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# The value of (10^8-10^2)/(10^7-10^3) is closest to which of

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Re: The value of (10^8-10^2)/(10^7-10^3) is closest to which of [#permalink]

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25 Feb 2014, 19:53
10^8 is way too high from 10^2, similarly 10^7 is way too high from 10^3
No need to make any further simplification calculation, just calculate 10^8 / 10^7 = 10 = Answer = B
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Re: The value of (10^8-10^2)/(10^7-10^3) is closest to which of [#permalink]

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08 Mar 2014, 19:49
Option B.
Factor the numerator and denominator.
{[(10^4)-10] [10^4+10]}/10^3(10^4-1)
Taking 10 common from each term in numerator.
{10^2[(10^3-1)(10^3+1)]}/10^3[(10^2-1)(10^2+1)]

After further factorization and cancellation We're left with
(111*91)/10*101=9.99 or 10

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Re: The value of (10^8-10^2)/(10^7-10^3) is closest to which of [#permalink]

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07 Apr 2015, 20:06
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Re: The value of (10^8-10^2)/(10^7-10^3) is closest to which of [#permalink]

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09 Sep 2015, 09:27
I think the easiest way to solve this is to use the quotient rule. Since all bases are the same (10), split the problem into two fractions, use the quotient rule on each, then subtract.

(10^8-10^2)/(10^7-10^3) =

(10^8/10^7) - (10^2/10^3) =

10 - (10^-1) =

10 - (1/10) =

10 - 0.1 =

9.9 =

B.
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Re: The value of (10^8-10^2)/(10^7-10^3) is closest to which of [#permalink]

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11 Jan 2016, 14:18
Why we can't simply eliminate 10^8 with 10^7 and so on?

I did in this way and this is what I got:

1) 10^8 - 10^2 / 10^7 - 10^3;
2) I eliminate 10^8 with 10^7 and I got 10 on the up left side;
3) then I eliminate 10^2 with 10^3 and got zero on the up ritghtside and 10 on the down right side;
4) so, basically I left with 10 - 0 / - 10;
5) 10 / -10 = -1;
Because there isn't -1 on the answer choices I pick 1 that is the closest one.

What is wrong with my line of reasoning? I saw many times calculations involving exponents elimination if there is a division.

Thanks in advance for the explanation
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The value of (10^8-10^2)/(10^7-10^3) is closest to which of [#permalink]

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07 Jan 2017, 21:45
As the question asks for approximation, let's tackle it in the same way :

Numerator : $$10^8-10^2$$ : $$10^2$$ is 0.00001% of $$10^8$$ ,which is negligible when compared to $$10^8$$
denominator: $$10^7-10^3$$ : $$10^3$$ is 0.0001% of $$10^7$$ ,which is negligible when compared to $$10^7$$

Hence ,($$10^8$$) - (negligible) / ($$10^7$$) - (negligible)= $$10^8$$/$$10^7$$ =10

Ans : B
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Re: The value of (10^8-10^2)/(10^7-10^3) is closest to which of [#permalink]

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09 Jan 2017, 14:29
$$\frac{10^{2}(10^{6} - {1})}{10^{3}(10^{4} - 1)}$$
$$\frac{10^{8}}{10^{7}}$$
10
B
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Re: The value of (10^8-10^2)/(10^7-10^3) is closest to which of   [#permalink] 09 Jan 2017, 14:29

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