Determining data sufficiency for identifying a specific day
Question
Let p, q, r and s be distinct positive integers. Let p, q be odd and r, s be even. Consider the following statements:
Which of the statements given above are correct?
Options
1 and 2 only
2 and 3 only
1 and 3 only
1, 2 and 3
Explanation
Apply standard parity rules (Odd/Even properties) to evaluate each expression [cite: 1643, 1644]:
Statement 1: (p-r)²(q-s). p - r = Odd - Even = Odd \implies Square = Odd. q - s = Odd - Even = Odd. Product = Odd × Odd = Odd. Thus, claiming it is even is Incorrect.
Statement 2: (q-s)q²s . Notice that s is an even number. Any integer expression multiplied by an even number automatically results in an even product. Statement 2 is Correct.
Statement 3: (q+r)²(p+s). q + r = Odd + Even = Odd \implies Square = Odd. p + s = Odd + Even = Odd. Product = Odd × Odd = Odd. Statement 3 is Correct.
Reviewing the logic, statements 2 and 3 are correct.
Answer: (b).
Question details
Year
2024
Paper
CSAT
Question
Q39
Section
Data Interpretation & Sufficiency
Sub-topic
Calendars
Type
Statement-based
Difficulty
Medium
Source hint
Data sufficiency evaluation
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