Anonymous wrote:If 0<x<y, what is the value of (x+y)^2 / (x-y)^2
(1) x^2 + y^2 = 3xy
(2) xy = 3
Answer is A
Thank you ~
you should either (a) memorize the expansions of (x + y)^2 and (x - y)^2, or (b) be able to generate those expansions within a few seconds on demand.
therefore, you should
immediately be able to rephrase the given question to "
what is (x^2 + 2xy + y^2) / (x^2 - 2xy + y^2) ?"
note that you don't
have to use the rephrased version once you've generated it; as with all other rephrases, you're free to go back and use the original version of the question.
--
statement (1):
use the expanded (rephrased) version of the fraction.
note that both the top and the bottom of the fraction contain the expression (x^2 + y^2), which, per statement (1), you can extract and replace with the expression 3xy.
therefore,
(
x^2 + 2xy
+ y^2) / (
x^2 - 2xy
+ y^2)
= (
3xy + 2xy) /
3xy - 2xy)
= 5xy / xy
= 5
sufficient.
--
statement (2):
attempt to substitute into the expanded (rephrased) version of the given fraction.
(x^2 +
2xy + y^2) / (x^2 -
2xy + y^2)
= (x^2 +
6 + y^2) / (x^2 -
6 + y^2)
this doesn't simplify further in any obvious (or non-obvious) way.
if you have time remaining, and you want to make sure that the value of this expression really
does vary depending on x and y, then substitute in values accordingly.
just make sure that you obey BOTH conditions: 0 < x < y (from the question prompt) and xy = 3 (from statement 2).
try x = 1, y = 3: (1 + 6 + 9) / (1 - 6 + 9) = 16/4 = 4.
note that,
in conjunction with statement 1, this already guarantees insufficiency, because the fraction
must be able to assume the value 5 (else the two statements would contradict each other). therefore, the fraction could be either 4 or 5; insufficient.
if you're using this statement first, try another set of numbers: x = 1/2, y = 6. that gives (1/4 + 6 + 36) / (1/4 - 6 + 36) = (42 1/4) / (30 1/4), which is most definitely not 4. there's no reason to actually calculate the value, since it's definitely different from the last value calculated (= 4); insufficient.
--
ans = (a)