GMAT Prep Question

Each statement alone is not sufficient as it only gives the value of one variable only.

Considering both statements together.

x < 8/9
y < 1/8

You can add these two to get:
x + y < 8/9 + 1/8 = 73/72
So for certain values of x & y x + y can be greater than 1.

Consider x = 7/9 & y = 1/9. This satisfies both the criteria and the sum (8/9) is < 1.
If x = 63.5/72 & y = 8.5/72. This satisfies the criteria but the sum = 72/72 = 1.

Hence both together are not sufficient.

Neither statement 1 alone nor statement 2 alone is sufficient, because you need to know the values of both of those variables to answer the question. Now try putting them together. The first step is to give them a common denominator; we'll use 72. If x is less that 8/9, then it is less than 64/72. [8/9 * 8/8 = 64/72]. If x is less than 1/8, it's less than 9/72 [1/8 * 9/9 = 9/72]. If we add the maximum values for x and y together, we have 63/72 + 8/72 = 71/72, and that is indeed less than 1. However, try using 720 for your common denominator, instead of 72. Then your maximum x value is 639/720, and your maximum y value is 89/720. Add those together and you get 728/720, which is more than one. So even together, the inequalities presented for x and y aren't sufficient.

Statement 1 is insufficient because it tells us nothing about y.

Statement 2 is insufficient because it tells us nothing about x.

Putting the two statements together, we have what I call a boundary question. In a boundary question, a value is given an upper or lower limit that it can't exceed. (Kind of like in Monopoly when you're told you can't pass "Go".) In this case, x and y are each given an upper limit: x < 8/9 and y < 1/8. A helpful technique for boundary questions:

Set the value equal to the boundary in order to see more clearly how the problem is restricted.

So let's say x = 8/9 and y = 1/8. Then x + y = 8/9 + 1/8 = 64/72 + 9/72 = 73/72.

This gives us the upper limit for x+y. Since x can't really equal 8/9 and y can't really equal 1/8, we know that x+y < 73/72.

This means that x+y can be ANYTHING smaller than 73/72:

If x+y = 1/72, is x+y < 1? Yes.
If x+y = 72/72 = 1, is x+y < 1? No.

Since the answer can be both yes and no, the two statements together are INSUFFICIENT.

The correct answer is E.

Thanks guys for your prompt help
p.s. princeton review technique is most "leveragable"