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# If 0.036*10^a/(0.09*10^b) = 4*10^5, then a - b =

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Joined: 02 Sep 2009
Posts: 58453
If 0.036*10^a/(0.09*10^b) = 4*10^5, then a - b =  [#permalink]

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05 Mar 2019, 02:41
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Difficulty:

45% (medium)

Question Stats:

59% (01:39) correct 41% (01:11) wrong based on 37 sessions

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If $$\frac{0.036*10^a}{0.09*10^b} = 4*10^5$$, then a - b =

A. 7
B. 6
C. 5
D. 4
E. 3

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Joined: 18 Nov 2018
Posts: 26
Re: If 0.036*10^a/(0.09*10^b) = 4*10^5, then a - b =  [#permalink]

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05 Mar 2019, 02:51
B is the answer. 0.036 = 0.4 x 0.09. Simplify the LHS and we get the equation of 4 x 10^(a-b-1) = 4 x 10^5. Hence a-b = 6

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If 0.036*10^a/(0.09*10^b) = 4*10^5, then a - b =  [#permalink]

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05 Mar 2019, 02:59
Bunuel wrote:
If $$\frac{0.036*10^a}{0.09*10^b} = 4*10^5$$, then a - b =

A. 7
B. 6
C. 5
D. 4
E. 3

Given,

$$\frac{0.036*10^a}{0.09*10^b} = 4*10^5$$

$$\frac{36*10^{a-3}}{9*10^{b-2}} = 4*10^5$$

$$4*10^{a-3 - b + 2} = 4*10^5$$

(a - 3 - b + 2) = 5

(a - b) = 6.

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Re: If 0.036*10^a/(0.09*10^b) = 4*10^5, then a - b =  [#permalink]

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05 Mar 2019, 09:16
Bunuel wrote:
If $$\frac{0.036*10^a}{0.09*10^b} = 4*10^5$$, then a - b =

A. 7
B. 6
C. 5
D. 4
E. 3

solve for expression

$$\frac{0.036*10^a}{0.09*10^b} = 4*10^5$$
we get
10^a-b = 10^6
a-b= 6
IMO B
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Re: If 0.036*10^a/(0.09*10^b) = 4*10^5, then a - b =  [#permalink]

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07 Mar 2019, 08:01
Bunuel wrote:
If $$\frac{0.036*10^a}{0.09*10^b} = 4*10^5$$, then a - b =

A. 7
B. 6
C. 5
D. 4
E. 3

If we re-express 0.036 as 36 x 10^-3 in the numerator and 0.09 as 9 x 10^-2 in the denominator, we obtain:

(36 x 10^-3 x 10^a)/(9 x 10^-2 x 10^b

Simplifying, we have:

(36 x 10^(a-3))/(9 x 10^(b-2)) = 4 x 10^5

36 x 10^(a-3) = (4 x 10^5)(9 x 10^(b-2))

36 x 10^(a-3) = 9 x 4 x 10^(5 + b - 2)

10^(a-3) = 10^(5 + b - 2)

a - 3 = 5 + b - 2

a - b = 6

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Re: If 0.036*10^a/(0.09*10^b) = 4*10^5, then a - b =   [#permalink] 07 Mar 2019, 08:01
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