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What is the area, in square meters, of the building plot shown in the figure above? – OGQR 2020 Question #218 with Solution

OGQR 2020: Question No. 218

What is the area, in square meters, of the building plot shown in the figure above?

  1. KM = MP = 30 meters
  2. JK = KL = LM = MN = NP = 15 meters
SourceOGQR 2020
TypeData Sufficiency
TopicGeometry
Sub-TopicPolygons
DifficultyMedium

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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