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## Comment on

Exponential Growth## Hi - regarding the below

GMAT practice question (difficulty level: 500 to 650) - Math Revolution

Which of the following is closest to (-3/4)^199？

A. -1

B. -1/2

C. 0

D. 1

E. 2

You guys say the OA is C... I understand that as the fraction's exponent increases, the magnitude will decrease and continue approaching zero. But given that the exponent is odd shouldn't the answer be B?

## You're right in that the odd

You're right in that the odd exponent means (-3/4)^199 equals some negative number. However that negative number is very close to 0.

Using a scientific calculator (which isn't provided on test day) we can calculate this.

We get: (-3/4)^199 ≈ -0.000000000000000000000000137

As you can see, this number if a lot closer to 0 than it is to -1/2

## Question link: https://www

Hi Brent,

How can a question have 2 correct answer choices? Here A and E both are logically correct.

## That question on BTG is

That question on BTG is poorly transcribed. I have changed the link to go here: https://gmatclub.com/forum/if-x-0-888-y-0-888-1-2-and-z-0-888-2-then-whi...

In the GMAT Club post, the answer choices are correctly transcribed.

Cheers,

Brent

## Ques.) X*Y = positive number?

Statement 1.) X^2 > 0 → it means a.) Anything greater than 0 is +ive value. b.) it could be possible that X = -ive value but becomes +ive value when squared. Therefore, Insufficient.

Statement 2.) |X| > 0 → means X = +ive value when inside |Modulus| [Like when X = +ive value when squared] . X without Modulus could be a -ive value. Since X exists in question’s equation without Modulus. Therefore, we can’t say X = +ive with certainty.

If X^2 or |X| is given we cannot say it with certainty whether their value is Positive or Negative.

Pls correct me If I’m wrong anywhere

## In the future please include

In the future please include a link to the question.

Your reasoning is perfectly valid.

If we know that x² > 0 and |x| > 0, there's no way to determine whether x is positive or negative.

For example, if x = 1, then it's true that x² > 0 and |x| > 0.

Likewise, if x = -1, then it's also true that x² > 0 and |x| > 0.

Aside: If the target question asks "Is xy positive?", then we can quickly see that the statements combined are not sufficient, since we aren't provided any information about y.

## I’d gladly add the link for

But I cooked up this question completely from my doubts.

## Ahhh, good to know!

Ahhh, good to know!

Cheers,

Brent

## Hi Brent,

Could you please help me to understand something?

I dont understand the written rule about Negative bases x<-1.

I understand as follows:

If exponent is even then the value of X^n increases as even exponent increases

If exponent is odd then the value of X^n decreases as add exponent increases.

Is my understanding correct?

## There are four different

There are four different cases (not two case)

These four cases are summarized at the end of the above video. They are as follows:

THE BASE (x) IS POSITIVE

Case i: The base is between 0 and 1

The value of x^n gets closer and closer to zero as n increases.

For example:

(0.1)^1 = 0.1

(0.1)^2 = 0.01

(0.1)^3 = 0.001

(0.1)^4 = 0.0001

etc

Case ii: The base is greater than 1

The value of x^n increases as n increases.

For example:

3^1 = 3

3^2 = 9

3^3 = 27

3^4 = 81

etc

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

THE BASE (x) IS NEGATIVE

Case iii: The base is between -1 and 0

The value of x^n OSCILLATES between positive and negative, and the MAGNITUDE of x^n gets closer and closer to zero as n increases.

For example:

(-0.1)^1 = -0.1

(-0.1)^2 = 0.01

(-0.1)^3 = -0.001

(-0.1)^4 = 0.0001

(-0.1)^5 = -0.00001

(-0.1)^6 = 0.000001

etc

Case iv: The base is less than -1

The value of x^n OSCILLATES between positive and negative, and the MAGNITUDE of x^n gets bigger as n increases.

For example:

(-2)^1 = -2

(-2)^2 = 4

(-2)^3 = -8

(-2)^4 = 16

(-2)^5 = -32

(-2)^6 = 64

etc

## Hi Brent,

Thank you for the reply. I have confusion with the negative base only.

Case iii: The base is between -1 and 0. The value of x^n will get closer to zero regardless if the exponent is even or odd?

Case iv: The base is less than -1. The value of x^n will get bigger if the exponent is even but if the exponent is odd the value is getting smaller. Is it correct? Ex. (-2)^1 = -2 and (-2)^3 = -8 in which -2 > -8, so I concluded that when N is odd the magnitude of x^n is getting smaller.

## Case iii: The base is between

Case iii: The base is between -1 and 0

You're right; I should have said: if the base is between -1 and 0, then the value of x^n OSCILLATES between positive and negative, and x^n gets closer to zero as the value of n increases.

Case iv: The base is less than -1

Magnitude refers to a number's DISTANCE from zero on the number line.

So, the MAGNITUDE of -10 is greater than the MAGNITUDE of 3.

So, the value of x^n OSCILLATES between positive and negative, and the MAGNITUDE of x^n gets bigger as n increases.

## that 650-800 I got it right,

## Question link: https:/

Question link: https://gmatclub.com/forum/is-x-y-1-z-2-y-2-x-z-235918.html

Nice work!

In some cases, you have to rely on a gut feeling about whether a statement is sufficient or not.