GMATPrep - Data Sufficiency Problems

This article walks through solving a DS problem: https://www.manhattanprep.com/gmat/blog ... ss-part-1/

A more detailed overview is also at the beginning of each of the MPrep Quant Strategy Guides.

I'll give a very quick outline here, and run through your second problem:

1. Understand the question. This might mean simplifying the math, translating the question into plain English, etc.

In the x-y plane, does y=3x+2 contain (r,s)?

You can tell that a line contains a point, if you can plug the coordinates of the point into the equation of the line, and get a correct result. So, what this is really asking is the following:

Does s = 3r + 2?

Also, note that this is a yes/no question. To answer it, you don't need to know the exact values of s and r. You only need to know whether s = 3r + 2 or not.

2. Pick a statement and understand it.

Statement 1: (3r+2-s)(4r+9-s)=0

This looks like a product of two expressions. I know that if the product of two expressions equals 0, then one or both of those expressions has to equal 0. So, what this is really telling me, is:

Either 3r + 2 - s = 0, OR 4r + 9 - s = 0, or both.

Simplify the math a bit:

Either s = 3r + 2, or s = 4r + 9.

3. Figure out whether that statement gives you enough info to answer the question. Eliminate wrong answers.

One possibility is that s = 3r + 2; in that case, the answer to the question would be 'yes'. But, there's another possibility, that s = 4r + 9. In that case, I don't know whether or not s = 3r + 2, so I couldn't answer the question. Since I'm not sure that I can answer the question, it's insufficient. So, I eliminate A and D (because 1 is insufficient.)

4. Repeat with the other statement:

(4r-6-s)(3r+2-s)=0

Either s = 4r + 6, or s = 3r + 2

But, I don't know which. So, insufficient as well. Eliminate B.

5. If necessary, put the two statements together.

I now know two things. First, I know that s equals either 3r + 2, or 4r + 9. Second, I know that s equals either 3r + 2, or 4r + 6.

The only possibility that matches both of these is that s equals 3r + 2. If s didn't equal 3r + 2, then it would have to equal 4r + 9 (to make the first statement true), but it would also have to equal 4r + 6 (to make the second statement true.) Since those can't both be true, that's impossible. So, the only possibility, given that both statements have to be true at the same time, is that s = 3r + 2. Since you know that, you know the answer to the question is 'yes', so the statements together are sufficient and the answer is C.