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

It is currently 22 Jul 2018, 09:47

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

The coordinates of the points P, Q, R and S are shown in the figure ab

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

Hide Tags

Expert Post
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 47182
The coordinates of the points P, Q, R and S are shown in the figure ab  [#permalink]

Show Tags

New post 18 Dec 2017, 21:46
00:00
A
B
C
D
E

Difficulty:

  5% (low)

Question Stats:

76% (00:59) correct 24% (01:04) wrong based on 130 sessions

HideShow timer Statistics

Image
The coordinates of the points P, Q, R and S are shown in the figure above. If PQ and RS are the diagonals of a square, what is the area of the square?

(A) 2√2
(B) 4
(C) 4√2
(D) 8
(E) 8√2

Attachment:
2017-12-19_0837_002.png
2017-12-19_0837_002.png [ 10.19 KiB | Viewed 1261 times ]

_________________

New to the Math Forum?
Please read this: Ultimate GMAT Quantitative Megathread | All You Need for Quant | PLEASE READ AND FOLLOW: 12 Rules for Posting!!!

Resources:
GMAT Math Book | Triangles | Polygons | Coordinate Geometry | Factorials | Circles | Number Theory | Remainders; 8. Overlapping Sets | PDF of Math Book; 10. Remainders | GMAT Prep Software Analysis | SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) | Tricky questions from previous years.

Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


What are GMAT Club Tests?
Extra-hard Quant Tests with Brilliant Analytics

BSchool Forum Moderator
User avatar
V
Joined: 26 Feb 2016
Posts: 2961
Location: India
GPA: 3.12
Premium Member
Re: The coordinates of the points P, Q, R and S are shown in the figure ab  [#permalink]

Show Tags

New post 18 Dec 2017, 21:54
If the figure is a square, diagonals are equal, length of which is 4.

If the length of the diagonal is 4, the length of the side is 4/√2 = 2√2

Area of the square is (2√2)^2 or 8(Option D)

Posted from my mobile device
_________________

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

Manager
Manager
avatar
B
Joined: 24 Nov 2016
Posts: 148
The coordinates of the points P, Q, R and S are shown in the figure ab  [#permalink]

Show Tags

New post 19 Dec 2017, 07:32
Bunuel wrote:
Image
The coordinates of the points P, Q, R and S are shown in the figure above. If PQ and RS are the diagonals of a square, what is the area of the square?

(A) 2√2
(B) 4
(C) 4√2
(D) 8
(E) 8√2

Attachment:
2017-12-19_0837_002.png


Distance between two points: \(\sqrt{(x2-x1)^2+(y2-y1)^2} = \sqrt{(5-1)^2+(5-5)^2}=√16=4\)

Side of square using the diagonal: \(diagonal = side*√2; (4) = side*√2; side = \frac{4}{√2}\)

Area of square: \(side^2=(\frac{4}{√2})^2=\frac{6}{2}=8\)

(D) is the answer.
Senior Manager
Senior Manager
User avatar
P
Joined: 12 Mar 2013
Posts: 296
Reviews Badge CAT Tests
Re: The coordinates of the points P, Q, R and S are shown in the figure ab  [#permalink]

Show Tags

New post 15 Jan 2018, 10:27
If the diagonals of a square is a and b, the the area is (a*b)/2
_________________

We Shall Overcome... One day...

Intern
Intern
avatar
B
Status: preparing for GMAT
Joined: 29 Nov 2017
Posts: 23
GPA: 3.55
WE: Military Officer (Military & Defense)
Re: The coordinates of the points P, Q, R and S are shown in the figure ab  [#permalink]

Show Tags

New post 15 Jan 2018, 20:48
I found the area of each triangle... (1/2 * base * height) * 4 (number of triangles in square)
Senior Manager
Senior Manager
User avatar
S
Status: love the club...
Joined: 24 Mar 2015
Posts: 278
Re: The coordinates of the points P, Q, R and S are shown in the figure ab  [#permalink]

Show Tags

New post 23 Feb 2018, 09:57
lets find the distance between SP, or PR, or RQ, or QS

the distance between any of them is √8

so area of the square is 8 = answer choice D

thanks
SC Moderator
avatar
D
Joined: 22 May 2016
Posts: 1835
Premium Member CAT Tests
The coordinates of the points P, Q, R and S are shown in the figure ab  [#permalink]

Show Tags

New post 23 Feb 2018, 23:41
Bunuel wrote:
Image
The coordinates of the points P, Q, R and S are shown in the figure above. If PQ and RS are the diagonals of a square, what is the area of the square?

(A) 2√2
(B) 4
(C) 4√2
(D) 8
(E) 8√2

Attachment:
2017-12-19_0837_002.png

Three ways to solve, below, are all based on the length of the diagonal.

