Given below is a question followed by two statements numbered (I) and (II), each containing some information. You have to decide which of the statements is/are sufficient to answer the question.

The sum of ages of X, Y and Z is 60 years. What is Y's age?

Statement:

(I) Y is 10 years older than X.
(II) Z is 30 years old.

Appeared in: NVS- 2025

Explanation

The initial problem provides one equation with three variables (X + Y + Z = 60), which cannot be solved alone.
Statement (I) provides a relationship between X and Y (Y = X + 10), and Statement (II) provides the value of Z (Z = 30).
By substituting the value of Z from Statement (II) into the main equation, we get a new equation with two variables: X + Y = 30.
Then, by substituting the relationship from Statement (I) (X = Y - 10) into this new equation, we can form a single equation with only one variable (Y).
The final equation becomes (Y - 10) + Y = 30, which simplifies to 2Y = 40, yielding Y = 20. Thus, both statements are necessary.

Option B: This is incorrect because, as demonstrated in the explanation, combining the two statements provides exactly enough information to find a single, unique value for Y.
Option C: Statement (II) alone is not sufficient. Knowing Z = 30 only simplifies the main equation to X + Y = 30. Since there are still two unknown variables (X and Y), you cannot determine the specific value of Y.
Option D: Statement (I) alone is not sufficient. Knowing the relationship Y = X + 10 allows you to substitute for X, but the resulting equation (2Y + Z = 70) still contains two unknown variables (Y and Z).

Clinical Relevance

Nursing practice connection: This is primarily an exam-oriented knowledge point with limited direct bedside application, so retain Data Sufficiency using Linear Equations as background academic context rather than a clinical decision trigger.
This question tests logical and analytical reasoning, a critical skill for nurses in clinical problem-solving, such as calculating multi-step drug dosages or interpreting trends in patient vital signs.
What if? - If Statement (I) was 'Y's age is the average of X's and Z's ages' (Y = (X+Z)/2), would the answer change? Yes. Combining this with Statement (II) (Z=30) would give two equations (X+Y=30 and Y=(X+30)/2), which is a solvable system. So, both would still be needed.

How to Approach the Question

First, translate the main question into a mathematical equation: X + Y + Z = 60. Identify that you need to find the value of Y and have one equation with three unknowns.
Second, evaluate Statement (I) by itself. Substitute Y = X + 10 into the main equation. This results in 2Y + Z = 70. Since there are still two variables, conclude that Statement (I) alone is not sufficient.
Third, evaluate Statement (II) by itself, ignoring Statement (I). Substitute Z = 30 into the main equation. This results in X + Y = 30. Since there are still two variables, conclude that Statement (II) alone is not sufficient.
Fourth, since neither statement is sufficient on its own, combine them. Use both Z = 30 and X = Y - 10.
Substitute both pieces of information into the original equation: (Y - 10) + Y + 30 = 60. This simplifies to a single-variable equation (2Y = 40), which can be solved for Y.
Finally, conclude that because a unique solution for Y can only be found by using both statements together, they are both necessary.

Concept Tested & Keywords

QmPIAJ1KlWT9dSh-uclj1U

Practise the full NVS- 2025

Attempt every question from this paper in a timed mock, then review the full solution for each one.