OGQR 2020: Question No. 218
What is the area, in square meters, of the building plot shown in the figure above?
- KM = MP = 30 meters
- JK = KL = LM = MN = NP = 15 meters
| Source | OGQR 2020 |
| Type | Data Sufficiency |
| Topic | Geometry |
| Sub-Topic | Polygons |
| Difficulty | Medium |
Solution
Steps 1 & 2: Understand Question and Draw Inferences
In this question, we are given:
- A diagram of the building plot
We need to find the area of the building plot.
Let us mark all the points of the building plot as shown.
- Area of the plot = Area of JLRS + Area of LMNR + Area of QRNP
= JL * LR + LM * MN + NP * QP (JLRS, LMNR, and QRNP are rectangles)
= JL * MN + LM * MN + NP * LM (LR = MN and LM = QP)
Hence, we need to find the lengths of JL, LM, MN, and NP.
With this understanding, let us now analyse the individual statements.
Step 3: Analyse Statement 1
“KM = MP = 30 meters”
- Area of the plot = JL * MN + LM * MN + NP * LM
- = JL * MN + LM (MN + NP)
- = JL * MN + LM * MP
- = JL * MN + LM * 30
However, we do not know the value of JL, MN, and LM.
Hence, we cannot find the answer from statement 1 alone.
Thus, statement 1 is not sufficient to answer the question.
Step 4: Analyse Statement 2
“JK = KL = LM = MN = NP = 15 meters”
- JL = JK +KL = 15 +15 = 30meters
- We are already given the value of LM, MN, and NP and we found the value of JL.
Hence, we can find the answer from this statement.
Thus, statement 2 is sufficient to answer the question.
Step 5: Combine Both Statements Together (If Needed)
Since we could determine the answer from statement 2 individually, this step is not required.
Hence, the correct answer is option B.
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