Each of the following questions is followed by two statements 1 If either of the statements I or II ...........

Math and Mental Ability Data Sufficiency

Each of the following questions is followed by two statements.

1.If either of the statements I or II alone but not the other is sufficient to answer the question.

2.If both the statements I or II alone are sufficient to answer the question.

3.If questions can be answered with the help of both statements together, but not with the help of either statement alone.

4.If question cannot be answered unless more information is provided.

What is the ratio of areas of two squares S1 and S2?

I. The ratio of the perimeters of the two squares is 3:2.

II.The ratio of the lengths of their diagonals is 3:2.

छोटे Courses बड़े Results

Master Data Sufficiency

Prepare through Micro-courses

Try Now

Explanation:

- Statement I: The perimeter of a square is proportional to its side length. If the ratio of the perimeters of two squares S1 and S2 is 3:2, then the ratio of their side lengths is also 3:2. Since the area of a square is the square of its side length, the ratio of the areas will be \( \left(\frac{3}{2}\right)^2 = \frac{9}{4} \). This statement alone is sufficient.

- Statement II: The length of the diagonal of a square is proportional to its side length. If the ratio of the diagonals of two squares S1 and S2 is 3:2, then the ratio of their side lengths is also 3:2. As in Statement I, this leads to an area ratio of \( \frac{9}{4} \). This statement alone is sufficient.

- Conclusion: Either Statement I or Statement II alone is sufficient to answer the question.

- Correct Option: 2. Both statements alone offer enough information.