Help plz!!

Post your questions about customer service issues, GMAT exam policies, and GMAT exam structure. Get an official answer from GMAC, the organization behind the GMAT test!
This topic has expert replies
User avatar
Junior | Next Rank: 30 Posts
Posts: 15
Joined: Thu Apr 27, 2017 2:55 am

Help plz!!

by Hmna » Thu Apr 27, 2017 3:00 am
If p and q are nonzero integers and 81p=27q what is the value of p\q
A)3/4
B)4/3
C)27/7
D)7/27
Image

GMAT/MBA Expert

User avatar
Elite Legendary Member
Posts: 10392
Joined: Sun Jun 23, 2013 6:38 pm
Location: Palo Alto, CA
Thanked: 2867 times
Followed by:511 members
GMAT Score:800

Help plz!!

by [email protected] » Thu Apr 27, 2017 4:36 pm
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
Contact Rich at [email protected]
Image

GMAT Instructor
Posts: 2630
Joined: Wed Sep 12, 2012 3:32 pm
Location: East Bay all the way
Thanked: 625 times
Followed by:119 members
GMAT Score:780

by Matt@VeritasPrep » Thu Apr 27, 2017 11:16 pm
One way:

(3�)ᴾ = (3³)ᴼ

3�ᴾ = 3³ᴼ

4p = 3q

p/q = 3/4

GMAT Instructor
Posts: 2630
Joined: Wed Sep 12, 2012 3:32 pm
Location: East Bay all the way
Thanked: 625 times
Followed by:119 members
GMAT Score:780

by Matt@VeritasPrep » Thu Apr 27, 2017 11:19 pm
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

GMAT Instructor
Posts: 2630
Joined: Wed Sep 12, 2012 3:32 pm
Location: East Bay all the way
Thanked: 625 times
Followed by:119 members
GMAT Score:780

by Matt@VeritasPrep » Thu Apr 27, 2017 11:21 pm
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!

GMAT Instructor
Posts: 2630
Joined: Wed Sep 12, 2012 3:32 pm
Location: East Bay all the way
Thanked: 625 times
Followed by:119 members
GMAT Score:780

by Matt@VeritasPrep » Thu Apr 27, 2017 11:21 pm
One way:

(3�)ᴾ = (3³)ᴼ

3�ᴾ = 3³ᴼ

4p = 3q

p/q = 3/4
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.)

GMAT Instructor
Posts: 2630
Joined: Wed Sep 12, 2012 3:32 pm
Location: East Bay all the way
Thanked: 625 times
Followed by:119 members
GMAT Score:780

by Matt@VeritasPrep » Thu Apr 27, 2017 11:22 pm
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
Same issue here, those super Os should super Qs. Hope the idea is still clear, though!

GMAT Instructor
Posts: 2630
Joined: Wed Sep 12, 2012 3:32 pm
Location: East Bay all the way
Thanked: 625 times
Followed by:119 members
GMAT Score:780

by Matt@VeritasPrep » Thu Apr 27, 2017 11:25 pm
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

GMAT Instructor
Posts: 2630
Joined: Wed Sep 12, 2012 3:32 pm
Location: East Bay all the way
Thanked: 625 times
Followed by:119 members
GMAT Score:780

by Matt@VeritasPrep » Thu Apr 27, 2017 11:28 pm
... 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 :D)