What is the remainder r when positive integer x is divided by 4?

Only possible remainders are 0, 1, 2, and 3

1) x is odd

Only possible remainders are 1 and 3

9/4 -> Remainder is 1
11/4 -> Remainder is 3
13/4 -> Remainder is 1
15/4 -> Remainder is 3

Insufficient

2) x is a multiple of 3

Multiples of 3 are : 3, 6, 9, 12
Possible remainders are

3/4 -> Remainder is 3
6/4 -> Remainder is 2
9/4 -> Remainder is 1
9/4 -> Remainder is 0

Insufficient

Together: x is odd and x is a multiple of 3

3, 9, 15, 21, 27, 33, 39 etc...

3/4 -> Remainder is 3
9/4 -> Remainder is 1
15/4 -> Remainder is 3
21/4 -> Remainder is 1

Togther: Insufficient

Therefore, answer is E

Hi Topspin!

What a great idea - I think you're onto something here.

Not to publish the recipe to the secret sauce, but my method for writing DS questions is basically this:

Step 1: Hey, I'm feeling bored - guess I'll try a few math problems.

Step 2: Ah, that one was easy - what's next?

Step 3: Wait, what the hell? I was wrong? That can't possibly be true! (*flipping smugly to the answer explanations*) Oh, it's because I assumed x was an integer? $#%^@!

Step 4: Hey, I'm going to write a DS problem using a trick just like that!

It certainly helps me avoid making the same mistake twice.

Remember that DS questions are all about tricking people into making easy, natural, and ultimately fatal assumptions: the test writers are measuring your ability to be skeptical of a seemingly good thing and thus review its implications before accepting it - obviously a pretty crucial skill in the often devious and ruthless world of business!