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

It is currently 25 Apr 2019, 07:05

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 points A(0, 0), B(0, 4a – 5) and C(2a + 1, 2a + 6) form a triangle

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

Hide Tags

 
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 54543
The points A(0, 0), B(0, 4a – 5) and C(2a + 1, 2a + 6) form a triangle  [#permalink]

Show Tags

New post 28 Jul 2017, 09:01
2
7
00:00
A
B
C
D
E

Difficulty:

  55% (hard)

Question Stats:

74% (03:01) correct 26% (03:16) wrong based on 77 sessions

HideShow timer Statistics

Intern
Intern
avatar
B
Joined: 03 Jun 2017
Posts: 15
Re: The points A(0, 0), B(0, 4a – 5) and C(2a + 1, 2a + 6) form a triangle  [#permalink]

Show Tags

New post 28 Jul 2017, 09:14
Given that triangle ABC is right angled at B, we know that the x coordinate of B and the x coordinate of C should be equal.

Equating both, we get a equals 5.5. Substitute into the points and the base comes out to be 17 units while the height is 12.

Area is 17*12/2 which is 102.

Sent from my ONE A2003 using GMAT Club Forum mobile app
Intern
Intern
avatar
B
Joined: 30 May 2017
Posts: 3
Re: The points A(0, 0), B(0, 4a – 5) and C(2a + 1, 2a + 6) form a triangle  [#permalink]

Show Tags

New post 29 Jul 2017, 01:54
1
We know that since Y coordinate of point B and y coordinate of point C is equal (Triangle ABC is 90 at B)

Therefore equating the the y coordinates of both the points B and C

i.e 4a - 5 = 2a + 6

We get, a = 11/2

Substituting the value of a in the coordinate points. Hence the points are now A (0,0), B (0,17) and C(12,17)

Area of triangle ABC = 1/2 x 12 x 17 = 102

Answer (A) = 102
Director
Director
User avatar
D
Affiliations: IIT Dhanbad
Joined: 13 Mar 2017
Posts: 724
Location: India
Concentration: General Management, Entrepreneurship
GPA: 3.8
WE: Engineering (Energy and Utilities)
Re: The points A(0, 0), B(0, 4a – 5) and C(2a + 1, 2a + 6) form a triangle  [#permalink]

Show Tags

New post 29 Jul 2017, 02:53
1
Bunuel wrote:
The points A(0, 0), B(0, 4a – 5) and C(2a + 1, 2a + 6) form a triangle. If angle ABC = 90°, what is the area of triangle ABC?

A. 102
B. 120
C. 132
D. 144
E. 256


ABC is a right angle triangle, right angled at B. ABC = 90°
Now A(0,0) and B (0, 4a-5) represents Y-axis..
So, BC must be perpendicular to Y - axis
i.e. BC must be parallel to X-axis

So. 4a-5=2a+6
-> 2a = 11
-> a = 5.5

So, 4a -5 = 17
2a+1 = 12
2a+6 = 17

So, the points are A(0,0) , B(0,17) and C(12,17)
AB = 17
BC = 12
Area (tria ABC) = 1/2*17*12 = 17 * 6 = 102

Answer A
_________________
CAT 2017 (98.95) & 2018 (98.91) : 99th percentiler
UPSC Aspirants : Get my app UPSC Important News Reader from Play store.

MBA Social Network : WebMaggu


Appreciate by Clicking +1 Kudos ( Lets be more generous friends.)



What I believe is : "Nothing is Impossible, Even Impossible says I'm Possible" : "Stay Hungry, Stay Foolish".
e-GMAT Representative
User avatar
D
Joined: 04 Jan 2015
Posts: 2812
Re: The points A(0, 0), B(0, 4a – 5) and C(2a + 1, 2a + 6) form a triangle  [#permalink]

Show Tags

New post 29 Jul 2017, 10:02
3
Bunuel wrote:
The points A(0, 0), B(0, 4a – 5) and C(2a + 1, 2a + 6) form a triangle. If angle ABC = 90°, what is the area of triangle ABC?

A. 102
B. 120
C. 132
D. 144
E. 256



Image

    • A very interesting testing our skill of visualization. :)
    • A is the origin and B lies on the y-axis.
      o If ABC is a right-angled triangle, that mean angle B = 90 degrees.
      o Also, line BC is a parallel to the x-axis.
         Thus, the y-cooridante of B and C would be the same.
      • \(4a – 5 = 2a + 6\)
      • \(2a = 11\)
      • \(a = 5.5\)
    • The area of the triangle \(= \frac{1}{2} * AB * BC = \frac{1}{2} * (4a -5) * (2a+1)\)
      o We know that \(a = 5.5\), substituting the value in the equation above, we get –
         \(Area = \frac{1}{2} * (22-5)*12\)
         \(Area = 102\)
    • And the correct answer is Option A.


Thanks,
Saquib
Quant Expert
e-GMAT

Register for our Free Session on Number Properties (held every 3rd week) to solve exciting 700+ Level Questions in a classroom environment under the real-time guidance of our Experts :)

[url=https://e-gmat.com/free-trial-registration/?utm_source=GC&utm_medium=post&utm_campaign=registration&utm_content=free_trial_registration&utm_term=wp_q1]Image[/url
_________________
GMAT Club Bot
Re: The points A(0, 0), B(0, 4a – 5) and C(2a + 1, 2a + 6) form a triangle   [#permalink] 29 Jul 2017, 10:02
Display posts from previous: Sort by

The points A(0, 0), B(0, 4a – 5) and C(2a + 1, 2a + 6) form a triangle

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


Copyright

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®.