Directions: Each of the questions below consists of a question and two…
2023
Directions: Each of the questions below consists of a question and two statements numbered I and II given below it. You have to decide whether the data provided in the statements are sufficient to answer the question. Read both the statements and
On which date in March was Pravin's father's birthday?
Statements:
I. Pravin correctly remembers that his father's birthday is after 14th but before 19th March.
II. Pravin's sister correctly remembers that their father's birthday is after 17th but before 21st March.
- A.
if the data in both the statements I and II together are not sufficient to answer the question.
- 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.
- C.
if the data in both the statements I and II together are necessary to answer the question.
- D.
if the data either in statement I alone or in statement II alone are sufficient to answer the question.
Show answer & explanation
Correct answer: C
In a data-sufficiency range problem, each statement restricts the unknown quantity to a set of possible values. A statement, or a combination of statements, is sufficient only when it narrows that set down to exactly one value; if more than one value remains possible, the answer cannot be pinned down.
Statement I: the birthday is after 14th and before 19th March, so the possible dates are 15th, 16th, 17th, or 18th - four candidates, not a single value.
Statement II: the birthday is after 17th and before 21st March, so the possible dates are 18th, 19th, or 20th - three candidates, not a single value.
Since each statement alone leaves more than one candidate date, neither statement alone is sufficient on its own.
Combining both statements means the birthday must satisfy both restrictions at once, i.e. it must lie in the overlap of {15, 16, 17, 18} and {18, 19, 20}.
The only date common to both sets is 18th March: 18 is after 14th and before 19th (satisfies statement I), and 18 is after 17th and before 21st (satisfies statement II). No other date from either set meets both conditions simultaneously.
So neither statement individually fixes the date, but together they narrow it down to a single value - 18th March. Data from both statements together are necessary to answer the question.