Last visit was: 20 Jul 2024, 15:49 It is currently 20 Jul 2024, 15:49
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
SORT BY:
Kudos
Tags:
Show Tags
Hide Tags
User avatar
Senior Manager
Senior Manager
Joined: 07 Apr 2014
Status:Math is psycho-logical
Posts: 335
Own Kudos [?]: 393 [19]
Given Kudos: 169
Location: Netherlands
GMAT Date: 02-11-2015
WE:Psychology and Counseling (Other)
Most Helpful Reply
GMAT Club Legend
GMAT Club Legend
Joined: 12 Sep 2015
Posts: 6804
Own Kudos [?]: 30842 [6]
Given Kudos: 799
Location: Canada
Send PM
General Discussion
e-GMAT Representative
Joined: 04 Jan 2015
Posts: 3711
Own Kudos [?]: 17344 [4]
Given Kudos: 165
Send PM
User avatar
Senior Manager
Senior Manager
Joined: 07 Apr 2014
Status:Math is psycho-logical
Posts: 335
Own Kudos [?]: 393 [1]
Given Kudos: 169
Location: Netherlands
GMAT Date: 02-11-2015
WE:Psychology and Counseling (Other)
Re: What are the coordinates of point B ? [#permalink]
1
Bookmarks
I hope it hasn't been posted before. I couldn't find it. It took me a while to solve it. I actually started solving before I even read the whole question, just by looking at the image. I find these questions tricky, just because I very often find myself solving them, when this is not necessary...
User avatar
Senior Manager
Senior Manager
Joined: 19 Apr 2013
Posts: 476
Own Kudos [?]: 277 [1]
Given Kudos: 537
Concentration: Strategy, Healthcare
Schools: Sloan '18 (A)
GMAT 1: 730 Q48 V41
GPA: 4
Send PM
Re: What are the coordinates of point B ? [#permalink]
1
Kudos
Bunuel, can you please explain this question?
Director
Director
Joined: 12 Nov 2016
Posts: 569
Own Kudos [?]: 118 [1]
Given Kudos: 167
Location: United States
Schools: Yale '18
GMAT 1: 650 Q43 V37
GRE 1: Q157 V158
GPA: 2.66
Send PM
Re: What are the coordinates of point B ? [#permalink]
1
Bookmarks
pacifist85 wrote:
What are the coordinates of point B ?

(1) The area of triangle ABC = 30
(2) Length(CB) = 13


Statement 1

Because this is a right triangle we only need the base and height in order to calculate the area; we know the height of the triangle so we must know the base

base x height/ 2 = 30
base x height =60
base x (5) =60
base= 60/5

Furthermore, because know the x coordinate (-3,4) we simply add 12 to the x value in order to find b-
l-3l + b =12

Statement 2

The diagram shows us that this is a right triangle- well, there is a Pythagorean Triplet 5 12 13- and because we know the height of the triangle we can easily deduce this is a 5 12 13 Pythagorean Right Triangle

Sufficient

Thus
"D"
GMAT Club Legend
GMAT Club Legend
Joined: 12 Sep 2015
Posts: 6804
Own Kudos [?]: 30842 [1]
Given Kudos: 799
Location: Canada
Send PM
What are the coordinates of point B ? [#permalink]
1
Kudos
Expert Reply
Top Contributor
churuand wrote:
Hi, I have a question. What if point B is on the left side of AC, then B will have a different location, leading to the point that there will be two locations of B in both statement 1 and 2? Correct me if I am wrong.


Great question!
This is one of those cases in which we can assume that point P lies to the right.
For more on assumptions we can make on GMAT geometry questions, watch the following video:


Cheers,
Brent
RC & DI Moderator
Joined: 02 Aug 2009
Status:Math and DI Expert
Posts: 11477
Own Kudos [?]: 34474 [0]
Given Kudos: 323
Send PM
Re: What are the coordinates of point B ? [#permalink]
Expert Reply
pacifist85 wrote:
What are the coordinates of point B ?

(1) The area of triangle ABC = 30
(2) Length(CB) = 13



hi pacifist,
you dont require to solve anything...
here you have a right angle triangle on x-y axis, where coord of two axis are given...
third vertex coord are reqd..
1) area would give us length of perpendicular.. and hence coord can be found..suff
2) length of hyp given.. vertex can be again found.. suff
ans D
avatar
Intern
Intern
Joined: 28 Oct 2014
Posts: 43
Own Kudos [?]: 228 [0]
Given Kudos: 1
Send PM
Re: What are the coordinates of point B ? [#permalink]
Hi

can some one help me how each STATEMENT for the above problem is sufficient ?

with the area and the distance formula . you can calculate the the length of AB ..but how do get the co ordinates or the point B?

and also how is the statement B alone also sufficient ?

please help?
RC & DI Moderator
Joined: 02 Aug 2009
Status:Math and DI Expert
Posts: 11477
Own Kudos [?]: 34474 [0]
Given Kudos: 323
Send PM
Re: What are the coordinates of point B ? [#permalink]
Expert Reply
viper1991 wrote:
Hi

can some one help me how each STATEMENT for the above problem is sufficient ?

with the area and the distance formula . you can calculate the the length of AB ..but how do get the co ordinates or the point B?

and also how is the statement B alone also sufficient ?

please help?


