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
Help plz!!
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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
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
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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
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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
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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!
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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
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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
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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
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... 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 )