Problem Solving

I just took my first diagnostic, so this may be a basic question.

One IR problem was:

"For all real values of x, the function f(x) has the form: f(x) = (x^2 - 4) ^-1. Select one value for v and one value for w that fulfills the condition that f(v) = w." Then it listed the options.

I was able to determine that if x=0, the f(x) = -1/4. However, in the answer choices, the correct answer is v = 0 and w = -1/4.

In these types of problems, am I supposed to sub in f(v) for f(x) and f(w) for (x^2 - 4)^-1? That's the only way to get those answers, but I'm confused on if this is something I should just be doing all the time throughout the GMAT.

Thanks in advance!

bml1105 wrote:I just took my first diagnostic, so this may be a basic question.

One IR problem was:

"For all real values of x, the function f(x) has the form: f(x) = (x^2 - 4) ^-1. Select one value for v and one value for w that fulfills the condition that f(v) = w." Then it listed the options.

I was able to determine that if x=0, the f(x) = -1/4. However, in the answer choices, the correct answer is v = 0 and w = -1/4.

In these types of problems, am I supposed to sub in f(v) for f(x) and f(w) for (x^2 - 4)^-1? That's the only way to get those answers, but I'm confused on if this is something I should just be doing all the time throughout the GMAT.

Thanks in advance!

Hi!

The most effective (and sometimes only) way to approach Two-part Analysis questions in IR is backsolving: using the choices to generate the matching pair of answers.

There's an infinite number of solutions for the problem, which is why you can't "front-solve" them. Instead of even trying to do so, take a quick look to see if you can eliminate any non-sensical choices, then backsolve the easier column and look for a match in the other.

In this particular question, you'd definitely want to plug in the value for v, since then you can just substitute into the function and see what value it would give you for w. As soon as you find a matching pair, you're finished!

Looking at the correct choices:

if v=0, then:

f(v) = f(0) = (0-4)^-1 = (-4)^1 = -(1/4)

Since f(v) = w, that means that when v=0, w=-(1/4). You always sub in for exactly where the variable appears in the equation.

Let me know if that clears things up!

Stuart

(As an aside, if a mod would move this thread to the IR section of the board, that would be great!)