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

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Vincen: Legendary Member; Posts: 2898; Joined: Thu Sep 07, 2017 2:49 pmFollowed by: 5 members; Thanked: 6 times

by Vincen » Thu Nov 02, 2017 8:27 am

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

A. 3
B. 9
C. 27
D. 108
E. 243

The OA is E.

Is there a way to solve it without trying option by option? Experts, may you help me please?

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Source: Beat The GMAT — Problem Solving | Thu Nov 02, 2017 8:27 am

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Brent@GMATPrepNow: GMAT Instructor; Posts: 16207; Joined: Mon Dec 08, 2008 6:26 pmFollowed by: 1268 members; Location: Vancouver, BC; Thanked: 5254 times; GMAT Score:770

by Brent@GMATPrepNow » Thu Nov 02, 2017 8:34 am

Vincen wrote:What number times (1â�„3)Â² will give the value of 3Â³?

A. 3
B. 9
C. 27
D. 108
E. 243

In other words, we want to solve the equation [(1â�„3)Â²]k = 3Â³ for k
First notice that 1/3 = 3^(-1)
So, (1â�„3)Â² = [3^(-1)]Â² = 3^(-2) [after we apply the Power of a Power law]

We have: [3^(-2)]k = 3Â³
Divide both side by 3^(-2) to get: k = 3Â³/3^(-2)
Apply Quotient law to get: k = 3^5 = 243

Answer: E

Cheers,
Brent

Brent Hanneson - Creator of GMATPrepNow.com

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Scott@TargetTestPrep: GMAT Instructor; Posts: 8137; Joined: Sat Apr 25, 2015 10:56 amFollowed by: 29 members; Location: Los Angeles, CA; Thanked: 43 times

by Scott@TargetTestPrep » Tue Dec 12, 2017 6:42 am

Vincen wrote:What number times (1â�„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

Scott Woodbury-Stewart
Founder and CEO
[email protected]

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