It is currently 30 Sep 2020, 20:38

### 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

# In the figure above, if the area of the smaller square regio

 Question banks Downloads My Bookmarks Reviews Important topics
Author Message
TAGS:
Founder
Joined: 18 Apr 2015
Posts: 13432
Followers: 292

Kudos [?]: 3418 [0], given: 12318

In the figure above, if the area of the smaller square regio [#permalink]  06 Jul 2018, 08:36
Expert's post
00:00

Question Stats:

80% (03:02) correct 20% (00:55) wrong based on 15 sessions
Attachment:

square.jpg [ 7.19 KiB | Viewed 699 times ]

In the figure above, if the area of the smaller square region is $$\frac{2}{3}$$ the area of the larger square region, then the diagonal of the larger square is how many inches longer than the diagonal of the smaller square?

A. $${\sqrt{2} - \frac{2\sqrt3}{3}$$

B. $$\frac{2}{3}$$

C. $$\frac{2\sqrt3}{3}$$

D. $$\frac{\sqrt2 - 2}{3}$$

E. $$\sqrt{3}$$
[Reveal] Spoiler: OA

_________________

Need Practice? 20 Free GRE Quant Tests available for free with 20 Kudos
GRE Prep Club Members of the Month: Each member of the month will get three months free access of GRE Prep Club tests.

VP
Joined: 20 Apr 2016
Posts: 1302
WE: Engineering (Energy and Utilities)
Followers: 22

Kudos [?]: 1315 [0], given: 251

Re: In the figure above, if the area of the smaller square regio [#permalink]  07 Jul 2018, 07:17
Carcass wrote:
Attachment:
square.jpg

In the figure above, if the area of the smaller square region is $$\frac{2}{3}$$ the area of the larger square region, then the diagonal of the larger square is how many inches longer than the diagonal of the smaller square?

A. $${\sqrt{2} - \frac{2\sqrt3}{3}$$

B. $$\frac{2}{3}$$

C. $$\frac{2\sqrt3}{3}$$

D. $$\frac{\sqrt2 - 2}{3}$$

E. $$\sqrt{3}$$

Here,

Side of the Larger square = 1 inch

Therefore Area Large square = $$1^2 =1$$

But we know Area of a square =$$\frac{diagonal^2}{2}$$

So 1 = $$\frac{diagonal^2}{2}$$

or diagonal = $$\sqrt{2}$$

And we know
smaller square region is $$\frac{2}{3}$$ the area of the larger square region

So it can be written as $$\frac{(Diagonal smaller square)^2}{2}= \frac{2}{3} * 1 = \frac{2}{3}$$ (Since the area of the Larger square = 1)

or $$(diagonal of smaller square)^2 = \frac{4}{3}$$

or diagonal of smaller square = $$\frac{\sqrt4}{\sqrt3} = \frac{2}{(\sqrt3)} = \frac{2}{\sqrt3} * \frac{\sqrt3}{\sqrt3} = \frac{2\sqrt3}{3}$$

Now,
Diagonal of the larger square is longer than the diagonal of the smaller square = $$\sqrt2 - \frac{2\sqrt3}{3}$$
_________________

If you found this post useful, please let me know by pressing the Kudos Button

Rules for Posting

Got 20 Kudos? You can get Free GRE Prep Club Tests

GRE Prep Club Members of the Month:TOP 10 members of the month with highest kudos receive access to 3 months GRE Prep Club tests

Re: In the figure above, if the area of the smaller square regio   [#permalink] 07 Jul 2018, 07:17
Display posts from previous: Sort by

# In the figure above, if the area of the smaller square regio

 Question banks Downloads My Bookmarks Reviews Important topics

 Powered by phpBB © phpBB Group Kindly note that the GRE® test is a registered trademark of the Educational Testing Service®, and this site has neither been reviewed nor endorsed by ETS®.