Data Sufficiency

Is x = y?

(1) (x + y) {(1/x) + (1/y)}= 4.

(2) (x – 50)^2 = (y – 50)^2.

1. (x + y) {(1/x) + (1/y)} = [(x + y)^2]/xy = 4. This means that (x + y)^2 = 4xy or that x^2 + y^2 + 2xy = 4xy. Take 4xy on the other side and you get that:
x^2 + y^2 - 2xy = 0
(x - y)^2 = 0
This is true onyl when x - y = 0 or x = y. So 1 is sufficient.

2. (x – 50)^2 = (y – 50)^2 means that you have two cases:
a. x - 50 = y - 50, making x = y
b. x - 50 = -(y - 50), making x <> y.
Since you can't tell between the two, then 2 is insufficient.

So I'd say A

DanaJ wrote:1. (x + y) {(1/x) + (1/y)} = [(x + y)^2]/xy = 4. This means that (x + y)^2 = 4xy or that x^2 + y^2 + 2xy = 4xy. Take 4xy on the other side and you get that:
x^2 + y^2 - 2xy = 0
(x - y)^2 = 0
This is true onyl when x - y = 0 or x = y. So 1 is sufficient.

2. (x – 50)^2 = (y – 50)^2 means that you have two cases:
a. x - 50 = y - 50, making x = y
b. x - 50 = -(y - 50), making x <> y.
Since you can't tell between the two, then 2 is insufficient.

So I'd say A

You are right DanaJ. Will you please explain me the art of hiding any text, by using spoiler?

)

It's not an art... You just use the spoiler function when you post (it's right over there under the title). Don't forget to un-tick the "Disable BBCode in this post" (right under the space where you write).

DanaJ wrote:)

It's not an art... You just use the spoiler function when you post (it's right over there under the title). Don't forget to un-tick the "Disable BBCode in this post" (right under the space where you write).

Thanks DanaJ, but I am still not sure what I am going to do with this. A link wanted me post OAs with my questions, so I am now going to try spoiler for the first time, check it out in my next few posts on "Problem Solving Forum"

sanju09 wrote:

DanaJ wrote:)

It's not an art... You just use the spoiler function when you post (it's right over there under the title). Don't forget to un-tick the "Disable BBCode in this post" (right under the space where you write).

Thanks DanaJ, but I am still not sure what I am going to do with this. A link wanted me post OAs with my questions, so I am now going to try spoiler for the first time, check it out in my next few posts on "Problem Solving Forum"

Sanju,

Thanks for taking effort to post OA..!! I saw your link with spoiler stuff..

I didn't mean that you post OA with question. What I meant is after the discussion you don't followup and post the correct Answer (obviously if there multiple Answers from the different peopel ). You can post it after discussion or follow up.

Anyway, I like your quesitons!! . What is source??
Do yo create them??

i fully agree with the above funda
btw this question is really deceptive
nice one