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## Comment on

Guessing Strategically## At 2:11 you say that the

## For statement 2, consider

For statement 2, consider these two cases:

Case a: x = -1. Notice that this satisfies the given inequality. Here, x < 3

Case b: x = 10. Notice that this satisfies the given inequality. Here, x > 3

So, statement 1 alone is not sufficient.

## Thank you!

## Solving statement 2: we get x

x(x-3)(x+3)>0 if we consider x=1, we will get a negative value, and if consider x=3 than we will get zero, only if we consider a value above 3 we will satisfy the second statement. The tricky part is when u combime statements for values of x=1,2 from statememt 1 you get negative values for statement 2 and end up marking option E as the answer. In order to avoid such mistakes using a number line can be one of the option. Great queation cheers!

## You're referring to the

You're referring to the question that starts at 1:30.

Just to be clear, the correct answer for this question is C (I wasn't sure if you were suggesting that the answer is actually E)

## Thanks for the response. I

## I figured so. Yes, a good

I figured so. Yes, a good point and great advice about the number line.

## What is number line? can you

## gary391 is referring how we

gary391 is referring how we can use a number line to help us solve higher-order inequalities.

This video (starting at 0:31) shows how this technique works: https://www.gmatprepnow.com/module/gmat-algebra-and-equation-solving/vid...

## Hi Brent,

What is the best way to solve the question that starts at 1.30? I plugged in values for x in statement 2 but it took me more than 2 min to solve it. Is there a way to solve it algebraically without testing values for x? What is the difficulty level of the question?

Thanks for a quick response to my previous doubts as well.

## Here's an algebraic solution

Here's an algebraic solution to the inequality in statement 2:

First, we'll solve the EQUATION: sqrt(x³ - 9x + 4) = 2

Square both sides to get: x^3 - 9x + 4 = 4

Subtract 4 from both sides to get: x^3 - 9x = 0

Factor: x(x² - 9) = 0

Factor more: x(x+3)(x-3) = 0

So, x = 0, 3 and -3 [for the EQUATION: sqrt(x³ - 9x + 4) = 2]

These values (0, 3 and -3) divide the number line into 4 REGIONS

REGION 1: x < -3

REGION 2: -3 < x < 0

REGION 3: 0 < x < 3

REGION 4: x > 3

-------------------------------------------------------------------

If x is in REGION 1, then it is NOT the case that sqrt(x³ - 9x + 4) > 2 (try replacing x with any value less than -3 and see what happens)

So, x is NOT in REGION 1

---------------------------------------------------------------------

If x is in REGION 2, then it IS the case that sqrt(x³ - 9x + 4) > 2

So, x COULD be in REGION 2

In other words, it COULD be the case that -3 < x < 0

---------------------------------------------------------------------

If x is in REGION 3, then it is NOT the case that sqrt(x³ - 9x + 4) > 2

So, x is NOT in REGION 3

---------------------------------------------------------------------

If x is in REGION 4, then it IS the case that sqrt(x³ - 9x + 4) > 2

So, x COULD be in REGION 4

In other words, it COULD be the case that x > 3

---------------------------------------------------------------------

STATEMENTS 1 & 2 COMBINED

Statement 2 tells us that EITHER -3 < x < 0 OR 3 > x

Statement 1 tells us that x > 0, which means we can RULE OUT the possibility that -3 < x < 0

So, it MUST BE the case that x > 3

Answer: C

Does that help?

Cheers,

Brent

## Yes, that helps a lot! Thank

## By the way, here's the video

By the way, here's the video on solving quadratic inequalities: https://www.gmatprepnow.com/module/gmat-algebra-and-equation-solving/vid...

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