If the HCF of p and q (p > q) is G, then which of the following statements is/are correct? I. HCF of p and (p + q) is G II. HCF of p and (p - q) is G Select the answer using the code given below:

CDS 2026 PYQ with Answer — If the HCF of p and q (p > q) is G, then which of the following state…

2026 · Q22

If the HCF of p and q (p > q) is G, then which of the following statements is/are correct?

IHCF of p and (p + q) is G
IIHCF of p and (p - q) is G Select the answer using the code given below:

Elementary MathematicsHCF and LCM

AI only
BII only
CBoth I and II
DNeither I nor II

Explanation

Any common divisor of p and p+q also divides their difference q, so gcd(p,p+q)=gcd(p,q)=G and statement I is correct. Likewise any common divisor of p and p−q divides q, so gcd(p,p−q)=G and statement II is correct. Both statements are correct, option C.