MGMAT fraction estimations question - wrong?

Question

Hi all

I noticed on an MGMAT fraction estimations question (from the Fractions, Decimals and Percents guide) that they 'estimated' 6/20 as being close to 1/3. Surely though, 6/20 is actually closer to 1/4 (i.e. 5/20) than 1/3 (i.e. 6/18). I therefore got the question wrong as I estimated 1/4 instead of 1/3.

Is there any reason they did this in this way? I can't think of any.

Thanks

mohater · Answer

The point of this is simplifying fractions to values that are easier to work with.

You're focused on one example (and this could be a bad example). The point to remember is don't get caught up on exact values during the test when dealing with a problem which appears overwhelming.

n2739178 · Answer

ok cool - thanks! must have been an error on MGMAT's behalf.

Cclay · Answer

Hi, I just talked with Dave Mahler, one of our instructors, who offered the following explanation:

"6/20 as a fraction reduces to 3/10, which is 0.3. 1/3 (0.333) is actually closer to 3/10 than is 1/4 (0.25) so 1/3 is actually a better estimate than is 1/4."

We do look over our books very carefully to make sure there are no errors in them!

Thanks!
Caitlin Clay
Student Services Associate
Manhattan GMAT

LoveTheGMAT · Answer

I am guessing you are talking about Manhattan Book 2 (FDPs) - In Action Problem #15?

At first, I wasn't sure about making 6/20 into 5/20 or 6/18 - probably because I am picky in math. But after I reduced the fraction to 3/10, which is 0.30 it was clear that 6/20I is closer to 1/3 (0.33) than 1/4 (0.25). So basically what Cclay said.

Personally, I like the technique #2 they discuss - since you can easily cancel out fractions, why get into decimals? I think Manhattan tells you somewhere to stay in fractions whenever possible to reduce errors.

Goodluck

n2739178 · Answer

I'm still confused by this

In the book (pg. 36 of FDP's) it says something about rounding errors when estimating fractions. The example question was 'What is 10/22 of 5/18 of 2000' -> they estimated 5/18 as 1/4 instead of 1/3 (i.e. 6/18) - but they said if you had rounded 5/18 to 6/18 = 1/3 then you would have rounded BOTH fractions up which would lead to a 'slight but systematic overestimation'. Thing is, what is do they mean by rounding fractions down, up etc. and how does it apply to this situation? Thanks!

esledge · Answer

To "round a fraction down" is to approximate with a more convenient fraction that is LESS than the original fraction.
So 5/18 was rounded down to 5/20, or 1/4.

To "round a fraction up" is to approximate with a more convenient fraction that is GREATER than the original fraction.
So 10/22 was rounded up to 10/20, or 1/2.

Any time you approximate or round, your number will be either too big or too small. The point about "systematic overestimation" is simply that if you round both fractions up, you are assured of getting a result that is too high. The error is compounded. But if you round one fraction up and the other down, the errors cancel out, at least partially.

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MGMAT fraction estimations question - wrong?

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