2019 · Q72
Consider the following statements:
- 1If p is relatively prime to each of q and r, then p is relatively prime to the product qr.
Which of the above statements is/are correct?
Elementary MathematicsNumber System
- A1 only
- B2 only
- CBoth 1 and 2
- DNeither 1 nor 2
Explanation
Note: the source stem omits statement 2; the keyed answer follows from statement 1 alone. Statement 1 is true: if gcd(p,q) = gcd(p,r) = 1, no prime divides both p and qr, so gcd(p,qr) = 1.