Q'1

On these types of questions, look to see if the triangle displays any of the "special" properties meaning it is isoceles or has sides that suggest 30/60/90 or equilateral, etc. This problem doesn't exhibit any special characteristics so you should assume you know nothing about the triangle.
Since you cannot make any assumptions about the triangle draw it super weird so you dont mistakenly interpret your own drawing and add hidden assumptions.

What info is given? Only the measure of two sides of the triangle - what triangle property deals with that? The only one I know of is the rule that the sum of any two sides of the triangle must be greater than the third side. In addition, we know that the largest angle in a triangle will be opposite the largest side so the question is: Which side has the longest length?

(1) y = x + 3

Now we know two sides: x + 3 and x + 2. But we do not know anything about the last side. It could anything in the range of 0.001 (repeating) to 2x + 4.9999999 (repeating) because none of these values would violate the rule. So this is INSUFFICIENT.

(2) x = 2

Given this information, we know one side PQ has a length of 4, but we have no info on PR and QR; they could be any values as long as they do not violate the rule. INSUFFICIENT.

(1+2) Together, from (1) we know the range of values for the last side fall within 0.0000001 to 2x + 4.99999 and from (2) we can determine a specific range: 0.00001 to 2(2) + 4.99999. We know that PQ = 2 + 2 = 4 and PR = y = x + 3 = 2 + 3 to 5. So two sides are 4 and 5, but we're still left with a range of values for the last side. INSUFFICIENT.

Is E the OA?

In any triangle, the largest angle is opposite the longest side. To determine the longest side it suffices to determine whether y > x + 2. Since x + 3 > x + 2, it follows from (1) that y > x + 2.

Statement (1) alone is therefore sufficient. From (2) it follows that PQ = 2 and QR = 4. Thus, y can be any value between 2 and 6; it follows that y > x, but it cannot be concluded that y > x + 2.

Statement (2) alone is therefore not sufficient.

Therefore, statement (1) ALONE is sufficient, but
statement (2) alone is not sufficient to answer the question.

suyog, how do you know the 3rd side of the triangle is not greater than x+3?

Guys can I say something?

in triangle PQR , if PQ = x + 2 and PR = y, which of the angles of triangle PQR has the greatest degree measure?

1. y = x + 3
2. x = 2

As per the question, if we take x = 2, then PQ = 4 and PR = y = 2 + 3 = 5 (Taking stmt 1 into account). So from these we can not say about RQ. [Initailly it came into my mind that RQ will be 3 then! But later I realize it can be 2 also]. So for me OA is E.

Here given all the data in the Q + the two statements, we cannot determine the third side of the triangle which may be greater than the two sides which are determinable, so the Data is not sufficient

hence my ans is alos E

i also marked ans as E.
but that the copy paste of the explanation given.
Its not my answer. was wondering how? so posted it...

Neways...shud we conclude the ans to be E?