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705-805 Level|   Geometry|      
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Is the measure of two exterior angles of a triangle PQR, each equal to 12 Apr 2018, 22:45
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Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!

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75% (hard)

Question Stats:

39% (01:24) correct 61% (01:32) wrong based on 128 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)
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D
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Is the measure of two exterior angles of a triangle PQR, each equal to 14 Apr 2018, 10:39
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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
exterior-angles-triangle.png [ 15.45 KiB | Viewed 4251 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 18 Apr 2018, 04:57
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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 :roll:

for gmat do we have to consider an equilateral triangle is isosceles from 3 sides ?? I think thats too much from GMAC. :sad:
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Is the measure of two exterior angles of a triangle PQR, each equal to 18 Apr 2018, 05:09
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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 :roll:

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

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.
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Is the measure of two exterior angles of a triangle PQR, each equal to 18 Apr 2018, 06:01
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[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 :roll:

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

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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Is the measure of two exterior angles of a triangle PQR, each equal to 18 Apr 2018, 06:41
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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

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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Is the measure of two exterior angles of a triangle PQR, each equal to 27 Apr 2018, 09:39
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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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Is the measure of two exterior angles of a triangle PQR, each equal to 05 May 2021, 06:24
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Exterior angle = 120 implies interior angle = 60. The only way to have 2 60 degree interior angles is to have an equilateral triangle (60, 60, 60)

1) Equilateral triangles are isosceles (two sides/angles are the same) by definition. Condition 1 negates that. Sufficient.
2) Violates condition that triangle is equilateral. Sufficient.

Alternative approach to 2)
The exterior angle of 70 is 110. The sum of the other two angles must be 110. The sum of the two exterior angles unaccounted for must be (180*2)-110 = 250, which makes it impossible to have two exterior angles of 120. Sufficient.
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