In 2008, a certain factory produced 30% more widgets

Lets assume no. of widgets in 07 = 100
Number of widgets in 08 = 130
Number of widgets in 09 = 169


Decrease required = \(\frac{169-100}{169} = \frac{69}{169}\)

= 41%

Answer is C.

Kudos Please... If my post helped.

I don't think you'll ever need to worry about this on the real GMAT - in real GMAT questions asking for estimates, the answers will usually be far enough apart that you can actually estimate fairly easily. But even in this case, there are a couple of interesting techniques we can use to bypass long division.

Here, if you can tell the right answer choice is either 39% or 41%, you really just need to know if 69/169 > 0.4 to pick the right answer. There are a few ways to make that decision quickly. You might locate a fraction which is exactly equal to 4/10 and that looks similar to 69/169. Notice if we multiply by 17 in the numerator and denominator, we find that 4/10 = 68/170. But notice now that 69/169 > 68/170, since 69/169 has both a larger numerator and a smaller denominator than 68/170. So 69/169 > 0.4, and 0.41 is a better estimate than 0.39.

Or you could notice that (0.4)*169/169 is exactly equal to 0.4 (just cancel the 169), and is exactly equal to 67.6/169. Since this is clearly smaller than 69/169, we can see that 69/169 is larger than 0.4.

If you prefer to avoid decimals, you can instead write down the following inequality (this method is mathematically the same as the one above, though) :

69/169 > 4/10

We want to know if this is true. If it is, then when we rewrite it, what we arrive at must be true. If you multiply by 169 and 10 on both sides, you find

690 > 4*169 = 676

and since this is true, the original inequality was true as well.

If you know that rounding 69/169 to 70/170 = 7/17 has only a negligible influence on the overall value of the fraction, then the above techniques are even easier to apply, but I've not done that here since it may not be clear how much that approximation will affect the fraction's value.
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That would be (C), the thoughts behind my choice set forth below:
Let it be:
2007 - x
2008 - x+0.3x=1.3x
2009 - 1.3x*1.3=1.69x
2010 - (x-1.69x)/1.69x = - 0.69x/1.69x = -0.408~-41%

The question is pretty easy, but if someone could highlight how to approximate 69/169 to 41%? There is a close answer choice of 39% as well, this takes up a lot of time in a real test and you end up getting a supposedly easy question wrong!

(69+1)/(169+1)>69/169
70/170>69/169
7/17>69/169
0.411>69/169

Therefore, 69/169 is slightly less than 0.411 or almost 0.41 (41%)

We can let the number of widgets produced in 2007 = 100. Thus, in 2008, 1.3 x 100 = 130 widgets were produced, and in 2009, 1.3 x 130 = 169 widgets were produced.

We need to determine the percentage decrease necessary to drop from 169 widgets to 100 widgets. Let’s use the percent change formula:

(100 - 169)/169 x 100% ≈ -40.8%

Answer: C
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thank you for sharing this explanation, this is very helpful

My pleasure!
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We can let the number of widgets produced in 2007 = 100. Thus, in 2008, 1.3 x 100 = 130 widgets were produced, and in 2009, 1.3 x 130 = 169 widgets were produced.


is this ok??

U r getting confused between "30% more produced as compared to 2007" and "130% of its production in 2008". Take a closer look both are same in context of the question.

In 2007 production = x
In 2008 production = 1.3x
In 2009 production = 1.3*1.3x = 1.69x
In 2010 production change = (1.69x-1x)/(1.69x) = approx 41%

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