thanhnguyen wrote:

Which of the followings is closest to \(({{9^{102}}/{{3^4}}) - {3^4}\)?

A. \({({3^2})^{49}}\)

B. \(3^{100}.3^{100}\)

C. \(9^{99}\)

D. \(9^{50}\)

E. \(9^{48}\)

Dear

thanhnguyen,

I'm happy to help with this.

You may find this blog article relevant to this problem:

http://magoosh.com/gmat/2012/adding-and ... -the-gmat/\(({{9^{102}}/{{3^4}}) - {3^4} = ({{(3^2)^{102}}/{{3^4}}) - {3^4}\)

\(= ({{(3)^{204}}/{{3^4}}) - {3^4}\)

\(= (3)^{200} - {3^4}\)

At this point, \((3)^{200}\) is a truly gargantuan number, more than an Avogadro's number of Avogadro's numbers, more than the number of elementary particles in the Visible Universe. Meanwhile,

3^4 = 81 is a mere pittance by comparison, so this latter term doesn't matter at all. The entire thing is closest to \((3)^{200} = (9)^{100}\).

Now, neither form is listed as a choice, but choice

(B) has

B. \(3^{100}.3^{100}\)

The decimal point is not a recognizable mathematical operator, but if by this, the author intended multiplication, then the correct way to write this would be:

B. \((3^{100})*(3^{100})\)

By computer convention, the * sign (shift-8 on a QWERTY keyboard) is the proper symbol for multiplication. If this is what is intended by

(B), then

(B) is the correct answer.

Does all this make sense?

Mike

_________________

Mike McGarry

Magoosh Test Prep