Lesson: Guessing Strategically

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At 2:11 you say that the correct answer is C. But why? When using the table-method I can see that x has to be at least 4. And if x would be -4, you cannot solve the equitation. So I think that the answer is B. What am I doing wrong?
gmat-admin's picture

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^3-9x>0 or x*(x^2-3^2)>0
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!
gmat-admin's picture

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 was able to understand the reasoning behind the correct choice (c). My comments were just to highlight a situation where someone could mark (E) as the answer.
gmat-admin's picture

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

What is number line? can you please elaborate?
gmat-admin's picture

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.
gmat-admin's picture

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 you so much Brent :)
gmat-admin's picture

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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