Question

Suppose that p and q are rational numbers and r is an irrational number. Which expression represents a rational number?

A. p+r

B. p+pr

C. p+q

D. p+qr

Answer 1

C.

Reason: The sum of two rationals is rational, so p+q is rational.

The others need not be:
- p+r is irrational (rational + irrational = irrational).
- p+pr = p(1+r) is irrational unless p = 0 (1+r is irrational).
- p+qr is generally irrational (qr is irrational unless q = 0).