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

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by Brent@GMATPrepNow » Thu Nov 02, 2017 8:34 am
Vincen wrote:What number times (1�3)² will give the value of 3³?

A. 3
B. 9
C. 27
D. 108
E. 243
In other words, we want to solve the equation [(1�3)²]k = 3³ for k
First notice that 1/3 = 3^(-1)
So, (1�3)² = [3^(-1)]² = 3^(-2) [after we apply the Power of a Power law]

We have: [3^(-2)]k = 3³
Divide both side by 3^(-2) to get: k = 3³/3^(-2)
Apply Quotient law to get: k = 3^5 = 243

Answer: E

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by Scott@TargetTestPrep » Tue Dec 12, 2017 6:42 am
Vincen wrote:What number times (1�3)^2 will give the value of 3^3?

A. 3
B. 9
C. 27
D. 108
E. 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

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