 # Managing Algebra-based Quantitative Comparison Questions on the GRE Part-II Let us look at a different dimension of the concept that we discussed in Part I.

Example 2A:

x is a real number greater than 5

Quantity A                       Quantity B

1/4x-7                                1/2x+3

Even if we want to plug in numbers for x, it may not be very convenient to do so with the question in its present form. A good idea is to multiply both sides by (4x – 7) (2x + 3)

We get

x is a real number greater than 5

Quantity A                       Quantity B

2x+3                                  4x-7

Use the same process as used in Examples 1A, 1B, and 1C, and you will get the answer (B).

The most important point to note here is that we are able to do this multiplication because we know that (4x – 7)(2x + 3) is always positive as both (4x – 7) and (2x + 3) are always positive.

Let’s look at a variation of this question.

Example 2B: x is a real number greater than 1

Quantity A                       Quantity B

1/4x-7                                1/2x+3

In this case, it will be erroneous to multiply both sides by (4x – 7) (2x + 3) as, although (2x + 3) is always positive, (4x – 7) can be either positive or negative, and, therefore, (4x – 7) (2x + 3) can be either positive or negative!

However, there’s still a way to simplify this to some extent. We can multiply both sides by (2x+3), and we get

x is a real number greater than 1

Quantity A                       Quantity B 2x+3/4x-7                        1

Now it may be a good idea to plug in values for x.

Quantity A                       Quantity B

2x+3/4x-7                        1

Put x = 1.1    5.2/-2.6

Quantity B is greater; cancel out (A) and (C).

Quantity A                       Quantity B

Put x = 2     7/1                 1

Let’s look at another variation of this question.

Example 2C:

x is a real number less than − 5

Quantity A                       Quantity B

1/4x-7                                1/2x+3

Now, we note that both (4x – 7) and (2x + 3) are always negative and, therefore, (4x – 7)(2x + 3) is always positive. We can just multiply both sides by (4x – 7)(2x + 3) and follow the same process.

We get

x is a real number less than − 5

Quantity A                       Quantity B

2x+3                                 4x-7

Use the same process as used in Examples 1A, 1B, and 1C.

This time, however, your answer will be (A) as x is a real number less than − 5

Here is one more variation — this time with a twist!

Example 2D:

x is a real number less than 7 but greater than −3

Quantity A                       Quantity B

1/x-7                                  1/x+3

Hey! Don’t just start putting values for x or start manipulating the expressions algebraically. This time you really don’t have to do anything. You just have to figure out that (x–7) is always negative and (x+3) is always positive. Consequently, your answer is (B). This one is really an easy question. You don’t have to do anything more.

As we say at Manya-The Princeton Review, “Work smarter, not harder. In subsequent parts, we will discuss quant comp questions involving more than one variable. See you: then.

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