square is inscribed. What fraction  [#permalink]

Show Tags

Bunuel wrote: In the 7-inch square above, another square is inscribed. What fraction of the larger square is shaded?

(A) $$\frac{3}{12}$$

(B) $$\frac{24}{49}$$

(C) $$\frac{1}{2}$$

(D) $$\frac{25}{49}$$

(E) $$\frac{7}{12}$$

Attachment:
Capture (2).JPG

The area of the larger square is 7^2 = 49. We see that each of the shaded regions is a right triangle that is a 3-4-5 right triangle. Thus, each of these right triangles has an area of ½ x 3 x 4 = 6, and the total area of the four triangles is 6 x 4 = 24. So the fraction of the larger square is shaded is 24/49.

_________________

Scott Woodbury-Stewart

Founder and CEO

Scott@TargetTestPrep.com

See why Target Test Prep is the top rated GMAT quant course on GMAT Club. Read Our Reviews

If you find one of my posts helpful, please take a moment to click on the "Kudos" button.

GMAT Club Legend  D
Joined: 18 Aug 2017
Posts: 4997
Location: India
Concentration: Sustainability, Marketing
GPA: 4
WE: Marketing (Energy and Utilities)
In the 7-inch square above, another square is inscribed. What fraction  [#permalink]

Show Tags

chetan2u ScottTargetTestPrep
I have question ; we are given that a square is inscribed in square ; we can notice that the digonal of the inside square = 7 so side of small square ; s=7/√2
area = 49/2
so shaded region ; 49-49/2 = 49/2
ratio ; 49/2 /49 = 1/2
IMO C

why is this approach and answer wrong?

chetan2u wrote:
Bunuel wrote: In the 7-inch square above, another square is inscribed. What fraction of the larger square is shaded?

(A) $$\frac{3}{12}$$

(B) $$\frac{24}{49}$$

(C) $$\frac{1}{2}$$

(D) $$\frac{25}{49}$$

(E) $$\frac{7}{12}$$

Attachment:
Capture (2).JPG

So every corner makes a right angled triangle with sides 3-4-5...
And hypotenuse of this triangle is the side of inner square, so 5..

Area of shaded region = $$7^2-5^2=49-25=24$$
Total area =7^2=49

Shaded region as a fraction of total =$$\frac{24}{49}$$

B
Board of Directors D
Status: QA & VA Forum Moderator
Joined: 11 Jun 2011
Posts: 4773
Location: India
GPA: 3.5
WE: Business Development (Commercial Banking)
Re: In the 7-inch square above, another square is inscribed. What fraction  [#permalink]

Show Tags

Archit3110 wrote:
chetan2u ScottTargetTestPrep
I have question ; we are given that a square is inscribed in square ; we can notice that the digonal of the inside square = 7 so side of small square ; s=7/√2
area = 49/2
so shaded region ; 49-49/2 = 49/2
ratio ; 49/2 /49 = 1/2
IMO C

why is this approach and answer wrong?

chetan2u wrote:
Bunuel wrote: In the 7-inch square above, another square is inscribed. What fraction of the larger square is shaded?

(A) $$\frac{3}{12}$$

(B) $$\frac{24}{49}$$

(C) $$\frac{1}{2}$$

(D) $$\frac{25}{49}$$

(E) $$\frac{7}{12}$$

Attachment:
Capture (2).JPG

So every corner makes a right angled triangle with sides 3-4-5...
And hypotenuse of this triangle is the side of inner square, so 5..

Area of shaded region = $$7^2-5^2=49-25=24$$
Total area =7^2=49

Shaded region as a fraction of total =$$\frac{24}{49}$$

B

The highlighted part is not correct, you can not calculate the diagonal of the square that way, chetan2u s approach is IMHO the most elegant way to solve the question...
_________________
Thanks and Regards

Abhishek....