Diagonal = length of line segment RS (or PQ, in which case use x-coordinates instead):
\((y_2 - y_1) = (7 - 3) = 4 = d\)

1. Area from diagonal alone:
\(A= \frac{d^2}{2}\)
Area of square = \(\frac{d^2}{2}=\frac{4^2}{2}=\frac{16}{2}=8\)

2. Area from \(s^2\), calculated from diagonal length
\(s\sqrt{2} = d\)
\(s=\frac{d}{\sqrt{2}}\)
\(s=\frac{4}{\sqrt{2}}\)
\(Area = s^2\)
\(Area = (\frac{4}{\sqrt{2}}*\frac{4}{\sqrt{2}})= \frac{16}{2} = 8\)

3. Area from sides and Pythagorean theorem

A square's diagonal is the hypotenuse of an isosceles right triangle. Use Pythagorean theorem:
\(s^2 + s^2 = d^2\)
\(2s^2 = 4^2\)
\(s^2 = \frac{4^2}{2}\)
\(Area = s^2 = \frac{4^2}{2}=\frac{16}{2}= 8\)

ANSWER D

*Note: obvious, but often overlooked. Do not solve for \(s\) in #3. Once you have \(s^2\), you have area.
_________________

In the depths of winter, I finally learned
that within me there lay an invincible summer.

-- Albert Camus, "Return to Tipasa"

Intern
Intern
User avatar
B
Joined: 26 Feb 2017
Posts: 24
Re: The coordinates of the points P, Q, R and S are shown in the figure ab  [#permalink]

Show Tags

New post 12 Mar 2018, 02:35
Bunuel wrote:
Image
The coordinates of the points P, Q, R and S are shown in the figure above. If PQ and RS are the diagonals of a square, what is the area of the square?

(A) 2√2
(B) 4
(C) 4√2
(D) 8
(E) 8√2

Attachment:
2017-12-19_0837_002.png



D1- diagonal one
D2=diagonal2
D1=√(5-1)^2 +(5-5)^2=4
D2=√(3-3)^2+(7-3)^2=4

Area=(D1*D2)/2=(4*4)/2=8
Manager
Manager
User avatar
G
Joined: 16 Sep 2016
Posts: 225
WE: Analyst (Health Care)
Premium Member CAT Tests
Re: The coordinates of the points P, Q, R and S are shown in the figure ab  [#permalink]

Show Tags

New post 12 Mar 2018, 03:04
ashisplb wrote:
Bunuel wrote:
Image
The coordinates of the points P, Q, R and S are shown in the figure above. If PQ and RS are the diagonals of a square, what is the area of the square?

(A) 2√2
(B) 4
(C) 4√2
(D) 8
(E) 8√2

Attachment:
2017-12-19_0837_002.png



D1- diagonal one
D2=diagonal2
D1=√(5-1)^2 +(5-5)^2=4
D2=√(3-3)^2+(7-3)^2=4

Area=(D1*D2)/2=(4*4)/2=8


Since it is GIVEN to be a square - you don't even need to calculate the length of both the diagonals... since the diagonals of a square are equal in length.

Could save a few precious seconds...
VP
VP
User avatar
D
Status: It's near - I can see.
Joined: 13 Apr 2013
Posts: 1155
Location: India
Concentration: International Business, Operations
GMAT 1: 480 Q38 V22
GPA: 3.01
WE: Engineering (Consulting)
Premium Member Reviews Badge CAT Tests
Re: The coordinates of the points P, Q, R and S are shown in the figure ab  [#permalink]

Show Tags

New post 11 Apr 2018, 09:41
Bunuel wrote:
Image
The coordinates of the points P, Q, R and S are shown in the figure above. If PQ and RS are the diagonals of a square, what is the area of the square?

(A) 2√2
(B) 4
(C) 4√2
(D) 8
(E) 8√2

Attachment:
2017-12-19_0837_002.png


Distance between PR = \(\sqrt{(3-1)^2 + (7-5)^2}\)

PR = \(\sqrt{4 + 4}\)

PR = \(2*\sqrt{2}\)

Distance between RQ = \(\sqrt{(3-5)^2 + (7-5)^2}\)

RQ = \(\sqrt{(-2)^2 + (2)^2}\)

RQ = \(2*\sqrt{2}\)

Area of square = PR * RQ

\(2\sqrt{2} * 2\sqrt{2}\)

Area = 8

Hence (D)
_________________

"Do not watch clock; Do what it does. KEEP GOING."

Re: The coordinates of the points P, Q, R and S are shown in the figure ab &nbs [#permalink] 11 Apr 2018, 09:41
Display posts from previous: Sort by

The coordinates of the points P, Q, R and S are shown in the figure ab

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

Events & Promotions

PREV
NEXT


GMAT Club MBA Forum Home| About| Terms and Conditions and Privacy Policy| 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®.