Data Sufficiency

vinni.k wrote:What is the value of x?

(1) 310x + 562y = 909
(2) 951x - 626y = 323

Here's another way to look at it.....
(1) 310x + 562y = 909
We can think of this as the equation of a line.
The x- and y-coordinates of all points on the line will satisfy the equation 310x + 562y = 909
Since there are infinitely many points on the line, there are infinitely many possible values of x
INSUFFICIENT

(2) 951x - 626y = 323
If we think of this as the equation of a line, we can also draw the same conclusion that statement 2 is INSUFFICIENT

(1 & 2 combined)
There are two possible cases to consider:
case a) The two equations represent the SAME line.
In this case, there are still infinitely many points (x, y) that will satisfy both equations, in which case the combined statements are not sufficient.

case b) The two equations represent DIFFERENT lines.
In this case, the two lines will intersect at exactly 1 point, which means there will only one pair of values (x, y) that satisfy both equations, in which case the combined statements are sufficient.

So, which is it?
Do the two equations represent the same line or different lines?
To find out, let's examine the slope of each line by rewriting the equations in slope y-intercept form.

(1) 310x + 562y = 909
562y = - 310x + 909
y = (-310/562)x + 909/562

(2) 951x - 626y = 323
951x = 323 + 626y
951x - 323 = 626y
(951/626)x - 323/626 = y
or... y = (951/626)x - 323/626

So, the slope of the 1st line is -310/562, and the slope of the 2nd line is 951/626
Since the slopes are different (one is positive and one is negative), the two equations CANNOT represent the same line.
As such, the two lines must intersect at ONE point.
So, IF we were to solve the system, we'd find exactly one solution.

This means the combined solutions must be SUFFICIENT.

Does that help?

Cheers,
Brent