OG 2020: Question No. 306
In the figure above, RST is a triangle with angle measures as shown and PRTQ is a line segment. What is the value of x + y?
- s = 40
- r = 70
| Source | OG 2020 |
| Type | Data Sufficiency |
| Topic | Geometry |
| Sub-Topic | Triangles |
| Difficulty | Easy – Medium |
Solution
Steps 1 & 2: Understand Question and Draw Inferences
In this question, we are given
- A diagram representing a triangle RST
- Angle SRT = r°, angle RTS = t° and angle TSR = s°
- PRTQ is a line segment
- Angle PRS = x° and angle QTS = y°
We need to determine
- The value of x + y
As PRTQ is a line segment, we can say
- x + r = t + y = 180°
- Therefore, x + r + t + y = 180 + 180 = 360
- Or, x + y = 360 – (r + t)
Hence, to find the value of x + y, we need to know either the individual values of r and t, or their sum.
With this understanding, let us now analyse the individual statements.
Step 3: Analyse Statement 1
As per the information given in statement 1, s = 40.
Also, because RST is a triangle, we can say r + s + t = 180
- Or, r + 40 + t = 180
Or, r + t = 180 – 40 = 140
As we can determine the value of r + t, we will be able to determine x + y also.
Hence, statement 1 is sufficient to answer the question.
Step 4: Analyse Statement 2
As per the information given in statement 2, r = 70
- From this statement, we do not get any information about the value of t.
Hence, statement 2 is not sufficient to answer the question.
Step 5: Combine Both Statements Together (If Needed)
Since we can determine the answer from statement 1 individually, this step is not required.
Hence, the correct answer choice is option A.
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