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Now, \(10^6-1\) is very close to \(10^6\) and \(10^4-1\) is very close to \(10^4\), hence \(\frac{10^6-1}{10*(10^4-1)}\approx{\frac{10^6}{10*10^4}=\frac{10^6}{10^5}=10}\).

Answer: B.

Or else you can notice that we need approximate value of a fraction. Now, \(10^{8}\) is much, much, much bigger than \(10^{2}\). So subtracting \(10^{2}\) from \(10^{8}\) will be very close to \(10^{8}\), basically \(10^{2}\) is negligible in this case. The same for for \(10^{7}\) and \(10^{3}\). So \(\frac{10^8-10^2}{10^7-10^3}\approx{\frac{10^8}{10^7}=10\).

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

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25 Jun 2010, 22:59

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Because the question asks for what value is "closest" the question invites approximation.

Let's look at the numerator:

10^8 - 10^2

10^8 is HUGE compared to 10^2.

So 10^8 - 10^2 is very close to 10^8 itself. (Just as 100 - 0.0001 is very close to 100 itself).

Likewise, 10^7 is HUGE compared to 10^3.

So 10^7 - 10^3 is very close to 10^7.

So we have:

10^8/10^7

or 10^(8-7) = 10.

Choose B.

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I think this is the quickest way to solve. If you see the point of the question, you can quickly solve it in this way without even having to do any scratchwork.

TAKEAWAY: don't assume algebraic approaches are always most efficient. And whenever a question asks for "approximation" or "close" be on the lookout to make deductions that will allow you to solve the question fast.

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

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18 Sep 2010, 14:03

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ok. without calculation you can probably guess 10^8 and 10^7 are SIGNIFICANTLY bigger than the numbers they are subtracting. so you can just do 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]

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18 Sep 2010, 15:28

shaselai wrote:

ok. without calculation you can probably guess 10^8 and 10^7 are SIGNIFICANTLY bigger than the numbers they are subtracting. so you can just do 10^8 / 10^7 = 10. B

Good quick thinking on your part . I took the more traditional approach of solving it the long way
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This gives 10. The great part is that you are dealing with such large numbers, that 1 and 10 are immaterial.

The point here is not accuracy, it is to get a sense of what is right or wrong. If you find you have to do long division, then you are definitely missing a trick. Even if a question seems fiendish, there is always a shortcut to the solution!

Hope this helps.

EDIT: Scrolled through Bunuel's post, who has hit the nail on the head

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

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02 Jul 2013, 02:01

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jcbruin wrote:

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

A. 1 B. 10 C. 10^2 D. 10^3 E. 10^4

The given expression can be written as : \(\frac {10^8(1-\frac{10^2}{10^8})} {10^7(1-\frac{10^3}{10^7})}\) = \(\frac {10^8(1-\frac{1}{10^6})} {10^7(1-\frac{1}{10^4})}\)

We know that \(\frac {1} {10^6}\ll1\) and similarly,\(\frac {1} {10^4}\ll1\), thus, we can safely approximate the given expression as\(\frac {10^8}{10^7}\) =10. B.
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