What is the area under the line GHI -- JKL in the given quadrilateral OPQR, knowing that all the small spaces are squares of the same area? I. Length ABCDEQ is greater than or equal to 60. II. Area OPQR is less than or equal to 1512.
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For area questions involving geometric grids, knowing both the edge dimension and total area helps determine row/column counts needed to isolate subregions.
If the question can be answered with the help of statement I alone.
If the question can be answered with the help of statement II alone.
If both the statement I and statement II are needed to answer the question.
If the question cannot be answered even with the help of both the statements.
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The Correct Option isC
Solution and Explanation
We are given a grid-based figure OPQR, subdivided into identical square units. We are to find the area under the path GHI–JKL, i.e., a subset of the entire quadrilateral OPQR.
Let the side of each square be 1 unit. Then:
- Total area of OPQR = total number of squares in the rectangle.
From Statement I:
Length ABCDEQ $\geq 60$ — this gives a lower bound for the number of units along that edge. But we cannot find area without width or total units.
From Statement II:
Area of OPQR $\leq 1512$ — this gives an upper bound for the total number of square units. But again, alone this does not tell us how many squares lie below line GHI–JKL.
Now combine both statements:
If we know:
- The length of one edge (from I), and
- The total area (from II),
we can compute the total number of rows/columns, and hence determine the dimensions of the grid and identify which rows/columns lie under the line GHI–JKL.
Thus, both statements together are sufficient to estimate or calculate the required area.
