peraspera wrote:

patedhav wrote:

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.

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.