## 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.

Source | OG 2020 |

Type | Data Sufficiency |

Topic | Geometry |

Sub-Topic | Quadrilateral |

Difficulty | Medium |

### Solution

__Steps 1 & 2: Understand Question and Draw Inferences__

__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__

__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 donāt 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__

__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)__

__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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