inequalities

[beater]

If xy > 0, does (x - 1) (y-1) = 1?

1. x + Y = xy
2. x = y

what does xy>0..mean?

[pepeprepa]

What does xy>0..mean?

"xy" means x and y are multiplied. If we want to totally write "a multiplied by b" which is the same as "b multiplied by a" we write: a x b or a * b. That's a multiplication.
xy>0 means that the result is positive. For example, if x=2 and y=3 we have: 2*3=6>0

[4meonly]

Answer is D?

[mim3]

I'm not postiive on this one, but I think it's A here.

1. x+y=xy
The only way this works is if x and y both equal 2 or 0. In both cases, the stem is proven. Sufficient

2. x=y
Just picking numbers and plugging into the stem, say x, y= 3 (3-1)(3-1) does not = 1 whereas (2-1)(2-1) = 1. Insufficient.

So I think it's A. What's the OA?

[Fab]

I would say A since,

For (x-1)(y-1)=1, there are only 2 possibilities:
1. x=0 y=0
2. x=2 y=2

In both cases x+y=xy

Option B could be anything...3=3, 4=4, 5=5....and so on..

[smithpa2]

One thing to consider is that xy>0, so both x and y are either positive or negative, but can't equal 0.

IMO A, b/c 2 is the only number that satisfies the criterion.

[4meonly]

(x-1)(y-1)=1 ?
makes the questionin such way: xy=x+y ?


(1)
xy=x+y
the same as we found
SUFF

(2)
x=y
from the main statement xy=x+y we have
yy=2y
y^2=2y
y=2 so x=2
(2-1)(2-1)=1
SUFF

Answer D

If I am wrong, pls somebody correct me

[schumi_gmat]

Ans is A

The second condition is possible only of x=y=2 but not true for any other number

Hence A is correct

[mim3]

[quote="4meonly"](x-1)(y-1)=1 ?
makes the questionin such way: xy=x+y ?


(1)
xy=x+y
the same as we found
SUFF

(2)
x=y
from the main statement xy=x+y we have
yy=2y
y^2=2y
y=2 so x=2
(2-1)(2-1)=1
SUFF

Answer D

If I am wrong, pls somebody correct me[/quote]

The stem was xy > 0, not xy=x+y, that was statement one.

[4meonly]

(x-1)(y-1)=1 ?
xy-x-y+1=1
xy=1-1+x+y
xy=x+y

So, the question can be rephrased in
Does xy=x+y ?

(1) Directly gives you the answer

(2) x=y
sustitute yy=y+y
y^2 = 2y
y = 2
2*2 = 2+2 or (2-1)(2-1)=1
According to xy>0? 2*2 > 0

Answer D

[beater]

OA - A. Thanks!

[Ian Stewart]

(x-1)(y-1)=1 ?
xy-x-y+1=1
xy=1-1+x+y
xy=x+y

So, the question can be rephrased in
Does xy=x+y ?

(1) Directly gives you the answer

(2) x=y
sustitute yy=y+y
y^2 = 2y
y = 2
2*2 = 2+2 or (2-1)(2-1)=1
According to xy>0? 2*2 > 0

Answer D

You are doing the math correctly, but you're answering a different question from the one that's being asked here. The question is:

Is (x-1)(y-1) = 1 ?

As you've done, you can rephrase the question:

Is xy = x + y ?

Still, that's the question. It's not a fact. Do not assume the answer to the question is 'yes', and use it as if it were a fact. This is crucially important, and it's a common trap people fall into when they first start doing DS questions.

So, you aren't trying to find x or y here; you are trying to decide, from Statement 2, whether xy = x+y must be true. If we know statement 2, we know that x = y, so we need to know whether x*x = x+x, that is whether x^2 = 2x. Well, x could be 2, and then x^2 = 2x, or x could be 3, and x^2 does not equal 2x. So we can't answer the question by only using 2) alone. As demonstrated above, Statement 1) is sufficient.

[sumithshah]

I agree with your explanation IAN but if an equation is simplified and found to be true, shouldlnt the un simplified equation be true also?

[Ian Stewart]

I agree with your explanation IAN but if an equation is simplified and found to be true, shouldlnt the un simplified equation be true also?

Yes, but I'm afraid I don't see the relevance of that to this question. We can rewrite or simplify the equation in the question all we want; using Statement 2 alone, we can't prove that it's true.