## OGQR 2020: Question No. 206

In the figure above, is the area of the triangular region ADE equal to the area of rectangular region ABCD?

- x = 10 and y = 5.
- x = 2y

Source | OGQR 2020 |

Type | Data Sufficiency |

Topic | Geometry |

Sub-Topic | Triangle/Polygons |

Difficulty | Medium |

### Solution

__Steps 1 & 2: Understand Question and Draw Inferences__

__Steps 1 & 2: Understand Question and Draw Inferences__

We are given a quadrilateral ABCD that includes

- ∆ADE and Rectangle ABCD
- Length of DE = x and DC = y

We need to determine:

- Whether the area of ∆ADE = area of rectangle ABCD or not.
- Or, 1/2 * AD * DE = AB * BC
- Or, 1/2 * AD * DE = CD * AD (Since ABCD is a rectangle, AB = CD = y and AD = BC)
- Or, 1/2 * AD * x = y * AD
- Or, 1/2 * x = y (Since AD is side length, it cannot be negative. Hence, we can divide both the sides of the inequality by AD)
- Or, x = 2y

- Therefore, if x = 2y then the answer is Yes, else the answer is No.

With this understanding let us analyze the statements.

__Step 3: Analyse Statement 1__

__Step 3: Analyse Statement 1__

*“x** = 10 and y = 5”*

- 10 = 2 * 5

Since x = 2y, the answer to the question is Yes.

Thus, statement 1 is sufficient to answer the question.

__Step 4: Analyse Statement 2__

__Step 4: Analyse Statement 2__

*“x** = 2y”*

Since x = 2y, the answer to the question is Yes.

Thus, 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 could determine the answer from either of the statements individually, this step is not required.

Hence, the correct answer is option D.

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