Hi viper..

firstly look at the figure and see what it tells us...
1) line AC is parallel to Y axis as the coord of both A and C have same value for X axis..
2) this means AB will be parallel to X axis and A and B will have same Y coord.. or B will be (x,4)

lets look at the statement..
1) it gives us area of triangle 30= base * perpendicular/2... AB=60/5=12 this will give us x as -3 + 12= 9.... sufficient
2)This gives us length of hypotenuse BC=13.. AC is 5 so AB is 12 again as in (1), x coord can be found.. sufficient
ans D
Intern
Intern
Joined: 03 Mar 2019
Posts: 31
Own Kudos [?]: 19 [0]
Given Kudos: 83
GMAT 1: 690 Q48 V37
GMAT 2: 640 Q45 V32
Send PM
Re: What are the coordinates of point B ? [#permalink]
GMATPrepNow wrote:
pacifist85 wrote:
What are the coordinates of point B ?

(1) The area of triangle ABC = 30
(2) Length(CB) = 13


IMPORTANT: For geometry Data Sufficiency questions, we are typically checking to see whether the statements "lock" a particular angle, length, or shape into having just one possible measurement. This concept is discussed in much greater detail in the following video: https://www.gmatprepnow.com/module/gmat-data-sufficiency?id=1103

Target question: What are the coordinates of point B ?

NOTE: points A and C are LOCKED in their positions. Since ∠CAB = 90º, we know that point B is SOMEWHERE along the line y = 4. So, some of the MANY possible cases are as follows:







Notice that, for EACH different position of point B, ∆ABC has a different area and side CB has a different length.

Okay, onto the statements...
Statement 1: The area of ∆ABC = 30
As I mentioned above, for EACH different position of point B, ∆ABC has a different area.
So, knowing that the area is 30, LOCKS point B into ONE AND ONLY ONE location.
In other words, statement 1 LOCKS IN the shape/dimensions of ∆ABC, which means there must be only one location for point B.
As such, statement 1 is SUFFICIENT

Statement 2: Length of CB = 13
As I mentioned above, for EACH different position of point B, side CB has a different length.
So, knowing that side CB has length 13 LOCKS point B into ONE AND ONLY ONE location.
In other words, statement 2 LOCKS IN the shape/dimensions of ∆ABC, which means there must be only one location for point B.
As such, statement 2 is SUFFICIENT

Answer =


Hi, I have a question. What if point B is on the left side of AC, then B will have a different location, leading to the point that there will be two locations of B in both statement 1 and 2? Correct me if I am wrong.
Senior Manager
Senior Manager
Joined: 16 Nov 2021
Posts: 472
Own Kudos [?]: 28 [0]
Given Kudos: 5901
Location: United Kingdom
Send PM
Re: What are the coordinates of point B ? [#permalink]
EgmatQuantExpert wrote:
Ergenekon wrote:
Bunuel, can you please explain this question?


Dear Ergenekon

Our first step here would be to observe that since the x- coordinate of both points A and C are the same, this means line AC is parallel to the y - axis.

And from the given diagram, it's clear than line AB is perpendicular to AC. What does this mean? That AB is parallel to x-axis. So, the y-coordinate of point B will be the same as the y-coordinate of point A.

This means, we can write point B as (x, 4)



So, we have only one unknown here: x. Let's see if St. 1 and 2 are sufficient to get us a unique value of x.

St. 1 says
The area of triangle ABC = 30


This means, \(\frac{1}{2}*AB*AC = 30\)

AC = 5 (because point A is 4 units above x-axis and point C is 1 units below x-axis. So, total length of AC = 5)

Similarly AB = 3 +x

So, we can write: \(\frac{1}{2}*(3+x)*5 = 30\)

Linear equation with one unknown. Sufficient to find a unique value of x.

St. 2 says
Length(CB) = 13


In right triangle BAC, using Pythagoras Theorem,

\(AB^2 + AC^2 = BC^2\)
\(AB^2 +5 ^2 = 13^2\)
\(AB^2 = 12^2\)

Since the length of a side cannot be negative, AB cannot be -12. So, the only value of AB that satisfies the above equation is AB = 12

This means, 3 + x = 12

From here, we get x. St. 2 is sufficient as well.

So, correct answer: D

Please let me know if something remains unclear. :)

Best Regards

Japinder


Great explanation EgmatQuantExpert, in St 1, not quite sure why is 3+x and not -3+x since x coordinate of point A is -3? Thanks Japinder
User avatar
Non-Human User
Joined: 09 Sep 2013
Posts: 34039
Own Kudos [?]: 853 [0]
Given Kudos: 0
Send PM
Re: What are the coordinates of point B ? [#permalink]
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
GMAT Club Bot
Re: What are the coordinates of point B ? [#permalink]
Moderator:
Math Expert
94433 posts