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Help plz!!

This topic has 8 expert replies and 0 member replies
Hmna Junior | Next Rank: 30 Posts
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15 messages

Help plz!!

Post 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
ttps://postimg.org/image/3su2nnkdt/" target="_blank">

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Post Thu Apr 27, 2017 11:22 pm
Quote:
81ᴾ = 27ᴼ

81ᴾ/27ᴼ = 1

(27ᴾ * 3ᴾ)/27ᴼ = 1

27ᴾ⁻ᴼ * 3ᴾ = 1

(3³)ᴾ⁻ᴼ * 3ᴾ = 1

3³ᴾ⁻³ᴼ * 3ᴾ = 3⁰

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!

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Post Thu Apr 27, 2017 11:25 pm
Another way of seeing the one above, if it's easier:

81ᴾ = 27ᴼ

(27 * 3)ᴾ = 27ᴼ

27ᴾ * 3ᴾ = 27ᴼ

27ᴾ/27ᴼ = 1/3ᴾ

27ᴾ⁻ᴼ = 3⁻ᴾ

3(p - q) = -p

p/q = 3/4

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Post 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 Very Happy)

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Post Thu Apr 27, 2017 11:21 pm
Quote:
One way:

(3⁴)ᴾ = (3³)ᴼ

3⁴ᴾ = 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.)

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Post Thu Apr 27, 2017 11:21 pm
Yet another way:

81ᴾ = 27ᴼ

Try the answers. Using A we have

81³ = 27⁴

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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Post Thu Apr 27, 2017 11:19 pm
Another way:

81ᴾ = 27ᴼ

81ᴾ/27ᴼ = 1

(27ᴾ * 3ᴾ)/27ᴼ = 1

27ᴾ⁻ᴼ * 3ᴾ = 1

(3³)ᴾ⁻ᴼ * 3ᴾ = 1

3³ᴾ⁻³ᴼ * 3ᴾ = 3⁰

3p - 3q + p = 0

4p = 3q

p/q = 3/4

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Post Thu Apr 27, 2017 11:16 pm
One way:

(3⁴)ᴾ = (3³)ᴼ

3⁴ᴾ = 3³ᴼ

4p = 3q

p/q = 3/4

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Post 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:

http://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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Contact Rich at Rich.C@empowergmat.com

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