Question : Find the area of a triangle.
Statements : I. One of its sides is 6 units.
II. It is an equilateral triangle.
Analysis of Triangle Area Data Sufficiency Question
The question asks to find the area of a triangle given two statements.
Statement I Analysis
Statement I says: "One of its sides is 6 units."
Knowing only the length of one side ($s=6$) is not enough to determine the area of a general triangle. Multiple triangles can have a side of length 6 but possess different areas.
Statement II Analysis
Statement II says: "It is an equilateral triangle."
Knowing that a triangle is equilateral is useful, but without knowing the side length, we cannot calculate a specific numerical area. The area ($A$) of an equilateral triangle is given by the formula $A = \frac{\sqrt{3}}{4} \times side^2$. We need the side length.
Combined Statement Analysis
Consider both statements together:
- Statement II tells us the triangle is equilateral.
- Statement I tells us one side length is 6 units.
If a triangle is equilateral, all its sides are equal. Therefore, combining both statements means the triangle is equilateral with all sides measuring 6 units.
We can now use the area formula for an equilateral triangle:
$ A = \frac{\sqrt{3}}{4} \times (6)^2 $
$ A = \frac{\sqrt{3}}{4} \times 36 $
$ A = 9\sqrt{3} \text{ square units} $
This calculation shows that the area can be uniquely determined.
Conclusion
Neither statement alone is sufficient to find the area of the triangle. However, using both statements together provides enough information to calculate the specific area. Therefore, both statements are required.
This corresponds to Option A.
Important Questions from Data Sufficiency (Notes)
- In light of the statements I and II choose the most appropriate option.
If a group comprises of five persons A, B, C, D and E, then how many persons are taller than E?
Statement (I) A is taller than B and B is shorter than A and E only.
Statement (II) C is shorter than A and A is shorter than E. - In light of the statements I and II choose the most appropriate option.
Eight boxes- A, B, C, D, P, Q, R and S are stacked vertically but not necessarily in the same order. Which among them is kept immediately above R?
Statement (I) Only three boxes are kept above D and only one box is kept between D and Q. Q is kept lower than D and is immediately below P.
Statement (II) Only one box is kept between A and C. C is kept three boxes above Q. As many boxes are kept above B as are kept below R. A question is followed by two statements numbered I and II. You have to decide whether the data provided in the statements are sufficient to answer the question. Read both the statements and select the most appropriate answer.
C, I, L, N, R, and Y live on six different floors of the same building. The lowermost floor in the building is numbered 1, the floor above it is numbered 2, and so on, till the topmost floor is numbered 6. Who among them lives immediately above Y?
(I) Only four people live between N and I. C lives immediately below I.
(II) Only one person lives between C and R. Y lives immediately above N.P and Q are children of S. Who is the father of P? To answer this question which of the statements (1) and (2) is/are necessary?
(1) R is the brother of P and the son of T.
(2) U is the mother of Q.Given below is a question followed by two statements, I and II, each containing some information. Decide which of the statements are sufficient to answer the question.
Question:
Rajesh's salary is Rs. 12,500. What is Arvind's salary?
Statements
I. Arvind gets $\frac{3}{5}$th of the total salary of his and Rajesh'
II. Two-thirds of Arvind's salary is equal to the average salary of both.
