Data Sufficiency on Quadrilateral Land Area
XAT 2025 · Quantitative Ability & Data Interpretation · Hard · Data Sufficiency
A farmer has a quadrilateral parcel of land with a perimeter of 700 feet. Two opposite angles of that parcel of land are right angles, while the remaining two are not. The farmer wants to do organic farming on that parcel of land. The cost of organic farming is Rs. 400 per square foot.
Consider the following two additional pieces of information: I. The length of one of the sides of that parcel of land is 110 feet. II. The distance between the two corner points where the non-perpendicular sides of that parcel of land intersect is 255 feet.
To determine the amount of money the farmer needs to spend to do organic farming on the entire parcel of land, which of the above additional pieces of information is/are MINIMALLY SUFFICIENT?
- A.
II only
- B.
I only
- C.
I and II together only
- D.
Either of I or II, by itself
- E.
The amount cannot be determined even with the additional pieces of information.
C
Explanation
Let the quadrilateral be with right angles at and . Diagonal is the hypotenuse for right-angled triangles and . Perimeter . Statement I gives ft. (Not sufficient alone). Statement II gives diagonal length ft. (Not sufficient alone). Combining both: In , . Then . Since is right-angled at , . We can uniquely determine and , and thus find the area of both triangles, giving the total area and total cost. Hence, I and II together are minimally sufficient.
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