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patedhav
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Geometry 16 Mar 2009, 07:54
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Q-1) Is QR the least side in triangle PQR?

1) Angle P = 60
2) Angle Q = 80

I came across this question while doing test in 4GMAT and as per my understanding answer should be A) but as per answer given they mentioned it's E) and I want to confirm by taking others opinions on this.

It is A) since if we know that one side is 60) then other two side will be added to 120) and so only in case of other sides are 60/60 then only side opposite to P) (QR) are going to be equal with others or else it will be greater than at least one side.

In case of all sides are same (equilateral triangle) QR will not be considered as least? (If all sides are same then it is not least).

Please respond with your thoughts.



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patedhav
Q-1) Is QR the least side in triangle PQR?

1) Angle P = 60
2) Angle Q = 80

I came across this question while doing test in 4GMAT and as per my understanding answer should be A) but as per answer given they mentioned it's E) and I want to confirm by taking others opinions on this.

It is A) since if we know that one side is 60) then other two side will be added to 120) and so only in case of other sides are 60/60 then only side opposite to P) (QR) are going to be equal with others or else it will be greater than at least one side.

In case of all sides are same (equilateral triangle) QR will not be considered as least? (If all sides are same then it is not least).

Please respond with your thoughts.
Show more



Why can't it be C

The side opposite to the least angle will be least.

From both, you know R = 40. So by triangle rule, side opposite to R should be least, that is PQ. SO we can say that QR is not least!!!
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patedhav
Q-1) Is QR the least side in triangle PQR?

1) Angle P = 60
2) Angle Q = 80

I came across this question while doing test in 4GMAT and as per my understanding answer should be A) but as per answer given they mentioned it's E) and I want to confirm by taking others opinions on this.

It is A) since if we know that one side is 60) then other two side will be added to 120) and so only in case of other sides are 60/60 then only side opposite to P) (QR) are going to be equal with others or else it will be greater than at least one side.

In case of all sides are same (equilateral triangle) QR will not be considered as least? (If all sides are same then it is not least).

Please respond with your thoughts.



Why can't it be C

The side opposite to the least angle will be least.

From both, you know R = 40. So by triangle rule, side opposite to R should be least, that is PQ. SO we can say that QR is not least!!!
Show more


Sorry, they have given "C" option but why not A, if all the sides are equal in case of equilateral triangle then can we consider all sides are least or none of them are least?
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patedhav
Q-1) Is QR the least side in triangle PQR?

1) Angle P = 60
2) Angle Q = 80

I came across this question while doing test in 4GMAT and as per my understanding answer should be A) but as per answer given they mentioned it's E) and I want to confirm by taking others opinions on this.

It is A) since if we know that one side is 60) then other two side will be added to 120) and so only in case of other sides are 60/60 then only side opposite to P) (QR) are going to be equal with others or else it will be greater than at least one side.

In case of all sides are same (equilateral triangle) QR will not be considered as least? (If all sides are same then it is not least).

Please respond with your thoughts.
Show more


I think it's not A for sure.
It could be so that e.g. P=60, q=10 and r=110. In this case PR is the smallest side.
It's not B for the same reasons.

However, I disagree that it is E. I think it's C.
If p=60 and Q=80, then R=40, and PQ should be the smallest side, so sufficient.
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I still do not understand why you say not A)? Can you give explanation?
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patedhav
I still do not understand why you say not A)? Can you give explanation?
Show more

P=60 from the statement.

That leaves us 180-60= 120 degrees for the remaining 2 angles. Which means the remaining 2 angles could be 60 and 60, or they could be 10 and 110, or 50 and 70, and so on. Since we have a multitude of choices for the smallest side as a result of trying different combinations of the remaining angles, the statement 1) is not sufficient.
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patedhav
I still do not understand why you say not A)? Can you give explanation?

P=60 from the statement.

