Question : What is Gagan's age ? Statements : I. Gagan, Vimal and Kunal are…
2024
Question : What is Gagan's age ?
Statements :
I. Gagan, Vimal and Kunal are all of the same age.
II. Total age of Vimal, Kunal and Anil is 32 years and Anil is as old as Vimal and Kunal together.
- A.
I alone is sufficient while II alone is not sufficient
- B.
II alone is sufficient while I alone is not sufficient
- C.
Neither I nor II is sufficient
- D.
Both I and II are sufficient
Attempted by 21 students.
Show answer & explanation
Correct answer: D
Concept: A Data Sufficiency question is solved by testing each statement independently first, and combining them only if neither alone yields a single, unique value for the quantity asked. A statement (or combination) is 'sufficient' only when it pins down exactly one numerical answer, not a range or multiple possibilities.
Statement I alone: Gagan, Vimal and Kunal are of the same age, so G = V = K. This only relates the three ages to each other — it fixes no numeric value for any of them — so Statement I alone is not sufficient.
Statement II alone: V + K + A = 32 and A = V + K. Substituting A = V + K into the first equation gives (V + K) + (V + K) = 32, i.e. 2(V + K) = 32, so V + K = 16. This fixes only the sum of Vimal and Kunal's ages, not their individual values, and says nothing about Gagan, so Statement II alone is not sufficient.
Combining I and II: From Statement I, V = K. Substituting into V + K = 16 (from Statement II) gives 2V = 16, so V = K = 8. From Statement I, G = V = K, so G = 8 — a single, unique value.
Cross-check: With V = K = 8, Statement II gives A = V + K = 16, and V + K + A = 8 + 8 + 16 = 32, matching the given total — confirming the result is consistent with both statements.
Result: Both statements together are required and sufficient to determine Gagan's age (8 years); neither statement alone suffices.