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# If x is a positive integer, and m=1^(x+1), then what is the value of

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Manager
Joined: 20 Jul 2018
Posts: 71
WE: Corporate Finance (Investment Banking)
If x is a positive integer, and m=1^(x+1), then what is the value of  [#permalink]

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06 Oct 2018, 10:10
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Difficulty:

45% (medium)

Question Stats:

68% (01:56) correct 32% (02:24) wrong based on 130 sessions

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If x is a positive integer, and $$m=3^{x+1}$$, then what is the value of $$9^{2x}$$ in terms of m?

a) $$\frac{m^2}{9}$$

b) $$\frac{m^2}{81}$$

c) $$\frac{m^3}{9}$$

b) $$\frac{m^4}{3}$$

e) $$\frac{m^4}{81}$$
Intern
Joined: 05 Jun 2018
Posts: 1
Re: If x is a positive integer, and m=1^(x+1), then what is the value of  [#permalink]

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06 Oct 2018, 11:41
1
m=3^(x+1)

=> m=3^x* 3

=> m/3 = 3^x

Also, 9^2x = 9^x *9^x => (3^x)^2 * (3^x)^2

=> (m/3)^2*(m/3)^2 => m^4/81

Hence Ans: E
Intern
Joined: 15 Jan 2014
Posts: 31
Location: India
Concentration: Technology, Strategy
Schools: Haas '19
GMAT 1: 650 Q49 V30
GPA: 2.5
WE: Information Technology (Consulting)
Re: If x is a positive integer, and m=1^(x+1), then what is the value of  [#permalink]

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06 Oct 2018, 12:20
Put $$x=1$$ in $$m$$=$$3^{x+1}$$ ==>$$m=3^2$$ ==> $$9$$

Now ,Put $$x=1$$ in $$9^{2x}$$ ==> $$81$$

Now put $$m=9$$ in answer options to get $$81$$

Only option E gives $$81$$

Please +1 kudos if you liked my post
Senior Manager
Joined: 12 Sep 2017
Posts: 302
Re: If x is a positive integer, and m=1^(x+1), then what is the value of  [#permalink]

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18 Jan 2019, 20:52
Hello!

Could someone please provide an algebraic solution?

Kind regards!
Director
Joined: 09 Mar 2018
Posts: 994
Location: India
Re: If x is a positive integer, and m=1^(x+1), then what is the value of  [#permalink]

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18 Jan 2019, 21:04
1
jfranciscocuencag wrote:
Hello!

Could someone please provide an algebraic solution?

Kind regards!

m=3^(x+1)

Can be written as => m = $$3^x$$ * 3 -----(a)

To find $$9^{2x}$$ in terms of m

lets expand the question a bit, $$3^{4x}$$

$$3^x * 3^x * 3^x * 3^x$$

Now you can manipulate (a) as $$3^x$$ = m / 3

Just substitute that back into the question, to get m^4 / 81

Does this help in any way ??
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Senior Manager
Joined: 12 Sep 2017
Posts: 302
If x is a positive integer, and m=1^(x+1), then what is the value of  [#permalink]

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19 Jan 2019, 12:32
1
KanishkM wrote:
jfranciscocuencag wrote:
Hello!

Could someone please provide an algebraic solution?

Kind regards!

m=3^(x+1)

Can be written as => m = $$3^x$$ * 3 -----(a)

To find $$9^{2x}$$ in terms of m

lets expand the question a bit, $$3^{4x}$$

$$3^x * 3^x * 3^x * 3^x$$

Now you can manipulate (a) as $$3^x$$ = m / 3

Just substitute that back into the question, to get m^4 / 81

Does this help in any way ??

Hello KanishkM !

Well no, it does not.

I¿m having problems to get to the answer from the easiest way.

Could you please explain to me how to solve it by plugging values, I have spent 2 hours but still don't know how to get the answer.

If x is a positive integer, and m=1^(x+1), then what is the value of   [#permalink] 19 Jan 2019, 12:32
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