That leaves us 180-60= 120 degrees for the remaining 2 angles. Which means the remaining 2 angles could be 60 and 60, or they could be 10 and 110, or 50 and 70, and so on. Since we have a multitude of choices for the smallest side as a result of trying different combinations of the remaining angles, the statement 1) is not sufficient.
Show more

I still do not agree with your explanation.

1) As you mentioned it leaves 180 - 60 = 120 and so there are number of combination for the size to be minimum but in all these conditions we are always sure that side opposite of P (60) is not going to be least except the case when we have equilateral triangle (60, 60, 60) but in this case do we consider the any side as least or all the sides are equal.

In short side opposite to 60 is not going to be the least unless it is equilateral triangle but as per my undersanding in equilateral triangle we cannot say any side as least side since all are equal.
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patedhav
Q-1) Is QR the least side in triangle PQR?

1) Angle P = 60
2) Angle Q = 80

I came across this question while doing test in 4GMAT and as per my understanding answer should be A) but as per answer given they mentioned it's E) and I want to confirm by taking others opinions on this.

It is A) since if we know that one side is 60) then other two side will be added to 120) and so only in case of other sides are 60/60 then only side opposite to P) (QR) are going to be equal with others or else it will be greater than at least one side.

In case of all sides are same (equilateral triangle) QR will not be considered as least? (If all sides are same then it is not least).

Please respond with your thoughts.


I think it's not A for sure.
It could be so that e.g. P=60, q=10 and r=110. In this case PR is the smallest side.
It's not B for the same reasons.

However, I disagree that it is E. I think it's C.
If p=60 and Q=80, then R=40, and PQ should be the smallest side, so sufficient.
Show more

Why r u trying to find the length of PR when the question is abt length of QR.

The question asks Is QR the least side in triangle PQR?
Stmt 1. With P= 60 we have Q + R = 120 i.e (q,r) = (61,59),(60,60),(59,61) These are the three cases possible.
(61,59) -> we have PQ as the least side => NO
(60,60) -> all sides are equal => NO
(59,61) -> we have PR as the least side => NO

in each of the cases, we answer the question "Is QR the least side in triangle PQR" and we get the same answer NO.
Hence sufficient.

Stmt 2. With Q= 80 we have P+R = 100 i.e (p,r) = (49,51),(50,50),(51,49)
(49,51) -> we have QR as the least side => YES
(50,50) -> we have QR as one of the least sides =>YES/NO
(51,49) -> we have PQ as the least side => NO
Hence insufficient.

So, IMO the answer should be A.
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patedhav
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patedhav
I still do not understand why you say not A)? Can you give explanation?

P=60 from the statement.

That leaves us 180-60= 120 degrees for the remaining 2 angles. Which means the remaining 2 angles could be 60 and 60, or they could be 10 and 110, or 50 and 70, and so on. Since we have a multitude of choices for the smallest side as a result of trying different combinations of the remaining angles, the statement 1) is not sufficient.

I still do not agree with your explanation.

1) As you mentioned it leaves 180 - 60 = 120 and so there are number of combination for the size to be minimum but in all these conditions we are always sure that side opposite of P (60) is not going to be least except the case when we have equilateral triangle (60, 60, 60) but in this case do we consider the any side as least or all the sides are equal.

In short side opposite to 60 is not going to be the least unless it is equilateral triangle but as per my undersanding in equilateral triangle we cannot say any side as least side since all are equal.
Show more

I think you right. If it's an equilateral triangle, then it's also sufficient, and QR is not the least, as all sides are equal. I guess it should be A. Thank you for an interesting problem.



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Hi there,
This topic has been closed and archived due to inactivity or violation of community quality standards. No more replies are possible here.
Where to now? Join ongoing discussions on thousands of quality questions in our Quantitative Questions Forum
Still interested in this question? Check out the "Best Topics" block above for a better discussion on this exact question, as well as several more related questions.
Thank you for understanding, and happy exploring!