Consider the following in respect of prime number p and composite number c. p + c/p - c can be even 2p + c can be odd pc can be odd. Which of the statements given above are correct?

Maths : Basic Numeracy

Q 105 / 370

UPSC CSE Prelims 2023

Consider the following in respect of prime number p and composite number c.

$\frac{p + c}{p - c}$ can be even
2p + c can be odd
pc can be odd.

Which of the statements given above are correct?

EXPLANATION

Correct Option (D)

All three statements are correct.

Statement 1: $\frac{p + c}{p - c}$ can be even
Consider a prime number p = 13 and a composite number c = 15. Then, $\frac{p + c}{p - c} = \frac{13 + 15}{13 - 15} = \frac{28}{- 2} = - 14$ . Since -14 is an even number, the statement holds true.
Statement 2: 2p + c can be odd
Consider a prime number p = 2 and a composite number c = 9. Then, $2 p + c = 2 (2) + 9 = 4 + 9 = 13$ . Since 13 is an odd number, the statement holds true.
Statement 3: pc can be odd
For the product of two integers to be odd, both integers must be odd. Consider a prime number p = 3 and a composite number c = 9. Then, $p c = 3 \times 9 = 27$ . Since 27 is an odd number, the statement holds true.

Incorrect Options:

Options (A), (B), and (C) are incorrect because they do not include all three statements as correct. As demonstrated above, statements 1, 2, and 3 are all possible under the given conditions for prime (p) and composite (c) numbers.