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Q3839/80Q40
Q39·CSAT · Prelims 2024

Determining data sufficiency for identifying a specific day

DI / DSCalendarsStatement-basedMedium

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:

1(p - r)²(q - s) is even.
2(q - s)q²s is even.
3(q + r)²(p + s) is odd.

Which of the statements given above are correct?

Options

a

1 and 2 only

b

2 and 3 only

c

1 and 3 only

d

1, 2 and 3

Answer

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.

In product expression checks, if any single term acting as a standalone multiplier is even, the entire product is guaranteed to be even.

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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