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
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
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)
$\displaystyle x^2 + xy/x$
simplify this first
$\displaystyle x \times x + y$
Now $\displaystyle x \times x$ is a whoole number (rule 3)
and $\displaystyle y$ 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