Number Properties Question

[ScottL236]

Hi, I have a question about 6th Edition Number Properties Question #10: "If c and d are integers, is c-3d even?"

(1) c and d are odd.
(2) c - 2d is odd.

The answer key says A but shouldn't it be E? Shouldn't (1) be insufficient? Since C and D could be odd multiples of each other, e.g. C = 9 and D = 3, leaving the possibility of a non-even answer (0).

Compared to the earlier example in the chapter on page 32: "Is the product of all the elements in Set S negative?"

(1) All of the elements in Set S are negative.
(2) There are 5 negative numbers in Set S.

The book says that (2) is insufficient since 0 could be one the of the possible numbers in the set, so shouldn't it follow that Question 10 recognizes the 0 possibility and how it creates an insufficiency?

Or am I missing something here?

[StaceyKoprince]

Hi! Welcome to the forums! Please take a look at the forum guidelines. This folder is for overall study strategy questions; questions about specific content go in the (relevant) Math folder. So your question, for example, would go in the MPrep non-CAT math folder.

I will give you a quick answer though. Actually, technically, I'm going to tell you to look something up—and then you're going to tell me what you find. (I'm making you do this because, if you figure it out yourself with a hint from me, you'll be more likely to remember it in future.)

Flip your NP guide to page 29. What does it say about 0 on this page?
(Note: If you have access to our Foundations of Math strategy guide, you can find similar material on page 16. Same question—what does it say about 0 on this page?)

If you find it, tell me how it applies to the question that you asked. If you don't find it, tell me and I'll give you another hint.