Hi Hmna,
In the future, you should make sure to post your questions in the appropriate sub-Forum. The Problem Solving Forum can be found here:
https://www.beatthegmat.com/problem-solving-f6.html
This question is all about exponent rules. When comparing exponents, it helps if the numbers have the same BASE. Here, the bases are 81 and 27, so we can rewrite those bases as (3^4) and (3^3). Now the given equation can be written as...
(3^4)^P = (3^3)^Q
We're raising 'a power to a power', so we can rewrite the equation one more step...
3^(4P) = 3^(3Q)
Now we know that 4P = 3Q
The question asks for the value of P/Q....
4P = 3Q
P = 3Q/4
P/Q = 3/4
Final Answer: A
GMAT assassins aren't born, they're made,
Rich
BREAKING: Target Test Prep releases Brand New 2026 On Demand GMAT prep course
Redeem
Featured Course
Target Test Prep GMAT OnDemand
Scott Woodbury-Stewart’s private virtual classroom — 400 hours of master-class video lessons for the GMAT Focus Edition.
- 715+ score guarantee — highest in the industry (99th percentile)
- 52 chapters · 1,500+ lessons · 4,000+ practice questions
- 400 hours of video · 1,500+ instructor-led HD smartboard lessons
- 300,000+ students accepted to Harvard, Stanford, Wharton, Booth & Sloan & more
- 24/7 live support + weekly Zoom office hours with GMAT instructors
- TTP AI Assist — 24/7 AI-powered virtual tutor for instant help
- 1,200+ flashcards + AI-powered study assistant & daily calendar
- OnDemand, LiveTeach & GMAT Bootcamp formats available
- Also: GRE, SAT Math & Executive Assessment courses
- MBA Admissions Consulting now available
- 🏆 2025 EdTech Breakthrough Award: Test Prep Solution Provider of the Year
- 200,000+ students served
- 5-day free trial — $0 to start, no auto-billing, cancel anytime
★★★★★
5.0
(559 reviews)
130-pt guarantee
$0 to start
then $127/mo
Help plz!!
Source: Beat The GMAT — Ask the Test Maker |
GMAT/MBA Expert
-
[email protected]
- Elite Legendary Member
- Posts: 10392
- Location: Palo Alto, CA
- Thanked: 2867 times
- GMAT Score:800
One way:
(3�)ᴾ = (3³)ᴼ
3�ᴾ = 3³ᴼ
4p = 3q
p/q = 3/4
(3�)ᴾ = (3³)ᴼ
3�ᴾ = 3³ᴼ
4p = 3q
p/q = 3/4
Another way:
81á´¾ = 27á´¼
81á´¾/27á´¼ = 1
(27á´¾ * 3á´¾)/27á´¼ = 1
27ᴾ�ᴼ * 3ᴾ = 1
(3³)ᴾ�ᴼ * 3ᴾ = 1
3³ᴾ�³ᴼ * 3ᴾ = 3�
3p - 3q + p = 0
4p = 3q
p/q = 3/4
81á´¾ = 27á´¼
81á´¾/27á´¼ = 1
(27á´¾ * 3á´¾)/27á´¼ = 1
27ᴾ�ᴼ * 3ᴾ = 1
(3³)ᴾ�ᴼ * 3ᴾ = 1
3³ᴾ�³ᴼ * 3ᴾ = 3�
3p - 3q + p = 0
4p = 3q
p/q = 3/4
Yet another way:
81á´¾ = 27á´¼
Try the answers. Using A we have
81³ = 27�
81 * 81 * 81 = 27 * 27 * 27 * 27
divide by 27 three times:
(81/27) * (81/27) * (81/27) = 27
3 * 3 * 3 = 27
This is true, so A is our answer!
81á´¾ = 27á´¼
Try the answers. Using A we have
81³ = 27�
81 * 81 * 81 = 27 * 27 * 27 * 27
divide by 27 three times:
(81/27) * (81/27) * (81/27) = 27
3 * 3 * 3 = 27
This is true, so A is our answer!
The formatting on this post is screwed up, the superscript O should be a superscript Q. (The forum gives an error glyph for the Q.)One way:
(3�)ᴾ = (3³)ᴼ
3�ᴾ = 3³ᴼ
4p = 3q
p/q = 3/4
Same issue here, those super Os should super Qs. Hope the idea is still clear, though!81á´¾ = 27á´¼
81á´¾/27á´¼ = 1
(27á´¾ * 3á´¾)/27á´¼ = 1
27ᴾ�ᴼ * 3ᴾ = 1
(3³)ᴾ�ᴼ * 3ᴾ = 1
3³ᴾ�³ᴼ * 3ᴾ = 3�
3p - 3q + p = 0
4p = 3q
p/q = 3/4
Another way of seeing the one above, if it's easier:
81á´¾ = 27á´¼
(27 * 3)á´¾ = 27á´¼
27á´¾ * 3á´¾ = 27á´¼
27á´¾/27á´¼ = 1/3á´¾
27ᴾ�ᴼ = 3�ᴾ
3(p - q) = -p
p/q = 3/4
81á´¾ = 27á´¼
(27 * 3)á´¾ = 27á´¼
27á´¾ * 3á´¾ = 27á´¼
27á´¾/27á´¼ = 1/3á´¾
27ᴾ�ᴼ = 3�ᴾ
3(p - q) = -p
p/q = 3/4
... and of course those should be superscript Qs again. Yeesh, I give up! (Why is super Q so hated by forum text? Must be a Scrabble thing 
)
)
