Directions : Each of the questions given below consists of a statement and / or a question and two statements numbered I and II given below it. You have to decide whether the data provided in the statement(s) is / are sufficient to answer the question. Read both the statements and choose the appropriate option. What is Reena's present age? I. Reena's present age is five times her son's present age. II. Reena's age two years hence will be three times her daughter's age at that time.

### Concept & Logic For a system of equations to be solvable, you need at least as many independent equations as you have variables. In age problems involving family members, verify carefully how many unique individuals (variables) are introduced. ### Step-by-Step Solution Let Reena's present age be $R$, her son's present age be $S$, and her daughter's present age be $D$. * **Evaluating Statement I alone:** "Reena's present age is five times her son's present age." $$R = 5S$$ This is one equation with two variables. We cannot solve for $R$. *Statement I alone is NOT sufficient.* * **Evaluating Statement II alone:** "Reena's age two years hence will be three times her daughter's age at that time." $$(R + 2) = 3(D + 2)$$ This is one equation with two different variables ($R$ and $D$). We cannot solve for $R$. *Statement II alone is NOT sufficient.* * **Evaluating Statements I and II together:** Combining the data gives us the following system: 1) $R = 5S$ 2) $R + 2 = 3D + 6 \Rightarrow R = 3D + 4$ We have 3 distinct variables ($R, S, D$) but only 2 equations. Because we don't have a third equation relating the son's age to the daughter's age (e.g., if they were twins), the system is underdetermined. It is mathematically impossible to find a unique value for Reena's age. ### Exam Strategy & Shortcut Variable counting is your best friend here. Scanning Statement I introduces 2 variables (Reena, Son). Scanning Statement II introduces a 3rd entirely new variable (Daughter). Since you only have 2 statements (2 equations) for 3 variables, it is an automatic "Cannot be determined" / "Not sufficient". You can deduce this in 5 seconds without writing a single equation. ### Common Pitfall Students often speed-read and subconsciously assume the "son" in Statement I and the "daughter" in Statement II are the same child, or assume they are twins without being told so. Always treat distinct nouns as distinct mathematical variables unless explicitly stated otherwise. ### Final Answer **Therefore, the correct answer is The data even in both Statements I and II together are not sufficient to answer the question.**