1. ## I don't really even understand what they are asking.

How do I find...
If x and y are nonzero integers, which of the following must be an integer?

A) x+ y/ x

B) x+y^2/ x

C) x^2 + xy/ x

D) x^2 + y^2/ x

2. Originally Posted by dnntau
How do I find...
If x and y are nonzero integers, which of the following must be an integer?

A) x+ y/ x

B) x+y^2/ x

C) x^2 + xy/ x

D) x^2 + y^2/ x
Dividing by an integer will not guarantee an integer hence you're looking for an expression where you can factor out x in the numerator

3. ## Plug in Numbers

A good idea is to plug in numbers for x and y. Pick nonzero integers as the problem says. For example, x = 3 and y = 2. Plug these values in for A, B, C, and D. See which one will give you an integer!

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How do I find...
If x and y are nonzero integers, which of the following must be an integer?

A) x+ y/ x

B) x+y^2/ x

C) x^2 + xy/ x

D) x^2 + y^2/ x

4. For these options please use brackets, your post is very confusing, for example is this

Originally Posted by dnntau

A) x+ y/ x
$\frac{x+ y}{ x}$ or $x+ \frac{y}{ x}$

Also show some working or ideas. It is not our job to do the whole problem for you. It is a "Help" forum.

5. A nonzero integer is a whole number other than zero (1,2,3,4,5.....,-1,-2,-3,-4,-5......).

The question gives you two whole numbers (x,y). It wants you to work out if the formulae given will also be whole numbers or not.

Some basic rules to remember are:
Rule1: A whole number plus a whole number is a whole number
Rule2: A whole number minus a whole number is a whole number
Rule3: A whole number times a whole number is a whole number

Rule4: A whole number divided by a whole number is a not always whole number

I'll do two of the options for you, see if you can do the other two yourself:

(A)
x + (y/x)

y/x is not necessarily a whole number (rule 4)

So we have (whole number) + (maybe not a whole number)
which is not always a whole number

(C)
$x^2 + xy/x$
simplify this first
$x \times x + y$

Now $x \times x$ is a whoole number (rule 3)
and $y$ is a whole number (from the question)

So we have (whole number) + (whole number) which gives a whole number

Although you have the answer (C), check you can show B & D are not the answer

6. Thanks.