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# The value of 3^(-2)+3^(-4)+3^(-6) is how many times the value of

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The value of 3^(-2)+3^(-4)+3^(-6) is how many times the value of  [#permalink]

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11 Apr 2017, 07:06
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The value of $$3^{-2} + 3^{-4} + 3^{-6}$$ is how many times the value of $$3^{-5}$$?

A. $$\frac{91}{3}$$

B. 27

C. $$\frac{31}{3}$$

D. 3

E. $$\frac{1}{3}$$

Source: GMAT Free

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Re: The value of 3^(-2)+3^(-4)+3^(-6) is how many times the value of  [#permalink]

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11 Apr 2017, 07:08
nguyendinhtuong wrote:
The value of $$3^{-2} + 3^{-4} + 3^{-6}$$ is how many times the value of $$3^{-5}$$?

A. $$\frac{91}{3}$$

B. 27

C. $$\frac{31}{3}$$

D. 3

E. $$\frac{1}{3}$$

Source: GMAT Free

Similar question: https://gmatclub.com/forum/the-value-of ... 30682.html
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Re: The value of 3^(-2)+3^(-4)+3^(-6) is how many times the value of  [#permalink]

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11 Apr 2017, 07:50
3^-2 = 1/3^2
Hence using this logic, rewriting the above equation, we get
1/3^2 + 1/3^4 + 1/3^6
= (3^4 + 3^2 + 1)/3^6
= 91/3^6
This is 91/3 times 1/3^5(Option A)

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Re: The value of 3^(-2)+3^(-4)+3^(-6) is how many times the value of  [#permalink]

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11 Apr 2017, 08:29
1
nguyendinhtuong wrote:
The value of $$3^{-2} + 3^{-4} + 3^{-6}$$ is how many times the value of $$3^{-5}$$?

A. $$\frac{91}{3}$$

B. 27

C. $$\frac{31}{3}$$

D. 3

E. $$\frac{1}{3}$$

Source: GMAT Free

You can divide (3^-2 + 3^-4 + 3^-6) by 3^-5

We get: 3^-2+5 + 3^1 + 3^-1 = 27 + 3 + 1/3 = 30 + 1/3 = 91/3 Hence A
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Re: The value of 3^(-2)+3^(-4)+3^(-6) is how many times the value of  [#permalink]

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11 Apr 2017, 12:19
1
1
nguyendinhtuong wrote:
The value of $$3^{-2} + 3^{-4} + 3^{-6}$$ is how many times the value of $$3^{-5}$$?

A. $$\frac{91}{3}$$

B. 27

C. $$\frac{31}{3}$$

D. 3

E. $$\frac{1}{3}$$

Source: GMAT Free

$$3^{-2} + 3^{-4} + 3^{-6}$$

= $$3^{-2} ( 1 + 3^{-2} + 3^{-4}$$ )

= $$\frac{1}{9} ( 1 + \frac{1}{9} + \frac{1}{81} )$$

= $$\frac{1}{9} ( \frac{81 + 9 + 1}{81} )$$

= $$\frac{91}{729}$$

Quote:
is how many times the value of $$3^{-5}$$?

So, $$\frac{91}{729}*\frac{243}{1}$$ = $$\frac{91}{3}$$

Hence, answer must be (A) $$\frac{91}{3}$$
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Re: The value of 3^(-2)+3^(-4)+3^(-6) is how many times the value of  [#permalink]

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11 Apr 2017, 12:29
Top Contributor
2
nguyendinhtuong wrote:
The value of $$3^{-2} + 3^{-4} + 3^{-6}$$ is how many times the value of $$3^{-5}$$?

A. $$\frac{91}{3}$$

B. 27

C. $$\frac{31}{3}$$

D. 3

E. $$\frac{1}{3}$$

Source: GMAT Free

Let's factor out $$3^{-5}$$

We get: $$3^{-2} + 3^{-4} + 3^{-6} = 3^{-5}(3^3 + 3^1 + 3^{-1})$$

$$= 3^{-5}(27 + 3 + \frac{1}{3})$$

$$= 3^{-5}(30 + \frac{1}{3})$$

$$= 3^{-5}(\frac{90}{3} + \frac{1}{3})$$

$$= 3^{-5}(\frac{91}{3})$$

Cheers,
Brent
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Re: The value of 3^(-2)+3^(-4)+3^(-6) is how many times the value of  [#permalink]

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13 Jul 2018, 08:03
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Re: The value of 3^(-2)+3^(-4)+3^(-6) is how many times the value of &nbs [#permalink] 13 Jul 2018, 08:03
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