What is the present age of Sanjeev? I. Sanjeev is 4 years older than Anuj. The…
2023
What is the present age of Sanjeev?
I. Sanjeev is 4 years older than Anuj. The ratio of the age of Anuj and Vipin is 4 : 5.
II. Vipin is 1 year older than Sanjeev and the present age of Anuj is 20 years.
III. The present age of Sanjeev is 5 years less than the age of Mohan.
- A.
The data in statements I and II are sufficient to answer the question,
while the data in statement III alone is not sufficient to answer the
question.
- B.
The data in statements II alone is sufficient to answer the question, while the data in statement I and III are not sufficient to answer the question.
- C.
The data in statements I alone or in statement II alone or Statement III alone is sufficient to answer the question.
- D.
The data in all the statements I, II and III are not sufficient to answer the question.
Attempted by 2 students.
Show answer & explanation
Correct answer: A
Concept: In a data sufficiency question, a statement (or a set of statements) is sufficient only when it pins the required quantity to one unique numerical value; if any unknown remains free, that statement (or combination) is insufficient.
Applying this to the given statements:
Statement I gives only a ratio: Anuj : Vipin = 4 : 5, so let Anuj = 4x and Vipin = 5x for some unknown x. It also gives Sanjeev = Anuj + 4 = 4x + 4 - but x is not fixed, so Sanjeev's value stays unknown. Statement I alone is insufficient.
Statement II gives Anuj = 20 and the relation Vipin = Sanjeev + 1 - one equation connecting two unknowns, Sanjeev and Vipin. With no second equation, Sanjeev cannot be pinned to a single value. Statement II alone is insufficient.
Statement III gives Sanjeev = Mohan - 5, but Mohan's age is never stated anywhere in the question. Statement III alone is insufficient, and it adds nothing even when paired with I or II, since Mohan's age still stays unknown.
Combine Statement I and Statement II: from Statement II, Anuj = 20. Substitute this into Statement I's ratio, Anuj : Vipin = 4 : 5, to get Vipin = (5/4) × 20 = 25. Statement II's own relation, Vipin = Sanjeev + 1, then gives Sanjeev = 25 - 1 = 24 - a single, unique value.
Cross-check the same result the other way: from Statement I, x = Anuj / 4 = 20 / 4 = 5, so Sanjeev = 4x + 4 = 4(5) + 4 = 24 - the two routes agree.
So Statement I and Statement II together fix Sanjeev's age uniquely, while Statement III alone (or added to either) never resolves it, since Mohan's age is never given.