In which year was Yashwi born? Statements: i. Yashwi at present is 25 years…

2025

In which year was Yashwi born?

Statements:

i. Yashwi at present is 25 years younger to her aunt.

ii. Yashwi’s brother, who was born in 1964, is 35 years younger to his aunt.

  1. A.

    If the data in statement I alone are sufficient to answer the question, while the data in statement II alone are not sufficient to answer the question

  2. B.

    If the data in statement II alone are sufficient to answer the question, while the data in statement I alone are not sufficient to answer the question

  3. C.

    If the data either in statement I alone or in statement II alone are sufficient to answer the question

  4. D.

    If the data given in both statements I and II together are not sufficient to answer the question

  5. E.

    If the data in both statements I and II together are necessary to answer the question

Attempted by 18 students.

Show answer & explanation

Correct answer: E

Concept: In Data Sufficiency, a statement is “sufficient” only if, used alone, it pins down exactly one value for the unknown asked in the question. A statement that gives only a relative/relational fact (an age gap, a ratio) with no anchor value is insufficient by itself — but two such relational facts that share a common reference point can together fix an absolute value that neither could alone.

Application:

  1. Let Aunt's birth year = A, Yashwi's birth year = Y, Brother's birth year = 1964 (given).

  2. Statement I alone: Y = A + 25 (Yashwi is 25 years younger than her aunt). Two unknowns, no anchor — Y cannot be found. Statement I alone is NOT sufficient.

  3. Statement II alone: 1964 = A + 35 (brother is 35 years younger than the aunt), so A = 1964 − 35 = 1929. This fixes the aunt's birth year, but gives no relation between Y and A — Y cannot be found. Statement II alone is NOT sufficient.

  4. Combine both: substitute A = 1929 (from Statement II) into Y = A + 25 (from Statement I): Y = 1929 + 25 = 1954.

Cross-check: Yashwi (1954) is 25 years younger than the aunt (1929): 1954 − 1929 = 25 ✓. The brother (1964) is 35 years younger than the same aunt (1929): 1964 − 1929 = 35 ✓. Both statements are mutually consistent and, together, uniquely fix Yashwi's birth year.

Result: Neither statement alone determines Yashwi's birth year, but the two together do — so both statements I and II together are necessary to answer the question.

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