Data Sufficiency

akpareek wrote:If ab=1, what is the value of (axb)(ayb)?

1. ax= by= 2
2. 2xy= 4

Dear akpareek,
I'm happy to help with this.

I will assume that, by say "axb", you simply mean those three variable multiplied together. The GMAT doesn't often use subscripts, but some practice sources us subscripts, and there's no straightforward way to render subscripts in the rtf of these posts. For example, if what you meant was (a-sub-x)*(b), that would be very different. I will assume you don't mean that, and that all the variables are simply multiplied.

We know ab = 1

We can rearrange & regroup multiplication in any order we like (the Commutative and Associative properties of multiplication), so ...

(axb)(ayb) = a*x*b*a*y*b = (a*b)*(a*b)*x*y = xy

That extraordinarily simplifies, because ab = 1. In other words, the prompt question is simply asking for the product of x and y.

Statement #1
ax=2 and by= 2, so multiply those equations ---

2*2 = 4 = (ax)*(by) = (ab)*(xy) = xy

This allows us to find the product of xy, so this statement, alone and by itself, is sufficient.

Statement #2
2xy= 4
xy = 2

This allows us to find the product of xy, so this statement, alone and by itself, is sufficient.

Both statement sufficient --- answer = [spoiler](D)[/spoiler]

Again, this answer depends on whether I am interpreting the font/format issue correctly.

Incidentally, it seems that the two different statements, while both sufficient, lead to two different answers for the value in the prompt question. Real GMAT questions and all high quality GMAT sources keep the standard that both DS statements lead to, or are at least consistent with, the same numerical answer.

Does all this make sense?
Mike