PLEASE FOLLOW THE RULES FOR POSTING IN QA AND VA FORUM AND USE SEARCH FUNCTION BEFORE POSTING NEW QUESTIONS

How to use Search Function in GMAT Club | Rules for Posting in QA forum | Writing Mathematical Formulas |Rules for Posting in VA forum | Request Expert's Reply ( VA Forum Only )
GMAT Club Legend  D
Joined: 18 Aug 2017
Posts: 4997
Location: India
Concentration: Sustainability, Marketing
GPA: 4
WE: Marketing (Energy and Utilities)
Re: In the 7-inch square above, another square is inscribed. What fraction  [#permalink]

Show Tags

Abhishek009
Could you please share reason why won't the diagonal of small square be 7 ? Is it because figure is not drawn to scale or some other reason?

Posted from my mobile device
Board of Directors D
Status: QA & VA Forum Moderator
Joined: 11 Jun 2011
Posts: 4773
Location: India
GPA: 3.5
WE: Business Development (Commercial Banking)
Re: In the 7-inch square above, another square is inscribed. What fraction  [#permalink]

Show Tags

Archit3110 wrote:
Abhishek009
Could you please share reason why won't the diagonal of small square be 7 ? Is it because figure is not drawn to scale or some other reason?

Posted from my mobile device

Bro , the sides of the square inscribed inside the square is 5 units and the sides of the bigger square is 7 units....
Attachment: Capture (2).JPG [ 16.57 KiB | Viewed 441 times ]

Thus the diagonal of the bigger square will be 7√2 and the diagonal of the smaller square will be 5√2

Hope this helps..
_________________
Thanks and Regards

Abhishek....

PLEASE FOLLOW THE RULES FOR POSTING IN QA AND VA FORUM AND USE SEARCH FUNCTION BEFORE POSTING NEW QUESTIONS

How to use Search Function in GMAT Club | Rules for Posting in QA forum | Writing Mathematical Formulas |Rules for Posting in VA forum | Request Expert's Reply ( VA Forum Only )
Manager  S
Joined: 15 Jul 2018
Posts: 62
Re: In the 7-inch square above, another square is inscribed. What fraction  [#permalink]

Show Tags

Hi Archit3110 , the diagonal of the inner square would have been 7 units if in the figure, all the points, where the inner square is touching the outer square are the midpoints of the sides of outer square

Posted from my mobile device
Target Test Prep Representative D
Status: Founder & CEO
Affiliations: Target Test Prep
Joined: 14 Oct 2015
Posts: 8069
Location: United States (CA)
Re: In the 7-inch square above, another square is inscribed. What fraction  [#permalink]

Show Tags

Archit3110 wrote:
chetan2u ScottTargetTestPrep
I have question ; we are given that a square is inscribed in square ; we can notice that the digonal of the inside square = 7 so side of small square ; s=7/√2
area = 49/2
so shaded region ; 49-49/2 = 49/2
ratio ; 49/2 /49 = 1/2
IMO C

why is this approach and answer wrong?

chetan2u wrote:
Bunuel wrote: In the 7-inch square above, another square is inscribed. What fraction of the larger square is shaded?

(A) $$\frac{3}{12}$$

(B) $$\frac{24}{49}$$

(C) $$\frac{1}{2}$$

(D) $$\frac{25}{49}$$

(E) $$\frac{7}{12}$$

Attachment:
Capture (2).JPG

So every corner makes a right angled triangle with sides 3-4-5...
And hypotenuse of this triangle is the side of inner square, so 5..

Area of shaded region = $$7^2-5^2=49-25=24$$
Total area =7^2=49

Shaded region as a fraction of total =$$\frac{24}{49}$$

B

Yes, your assumption is wrong. From the picture, you can actually see that the diagonal of the inscribed square is slanted, that is, it’s actually longer than a side of the circumscribed square. The only way the diagonal of the inscribed square is equal to the side length of the circumscribed square is when the vertices of the inscribed square are the midpoints of the sides of the circumscribed square. However, that is not the case here. You can see that the vertices of the inscribed square are a little off from the midpoints of the sides of the circumscribed square.
_________________

Scott Woodbury-Stewart

Founder and CEO

Scott@TargetTestPrep.com

See why Target Test Prep is the top rated GMAT quant course on GMAT Club. Read Our Reviews

If you find one of my posts helpful, please take a moment to click on the "Kudos" button. Re: In the 7-inch square above, another square is inscribed. What fraction   [#permalink] 06 Jun 2019, 17:59
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

 Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne  