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# Is the measure of two exterior angles of a triangle PQR, each equal to

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DS Forum Moderator
Joined: 21 Aug 2013
Posts: 1432
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Is the measure of two exterior angles of a triangle PQR, each equal to  [#permalink]

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12 Apr 2018, 21:45
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75% (hard)

Question Stats:

35% (01:20) correct 65% (01:33) wrong based on 65 sessions

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Is the measure of two exterior angles of a triangle PQR, each equal to 120 degrees?

(1) PQR is NOT an isosceles triangle.

(2) Measure of angle P is 70 degrees.

(Inspired by a Bunuel's question)
Senior Manager
Joined: 22 Feb 2018
Posts: 416
Is the measure of two exterior angles of a triangle PQR, each equal to  [#permalink]

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14 Apr 2018, 09:39
1
amanvermagmat wrote:
Is the measure of two exterior angles of a triangle PQR, each equal to 120 degrees?

(1) PQR is NOT an isosceles triangle.

(2) Measure of angle P is 70 degrees.

(Inspired by a Bunuel's question)

OA:D
First simplify the question:Is the measure of two exterior angles of a triangle PQR, each equal to 120 degrees?
For a given triangle, Sum of all exterior angle is $$360^{\circ}$$.
Attachment:

exterior-angles-triangle.png [ 15.45 KiB | Viewed 668 times ]

if two exterior angles of a triangle PQR are to be 120 degrees i.e total $$2*120^{\circ} =240^{\circ}$$,Third exterior angle should be also $$360^{\circ}-240^{\circ}=120^{\circ}$$
$$\angle$$P=$$\angle$$Q=$$\angle$$R= $$180^{\circ}-120^{\circ}$$($$120^{\circ}$$ being exterior angle)
$$\angle$$P=$$\angle$$Q=$$\angle$$R=$$60^{\circ}$$
Question is reduced to whether $$\triangle$$PQR is an equilateral triangle or not?

Statement 1 : PQR is NOT an isosceles triangle.
If PQR is not even isosceles triangle , it cannot be equilateral triangle.
So Statement 1 alone is sufficient to answer whether $$\triangle$$PQR is an equilateral triangle or not?

Statement 2 :Measure of angle P is 70 degrees.
Measure of $$\angle$$ P is not $$60^{\circ}$$, so PQR is not an equilateral triangle.
So Statement 2 alone is sufficient to answer whether $$\triangle$$PQR is an equilateral triangle or not?

so OA should be D
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Is the measure of two exterior angles of a triangle PQR, each equal to  [#permalink]

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18 Apr 2018, 03:57
Princ wrote:
amanvermagmat wrote:
Is the measure of two exterior angles of a triangle PQR, each equal to 120 degrees?

(1) PQR is NOT an isosceles triangle.

(2) Measure of angle P is 70 degrees.

(Inspired by a Bunuel's question)

OA:D
First simplify the question:Is the measure of two exterior angles of a triangle PQR, each equal to 120 degrees?
For a given triangle, Sum of all exterior angle is $$360^{\circ}$$.
Attachment:
exterior-angles-triangle.png

if two exterior angles of a triangle PQR are to be 120 degrees i.e total $$2*120^{\circ} =240^{\circ}$$,Third exterior angle should be also $$360^{\circ}-240^{\circ}=120^{\circ}$$
$$\angle$$P=$$\angle$$Q=$$\angle$$R= $$180^{\circ}-120^{\circ}$$($$120^{\circ}$$ being exterior angle)
$$\angle$$P=$$\angle$$Q=$$\angle$$R=$$60^{\circ}$$
Question is reduced to whether $$\triangle$$PQR is an equilateral triangle or not?

Statement 1 : PQR is NOT an isosceles triangle.
If PQR is not even isosceles triangle , it cannot be equilateral triangle.
So Statement 1 alone is sufficient to answer whether $$\triangle$$PQR is an equilateral triangle or not?

Statement 2 :Measure of angle P is 70 degrees.
Measure of $$\angle$$ P is not $$60^{\circ}$$, so PQR is not an equilateral triangle.
So Statement 2 alone is sufficient to answer whether $$\triangle$$PQR is an equilateral triangle or not?

so OA should be D

(1) PQR is NOT an isosceles triangle.

As above statement (1) says triangle is not isosceles how can we conclude that such triangle is not equilateral

for gmat do we have to consider an equilateral triangle is isosceles from 3 sides ?? I think thats too much from GMAC.
DS Forum Moderator
Joined: 21 Aug 2013
Posts: 1432
Location: India
Re: Is the measure of two exterior angles of a triangle PQR, each equal to  [#permalink]

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18 Apr 2018, 04:09
GMAT215 wrote:
Princ wrote:
amanvermagmat wrote:
Is the measure of two exterior angles of a triangle PQR, each equal to 120 degrees?

(1) PQR is NOT an isosceles triangle.

(2) Measure of angle P is 70 degrees.

(Inspired by a Bunuel's question)

OA:D
First simplify the question:Is the measure of two exterior angles of a triangle PQR, each equal to 120 degrees?
For a given triangle, Sum of all exterior angle is $$360^{\circ}$$.
Attachment:
exterior-angles-triangle.png

if two exterior angles of a triangle PQR are to be 120 degrees i.e total $$2*120^{\circ} =240^{\circ}$$,Third exterior angle should be also $$360^{\circ}-240^{\circ}=120^{\circ}$$
$$\angle$$P=$$\angle$$Q=$$\angle$$R= $$180^{\circ}-120^{\circ}$$($$120^{\circ}$$ being exterior angle)
$$\angle$$P=$$\angle$$Q=$$\angle$$R=$$60^{\circ}$$
Question is reduced to whether $$\triangle$$PQR is an equilateral triangle or not?

Statement 1 : PQR is NOT an isosceles triangle.
If PQR is not even isosceles triangle , it cannot be equilateral triangle.
So Statement 1 alone is sufficient to answer whether $$\triangle$$PQR is an equilateral triangle or not?

Statement 2 :Measure of angle P is 70 degrees.
Measure of $$\angle$$ P is not $$60^{\circ}$$, so PQR is not an equilateral triangle.
So Statement 2 alone is sufficient to answer whether $$\triangle$$PQR is an equilateral triangle or not?

so OA should be D

(1) PQR is NOT an isosceles triangle.

As above statement (1) says triangle is not isosceles how can we conclude that such triangle is not equilateral

for gmat do we have to consider an equilateral triangle is isosceles from 3 sides ?? I think thats too much from GMAC.

Hello

Its simple if we look at it this way:

If a triangle is not isosceles, then it obviously cannot be equilateral. An isosceles triangle is one where two of its sides are equal. So if a triangle has no 2 sides equal, then obviously it cannot have its all 3 sides equal. Question answered.
Manager
Joined: 26 Sep 2017
Posts: 97
Re: Is the measure of two exterior angles of a triangle PQR, each equal to  [#permalink]

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18 Apr 2018, 05:01
amanvermagmat wrote:
GMAT215 wrote:
Princ wrote:
[quote="amanvermagmat"]Is the measure of two exterior angles of a triangle PQR, each equal to 120 degrees?

(1) PQR is NOT an isosceles triangle.

(2) Measure of angle P is 70 degrees.

(Inspired by a Bunuel's question)

OA:D
First simplify the question:Is the measure of two exterior angles of a triangle PQR, each equal to 120 degrees?
For a given triangle, Sum of all exterior angle is $$360^{\circ}$$.
Attachment:
exterior-angles-triangle.png

if two exterior angles of a triangle PQR are to be 120 degrees i.e total $$2*120^{\circ} =240^{\circ}$$,Third exterior angle should be also $$360^{\circ}-240^{\circ}=120^{\circ}$$
$$\angle$$P=$$\angle$$Q=$$\angle$$R= $$180^{\circ}-120^{\circ}$$($$120^{\circ}$$ being exterior angle)
$$\angle$$P=$$\angle$$Q=$$\angle$$R=$$60^{\circ}$$
Question is reduced to whether $$\triangle$$PQR is an equilateral triangle or not?

Statement 1 : PQR is NOT an isosceles triangle.
If PQR is not even isosceles triangle , it cannot be equilateral triangle.
So Statement 1 alone is sufficient to answer whether $$\triangle$$PQR is an equilateral triangle or not?

Statement 2 :Measure of angle P is 70 degrees.
Measure of $$\angle$$ P is not $$60^{\circ}$$, so PQR is not an equilateral triangle.
So Statement 2 alone is sufficient to answer whether $$\triangle$$PQR is an equilateral triangle or not?

so OA should be D

(1) PQR is NOT an isosceles triangle.

As above statement (1) says triangle is not isosceles how can we conclude that such triangle is not equilateral

for gmat do we have to consider an equilateral triangle is isosceles from 3 sides ?? I think thats too much from GMAC.

Hello

Its simple if we look at it this way:

If a triangle is not isosceles, then it obviously cannot be equilateral. An isosceles triangle is one where two of its sides are equal. So if a triangle has no 2 sides equal, then obviously it cannot have its all 3 sides equal. Question answered.[/quote]It is given pqr is not an isoceles might be it is equlitateral which is not termed as isoceles , so how
Stment 1 suffices i also dont think so.

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Senior Manager
Joined: 22 Feb 2018
Posts: 416
Re: Is the measure of two exterior angles of a triangle PQR, each equal to  [#permalink]

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18 Apr 2018, 05:41
1
Princ wrote:
amanvermagmat wrote:
Is the measure of two exterior angles of a triangle PQR, each equal to 120 degrees?

(1) PQR is NOT an isosceles triangle.

(2) Measure of angle P is 70 degrees.

(Inspired by a Bunuel's question)

OA:D
First simplify the question:Is the measure of two exterior angles of a triangle PQR, each equal to 120 degrees?
For a given triangle, Sum of all exterior angle is $$360^{\circ}$$.
Attachment:
exterior-angles-triangle.png

if two exterior angles of a triangle PQR are to be 120 degrees i.e total $$2*120^{\circ} =240^{\circ}$$,Third exterior angle should be also $$360^{\circ}-240^{\circ}=120^{\circ}$$
$$\angle$$P=$$\angle$$Q=$$\angle$$R= $$180^{\circ}-120^{\circ}$$($$120^{\circ}$$ being exterior angle)
$$\angle$$P=$$\angle$$Q=$$\angle$$R=$$60^{\circ}$$
Question is reduced to whether $$\triangle$$PQR is an equilateral triangle or not?

Statement 1 : PQR is NOT an isosceles triangle.
If PQR is not even isosceles triangle , it cannot be equilateral triangle.
So Statement 1 alone is sufficient to answer whether $$\triangle$$PQR is an equilateral triangle or not?

Statement 2 :Measure of angle P is 70 degrees.
Measure of $$\angle$$ P is not $$60^{\circ}$$, so PQR is not an equilateral triangle.
So Statement 2 alone is sufficient to answer whether $$\triangle$$PQR is an equilateral triangle or not?

so OA should be D

viv007 GMAT215
As per GMAT Official Guide Quantitative Review 2018 (Page : 37)
Quote:
An equilateral triangle has all sides of equal length. All angles of an equilateral triangle have equal measure. An isosceles triangle has at least two sides of the same length.

So as per GMAC, Equilateral triangles are subset of Isosceles triangles.
All Equilateral triangle are Isosceles triangle as per GMAC, but opposite is not true.
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Joined: 02 Oct 2017
Posts: 735
Re: Is the measure of two exterior angles of a triangle PQR, each equal to  [#permalink]

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27 Apr 2018, 08:39
I) triangle is not isosceles means two interior angles of triangle are not equal.
If two interior angles of triangle are not equal their exterior angles are also not equal.
Sufficient

2) P=70
Then max value of other two angles of triangle is 55 if they are isosceles
But they are not so exterior angles will not be equal to 120
Sufficient

Ans D

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Re: Is the measure of two exterior angles of a triangle PQR, each equal to &nbs [#permalink] 27 Apr 2018, 08:39
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