60% electronic errors are in paper errors, 75% paper errors

Question

60% electronic errors are in paper errors, 75% paper errors are in electronic errors, 3% all errors is both electronic errors and paper errors. How many % correct in both electronic and paper.

jpv · Answer

quite convoluted.... 

Took me 8 minutes.. Let me know whether I am correct...

Say... Total 100 errors..

e - electronic errors
p - paper errors

question stem says - 0.6e = 0.75p = 3 ( 3 % of 100)
e = 5
p = 4

Total error = e + p - (common to e and p i.e. 3)
Total error = 5 + 4 - 3 = 6

Total Correct = 100 - 6 = 94% (ans)

ian7777 · Answer

Yeah, I also think this is pretty convoluted. The wording is too ambiguous to be on the real test.

But I got the same answer as JPV, but a little different method (though I think his is great, here's just what I did):

I converted the percents to fractions, and made x and y be the two groups:

3/5x=3/4y

Then I chose a number that works with 3, since that's the same numerator, so I chose 18. That meant there were 30 x's and 24 y's, each sharing 18. 

I put that into a ven diagram, with 18 in the middle. If 18 represents 3% of all the error, then there were 600 errors in all. 30 + 24 - 18 = 36, and (600-36)/600=94%.

But I would think that's 94% errors that were neither electronic nor paper, not % correct that were.

boksana · Answer

you guys are great! I stuck with this question. BTw, in fact this is the type of GMAT questions

ian7777 · Answer

You're welcome! glad to help. You're right, it is a real question topic, but the wording isn't very GMAT. The question would just be a little more suscinct.

jpv · Answer

If it is really GMAT type question then, timing need to improve. 
I am bit worried. Any suggestion? IAN!! or anybody...

boksana · Answer

Don't worry. As Ian noticed wording, perhaps, on the exam will be more coincise. :wink:

I guess the main problem here was to understand the fraction, and the rest is simple.

ian7777 · Answer

jpv, you need to be prepared to get something you've never seen before. That's what you're doing on this forum. Your method was great, and you got the right answer, and i'd rather have it take you 8 minutes now than on the test.

As Boksana said, the wording will be more concise on the real test, so you should have a clearer goal. And while the test will be hard, after all the work you're doing, nothing should genuinely shock you, you'll just have to apply what you know in different ways.

Now, on a personal note, I love fractions. I use them whenever I can. I think the test mostly makes any fraction or percent look worse than it is, and as a fraction, all the numbers usually cancel out. That's why I did this in fractions, and I saw that both fractions were three out of something, which makes life easy to work with.

Here's another fraction trick:

Did you know that 80% and 125% cancel each other out? That's because they're 4/5 and 5/4. Same thing with 75% and 133 1/3% (3/4 and 4/3). Same thing with 66 2/3% and 150%. And how simple is 150% as a fraction? 3/2 --> half the numbers in the universe divide by 2!

For a quick example of this, see the OG, PS68. Work it out right, and you'll see that x=z.

So if there was anything that I'd take away from this problem, it's to use fractions as much as possible and you'll see your time improving.

60% electronic errors are in paper errors, 75% paper errors

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