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

 It is currently 21 Oct 2019, 23:38 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

Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.  In an isosceles triangle PQR, if ∠Q = 80 degrees, then what is the ...

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

Hide Tags

e-GMAT Representative V
Joined: 04 Jan 2015
Posts: 3078
In an isosceles triangle PQR, if ∠Q = 80 degrees, then what is the ...  [#permalink]

Show Tags 00:00

Difficulty:   65% (hard)

Question Stats: 44% (01:01) correct 56% (00:56) wrong based on 64 sessions

HideShow timer Statistics

In an isosceles triangle PQR, if ∠Q = 80 degrees, then what is the sum of all possible values of ∠P?

A. 70
B. 80
C. 100
D. 130
E. 150

_________________
Director  G
Joined: 09 Mar 2018
Posts: 994
Location: India
In an isosceles triangle PQR, if ∠Q = 80 degrees, then what is the ...  [#permalink]

Show Tags

1
EgmatQuantExpert wrote:
In an isosceles triangle PQR, if ∠Q = 80 degrees, then what is the sum of all possible values of ∠P?

A. 70
B. 80
C. 100
D. 130
E. 150

IMO E

Now PQR is an isosceles triangle, < Q = 80

3 Cases
1) when <P = < R = 50
2) when <Q = <P = 80
3) when <Q = <R = 80, <P = 20

Sum = 150
_________________
If you notice any discrepancy in my reasoning, please let me know. Lets improve together.

Quote which i can relate to.
Many of life's failures happen with people who do not realize how close they were to success when they gave up.

Originally posted by KanishkM on 06 Feb 2019, 20:13.
Last edited by KanishkM on 06 Feb 2019, 20:49, edited 1 time in total.
Director  V
Joined: 06 Jan 2015
Posts: 689
Location: India
Concentration: Operations, Finance
GPA: 3.35
WE: Information Technology (Computer Software)
Re: In an isosceles triangle PQR, if ∠Q = 80 degrees, then what is the ...  [#permalink]

Show Tags

1
KanishkM wrote:
EgmatQuantExpert wrote:
In an isosceles triangle PQR, if ∠Q = 80 degrees, then what is the sum of all possible values of ∠P?

A. 70
B. 80
C. 100
D. 130
E. 150

IMO E

Now PQR is an isosceles triangle, < Q = 80

3 Cases
1) when <P = < R = 50
2) when <Q = <P = 80
3) when <Q = <R = 160, <P = 20

Sum = 150

Hey KanishkM,

3) when <Q = <R = 160, <P = 20 How is it possible? While Sum of angles of triangle is 180 _________________
आत्मनॊ मोक्षार्थम् जगद्धिताय च

Resource: GMATPrep RCs With Solution
Director  G
Joined: 09 Mar 2018
Posts: 994
Location: India
In an isosceles triangle PQR, if ∠Q = 80 degrees, then what is the ...  [#permalink]

Show Tags

NandishSS wrote:
KanishkM wrote:

IMO E

Now PQR is an isosceles triangle, < Q = 80

3 Cases
1) when <P = < R = 50
2) when <Q = <P = 80
3) when <Q = <R = 160, <P = 20

Sum = 150

Hey KanishkM,

3) when <Q = <R = 160, <P = 20 How is it possible? While Sum of angles of triangle is 180 hahahah NandishSS

I think i did some big time typo , let me correct it now
_________________
If you notice any discrepancy in my reasoning, please let me know. Lets improve together.

Quote which i can relate to.
Many of life's failures happen with people who do not realize how close they were to success when they gave up.
Intern  S
Joined: 05 Jan 2017
Posts: 32
Re: In an isosceles triangle PQR, if ∠Q = 80 degrees, then what is the ...  [#permalink]

Show Tags

This is an isosceles triangle, so two sides are equal and two angles must be of the same measure.

There are three cases:

1) angle Q is formed by two equal sides, so the other two angles (P and R) must be the same.

$$80 (angle Q) + angle P + angle R = 180$$ (sum of all angles in a triangle)

$$angle P + angle R = 100$$

As mentioned before, angle P and angle R must be equal, hence P = 50 and R = 50.

2) angle Q is formed by the base and one of the sides, and the angle (let's say R) is formed by the base and the other side. It means, that Q=R, so $$P = 180-80-80 = 20$$

3) angle Q is formed by the base and one of the sides, and the angle (this time it's P) is formed by the base and the other side. It means, that Q=P, so P = 80

Sum of all possible values of angle $$P = 50 + 20 + 80 = 150$$.

Manager  S
Joined: 22 Sep 2018
Posts: 240
Re: In an isosceles triangle PQR, if ∠Q = 80 degrees, then what is the ...  [#permalink]

Show Tags

EgmatQuantExpert wrote:
In an isosceles triangle PQR, if ∠Q = 80 degrees, then what is the sum of all possible values of ∠P?

A. 70
B. 80
C. 100
D. 130
E. 150

P can be equal to 80, if side PR is the same length as QR.

P can be 20 if side PQ is the same as PR

P can be 50 if side PQ and RQ are the same.

total is 150
e-GMAT Representative V
Joined: 04 Jan 2015
Posts: 3078
Re: In an isosceles triangle PQR, if ∠Q = 80 degrees, then what is the ...  [#permalink]

Show Tags

Solution

Given:
• PQR is an isosceles triangle
• ∠Q = 80 degrees

To find:
• Sum of all possible values of ∠P

Approach and Working:
We know that in an isosceles triangle two angles are equal
Case 1: If ∠Q = ∠P, then ∠P = 80 degrees
Case 2: If ∠Q = ∠R, then ∠P = 180 – 80 – 80 = 20 degrees
Case 3: If ∠P = ∠R, then ∠P = $$\frac{(180 – 80)}{2} = 50$$ degrees

Therefore, sum of all possible values of ∠P = 80 + 50 + 20 = 150

Hence the correct answer is Option E.

_________________ Re: In an isosceles triangle PQR, if ∠Q = 80 degrees, then what is the ...   [#permalink] 08 Feb 2019, 00:09
Display posts from previous: Sort by

In an isosceles triangle PQR, if ∠Q = 80 degrees, then what is the ...

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

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