In the figure above, RST is a triangle with angle measures as shown an

Given: RST is a triangle with angle measures as shown and PRTQ is a line segment

Target question: What is the value of x + y ?

Statement 1: s = 40
Since angles in a triangle add to 180°, we know that r° + t° = 140°
Since angles on a line add to 180°, we know that x° + r° = 180°, and we know that t° + y° = 180°
So, we can write: x° + r° + t° + y° = 180° + 180°
Rearrange: x° + y° + r° + t° = 360°
Substitute to get: x° + y° + 140° = 360°
Subtract 140° from both sides to get: x° + y° = 220°
Since we can answer the target question with certainty, statement 1 is SUFFICIENT

Statement 2: r = 70
This tells us that x° = 110°, however we have no information about the value of any other angle.
Statement 2 is NOT SUFFICIENT

Answer: A

Cheers,
Brent
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The original question: \(x+y=?\) Imagine x and y as angle measures of supplementary angles.
The rephrased question: \((180-r)+(180-t)=? \implies 360-(r+t)=? \implies r+t=?\)

1) We know that \(s=40\) and \(r+t+s=180\), so \(r+t=140\). Thus, the answer to the rephrased question is a unique value. \(\implies\) Sufficient

2) We know that \(r=70\), and all we can infer is that \(70<r+t<180\). Thus, we can't get a unique value to answer the rephrased question. \(\implies\) Insufficient

Answer: A
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Should be a, x+y would be equal to r+2s+t
R+2s+t= r+t+s+s= 180+s, hence option a

Posted from my mobile device

from given info
x=s+t
y=s+r
and s+t+r = 180
t+r= 140
and x+y= 2s+t+r
so x+y = 80+140 ; 220
sufficient
from2 r=70 , insufficeint
IMO A

Since x and y are exterior angles or r and t respectively, we can represent x and y as 180 - r and 180 - t.
So we need to determine (180 - r) + (180 - t) = 360 - r - t = 360 - (r + t)

Statement One Alone:

s = 40

Since = 40, r + t = 180 - 40 = 140.

Thus, x + y = 360 - 140 = 220.

Statement one alone is sufficient to answer the question.

Statement Two Alone:

r = 70

We see that x is 180 - 70 = 110.

However, we can’t determine the value of y since we don’t know the value of t or s. Statement two alone is not sufficient to answer the question.

Answer: A
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Hi All,

We're told that in the figure above, RST is a triangle with angle measures as shown and PRTQ is a line segment. We're asked for the value of (X+Y). This question is built around a couple of Geometry rules involving Triangles and Lines. To start, the angles in the triangle (re: s, r and t) total 180 degrees and so do the pairs of angles (x+r) = 180 and (t+y) = 180.

(1) s = 40

With angle s, we know that r+t must total 140 degrees. Those two angles are part of the two 180 degree totals on the line, meaning that r+t+x+y = 360 degrees. We now know that r+t = 180, so....
r+t+x+y = 360
180+x+y = 360
x+y = 180
Fact 1 is SUFFICIENT

(2) r = 70

Fact 2 helps us to determine the value of angle x (since x+r = 180, we know that x = 110 degrees), but we don't know the value of y.
Fact 2 is INSUFFICIENT

Final Answer:

GMAT assassins aren't born, they're made,
Rich
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Why can we not assume that r is equivalent to t since sides ST and SR appear equivalent, hence allowing us to solve for (X+Y)?

Even before looking at options 1&2,

We can calculate:

x+r+y+t=360; 360-r-t=x+y ------------------------eq.1

r+t+s=180 ; 180-r-t = s -----------------eq.2

For eq.2 if we add 180 on both sides, we get 360-r-t = 180+s -------------------eq.3

from eq.1 and eq.3, we get 180+s = x+y.

So, we only need the option which has the value of s in it to calculate x+y.

so (1) is sufficient.

Consider Statement (2)

r alone is not going to be sufficient because s will always influence t's value and without knowing s, we cant find x+y. So individual values of X&Y need to be found, which is not possible without using (1) also.

