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E
We dont know anything about RQ
1. RQ can be anything between >1 and <2x+3 The largest angle is always oppostite to the largest side ... insufficient as we cant say for sure which side is largest
2. insufficient
Together ... insufficient same reason as above!

from mba.com Gmat Free Prep Test Software GMAT Practice Test 1

Figure: A right triangle with points S (the right angle), P and Q. from point P, another line extends ending between Q and S. The endpoint of this line is point R.

Basically, the figure has two right triangles - Triangle PSQ and Triangle PRS with Triangle PRS inside Triangle PSQ.

In the figure shown, the measure of angle PRS is how many degrees greater than the measure of angle PQR?

(1) The measure of angle QPR is 30 degrees. (2) The measure of angles PQR and PRQ combined are 150 degrees.

Any help?

Hopefully I drew the triangle right... anyway,

(1) From this we know the angle of SPQ (60), but we don't know where point R falls along line SQ, so (1) isn't enough. (2) From this we know RPQ is 30, I don't think we can be sure of anything else... (Combined) We can find QPR & we can find out PRS, this is enough.

I would probably go with answer (C), but I still have a nagging feeling that we could find out from (2) alone, so I'm not entirely sure.

Okay... now I've figured it out (well, my mom figured it out)... the CORRECT answer is (B), you can indeed find out the answer from (2)alone.

We can solve this algebraically: Let PQR=A; Let PRQ=B; Let PRS=C;

We'll subtract the first equation from the second equation, this would eliminate B on the left side of the equal sign, and leave us with 30 degrees on the right side. This leaves us with: A-C = 30 degrees. We don't know the precise values of A & C, but we don't need to know, we've algebraically proven that the difference is 30 degrees (correction, my mom has proven that the difference is 30).

great solution, but doesnt statement 1 and 2 give us the same information, wouldnt the answer be D?

(1) y=x+3 x+3>x+2 The angle opposite to the longest side of the triangle is greatest. \(\angle PQR\) is the greatest.

Sufficient.

(2) x=2; x+2=4; 2<y<6

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. Not Sufficient.

(1) y=x+3 x+3>x+2 The angle opposite to the longest side of the triangle is greatest. \(\angle PQR\) is the greatest.

Sufficient.

(2) x=2; x+2=4; 2<y<6

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. Not Sufficient.

Ans: "A"

You are great as always. But I didn't understand why you suppose y>x+2 ?

(1) y=x+3 x+3>x+2 The angle opposite to the longest side of the triangle is greatest. \(\angle PQR\) is the greatest.

Sufficient.

(2) x=2; x+2=4; 2<y<6

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. Not Sufficient.

Ans: "A"

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; x,x+2,y 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 \(\angle PQR\).

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.

That's all!!

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; x=2 x+2=4

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) means (4-2) < y < (4+2) 2<y<6

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. Not sufficient.
_________________

I fail to see how (1) provides the same information as (2). Could anyone explain?

From what someone said ("(1) From this we know the angle of SPQ (60), but we don't know where point R falls along line SQ, so (1) isn't enough."), I don't see that one either. How should we know anything about SPQ just by statement 1?

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