Multiple choice

If both ac and bc are integers, which of the following must also be an integer? I. a + c II. abc III. (a2 + b2) c2

  1. I only

  2. III only

  3. I, II and III

  4. II and III only

  5. I and III only
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Consistent with the given condition (a, b, c) can be 1/2, 1/3 and 6. So, I need not be true. Similarly, (a, b, c) can be (1/2, 1/2, 2). So, II need not be true. If ac and bc are both integers, then (ac)2 + (bc)2 must also be an integer. So, III must always be true. So, (3) is the answer.

Keep practicing — related questions