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
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
“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
“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)
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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