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

 It is currently 16 Dec 2018, 13:08

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

Events & Promotions

Events & Promotions in December
PrevNext
SuMoTuWeThFrSa
2526272829301
2345678
9101112131415
16171819202122
23242526272829
303112345
Open Detailed Calendar
• Free GMAT Prep Hour

December 16, 2018

December 16, 2018

03:00 PM EST

04:00 PM EST

Strategies and techniques for approaching featured GMAT topics
• FREE Quant Workshop by e-GMAT!

December 16, 2018

December 16, 2018

07:00 AM PST

09:00 AM PST

Get personalized insights on how to achieve your Target Quant Score.

In the figure above, each of the four squares has sides of length x.

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

Hide Tags

Math Expert
Joined: 02 Sep 2009
Posts: 51229
In the figure above, each of the four squares has sides of length x.  [#permalink]

Show Tags

05 Jul 2018, 04:11
00:00

Difficulty:

25% (medium)

Question Stats:

95% (01:23) correct 5% (02:46) wrong based on 26 sessions

HideShow timer Statistics

In the figure above, each of the four squares has sides of length x. If ∆PQR is formed by joining the centers of three of the squares, what is the perimeter of ∆PQR in terms of x ?

(A) $$2x \sqrt{2}$$

(B) $$\frac{x\sqrt2}{2}$$ $$+ x$$

(C) $$2x + \sqrt{2}$$

(D) $$x \sqrt{2} + 2$$

(E) $$2x + x \sqrt{2}$$

Attachment:

square (1).jpg [ 14.04 KiB | Viewed 373 times ]

_________________
Director
Status: Learning stage
Joined: 01 Oct 2017
Posts: 931
WE: Supply Chain Management (Energy and Utilities)
Re: In the figure above, each of the four squares has sides of length x.  [#permalink]

Show Tags

05 Jul 2018, 04:44
Bunuel wrote:

In the figure above, each of the four squares has sides of length x. If ∆PQR is formed by joining the centers of three of the squares, what is the perimeter of ∆PQR in terms of x ?

(A) $$2x \sqrt{2}$$

(B) $$\frac{x\sqrt2}{2}$$ $$+ x$$

(C) $$2x + \sqrt{2}$$

(D) $$x \sqrt{2} + 2$$

(E) $$2x + x \sqrt{2}$$
Attachment:
square (1).jpg

We have, PQ=$$\frac{x}{2}+\frac{x}{2}=x$$
and QR=$$\frac{x}{2}+\frac{x}{2}=x$$
in the right angled triangle $$RP^2=PQ^2+QR^2=x^2+x^2=2x^2$$
So, $$RP=x\sqrt{2}$$

Perimeter of $$∆PQR=PQ+QR+RP=x+x+x\sqrt{2}$$=$$2x + x \sqrt{2}$$

Ans. (E)
_________________

Regards,

PKN

Rise above the storm, you will find the sunshine

Senior PS Moderator
Joined: 26 Feb 2016
Posts: 3327
Location: India
GPA: 3.12
In the figure above, each of the four squares has sides of length x.  [#permalink]

Show Tags

05 Jul 2018, 05:09

Since this triangle is formed by joining the centers of three triangles, the sides
PQ and QR will super-impose into any of the squares. The triangle ∆PQR is half
the square, where the third side(PR) is the diagonal of the square, which is $$x\sqrt{2}$$

Therefore, the perimeter of the triangle(∆PQR) is $$x + x + x\sqrt{2} = 2x + x\sqrt{2}$$ (Option E)

_________________

You've got what it takes, but it will take everything you've got

In the figure above, each of the four squares has sides of length x. &nbs [#permalink] 05 Jul 2018, 05:09
Display posts from previous: Sort by

In the figure above, each of the four squares has sides of length x.

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

 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®.