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## Comment on

Negative Exponents## Hi Brent

If x is an integer, is x|x|<2^x?

(1)x<0

(2)x=-10

Pls explain i couldn't understand how to substitute values for |x| should i take -ve or + ve

## In both statements you are

In both statements you are told that x is negative. So, if you're going to plug in (test) values of x, you must use negative values.

The key thing to recognize here is that 2^x IS POSITIVE for ALL values of x (positive or negative)

For example, if x = 5, then 2^x = 2^5 = 32

And if x = -3, then 2^x = 2^(-3) = 1/8

(1) If x < 0, then x is NEGATIVE

So, we get: (NEGATIVE)(|NEGATIVE|) < 2^NEGATIVE

Evaluate to get: (NEGATIVE)(POSITIVE) < POSITIVE

Simplify: NEGATIVE < POSITIVE

Perfect!

2) Same process here as for statement 1.

Answer: D

Here's a thread discussing this question at greater length: https://gmatclub.com/forum/if-x-is-an-integer-is-x-x-2-x-144342.html

## Hi Brent. Can you walk

https://gmatclub.com/forum/if-5n-4n-x-0-788-then-x-n-259657.html

And why/how can you flip each fraction?

Your answer to the question:

Given: 5n/(4n - x) = (0.788)^(-1)

Rewrite as: 5n/(4n - x) = 1/0.788

Flip each fraction: (4n-x)/5n = 0.788

Apply above property: 4n/5n - x/5n = 0.788

Simplify: 4/5 - x/5n = 0.788

Simplify: 0.8 - x/5n = 0.788

So: x/5n = 0.012

Multiply both sides by 5 to get: x/n = 0.06

Rewrite as fraction: x/n = 6/100 = 3/50

## Question link: https:/

Question link: https://gmatclub.com/forum/if-5n-4n-x-0-788-then-x-n-259657.html

The main property here is as follows:

If wxyz ≠ 0 and w/x = y/z, then it must also be true that: x/w = z/y

For example, since 4/8 = 1/2, it must also be true that 8/4 = 2/1

Likewise, since 9/6 = 3/2, it must also be true that 6/9 = 2/3

So, when I got to this point: 5n/(4n - x) = 1/0.788...

...I could see that flipping both sides was going to make it much easier to solve the equation.

Does that help?

Cheers,

Brent

## Hi Brent,

Could you please show how to solve the question by using just variables?

https://gmatclub.com/forum/x-1-y-1-xy-1-x-y-316172.html

How did you know that x can be 2 and y can be 4?

## Since there are no

Since there are no restrictions on the values of x and y, we can assign any values we wish.

I chose x = 2 and y = 4, because they're easy numbers to work with.

I could have also chosen to use x = 6.215 and y = -0.004213, and the algebraic expression would still evaluate to be -1 (but the calculations would be a lot harder to complete.)

https://gmatclub.com/forum/x-1-y-1-xy-1-x-y-316172.html#p2546544

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