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

It is currently 18 Oct 2019, 21:53

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

What is the area of triangle PQR? (1) angle PQR is 120 degrees

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

Hide Tags

Find Similar Topics 
Intern
Intern
avatar
B
Joined: 12 May 2017
Posts: 6
What is the area of triangle PQR? (1) angle PQR is 120 degrees  [#permalink]

Show Tags

New post 16 Mar 2018, 07:12
00:00
A
B
C
D
E

Difficulty:

  45% (medium)

Question Stats:

63% (01:12) correct 37% (01:20) wrong based on 83 sessions

HideShow timer Statistics

What is the area of triangle PQR?

(1) angle PQR is 120 degrees

(2) PQ=5 units and PR=10 units
Intern
Intern
avatar
Joined: 25 Jan 2018
Posts: 1
Re: What is the area of triangle PQR? (1) angle PQR is 120 degrees  [#permalink]

Show Tags

New post 16 Mar 2018, 07:38
area of triangle ab sin(theta) , where a and b are the sides of the triangle and theta is the angle between them. so my answer is 25
VP
VP
avatar
V
Joined: 30 Jan 2016
Posts: 1159
Reviews Badge CAT Tests
Re: What is the area of triangle PQR? (1) angle PQR is 120 degrees  [#permalink]

Show Tags

New post 18 Mar 2018, 11:23
What is the area of triangle PQR?

(1) angle PQR is 120 degrees - dimensions of the triangle are given - not sufficient

(2) PQ=5 units and PR=10 units. Side QR can be any value from 5< QR< 15 - not sufficient.

(1) + (2) SSA condition. As angle PQR is obtuse, QR can take only 1 value. Therefore, we can calculate the area of the square. Sufficient
_________________
Non progredi est regredi
Manager
Manager
User avatar
S
Joined: 23 May 2017
Posts: 234
Concentration: Finance, Accounting
WE: Programming (Energy and Utilities)
Re: What is the area of triangle PQR? (1) angle PQR is 120 degrees  [#permalink]

Show Tags

New post 18 Mar 2018, 12:57
1
Here we are not given the angle between the two sides: hence we can't use the Sine formula here.

We are just given two adjacent sides and non-including angle

Ans:C
Attachments

Screen Shot 2018-03-18 at 19.55.17.png
Screen Shot 2018-03-18 at 19.55.17.png [ 96.55 KiB | Viewed 1432 times ]


_________________
If you like the post, please award me Kudos!! It motivates me
VP
VP
avatar
V
Joined: 30 Jan 2016
Posts: 1159
Reviews Badge CAT Tests
Re: What is the area of triangle PQR? (1) angle PQR is 120 degrees  [#permalink]

Show Tags

New post 19 Mar 2018, 10:15
Quote:
Here we are not given the angle between the two sides: hence we can't use the Sine formula here.

We are just given two adjacent sides and non-including angle


Hi Leo8,

Awesome explanation.

Just wanna add that SSA gives 2 solutions using the law of sines. I'm not sure if we can use the law of sines given that PQR is obtuse?
https://www.mathsisfun.com/algebra/trig ... ngles.html
_________________
Non progredi est regredi
Retired Moderator
User avatar
V
Joined: 27 Oct 2017
Posts: 1259
Location: India
Concentration: International Business, General Management
GPA: 3.64
WE: Business Development (Energy and Utilities)
Re: What is the area of triangle PQR? (1) angle PQR is 120 degrees  [#permalink]

Show Tags

New post 20 Mar 2018, 06:55
1
Hi

Please see this similar question: https://gmatclub.com/forum/what-is-the- ... l#p2027164

This Question is based on a very IMPORTANT EXCEPTION:

The SSA condition (Side-Side-Angle) which specifies two sides and a non-included angle (also known as ASS, or
Angle-Side-Side) does not always prove congruence, even when the equal angles are opposite equal sides.

Specifically, SSA does not prove congruence when the angle is acute and the opposite side is shorter than the
known adjacent side but longer than the sine of the angle times the adjacent side. This is the ambiguous case. In
all other cases with corresponding equalities, SSA proves congruence.

