Given x+y=a+b, is x> y ? x, y, a, b are real numbers

[Guest]

1) x>a
2) y<b

Source Gmat Guru 2. OA E)

Don't know how to attack this type of problem. :?

[JonathanSchneider]

There are two ways of going about this. The first is to substitute. This requires a bit of flexibility. Here's how I would do it:

First, write out the given equation:
x + y = a + b
Next, use the info from statement 1 to substitute:
(greater than a) + y = a + b
Now solve for y:
y = a + b - (greater than a)
y = b + a - (greater than a)
y = less than b
y < b

Now, notice that this is the same as Statement 2. In fact, if you were to start with statement 2 instead, you'd solve to get x > a, what you're given in statement 1. Why? Because the two things must go together.

Now, the easier way to solve this question is to get an understanding of what the info means.

The given equation tells us that the sum of two variables is equal to the sum of two other variables. We have no idea which variable is larger on either side, however.
We are next told (in the separate statements) that a variable on one side is larger, or smaller, than a variable on the other side. Well, this can only mean that in order to equal the same sum, the other variable must account for that difference. In other words, if x<a then y>b, etc. But do we have any idea which variable, x or y, is larger? No.

Again, a Number Properties question, in a way, with some algebra/inequalities stuff thrown in.

[Guest]

Awesome Jonhatan! Tks!!!!!!!!!!

[JonathanSchneider]

: )