|
|
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
Track
Your Progress
Practice
Pays
Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.
29 Mar 2019, 00:38
Kudos
Bookmarks
C
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
65%
(hard)
Question Stats:
62% (02:33) correct
38%
(02:36)
wrong
based on 113
sessions
History
Date
Time
Result
Not Attempted Yet
Five unit squares are arranged in the coordinate plane as shown, with the lower left corner at the origin. The slanted line, extending from (a,0) to (3,3), divides the entire region into two regions of equal area. What is a?
(A) 1/2
(B) 3/5
(C) 2/3
(D) 3/4
(E) 4/5
Attachment:
6bc7311ff3d3544995cdcaf4af10e95b690b3f22.png [ 26.46 KiB | Viewed 5356 times ]
Archit3110
Updated on: 30 Mar 2019, 00:35
Originally posted by Archit3110 on 29 Mar 2019, 07:28.
Last edited by Archit3110 on 30 Mar 2019, 00:35, edited 1 time in total.
Last edited by Archit3110 on 30 Mar 2019, 00:35, edited 1 time in total.
Kudos
Bookmarks
Bunuel
total area of the square region = 1*1*5 ; 5
line (a,0) to (3,3) forms a triangle and its area
1/2 * (3-a) * 3 ----(1)
a 6th square will be a part of this triangle so we need to subtract it from (1)
1/2 *9-3a -1
7-3a / 1/2 --(B)
given that line The slanted line, extending from (a,0) to (3,3), divides the entire region into two regions of equal area viz.
area of triangle is equal to half the area of 5 squares
i.e
7-3a / 1/2 = 1/2 * 5 *1*1
solve for a
a = 2/3
IMO C
anshkool4u
Current Student
Joined: 18 Oct 2018
Last visit: 22 Oct 2022
Posts: 91
Given Kudos: 23
Location: India
Concentration: Finance, Operations
Schools: IIMA PGPX'23 (A)
GMAT 1: 710 Q50 V36
GPA: 4
WE:Business Development (Retail Banking)
29 Mar 2019, 08:16
Kudos
Bookmarks
The area of entire figure is 5 unit^2.
The area of shaded region will be half of the area of entire figure= 5/2=2.5 unit^2.
Now,area of shaded figure can also be thought of as 0.5*3*(3-a) -1 unit^2 = 3.5-1.5a ( we can consider the shaded area as comprising of one more unit square ,which makes the shaded region a right angled triangle.Later to find the area of actual shaded region,subtract the area of that additional square)
Therefore,2.5=3.5-1.5a
Hence ,a=1/1.5= 2/3
Posted from my mobile device
The area of shaded region will be half of the area of entire figure= 5/2=2.5 unit^2.
Now,area of shaded figure can also be thought of as 0.5*3*(3-a) -1 unit^2 = 3.5-1.5a ( we can consider the shaded area as comprising of one more unit square ,which makes the shaded region a right angled triangle.Later to find the area of actual shaded region,subtract the area of that additional square)
Therefore,2.5=3.5-1.5a
Hence ,a=1/1.5= 2/3
Posted from my mobile device
Attachments
IMG_20190329_205339.jpg [ 4.62 MiB | Viewed 4620 times ]
...
