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# If (0.0024*10^j)/(0.08*10^r) = 3*10^6, then j – r equals which of the

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Math Expert
Joined: 02 Sep 2009
Posts: 52161
If (0.0024*10^j)/(0.08*10^r) = 3*10^6, then j – r equals which of the  [#permalink]

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10 May 2017, 11:30
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25% (medium)

Question Stats:

79% (01:49) correct 21% (01:51) wrong based on 74 sessions

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If $$\frac{(0.0024*10^j)}{(0.08*10^r)}= 3*10^6$$, then j – r equals which of the following?

(A) 9
(B) 8
(C) 7
(D) 6
(E) 5

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Location: India
Re: If (0.0024*10^j)/(0.08*10^r) = 3*10^6, then j – r equals which of the  [#permalink]

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10 May 2017, 11:41
Bunuel wrote:
If $$\frac{(0.0024*10^j)}{(0.08*10^r)}= 3*10^6$$, then j – r equals which of the following?

(A) 9
(B) 8
(C) 7
(D) 6
(E) 5

Equation will boil down to (3*10^j+2)/(10^r+4).
Finally we have 10^j+2-r-4=6
j-r=8

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Re: If (0.0024*10^j)/(0.08*10^r) = 3*10^6, then j – r equals which of the  [#permalink]

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10 May 2017, 11:45
$$\frac{(0.0024*10^j)}{(0.08*10^r)}= 3*10^6$$

= $$\frac{(24*10^j)}{(8*10^{r + 2})}= 3*10^6$$

= $$[fraction](3*10^{j-r-2})[/fraction]= 3*10^6$$

Hence, j-r-2 = 6
j-r = 8(Option B)
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Re: If (0.0024*10^j)/(0.08*10^r) = 3*10^6, then j – r equals which of the  [#permalink]

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15 May 2017, 16:34
1
Bunuel wrote:
If $$\frac{(0.0024*10^j)}{(0.08*10^r)}= 3*10^6$$, then j – r equals which of the following?

(A) 9
(B) 8
(C) 7
(D) 6
(E) 5

Let’s express 0.0024 and 0.08 as whole numbers:

0.0024 x 10^j = 24 x 10^-4 x 10^j = 24 x 10^(j-4)

0.08 x 10^r = 8 x 10^-2 x 10^r = 8 x 10^(r-2)

So, we have:

[24 x 10^(j-4)]/[8 x 10^(r-2)] = 3 x 10^6

24 x 10^(j-4) = (3 x 10^6)(8 x 10^(r-2))

24 x 10^(j-4) = 24 x 10^(6 + r - 2)

10^(j-4) = 10^(6 + r - 2)

Because the bases are equal, we can equate just the exponents:

j - 4 = 6 + r - 2

j - r = 8

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Re: If (0.0024*10^j)/(0.08*10^r) = 3*10^6, then j – r equals which of the &nbs [#permalink] 15 May 2017, 16:34
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