Is this considered arithmetic or number properties?

[mayonnai5e]

Hello,

Just wondering whether this is categorized as an arithmetic DS problem or number properties?

If x, y are integers, is x = y?
(1) xy = y^2
(2) x^2 = y^2

I've been considering it as number properties since you have to think about the properties of certain numbers that could be used and how they change when squared. The answer, by the way, is C. (1) is insufficient because when y = 2, the answer is yes and when y = 0, the answer is no (since x can be any integer in this case). (2) is insufficient because x can be -2 while y is 2 and the statement still holds true or x = 2 and y = 2 and the statement still holds true. (1) and (2) together are sufficient since y can no longer be 0 with x being any other integer in statement (1) because statement (2) would not hold true.

[mayonnai5e]

Seems like numbers properties to me. Is it important to know how these questions would be labeled?

It's important to me because I am systematically categorizing my mistakes into question types to discover which are the most problematic for me. So mislabeling a question type could skew a particular category to look like a weakness when it actually is not.

[ricaototti]

wait,
shouldnt the answer be A?

Because y can not be 0 in number one. If y = 0 then, xy=y^2 is not possibe since x=y^2/y is impossible.

Can someone please explain it better.

[smclean23]

(1) is insufficient because when y = 2, the answer is yes and when y = 0, the answer is no (since x can be any integer in this case).

PLEASE EXPLAIN.....

[mayonnai5e]

(1) xy = y^2

y = 2: x*2 = 2^2 --> 2x = 4 --> x = 2 so x = y (YES)
y = 0: x*0 = 0^2 --> 0*x = 0 --> so x can be -1, 0, 1, 2, etc because any number times 0 equals 0, which means that x does not have to be equal to y (NO)

Since you can determine two values for y that yield different answers, (1) is INSUFF.

[gmatutor]

You can go around with this question for a while. The study of arithmetic is the study of number properties. So the classification could be done in using either arithmetic or number properties as the category. I would suggest you call this number properties as the OG makes number properties a subcategory of Arithmetic.

[cramya]

Keeping the post current by posting a comment for everyone's benefit...


If x, y are integers, is x = y?
(1) xy = y^2
(2) x^2 = y^2



The key to stmt I is to not divide each side by y but factorize

Stmt I

xy-y^2 = 0

y(x-y) = 0

y-0 or x=y

INSUFF

Stmt II

x^2 = y ^ 2

x= +y or x = -y

INSUFF

Together

X=Y

Looks like a very simple problem but slightly tricky... IMO

Regards,
CR