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# If 0.000027*10^x/900*10^(-4) = 0.03*10^11, what is the value of x?

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Math Expert
Joined: 02 Sep 2009
Posts: 50583
If 0.000027*10^x/900*10^(-4) = 0.03*10^11, what is the value of x?  [#permalink]

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26 Aug 2018, 05:35
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Difficulty:

35% (medium)

Question Stats:

75% (01:09) correct 25% (01:44) wrong based on 26 sessions

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If $$\frac{0.000027*10^x}{900*10^{-4}}= 0.03*10^{11}$$, what is the value of x?

(A) 13
(B) 14
(C) 15
(D) 16
(E) 17

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Joined: 25 Aug 2018
Posts: 4
Re: If 0.000027*10^x/900*10^(-4) = 0.03*10^11, what is the value of x?  [#permalink]

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26 Aug 2018, 05:45
27/(9×10^8)*10^(x+4)=3*10^9
3×10^(x-4)=3×10^9
X-4=9
X=13

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Director
Joined: 31 Oct 2013
Posts: 777
Concentration: Accounting, Finance
GPA: 3.68
WE: Analyst (Accounting)
If 0.000027*10^x/900*10^(-4) = 0.03*10^11, what is the value of x?  [#permalink]

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26 Aug 2018, 09:56
Bunuel wrote:
If $$\frac{0.000027*10^x}{900*10^{-4}}= 0.03*10^{11}$$, what is the value of x?

(A) 13
(B) 14
(C) 15
(D) 16
(E) 17

$$\frac{0.000027 * 10^x}{900 * 10^{-4}}$$= $$0.03*10^{11}$$

$$\frac{0.000027 * 10^{x+4}}{900}$$ = $$3 * 10^9$$

$$\frac{27 * 10^{x + 4 - 6}}{900}$$ = $$3* 10^9$$

$$\frac{9 * 10^{x + 4 - 6}}{900}$$ = $$10^9$$

$$\frac{10^{x + 4 - 6}}{100}$$= $$10^9$$

$$\frac{10^{x - 2}}{10^2}$$= $$10^9$$

$$10^{x - 2 -2} = 10^9$$

x - 4 = 9

x = 13.

Thus the best answer is A.
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Status: Learning stage
Joined: 01 Oct 2017
Posts: 930
WE: Supply Chain Management (Energy and Utilities)
Re: If 0.000027*10^x/900*10^(-4) = 0.03*10^11, what is the value of x?  [#permalink]

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26 Aug 2018, 09:59
Bunuel wrote:
If $$\frac{0.000027*10^x}{900*10^{-4}}= 0.03*10^{11}$$, what is the value of x?

(A) 13
(B) 14
(C) 15
(D) 16
(E) 17

$$\frac{0.000027*10^x}{900*10^{-4}}= 0.03*10^{11}$$
Or, $$\frac{27*10^{-6}*10^x}{9*10^2*10^{-4}}= 3*10^{-2}*10^{11}$$
Or, $$\frac{27*10^{-6+x}}{9*10^{2+(-4)}}= 3*10^{-2+11}$$
Or, $$\frac{27*10^{-6+x}}{9*10^{-2}}= 3*10^9$$
Or, $$3*10^{-6+x-(-2)}= 3*10^9$$
Or, $$10^{-4+x}=10^9$$
Or, -4+x=9
Or, x=9+4=13

Ans. (A)
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PKN

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Re: If 0.000027*10^x/900*10^(-4) = 0.03*10^11, what is the value of x? &nbs [#permalink] 26 Aug 2018, 09:59
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