Exponent Question..

[rahul26]

If 3^6x = 8,100, what is the value of (3x – 1)^3 ?

A. 90
B. 30
C. 10
D. 10 / 3
E. 10 / 9

[Feep]

The answer should be B. 30.

There might be some wonderfully elegant algebraic solution to this problem, but I highly doubt it. This question tests your ability to do quick math and ballpark your answers.

Some quick multiplying-by-3 shows that we need a little more than 8 in the exponent to reach 8,100. (1, 3, 9, 27, 81, 243, 729, 2200ish, 6600ish). So, let's say 8.2ish. So, x equals 8.2/6.

Substituting into the second equation, we get (8.2/2 - 1)^3 = 3.1^3. You can multiply out, or you can see it'll be a bit more than 3^3, which is 27. So, 30.

Sometimes, you just gotta put your head down and power through. = P

Edit: The actual question is written differently, (3^(x-1))^3. The answer is D, in this case, and has a much more elegant solution. Please see the link below.

[Musiq]

To the OP (Rahul?),

This is not a good representation of a GMAT question. As Feep admirably shows you how to get to the answer using approximation, similarly the testmaker MUST let us know that they need an approximate value.

Did you miss that out of your question? Or is the question correct as is?

Also, is the left hand side of the equation (3^6 ) ( X) or (3) ^ (6X)?

Please let us know since this considerably chnages the approach to the problem.

Thanks in advance!

[moutar]

I think this is the actual question.

https://www.beatthegmat.com/ps-t33962.html

[Musiq]

I think this is the actual question.

https://www.beatthegmat.com/ps-t33962.html

Elegant solution!

Thanks for responding.

To Rahul, please follow link that Moutar has posted...and go straight to his solution.

[moutar]

Elegance is the way forward.

[logitech]

3^6x = 8,100

9,16,25,35,..81,100 should always ring the perfect square ring.

3^3X=90

The question asks: 3^x/3^3 = 90/27=10/3