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Decimal Calculation Problems - Most Efficient Way to Solve?

Problem Solving — algebra and arithmetic (GMAT Focus Edition)
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Location: Arlington, VA
by jlaurenj » Fri Nov 23, 2012 7:09 pm
Hi Everyone,
I've started studying for the GMAT, and I'm trying to focus on not only getting the answer right but also learning the most efficient way to solve the problems. My questions below:

1) What is the result if 0.0777 is multiplied by 990/7? Answer - 11

2) What is the result if 0.00667/800 is divided by 0.025/3000? Answer - 1

I've tried to get the problems down to the simplest form by using scientific notation and crossing out the equivalent notation found in the numerator and/or denominator (i.e. .00667 = 1/6 times 10 ^ -5 ), but I'm having no luck at arriving at the answers.

Can someone help provide a strategy to efficiently solve the problems above?

Thanks!
Lauren
Prospective MBA Candidate '16
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Source: — Quantitative Reasoning |
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by David Chong » Thu Nov 29, 2012 11:26 am
Lauren:

The approach that you are taking to the problem is an effective one. The difficulty you are encountering is a matter of mechanics. For example:
  • 0.00667 DOES NOT EQUAL (1/6) * (10^-5)
Since 1/6 = 0.1667, it follows that:
  • (1/6) * (10^-5) = 0.000001667
You'll want to get good at recognizing decimal-fraction equivalents. The relevant equivalences for this problem are 2/3 = 0.667 and 1/4 = 0.25. Thus:
  • 0.00667 = (2/3) * (10^-2)
Understood in this way, the numerator can be rewritten as:
  • [(2/3) * (10^-2)] / 800
and the denominator can be rewritten as:
  • [(1/4) * (10^-1)] / 3000
From here, you should be able to knock out the rest of the problem (I'd hate to rob you of the satisfaction!).

Hope this helps, and best of luck with your preparation!


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David Chong
Manhattan GMAT
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