The SSA condition proves congruence if the angle is obtuse or right. In the case of the right angle (also known
as the HL (Hypotenuse-Leg) condition or the RHS (Right-angle-Hypotenuse-Side) condition), we can calculate the
third side and fall back on SSS.

If any triangle follows laws of Congruency, it means it can be drawn Uniquely. Hence sufficient.

Akela wrote:
Quote:
Here we are not given the angle between the two sides: hence we can't use the Sine formula here.

We are just given two adjacent sides and non-including angle


Hi Leo8,

Awesome explanation.

Just wanna add that SSA gives 2 solutions using the law of sines. I'm not sure if we can use the law of sines given that PQR is obtuse?
https://www.mathsisfun.com/algebra/trig ... ngles.html

Attachments

WhatsApp Image 2018-03-09 at 21.13.07 %281%29.jpeg
WhatsApp Image 2018-03-09 at 21.13.07 %281%29.jpeg [ 109.55 KiB | Viewed 1351 times ]


_________________
Intern
Intern
avatar
B
Joined: 29 Aug 2017
Posts: 32
Location: India
GMAT ToolKit User
Re: What is the area of triangle PQR? (1) angle PQR is 120 degrees  [#permalink]

Show Tags

New post 22 Mar 2018, 23:35
Akela wrote:
What is the area of triangle PQR?

(1) angle PQR is 120 degrees - dimensions of the triangle are given - not sufficient

(2) PQ=5 units and PR=10 units. Side QR can be any value from 5< QR< 15 - not sufficient.

(1) + (2) SSA condition. As angle PQR is obtuse, QR can take only 1 value. Therefore, we can calculate the area of the square. Sufficient



Can you please elaborate. I am not convinced with the similarity and the area formula that has been used below
Retired Moderator
User avatar
V
Joined: 27 Oct 2017
Posts: 1259
Location: India
Concentration: International Business, General Management
GPA: 3.64
WE: Business Development (Energy and Utilities)
Re: What is the area of triangle PQR? (1) angle PQR is 120 degrees  [#permalink]

Show Tags

New post 23 Mar 2018, 00:11
Hi
First remember if you can draw a triangle or any figure uniquely, you can find any parameter related to the figure, it's area, perimeter, any angle, side, diagonal etc.

Now remember, if any triangle satisfy the law of congruency, it can be drawn uniquely.

In this question , we have proved that it is a unique triangle drawn as per given conditions. Hence area can be found out.

Let me know what u haven't understood?

Tanvi94 wrote:
Akela wrote:
What is the area of triangle PQR?

(1) angle PQR is 120 degrees - dimensions of the triangle are given - not sufficient

(2) PQ=5 units and PR=10 units. Side QR can be any value from 5< QR< 15 - not sufficient.

(1) + (2) SSA condition. As angle PQR is obtuse, QR can take only 1 value. Therefore, we can calculate the area of the square. Sufficient



Can you please elaborate. I am not convinced with the similarity and the area formula that has been used below


Posted from my mobile device
_________________
VP
VP
avatar
V
Joined: 30 Jan 2016
Posts: 1159
Reviews Badge CAT Tests
Re: What is the area of triangle PQR? (1) angle PQR is 120 degrees  [#permalink]

Show Tags

New post 23 Mar 2018, 08:22
Quote:
Can you please elaborate. I am not convinced with the similarity and the area formula that has been used below


Hi!

So, st. 1 itself is not sufficient.

St. 2 PQ =5, PR =10 => we can make infinite number of triangles (see attached pic)

St 1 + st 2. If angle PQR = 120, PQ=5, PR=10, we can draw only one triangle. Not sure? Try to draw another type :)
Therefore, we can find the area of the triangle. Please note that in DS questions we do not have to find the value of the area like in PS. We just have to know whether we CAN find the area with the data provided. So, as we can draw only ONE triangle with given values we will be able to calculate the area.

Hope this helps!
Attachments

Untitled.png
Untitled.png [ 14.51 KiB | Viewed 1222 times ]


_________________
Non progredi est regredi
GMAT Club Bot
Re: What is the area of triangle PQR? (1) angle PQR is 120 degrees   [#permalink] 23 Mar 2018, 08:22
Display posts from previous: Sort by

What is the area of triangle PQR? (1) angle PQR is 120 degrees

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





Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne