## OG 2020: Question No. 324

Is quadrilateral PQRS a parallelogram?

- Adjacent sides PQ and QR have the same length.
- Adjacent sides RS and SP have the same length.

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 asked to determine

- Whether the quadrilateral PQRS is a parallelogram or not.

If PQRS is a parallelogram, then the opposite sides of PQRS will be parallel and equal to each other.

However, from the question statement, we do not get any such relevant information.

Hence, let us now analyse the individual statements.

__Step 3: Analyse Statement 1__

__Step 3: Analyse Statement 1__

As per the information given in statement 1, adjacent sides PQ and QR have the same length.

- However, from this information, we cannot make any conclusion whether PQRS is a parallelogram or not, as we do not have any relevant information regarding the opposite side pair.

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, adjacent sides RS and SP have the same length.

- However, from this information, we cannot make any conclusion whether PQRS is a parallelogram or not, as we do not have any relevant information regarding the opposite side pair.

Hence, statement 2 is not sufficient to answer the question.

__Step 5: Combine Both Statements Together (If Needed)__

__Step 5: Combine Both Statements Together (If Needed)__

Combining the information from both statements, we get

- PQ = QR
- RS = SP

However, we cannot say whether PQ = RS and QR = SP, and whether the opposite sides are parallel to each other or not.

Therefore, even after combining both statements we cannot get the answer.

Hence, the correct answer is option E.