GMAT Quant: Algebra – Absolute Value

Algebra: Absolute Value

We all have studied absolute value in our schools but with time it became a bit complex. Down the line what we basically learnt in absolute value is:

|positive| = positive

As well as,

|negative| = positive

But, GMAT is never going to ask you such an easy question.

In GMAT Exam, you can expect the following types of questions:

  •  |3x + 8| = 42

So, 3x + 8 = 42 or, 3x + 8 = -42

3x = 34        or, 3x = -50

x = 11.333    or,  x = -16.666

Let’s solve some more complex questions and see what GMAT actually tests.

1. Find the value of x in:

|x + 2| + |x – 3| = |2x + 3|

  1. -5
  2. -2
  3. 1
  4. 4
  5. 7

Solution:

If we suddenly look at this question, we won’t have any idea of solving it.

So, let’s solve it step-by-step.

  • There is a variable in this question.
  • When a variable is here, we can simply plug-in any number at its place.
  • Value of x is one of the given options. So, let’s substitute these options and check which one fulfills the constraints.

|-5 + 2| + |-5 – 3| = |2 (-5) + 3|

Not equal.

|-2 – 2| + |-2 + 3| = |2 (-2) + 3|

Not equal

|1 + 2| + |1 – 3| = |21+3|

Equal

So, C is the answer.

Tip: Solving a problem in traditional way can eat-up a lot of your time. So, try different approaches.

  1. If m + |m| = 0, then m is,
  2. positive
  3. 0
  4. Negative

Let’s check each possibility,

Case1. m is positive.

|m| = m

So, m + |m| = 0

m + m = 0

So this case is not possible.

Case2. m is 0

So, |m| = 0

0 + 0 = 0

So this is a possible case

Case3. m is negative.

|m| = -m

|m| + m = 0

-m + m = 0

So, m is either 0 or negative.

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