GRE Quant - rounding in calculations

[okProteus]

Working through Manhattan practice tests. Have noticed a few times that reasonable rounding (and by reasonable I mean endorsed by Manhattan's explanation) creates numbers different enough from the answer options that, during the test, I second-guessed my calculations.

Example: actual answer 6.8% (supported by full calculations); answer produced by Manhattan's suggested rounding technique: 3.1%. Manhattan's explanation says that, because 3.1% is much closer to 6.8% than the other options (0.7% and 31.3% were the next-closest), I should assume that 6.8% is correct. However, 6.8% is not only twice the answer produced by estimation; it's also not even the closest answer!

On another problem, I rounded the following: (.304 + .012) x 1,027 --> .31 x 1,000 --> 310, and (.452+.055) x 851 --> .45 x 850 --> 430. (I'm aware that this was slightly imprecise, but just slightly.) This produced the answer 39% (it was difference between the numbers divided by the smaller one). The answer choices included 33% and 45%, and this literally splits them right down the middle.

It appears that, to be confident in my answers, I must quit rounding (or be extremely conservative in my rounding).

My question: are the actual GRE questions also structured in such a way that similar rounding produces similarly ambiguous answers?

Edited November 26, 2012 by dwdptok

[TakeruK]

Rounding can be hard when the numbers aren't spaced far apart. So maybe a good strategy is to only use rounding when the choices are like...an order of magnitude apart (e.g. 0.2, 2.0, 20 etc.) instead of 11, 13, 15 etc.

For your specific example, I notice that rounding 0.452 + 0.055 to 0.45 is not a good idea. I don't think you should ever just remove an entire number. Rounding 0.452 + 0.055 to 0.50 is a much better (and easier compute 0.50 times something anyways). One rule of thumb you could use is to only round off one digit. So for the sums, instead of keeping all three decimal places, bump it down to just 2 decimal places (e.g. 0.31 and 0.50). When I did this, my answer came to 37% which is closer to 33%, the correct answer (of course, you'd wouldn't know the real answer so that is not really a useful statement).

Another rule of thumb is to keep track of whether you are underestimating or overestimating. For example, "430" for the second number is pretty accurate. But rounding 1027 down to 1000 is a bigger leap. This means your 310 number is an underestimate. Since you will be taking the difference of 310 and 430, underestimating 310 means that you are overestimating the numerator. Also, since you are dividing by 310, you are underestimating the denominator. The combination of overestimating the numerator and underestimating the denominator means that your overall answer is an overestimate. So, if you get e.g. 39% and the two choices are 33% and 45%, it's more likely that 33% is the correct answer since you know you are overestimating!

This is a bit more work and it might cancel out the time you save by rounding in the first place! It depends what you are comfortable with. One thing you can do is to first simply round the way you've been doing, and see if your answer is one of the choices. If it lies in between two numbers, then analyse your over/under estimates and decide if your overall rounded guess is too high or too low! Sometimes you might purposely round a certain way just to ensure that you are consistently under- (or over-) estimating.

[okProteus]

Thank you for your detailed suggestions.

I can see that my rounding was a bit sloppy in the second example.

It's still hard to understand why, in the first example, the Manhattan-endorsed approach was so ambiguous.

Very limited rounding obviously eliminates that danger. Maybe that's the safest route.

[iowaguy]

Another thought is to use rounding to get through those types of questions quickly, but mark them for review (especially if the answer choices are fairly close together as TakerUK mentioned). Then if you have enough time leftover at the end you can go back and use the calculator, etc to be sure of your answer. If you don't have enough time at the end, you can rest assured that you probably got the right answer in the least amount of time...

IMHO it's better to round/estimate, yet not be 100% sure, but get through the entire test; than to get too anal retentive about exactly calculating every answer yet not get to the last several questions (particularly relevant on a 2nd "tough" quant section where every second counts).

[okProteus]

IMHO it's better to round/estimate, yet not be 100% sure, but get through the entire test; than to get too anal retentive about exactly calculating every answer yet not get to the last several questions (particularly relevant on a 2nd "tough" quant section where every second counts).

Excellent point.