When the positive integer x is divided by 4,

[griffin.811]

When the positive integer x is divided by 4, is the remainder equal to 3?

(1) When x is divided by 2, the remainder is 1.

(2) x is divisible by 3.

Answer:E

Source: MGMAT CAT#3

For this question, I began by examining statement 1. I tested numbers. My question is does it make sense to test 3? or do I need to assume that x is greater than 4 (based on the question).

I tested 3 and saw that it satisfied statement 1, and there was no remainder. Do I need to test a number that will yield a remainder?

Thanks

[JeffM187]

When X = 3, 7, 11, 15, 19... the remainder will be 1 when you divide 2 into X or 3 when you divide 4 into X.

When X = 5, 9, 13, 17... the remained will be 1 when you divide either 2 or 4 into X.

Since the remainder changes when you divide 4 into certain numbers but 2's remainder remains constant, this means statement 1 is not sufficient.

You can test 3, but you also need to test other numbers.

Hope that's right!

[RonPurewal]

If you divide 3 by 4, the remainder is 3.

If that doesn't make sense, think about making "packs of 4" of some item. (I still have to do this, even though I first learned about remainders 30 years ago.) If you have 3 items, then that's zero packs of 4, with 3 items left over.

For the same reason, dividing N by anything bigger than N (regardless of what N actually is) will leave N as a remainder. Because you make zero "packs", and the whole stock of N items is still left over.

[RonPurewal]

More importantly—the official problems WILL NOT depend on "unusual" cases like this.
If a statement technically applies to the number 3, then, sure, you can test the number 3. But, if you're dealing with an official problem, it will always turn out the same way it'd have turned out if you hadn't considered the "unusual" case.

E.g., in this problem, the answer is E.
If you ignore 3, the answer is ... still E.

Simply put, the GMAT doesn't contain "tricks".
When most people learn about remainders, they don't ever consider the case of dividing a smaller number by a bigger one. So, the GMAT will not contain a problem predicated on such a thing. (Even if some rogue question writer wrote one, it would fail the "experimental" stage.)

[griffin.811]

Thanks, and the 0 packs of 4, with three remaining makes sense. I've just never though of it that way.

[tim]

Let us know if there are any further questions on this one.

[RonPurewal]

Thanks, and the 0 packs of 4, with three remaining makes sense. I've just never though of it that way.

Just remember that cases like this one ^^ aren't going to be essential for this exam anyway.

Basically—If you didn't learn about something when you first learned the concept, then you're not going to need it here.

This test is quite challenging, but it's definitely not "sneaky". Lots of artillery, but no secret weapons.