OG 2020: Question No. 335
In the figure above, PQRT is a rectangle. What is the length of segment PQ?
- The area of region PQRS is 39 and TS = 6.
- The area of region PQRT is 30 and QR = 10.
Steps 1 & 2: Understand Question and Draw Inferences
In this question, we are given
- A diagram of a quadrilateral PQRS, of which PQRT is a rectangle
We need to determine
- The length of segment PQ
Since PQRT is a rectangle we can say the side QR and PT are parallel to each other.
- Therefore, we can say that PQRS is a trapezium.
With this understanding, let us know analyse the individual statements.
Step 3: Analyse Statement 1
As per the information given in statement 1, the area of region PQRS is 39 and TS is equal to 6.
- Area of PQRS = (1/2) (QR + PS) (PQ) = 39
Or, (QR + PS) (PQ) = 78
Or, (PT + PT + TS) (PQ) = 78
Or, (2PT + 6) (PQ) = 78
As we don’t know the value of PT, we cannot determine the value of PQ.
Hence, statement 1 is not sufficient to answer the question.
Step 4: Analyse Statement 2
As per the information given in statement 2, the area of region PQRT is 30 and QR is equal to 10.
- PQ * QR = 30
Or, PQ * 10 = 30
Or, PQ = 3
As we can determine the value of PQ, statement 2 is sufficient to answer the question.
Step 5: Combine Both Statements Together (If Needed)
Since we can determine the answer from statement 2 individually, this step is not required.
Hence, the correct answer choice is option B.
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