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0.0027x10^x/0.09x10^y=3x10^8 What is the value of y less than x?

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0.0027x10^x/0.09x10^y=3x10^8 What is the value of y less than x? [#permalink]

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Updated on: 24 Sep 2017, 14:13
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Question Stats:

83% (01:33) correct 17% (02:07) wrong based on 48 sessions

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$$\frac{0.0027x10^x}{0.09x10^y}$$=3 x 10^8 What is the value of y less than x?

A 9
B 10
C 11
D 12
E 13

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Last edited by SajjadAhmad on 24 Sep 2017, 14:13, edited 1 time in total.
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Joined: 22 May 2016
Posts: 1825
Re: 0.0027x10^x/0.09x10^y=3x10^8 What is the value of y less than x? [#permalink]

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24 Sep 2017, 13:54
2
$$\frac{0.0027x10^x}{0.09x10^y}$$=3x10^8 What is the value of y less than x?

A 9
B 10
C 11
D 12
E 13

In stages

$$\frac{0.0027*10^x}{0.09*10^y}$$=$$3*10^8$$ REWRITE

$$\frac{27*10^{-4}*10{^x}}{9*10^{-2}*10{^y}}$$ =$$3*10^8$$

Switch the negative powers of 10:

$$\frac{27*10^{2}*10^{x}}{9*10^{4}*10^{y}}$$ =$$3*10^8$$

DIVIDE:

$$3*10^{(2-4)}*10^{(x-y)} = 3*10^8$$

Factor out 3

$$10^{(2-4)}*10^{(x-y)} = 10^8$$

Divide by $$10^{-2}$$

$$\frac{10^{-2}*10^{(x-y)}}{10^{-2}} = \frac{10^8}{10^{-2}}$$

Simplify:

$$10^{(x-y)} = 10^{(8- (-2))}$$

$$10^{(x-y)} = 10^{10}$$

"y less than x" means "$$x - y$$"

Bases are identical, set the exponents equal. The value of y less than x is

$$x - y = 10$$

In fewer steps

$$\frac{0.0027*10^x}{0.09*10^y}$$=$$3*10^8$$

$$(.03)*10^{x-y} = 3 * 10^8$$

$$3*10^{-2}*10^{x-y} = 3 * 10^8$$

$$10^{x-y} = 10^{10}$$

$$x - y = 10$$

SajjadAhmad , thank you for the question. I had a hard time differentiating between what I thought was variable $$x$$, and "x" as multiplication. I think it might be better to use an asterisk, as I did. JMO.
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SVP
Status: Preparing for the GMAT
Joined: 02 Nov 2016
Posts: 1595
Location: Pakistan
GPA: 3.39
0.0027x10^x/0.09x10^y=3x10^8 What is the value of y less than x? [#permalink]

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24 Sep 2017, 14:17
[/quote]"thank you for the question. I had a hard time differentiating between what I thought was variable $$x$$, and "x" as multiplication. I think it might be better to use an asterisk, as I did. JMO. [/quote]

Done... Thanks
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Joined: 06 Aug 2017
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GMAT 1: 570 Q50 V18
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Re: 0.0027x10^x/0.09x10^y=3x10^8 What is the value of y less than x? [#permalink]

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24 Sep 2017, 14:21
$$\frac{0.0027x10^x}{0.09x10^y}$$=3 x 10^8 What is the value of y less than x?

A 9
B 10
C 11
D 12
E 13

The answer should be B as follows.

$$\frac{0.0027*10^x}{0.09*10^y}$$=3 * 10^8 ==> $$\frac{27*10^(x-4)}{9*10^(y-2)}$$=3 * 10^8 ==> $$[fraction]3*10^(x-4-y+2)$$=3 * 10^8

Comparing the power of 10 on both the sides, we get

x-4-y+2=8 ==>x-y-2=8 ==>x-y=10

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Re: 0.0027x10^x/0.09x10^y=3x10^8 What is the value of y less than x?   [#permalink] 24 Sep 2017, 14:21
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