What number times (1⁄3)^2 will give the value of 3^3?

Hi All,

The speed with which you can answer many Quant questions on Test Day will come down to how you use the available information you're given AND in how you 'see' the math involved. While this question can certainly be solved using exponent rules, we can do a little math and use the answer choices to our advantage to avoid the rest of that math.

We're asked what number times (1⁄3)^2 will give the value of 3^3.

So... what numbers times 1/9 will get us 27.

(X)(1/9) = 27

If we multiply both sides by 9, we get...

X = (27)(9)

Since (27)(10) = 270, looking at the answer choices, there's really only one answer that makes sense...

Final Answer:

GMAT assassins aren't born, they're made,
Rich

My Take:
Indeed it's E) 243

let that number is P
(1/3)^2 X P = 3^2 (given)

P = 3^5 = 243

We can create the following equation in which k = the number:

k(1/3)^2 = 3^3

k(1/9) = 27

k = 243

Answer: E

\((1⁄3)^2 = 3^{-2}\)

We have : \(3^{-2}*3^k = 3^3\)

So, k = 5

Thus, 3^5 = 243

Answer will hence be (E) 343