Introduction
Age-based Data Sufficiency problems test your ability to determine whether the given information is enough to find a person’s or group’s age(s). These questions often involve relationships between present, past, or future ages. The goal is not to calculate the exact age, but to check if the given statements are sufficient to determine it uniquely.
This pattern is important because it combines arithmetic reasoning with logical analysis - both key skills for aptitude and reasoning exams.
Pattern: Age-Based Data Sufficiency
Pattern
Key idea - Translate verbal relations (“older than,” “after 5 years,” “twice as old,” etc.) into equations and check whether one or both statements can uniquely determine the required age.
Typical stems include questions like “What is X’s present age?” or “What is the ratio of ages of A and B?”. Each statement gives partial age relationships - you must judge if that data alone or combined is sufficient.
Step-by-Step Example
Question
What is Riya’s present age?
(I) Riya is 5 years younger than her brother.
(II) Her brother’s age after 5 years will be 25.
Solution
-
Step 1: From (I)
Riya = Brother - 5. The brother’s current age is not known, so (I) alone is insufficient. -
Step 2: From (II)
Brother’s age after 5 years = 25 ⇒ Present age of brother = 25 - 5 = 20. But Riya’s relation to him is not given → insufficient alone. -
Step 3: Combine (I) and (II)
From (II): Brother = 20. From (I): Riya = 20 - 5 = 15. Both statements together determine Riya’s age uniquely. -
Final Answer:
Both statements together are necessary -
Quick Check:
Combine → Brother = 20 → Riya = 15 ✅
Quick Variations
1. Two-person relationships (like father-son, husband-wife, or friends).
2. Multi-step age differences involving “years ago” or “years hence.”
3. Ratio-based age questions where current ages are expressed as multiples or fractions of each other.
4. Questions involving total or combined ages.
Trick to Always Use
- Step 1 → Express each statement as an equation in variables (e.g., A = B + 5).
- Step 2 → Check if one equation alone can give a unique value of the target variable.
- Step 3 → If not, see if combining both gives a solvable pair of equations.
Summary
Summary
- Translate every age relation into an algebraic equation.
- Statement sufficiency ≠ solving the question - only check if you *can* solve uniquely.
- Single relation = insufficient; two independent relations = usually sufficient.
- Always consider “years ago” and “years hence” carefully - adjust each age accordingly.
Example to remember:
(I) Riya = Brother - 5; (II) Brother after 5 years = 25 ⇒ Both together give Riya = 15.
Hint: Use 'years ago' to find present age, then apply difference relation.
Common Mistakes: Assuming one relational statement without a numeric value can yield exact age.