Hi didieravoaka,
You should have posted this in the DS Forum, but I'll still help you walk through it.
We're told that a square has an area of 9, so we know its sides all equal 3. We're told two opposite sides of the square are lengthened. We're asked how much they're lengthened.
1) The diagonal of the resulting rectangle is 5.
With this Fact, we'll have a rectangle with a side of 3, a side of X and a diagonal of 5. Since the diagonal 'cuts' the rectangle into two right triangles, we can determine the value of X - we'll have a 3/4/5 right triangle, so X MUST be 4 and the two side lengths were each lengthened by 1.
Fact 1 is SUFFICIENT
2) The resulting rectangle can be cut into three rectangles of equal size.
It's important to keep in mind that this Fact does NOT state that the dimensions of those 3 rectangles have to be integers nor does it tell us how we're supposed to 'cut' the rectangle (lengthwise or widthwise).
For example, draw a rectangle that is 3x4 and another that is 3x6. Now cut each of those rectangles into 3 smaller, equal rectangles. You'll see that each rectangle can be cut in two possible ways and that there's more than one possible end result, so the increase in side lengths can be any value.
Fact 2 is INSUFFICIENT
Final Answer: A
GMAT assassins aren't born, they're made,
Rich
