Lesson: Challenging Problem Solving - 13t01

Advanced Number Properties: Know The Rules

[Page 13 of 37]

Picking Numbers works well on many Number Properties questions, but sometimes it's necessary to know Number Property rules in order to solve a problem. At other times, familiarity with the rules will help get you to the correct answer more efficiently. For the following Roman Numeral question, we will focus on the Number Property rules that are being tested. Review the question and then proceed to the task below.

If the sum of prime numbers x and y is an odd number, which of the following CANNOT be true?

I. y2 is odd
II. x – y is odd
III. is an integer

None
I only
III only
I and II
II and III
This question stem suggests that two Number Properties concepts will be central to solving this problem. What are they?

1:

2:

Our question stem explicitly mentions two Number Properties concepts we must consider in answering this question—odd/even addition rules, and the definition of a prime number. If we can recall the basics facts regarding odd, even, and prime numbers, then we can get through this question easily.
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