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

 It is currently 23 Oct 2019, 17:15

### 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

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

# If the vertices of a triangle have coordinates (x,1), (5,1),

Author Message
TAGS:

### Hide Tags

Director
Joined: 16 Jul 2009
Posts: 775
Schools: CBS
WE 1: 4 years (Consulting)
If the vertices of a triangle have coordinates (x,1), (5,1),  [#permalink]

### Show Tags

Updated on: 22 Apr 2012, 02:20
5
12
00:00

Difficulty:

95% (hard)

Question Stats:

42% (02:15) correct 58% (02:30) wrong based on 219 sessions

### HideShow timer Statistics

If the vertices of a triangle have coordinates (x,1), (5,1), and (5,y) where x<5 and y>1, what is the area of the triangle?

(1) x=y
(2) Angle at the vertex (x,1) is equal to angle at the vertex (5,y)

_________________
The sky is the limit
800 is the limit

GMAT Club Premium Membership - big benefits and savings

Originally posted by noboru on 03 Nov 2009, 13:49.
Last edited by Bunuel on 22 Apr 2012, 02:20, edited 2 times in total.
Edited the question and added the OA
Math Expert
Joined: 02 Sep 2009
Posts: 58464

### Show Tags

03 Nov 2009, 13:56
8
If the vertices of a triangle have coordinates (x,1), (5,1), and (5,y) where x<5 and y>1, what is the area of the triangle?

Look at the diagram below:

Notice that vertex (x,1) will be somewhere on the green line segment and the vertex (5,y) will be somewhere on the blue line segment. So, in any case our triangle will be right angled, with a right angle at vertex (5, 1). Next, the length of the leg on the green line segment will be $$5-x$$ and the length of the leg on the blue line segment will by $$y-1$$. So, the area of the triangle will be: $$area=\frac{1}{2}*(5-x)*(y-1)$$

(1) x=y --> since $$x<5$$ and $$y>1$$ then both x and y are in the range (1,5): $$1<(x=y)<5$$. If we substitute $$y$$ with $$x$$ we'll get: $$area=\frac{1}{2}*(5-x)*(y-1)=\frac{1}{2}*(5-x)*(x-1)$$, different values of $$x$$ give different values for the area (even knowing that $$1<x<5$$). Not sufficient.

(2) Angle at the vertex (x,1) is equal to angle at the vertex (5,y) --> we have an isosceles right triangle: $$5-x=y-1$$. Again if we substitute $$y-1$$ with $$5-x$$ we'll get: $$area=\frac{1}{2}*(5-x)*(y-1)=\frac{1}{2}*(5-x)*(5-x)$$, different values of $$x$$ give different values for the area. Not sufficient.

(1)+(2) $$x=y$$ and $$5-x=y-1$$ --> solve for $$x$$: $$x=y=3$$ --> $$area=\frac{1}{2}*(5-3)*(3-1)=2$$. Sufficient.

_________________
##### General Discussion
Manager
Joined: 16 Jul 2009
Posts: 176

### Show Tags

11 Nov 2009, 06:35
Good explanation Bunnel!
Math Expert
Joined: 02 Aug 2009
Posts: 8023

### Show Tags

16 Dec 2009, 07:31
hi tania..ill try.. firstly the 3 set of coord tells us that it is a right angled triangle(right angle is at vertex(5,1))
SI tells us that x=y....x and y can be any values...not suff..
SII tells us the angles at two other vertices are 45...so the other two sides are equal...can have many values.. eq we get from it is 5-x=y+1.... not suff
combined 5-x =x+1... so x=y=3.. suff.. C ans
_________________
Intern
Joined: 23 Nov 2009
Posts: 31

### Show Tags

21 Dec 2009, 18:35
Distance formula for area:
A = 1\2\sqrt{(5-x)^2 (x-1)^2}

_________________
A kudos would greatly help

Tuhin
Intern
Joined: 18 Sep 2013
Posts: 7

### Show Tags

06 Mar 2014, 11:45
Dear Bunuel

Can we have B as the answer, since we know that angles are equal, the only coordinate that will give same the distance will be 3. Hence, we dont need option A for any support. Kindly help!

Regards
Math Expert
Joined: 02 Sep 2009
Posts: 58464

### Show Tags

07 Mar 2014, 02:14
ShantnuMathuria wrote:
Dear Bunuel

Can we have B as the answer, since we know that angles are equal, the only coordinate that will give same the distance will be 3. Hence, we dont need option A for any support. Kindly help!

Regards

That's not correct. Any $$x<5$$ and $$y>1$$, which satisfy $$5-x=y-1$$ ($$x+y=6$$) will give equal legs and thus equal angles. For example, $$x=4$$, $$y=2$$, or $$x=3.5$$, $$y=2.5$$, ...

Hope it's clear.
_________________
Non-Human User
Joined: 09 Sep 2013
Posts: 13421
Re: If the vertices of a triangle have coordinates (x,1), (5,1),  [#permalink]

### Show Tags

09 Mar 2019, 07:18
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.
_________________
Re: If the vertices of a triangle have coordinates (x,1), (5,1),   [#permalink] 09 Mar 2019, 07:18
Display posts from previous: Sort by