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.

Guest · Posted: Mon Jul 23, 2007 9:26 pm Post subject:

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

mayonnai5e · Posted: Thu Jul 26, 2007 3:49 am Post subject:

ricaototti · Posted: Thu Aug 28, 2008 10:17 pm Post subject: but y cant be = 0 in A

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

[quote="mayonnai5e"](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). [quote]

PLEASE EXPLAIN.....

mayonnai5e · Posted: Tue Sep 02, 2008 3:25 pm Post subject:

(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 · Posted: Thu Sep 04, 2008 6:24 am Post subject:

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.