Question: is y>x+2
The angle opposite to the longest side of the triangle is greatest.
\(\angle PQR\) is the greatest.
If y is about 2; the angle opposite y will be smaller than angle opposite x+2.
If y is about 6; the angle opposite y will be the greatest.
You are great as always. But I didn't understand why you suppose y>x+2 ?
No, I didn't suppose so. I just rephrased what's asked in the question. The question asks
which angle is the greatest among the three angles.
What sides are there;
What angles are opposite these sides;
opposite x -> \(\angle QRP\)
opposite x+2 -> \(\angle QPR\)
opposite y -> \(\angle PQR\)
x+2 will always be greater than x. So; angle opposite to side x+2 will be greater than the
angle oppsite to x.
\(\angle QPR\) will always be greater than \(\angle QRP\). We need to know about
The only question then stands, "Is y> x+2 or y<x+2"
If y> x+2; then y becomes the longest side and the angle opposite to it will become the greatest angle.
If y< x+2; then x+2 becomes the longest side and the angle opposite to it will become the greatest angle.
1) This statements tells us that y=x+3
For any value of x;
y will be the longest side and the angle oppsite y will be the greatest.
2) This statement tells us that;
y is any value between 2 and 6(if one side of the triangle is 2 and other side 4; the third side will be between the difference
and sum of the other two sides)
(4-2) < y < (4+2)
y can be 3 which is less than x+2. x+2 becomes longest.
y can be 5 which is greater than x+2. y becomes longest.
So; we don't definitely know whether y>x+2.
GMAT Club Premium Membership - big benefits and savings