So IMO A

Hi Eagles1795,

When dealing with pictures of shapes in DS questions, we CANNOT assume that the picture is 'drawn to scale.' Thus, while ST and SR might be the same length (meaning that angles r and t are equal), it's possible that one of those sides is longer than the other (meaning that angles r and t are NOT equal). With DS questions, we will ALWAYS need more information to answer the question than the initial prompt provides. In my post (directly above yours), I explain how to get to the correct answer.

GMAT assassins aren't born, they're made,
Rich
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(1) \(s=40, so, r+t=140\)

\(∴ x+r+t+y=180+180\)

\(⇒ x+y+r+t=360\)

\(⇒ x+y+140=360\)

\(⇒ x+y=360-140=220\); Sufficient

(2) No relation found among s, t and y. Insufficient.

The answer is A
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So I got stumped b/c I told myself to never assume that lines are parallel, perpendicular, etc.

How can we be sure in this instance that PRTQ is completely parallel?
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I think you mean "how can we assume that points P, R, Q and T are collinear, (on the same straight line)?"

OFFICIAL GUIDE:

Problem Solving
Figures: All figures accompanying problem solving questions are intended to provide information useful in solving the problems. Figures are drawn as accurately as possible. Exceptions will be clearly noted. Lines shown as straight are straight, and lines that appear jagged are also straight. The positions of points, angles, regions, etc., exist in the order shown, and angle measures are greater than zero. All figures lie in a plane unless otherwise indicated.

Data Sufficiency:
Figures:
• Figures conform to the information given in the question, but will not necessarily conform to the additional information given in statements (1) and (2).
• Lines shown as straight are straight, and lines that appear jagged are also straight.
• The positions of points, angles, regions, etc., exist in the order shown, and angle measures are greater than zero.
• All figures lie in a plane unless otherwise indicated.

Hope it helps.
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Answer: Option A

Video solution by GMATinsight



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Simplifying the Q prompt helped me a ton
Approach:
x+y is asked
x=s+t and y=s+r (By Exterior Angle Theorem)
We are supposed to find x+y=2s+r+t=s+r+t+s=180+s(Sum of all angles=180)
Thus all we need for proving sufficiency is the value of s
Statement A Sufficient
Statement B Insufficient as just r is not enough to ans
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The question can be solved with two different properties:

Traps to watch out for:
- Unless given otherwise, figures are not drawn to the scale
- Lines are still lines, triangles are still triangles

We need to apply one of the first two theorems & the theorem 3:

Theorem 1:
Adjacent angles on the same line are supplementary (x,r and t,y are supplementary => their sum is 180) (Learn more about this theorem here)
Theorem 2:
External angle is equal to the sum of two internal angles (Triangle theorems: external angle and internal opposite angles)

Theorem 3:
Internal angles of a triangle are supplementary (sum = 180)

Lets apply theorem 2 and rephrase the question:

From the theorem:
x = s+t
y = s+r

Since we need x+y, lets add the two
x+y = s + s+t+r = 180 + s (Since s+t+r = 180 by Theorem 3)

So the answer depends only on s.

1) Gives s, so we can find x+y. SUFF
2) Gives only r, but doesnt give us any other angle. To get to s we need atleast t also. INSUFF

If someone prefers video format - I have discussed the common mistakes and solution in detail:



Hence A
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Why isn't statement 2 sufficient? Is it because we can't assume the bottom line is at 90 degrees?

Hi thesip2323,

When dealing with pictures of shapes in DS questions, we CANNOT assume that the picture is 'drawn to scale.' Thus, while ST and SR might be the same length (meaning that angles r and t are equal), it's possible that one of those sides is longer than the other (meaning that angles r and t are NOT equal). Thus, we don't know the value of Angle T or Angle Y, so Fact 2 is Insufficient.

GMAT assassins aren't born, they're made,
Rich
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Hey guys, quick Q to why (2) is insufficient. If i were to draw a triangle from P-S and S-Q i'd be able to calculate x still. The angle in Ps corner would be 60, since all the angles in the corners would have to add up to 180. From there i could easily calculate the angle of S. So why would that make (2) not sufficient on its own? Appreciate your help