Last visit was: 15 Jul 2025, 15:57 It is currently 15 Jul 2025, 15:57
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
User avatar
Crytiocanalyst
Joined: 16 Jun 2021
Last visit: 27 May 2023
Posts: 951
Own Kudos:
Given Kudos: 309
Posts: 951
Kudos: 202
Kudos
Add Kudos
Bookmarks
Bookmark this Post
User avatar
rajshreeasati
Joined: 11 Jul 2018
Last visit: 16 Mar 2025
Posts: 78
Own Kudos:
Given Kudos: 43
Schools: ISB '27 (A)
Schools: ISB '27 (A)
Posts: 78
Kudos: 28
Kudos
Add Kudos
Bookmarks
Bookmark this Post
User avatar
Noida
Joined: 27 Apr 2021
Last visit: 30 Jul 2024
Posts: 71
Own Kudos:
Given Kudos: 72
Posts: 71
Kudos: 47
Kudos
Add Kudos
Bookmarks
Bookmark this Post
User avatar
BrushMyQuant
Joined: 05 Apr 2011
Last visit: 15 Jul 2025
Posts: 2,247
Own Kudos:
Given Kudos: 100
Status:Tutor - BrushMyQuant
Location: India
Concentration: Finance, Marketing
Schools: XLRI (A)
GMAT 1: 700 Q51 V31
GPA: 3
WE:Information Technology (Computer Software)
Expert
Expert reply
Schools: XLRI (A)
GMAT 1: 700 Q51 V31
Posts: 2,247
Kudos: 2,463
Kudos
Add Kudos
Bookmarks
Bookmark this Post
\(|\frac{x}{2}| + |\frac{y}{2}| = 5\)

Multiplying with 2 on both the sides we get

\(|\frac{2x}{2}| + |\frac{2y}{2}| = 2*5\)

=> |x| + |y| = 10

We can open |x| + |y| = 10 in four cases

Case 1 and 2 which is Quadrant I and Quadrant II
Quadrant I : x ≥ 0, y ≥ 0

=> |x| = x, | y| = y
=> x + y = 10
=> x = 0, y = 10 and y = 0, x = 10

So, the line will pass through the points (0,10) and (10,0) in Quadrant I
Quadrant II : x 0, y ≥ 0

=> |x| = -x, | y| = y
=> -x + y = 10
=> x = 0, y = 10 and y = 0, x = -10

So, the line will pass through the points (0,10) and (-10,0) in Quadrant II

Case 3 and 4 which is Quadrant III and Quadrant IV
Quadrant III : x 0, y 0

=> |x| = -x, | y| = -y
=> -x - y = 10
=> x = 0, y = -10 and y = 0, x = -10

So, the line will pass through the points (0,-10) and (-10,0) in Quadrant III
Quadrant IV : x 0, y 0

=> |x| = x, | y| = -y
=> x - y = 10
=> x = 0, y = -10 and y = 0, x = 10

So, the line will pass through the points (0,-10) and (10,0) in Quadrant IV

Attachment:
ABS-42-1.jpg
ABS-42-1.jpg [ 18.71 KiB | Viewed 55 times ]

So, Area of the enclosed figure = Area of the Two triangles with base = (10 - (-10)) = 20 and Height = 10

Attachment:
ABS-42-2.jpg
ABS-42-2.jpg [ 21.6 KiB | Viewed 56 times ]

=> Area of the enclosed figure = 2 * \(\frac{1}{2}\) * 20 * 10 = 200

So, Answer will be D
Hope it helps!

Watch the following video to MASTER Absolute Value Problems

   1   2 
Moderators:
Math Expert
102582 posts
PS Forum Moderator
695 posts