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Percents and Fractions, just can't beat them

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Percents and Fractions, just can't beat them [#permalink] New post 18 Dec 2011, 18:18
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I noticed something interesting in my 4 MGMAT Quant practice tests and wanted to get some expert opinion about it. All my 4 tests started with Percent or Fraction question. Is it some kind of fascination on the part of Mr.Manhattan towards Percent/Fractions or is it representative of GMAT it self? (recent test takers' and experts' opinion is most welcome)

I wouldn't have noticed it at all if I was not as bad as I am in Percents/Fractions. I just freeze every time I see a P/F question (especially in a timed test). In un-timed tests, I take a 2.5 to 3 mins (very optimistic estimate) for these questions but most times solve it right. Coupled with my starting jitters, I am invariably getting the first question wrong in every test. My confidence and timing are taking a beating very early in each test and its effecting my scores.

I know that all the griping above might dilute the essence of the post, but I had to vent it somewhere and why not vent it in front of the experts?

Coming to the real issue at hand, are there any resources (guides, question banks, websites etc) that can give me a quick fix for the percentage problems. I know its fixable because I am good at writing equations from the information given and solving the questions (and get about 95% right un-timed). Its just taking more time than GMAT allows. The words are what trip me often. I have downloaded the question set posted by "MBAhereICome" and solved all questions (average time 3.5mins). I guess I am just looking for more questions and if available, some enlightening in my way of thinking about percents/fractions that can help me fix the problem. Other than that, I just plan to solve every percent/fraction problem I come across 10 times till I can solve them with my hands tied.

Also, are there any other PF retards out there or am I alone in this battle?
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Re: Percents and Fractions, just can't beat them [#permalink] New post 19 Dec 2011, 23:52
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You are not alone at all. Many of my students find that percent and fraction word problems can be very time-consuming and difficult!

I recommend that you start back at square one. Get the Manhattan Foundations of Math book (the new 5th edition guide), and work through all of the % and fraction material. There are drills for mechanics (just manipulating percents and fractions) and setting up word problems. The goal should be to get very automatic with the underlying skills, so you can focus all your brainpower on understanding the problem and working for accuracy. I also highly recommend that you try to set up a solution expression in advance. For instance, let's say you are working on the following problem:

Andres is eating a snack mix that consists of almonds, pistachios, and chocolate chips. The quantity of chocolate chips, by weight, is 1/3 the quantity of pistachios. The quantity of almonds is four times the combined quantities of chocolate chips and pistachios. What fraction of the mix, by weight, consists of chocolate chips?

Even if we're not sure exactly where to start on this problem, if we understand the final question, we can set up a solution expression:

weight of chocolate chips/total weight =

If we assign variables to represent each quantity (a,p,c), this becomes

c/(a+p+c) =

The importance of this is that it gives us a focus for our work, and it often helps to prevent errors later in the process, when we may have lost sight of what we're actually trying to do. Now, let's solve. We'll start by translating the statements into equations:

The quantity of chocolate chips, by weight, is 1/3 the quantity of pistachios.

c=(1/3)p

The quantity of almonds is four times the combined quantities of chocolate chips and pistachios.

a=4(c+p)

Now let’s try to combine this information. Note that c appears in both equations, and we want it in our numerator. We might be tempted to solve for c right away, but we should do the opposite. Since we want to have c at the end, we should get the other variables out of the way by solving for them in terms of c, like this:

c=(1/3)p
3c=p

a=4(c+p)
a=4(c+(3c))
a=4(4c)
a=16c

We now have all of our variables in terms of the desired quantity, c. Now we just have to drop these values into our solution expression.

c/(a+p+c) =
c/(16c+3c+c) =
c/20c=
1/20

I hope this helps. Definitely check out our Foundations book, and best of luck with your fraction odyssey!
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Dmitry Farber | Manhattan GMAT Instructor | New York


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Re: Percents and Fractions, just can't beat them [#permalink] New post 20 Dec 2011, 06:35
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Thanks Dmitry. That is really a great explanation. And you are right, my main issue is figuring out where to start. I will certainly follow the approach that you just showed in my practice for the next couple of weeks and see if I notice any progress.

As far as the foundation book is concerned, I did the opposite I guess. I just ordered the Advanced Math Guide as I already have the 8 MGMAT guides. I will first apply your approach and see if I become any better at these problems and if I am still struggling, then I will go ahead and order the book.

Thanks for the detailed example and explanation.
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Re: Percents and Fractions, just can't beat them   [#permalink] 20 Dec 2011, 06:35
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Percents and Fractions, just can't beat them

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