SAT Mean, Median, and Mode

Probability Level 1

What is the average (arithmetic mean) of $3^{15}, 3^{20},$ and $3^{25}?$

(A) $\ \ 20$
(B) $\ \ 60$
(C) $\ \ 3^{20}$
(D) $\ \ 3^{14} + 3^{19} + 3^{24}$
(E) $\ \ 3^{16} + 3^{21} + 3^{26}$

A B C D E

2 solutions

Tatiana Georgieva Staff
Mar 18, 2015

Correct Answer: D

Solution:

Tip: The average of $n$ numbers is the sum of the numbers divided by $n.$
Tip: Know the Rules of Exponents.

$\frac{3^{15} + 3^{20} + 3^{25}}{3} = \frac{3^{15}}{3} + \frac{3^{20}}{3} + \frac{3^{25}}{3} = 3^{14} + 3^{19} + 3^{24},$

where we applied the exponent rule $\frac{a^{m}}{a^{n}}=a^{m-n}.$

Incorrect Choices:

(A)
This is the average of the exponents, not of the given numbers.

(B)
This is the sum of the exponents, not the average of the three numbers in the prompt.

(C)
Here, 3 is brought to a power equal to the average of the three exponents.

(E)
Here, instead of dividing the sum of the three numbers by three, the sum of the three numbers is multiplied by 3.

So ma'am , are you responsible for the SAT Prep division ?

Also I've wanted to ask this to a staff member for a long time , what goes on in your mind when you are making a question ?

I for example try to incorporate those concepts in which I had(or have) trouble with in my questions . Is it a right thing to do or is there any better way of making questions ?

Thanks a lot ma'am $\ddot\smile$

A Former Brilliant Member - 6 years, 2 months ago

Elijah Frank
Dec 1, 2020

It’s (-1) factor because if we simplified the 3^x the we want 3^x-1 so we need that the This is 3 and in This case the average is -1 ( 3) there times for the same factor

SAT Mean, Median, and Mode

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