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# If 27^(1/m) = 3^(3m) and 4m > 1, then what is the value of m ?

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Math Expert
Joined: 02 Sep 2009
Posts: 58402
If 27^(1/m) = 3^(3m) and 4m > 1, then what is the value of m ?  [#permalink]

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10 Apr 2019, 21:37
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5% (low)

Question Stats:

83% (01:11) correct 17% (01:39) wrong based on 124 sessions

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If $$\sqrt[m]{27} = 3^{3m}$$ and 4m > 1, then what is the value of m ?

(A) –1
(B) –1/4
(C) 0
(D) 1/4
(E) 1

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Joined: 18 Aug 2017
Posts: 5008
Location: India
Concentration: Sustainability, Marketing
GPA: 4
WE: Marketing (Energy and Utilities)
Re: If 27^(1/m) = 3^(3m) and 4m > 1, then what is the value of m ?  [#permalink]

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11 Apr 2019, 00:33
1
1
1
Bunuel wrote:
If $$\sqrt[m]{27} = 3^{3m}$$ and 4m > 1, then what is the value of m ?

(A) –1
(B) –1/4
(C) 0
(D) 1/4
(E) 1

for 4m > 1
m=1
IMO E
Intern
Joined: 11 Apr 2019
Posts: 13
Re: If 27^(1/m) = 3^(3m) and 4m > 1, then what is the value of m ?  [#permalink]

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20 Apr 2019, 03:07
Archit3110 wrote:
Bunuel wrote:
If $$\sqrt[m]{27} = 3^{3m}$$ and 4m > 1, then what is the value of m ?

(A) –1
(B) –1/4
(C) 0
(D) 1/4
(E) 1

for 4m > 1
m=1
IMO E

How do you get to m=1 from 4m > 1 ?
GMAT Club Legend
Joined: 18 Aug 2017
Posts: 5008
Location: India
Concentration: Sustainability, Marketing
GPA: 4
WE: Marketing (Energy and Utilities)
Re: If 27^(1/m) = 3^(3m) and 4m > 1, then what is the value of m ?  [#permalink]

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20 Apr 2019, 03:13
1
vargamartin1031 wrote:
Archit3110 wrote:
Bunuel wrote:
If $$\sqrt[m]{27} = 3^{3m}$$ and 4m > 1, then what is the value of m ?

(A) –1
(B) –1/4
(C) 0
(D) 1/4
(E) 1

for 4m > 1
m=1
IMO E

How do you get to m=1 from 4m > 1 ?

vargamartin1031
given 4m>1
browsing answer options we can say m has to be 1 then only 4*1>1 is valid
Manager
Joined: 15 Jan 2018
Posts: 60
Re: If 27^(1/m) = 3^(3m) and 4m > 1, then what is the value of m ?  [#permalink]

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30 Apr 2019, 15:55
1
Bunuel wrote:
If $$\sqrt[m]{27} = 3^{3m}$$ and 4m > 1, then what is the value of m ?

(A) –1
(B) –1/4
(C) 0
(D) 1/4
(E) 1

This can be rewritten as $$3^{3/m} = 3^{3m}$$

We see here that 1 is really the only number that works here.

Using 4m > 1, we can easily see that 1 must be the answer
Manager
Joined: 19 Feb 2019
Posts: 74
Concentration: Marketing, Statistics
Re: If 27^(1/m) = 3^(3m) and 4m > 1, then what is the value of m ?  [#permalink]

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28 Aug 2019, 10:12
what happened to m root of 27 ??
How does 1 satisfy this equation?
1 satisfies only 4m>1
If m is put in the m root 27 = 3^3m equation how can the equation be solved???
Pls explain
Manager
Joined: 15 Jan 2018
Posts: 60
If 27^(1/m) = 3^(3m) and 4m > 1, then what is the value of m ?  [#permalink]

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28 Aug 2019, 11:15
devavrat wrote:
what happened to m root of 27 ??
How does 1 satisfy this equation?
1 satisfies only 4m>1
If m is put in the m root 27 = 3^3m equation how can the equation be solved???
Pls explain

It looks like you'll need to brush up on exponents.

$$\sqrt[m]{27}$$ = $$(3^{3})^{1/m} = 3^{3*(1/m)} = 3^{3/m}$$

They're telling us that $$3^{3/m} = 3^{3m}$$

For which answer choices does m satisfy 4m > 1?
(A) –4 > 1
(B) –1 > 1
(C) 0 > 1
(D) 1 > 1

(E) 1

$$3^{3/m} = 3^{3m}$$ if we use 1 or -1 for m (using 0 gives us an invalid equation). So if we know that 4m > 1, then E must be the answer.
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Re: If 27^(1/m) = 3^(3m) and 4m > 1, then what is the value of m ?  [#permalink]

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02 Sep 2019, 19:23
Bunuel wrote:
If $$\sqrt[m]{27} = 3^{3m}$$ and 4m > 1, then what is the value of m ?

(A) –1
(B) –1/4
(C) 0
(D) 1/4
(E) 1

Rewriting the equation, we have:

3^(3/m) = 3^(3m)

3/m = 3m

3 = 3m^2

1 = m^2

m = 1 or m = -1

However, since 4m > 1, m must be 1.

Alternate solution:

Since 4m > 1, m > 1/4. Looking at the multiple choices, only choice E can be correct.

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Manager
Joined: 02 Nov 2018
Posts: 50
Re: If 27^(1/m) = 3^(3m) and 4m > 1, then what is the value of m ?  [#permalink]

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10 Sep 2019, 15:10
Bunuel wrote:
If $$\sqrt[m]{27} = 3^{3m}$$ and 4m > 1, then what is the value of m ?

(A) –1
(B) –1/4
(C) 0
(D) 1/4
(E) 1

I got to:

27^(1/m) = 3^(3m)
(3^3)^1/m = (3^3)^m

So surely based on the above 1/m = m which means m can only be 1 so E is the answer. However, is this thought process correct?
Re: If 27^(1/m) = 3^(3m) and 4m > 1, then what is the value of m ?   [#permalink] 10 Sep 2019, 15:10
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