The positive integer n is divisible by

Allan Carlo Ramos

So in this video... if you can make sure that the inequality are positive numbers -- it is safe to square both sides.?

6 > 5
6^5 > 5^5

5 < 6
5^5 < 6^5

How about negative numbers? are there rules for squaring them? Do we flip the inequality sign?

(-5) > (-6)
(-5) ^ 5 _____ (-6) ^ 5

Could someone give me some tips on this inequality sign flipping? ^_^

Feb 12, 2016 • Reply

Cydney Seigerman, Magoosh Tutor

Hi Allan :)

Good question! There are a couple ways to consider these types of inequalities. One way is to remember that when a negative number is raised to an even power, the final value will be positive. In that case, we can compare the absolute values of the original number. For example,

(-5)^2 ? (-6)^2
|(-5)| ? |(-6)|
5 < 6

Therefore: (-5)^2 < (-6)^2

which we can see is true if we square each base:

(-5)^2 = 25
(-6)^2 = 36
25 < 36

On the other hand, when we have a negative number raised to an odd power, the answer will be negative. In those cases, we want to compare the original base and not the absolute value. For example,

(-5)^5 ? (-6)^5
(-5) > (-6)

Therefore: (-5)^5 > (-6)^5

Again, we can see this is true by finding the actual values of the two expressions:

(-5)^5 = -3125
(-6)^5 = -7776
-3125 > -7776

I hope this helps :)

Feb 15, 2016 • Reply

Allan Carlo Ramos

I'll try to study this more.

But, it is tricky for multiplication and divisions / squaring / getting square roots, I believe.

If you have more resources on inequalities strategies. Please don't hesitate to share.

Mar 30, 2016 • Reply

Cydney Seigerman, Magoosh Tutor

Hi Allan :)

For more strategies to approach questions on inequalities and other concepts that will be tested on the quant section, I'd recommend checking out the Math sections of both our GMAT and GRE blogs :) Here are a couple of blog posts to get you started:

* http://magoosh.com/gre/2012/gre-math-inequalities/
* http://magoosh.com/gmat/2013/gmat-quant-arithmetic-with-inequalities/
*http://magoosh.com/gmat/2012/gmat-quadratic-inequalities/

Hope this helps! Happy studying :D

Apr 15, 2016 • Reply