Question

Find the value of X in terms of ‘a’.
[I.] Arithmetic mean of X and Y is ‘a’ while the geometric mean is also ‘a’.
[II.] $\dfrac{X}{Y} = R$; $X - Y = D$

• A. if the question can be answered with the help of any one statement alone but not by the other statement.
• B. if the question can be answered with the help of either of the statements taken individually.
• C. if the question can be answered with the help of both statements together.
• D. if the question cannot be answered even with the help of both statements together.

Hint:

When two distinct types of means are equal, it imposes a strong constraint — use it directly.

Answer 1

The Correct Option is A

From Statement I: \[ \text{Arithmetic Mean: } \dfrac{X+Y}{2} = a,\quad \text{Geometric Mean: } \sqrt{XY} = a \] Solving these two equations gives unique values of X and Y in terms of 'a'. Hence, this is sufficient. Statement II gives two equations with two variables but with unknown constants \( R \) and \( D \), which cannot be resolved in terms of ‘a’.