Lesson: Exponential Growth

Comment on Exponential Growth

Hi - regarding the below question from
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?
gmat-admin's picture

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

Hi Brent, how would you calculate a number like (1.03)^8 fast on the gmat? I find it difficult to quickly solve compound interest questions due this step.
Thanks,
gmat-admin's picture

The GMAT would never require you to evaluate (1.03)^8

For compound interest questions, there are two possibilities:

1) There will be 2 compoundings, in which case you may be asked to evaluate something like (1.1)^2
Example: https://gmatclub.com/forum/kevin-invested-8-000-for-one-year-at-a-simple...

2) There will be more than 2 compoundings, in which case the answer choices will be expressed as powers.
Example: https://gmatclub.com/forum/if-1-were-invested-at-8-percent-interest-comp...

Cheers,
Brent

thank you.

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