Last visit was: 21 Nov 2024, 16:22 It is currently 21 Nov 2024, 16:22

Close

GRE Prep Club Daily Prep

Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track
Your Progress

every week, we’ll send you an estimated GRE score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.

Close

Request Expert Reply

Confirm Cancel
Verbal Expert
Joined: 18 Apr 2015
Posts: 30003
Own Kudos [?]: 36341 [0]
Given Kudos: 25927
Send PM
avatar
Director
Director
Joined: 03 Sep 2017
Posts: 518
Own Kudos [?]: 703 [0]
Given Kudos: 0
Send PM
avatar
Intern
Intern
Joined: 14 Jan 2019
Posts: 31
Own Kudos [?]: 21 [0]
Given Kudos: 0
Send PM
User avatar
Intern
Intern
Joined: 25 Aug 2019
Status:Trying to get rich every single day.
Affiliations: Me.
Posts: 21
Own Kudos [?]: 61 [0]
Given Kudos: 0
Location: Netherlands
More precise location: Amsterdam
Send PM
Re: If a = (27)(3^–2^ ) and x = (6)(3 ^–1^ ), then which of the [#permalink]
1
This is a tricky question, but much then again.
The main thing which this question tests if do you know the "negative powers" rule
Image

Negative powers/exponents:
https://www.mathsisfun.com/algebra/nega ... nents.html
Retired Moderator
Joined: 10 Apr 2015
Posts: 6218
Own Kudos [?]: 12196 [0]
Given Kudos: 136
Send PM
Re: If a = (27)(3^–2^ ) and x = (6)(3 ^–1^ ), then which of the [#permalink]
1
Carcass wrote:

The last collection of questions for the GRE Quant - 2019



If a = \((27)(3^{-2} )\) and x = \((6)(3^{-1} )\), then which of the following is equivalent to \((12)(3^{-x} ) * (15)(2^{-a} )\) ?

A) \(5(-2245)(320)\)

B) \(\frac{2}{5}\)

C) \(\frac{5}{2}\)

D) \(5(24)(38)\)

E) \(5(2245)(320)\)


GIVEN: \(a = (27)(3^{-2})\)

Rewrite as: \(a = (3^3)(3^{-2})\)

Apply Product rule to get: \(a = 3^{3 + (-2)} = 3^1 = 3\)


GIVEN: \(x = (6)(3^{-1} )\)

Rewrite as: \(a = (6)(\frac{1}{3^1}) = \frac{6}{3} = 2\)


So, \(a=3\) and \(x=2\)


Now take: \((12)(3^{-x} ) * (15)(2^{-a} )\)

Replace a and x to get: \((12)(3^{-2} ) * (15)(2^{-3} )\)

Evaluate each part to get: \((12)(\frac{1}{3^2}) * (15)(\frac{1}{2^3})\)

Simplify: \((12)(\frac{1}{9}) * (15)(\frac{1}{8})\)

Simplify: \((\frac{12}{9})(\frac{15}{8})\)

Evaluate: \(\frac{180}{72}\)

Simplify: \(\frac{5}{2}\)

Answer: C
Prep Club for GRE Bot
Re: If a = (27)(3^–2^ ) and x = (6)(3 ^–1^ ), then which of the [#permalink]
Moderators:
GRE Instructor
84 posts
GRE Forum Moderator
37 posts
Moderator
1111 posts
GRE Instructor
234 posts

Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne