Question 23

This appears to be a straight one variable equation simply crying out to be solved. Those of you who see the GMAT as a math test see this question and immediately hear:

Solve Me! Solve Me!

As always we can use our mathematical solution. But, our "Multiple Choice Is Our Friend Solution" will work much better here.

As always let's begin by reading the question carefully. It is important to note specifically that "x" is a positive number!

Mathematical Solution

To solve for x is to isolate x by itself. To isolate x we must first isolate the term in which x appears. Here we go.

1. We start with 1/x - x = 3/2

2. Let's multiply the whole thing through by x:

x/x - x*x = 3x/2

1 - x*x = 3x/2

3. Now let's multiply through by 2:

2 - 2x*x = 3x

4. What we do to one side of the equation we do to the other:

I.e. 2x*x + 3x - 2 = 0

5. To solve now involves taking the roots of a quadratic equation. As only a small group of you remember you solve a quadratic equation by taking the roots as follows:

If (ax*x + bx - c = 0) then

x = [-b +/- the square root of b*b - 4ac]/2a.

To substitute, this means x = [-3 +/- the square root of 9 - (4(2)(-2))]/4.

To continue: x = [-3 +/- root 25]/4

In terms of the math we now have two possible values for x:

1. x = [-3 + 5]/4 = 2/4 = 1/2 or

2. x = [-3 - 5]/4 = -8/4 = -2.

But, the question makes it clear that x is a positive number. Hence, 1/2 or choice (A) is the answer. Aren't you happy to see the mathematical solution? It is completely useless under the time constraints.

Comment: This question clearly underscores the importance of remembering that "Multiple Choice Is Your Friend."

Multiple Choice Is Your Friend Solution

Alternative 1 - Let's Range The Answer Choices

Let's let some common sense prevail.

First, If (x is a positive number and

1/(positive number) - positive number = 3/2) then

3/2 + positive number = 1/positive number).

Therefore, 1/(positive number) is greater than 3/2.

Second, since 1/(positive number) is greater than 0 the "positive number" must be less than 1.

Third, let's look at our choices. (B), (C), (D) and (E) can be eliminated because they are not less than 1. This leaves us with (A). Let's just take it!

(A) is the correct answer.

Alternative 2 - Let's Backsolve

Backsolving is a process where you simply "plug in" the answer choices until you find one that works. In this particular case, it is obvious that 1/2 is the only answer choice that satisfies the equation given. In this way you can recognize that it is correct even if have no idea how to solve mathematically.

In general, I advocate "Multiple Choice Is Your Friend" approaches over any mathematical approach!