Confusion in estimation

[RAHULZ400]

Hi Ron,

I have a confusion in using estimation in certain cases where I land up with a completely different answer and end up selecting the wrong one. Here is an example of a self created question taking idea from other GMAT sources e.g. iphone app example.

Now lets suppose company ABC received had a profit of $ 4 million for a sale of $ 23 million while company XYZ had a profit of $15 million in $300 million. By approximately what percent did the ratio of profits to sales decrease from 1st case to the second.

(A) 50%
(B) 52%
(C) 60%
(D) 45%
(E) 20%

Now if we do the problem via estimation there are multiple ways (I made these attempts) First of all what I did was I took 23 as 20 so that the fraction becomes 4/20 i.e.1/5 so 15/300 i.e.(1/12-1/5)/(1/5)*100 = 58.3% so in that case I will mark my answer as (C) i.e. 60%. Also when I took 23 as 24 (more convenient) I got (1/12-1/6)/(1/6)*100 = 50% so I marked the answer as (A). Also now if approximate 23 to 24 and to balance out rounding off errors I round of 12 to 10 (one increase other decrease) then (1/10-1/6)/(1/6) = 40% decrease so answer should have been (D) i.e. 45%. As advised in the guide we should round one quantity up and other down to balance.

However by exactly calculating and following the conventional steps we get {(1/12 - 4/23)/(4/23)} * 100 = 52.08% approx so the correct ans as (B).
There are times when if there are two fractions and I just round off denominator to nearest multiple of numerator (e.g. 3/20 I can round it off to 3/18 instead of 3/21) i.e. 1/6 instead of 1/7 and if I am using this fraction in a problem then the ultimate answer differs and at times by a huge margin. So when faced with two fractions and computing a problem as above wherein this sort of scenario is there so how do I now estimate and pick the right answer?

[RonPurewal]

...aaaaaand this is why you shouldn't make up your own examples. when you try to invent your own problems, you will have "issues" that are non-issues on the actual exam.

in this problem, you have values that are EXTREMELY close together -- 45, 50, and 52 percent -- yet you are asking for an approximation.
the official problems won't do that, because the official problems are not "tricky" and do not engage in misdirection. if an official problem asks you to approximate an answer, then you'll actually be able to approximate the answer without this kind of danger.

[RAHULZ400]

Hi Ron,

I understand that the GMAT will not perhaps provide the answer choices as close as given above however even if we neglect this still there is quite a big difference between the 3 values I got using three methods i.e. 58.3%, 50% and 40%. Even if the choices given be lets say:

A)52
B) 60
C) 45
D) 30
E) 25

Now there is quite a gap between them still we will end up getting the above 3 answers and then mark them as B(60), A(52), C(45) respectively as per the three answers computed above (58.3, 50, 40). Basically I wanted to confirm what kind of approximation can we take out of the three ways suggested above i.e. at times changing the denominator of just one fraction without the need to change other can suffice and there are multiple scenarios to this based on the fraction.Basically the fraction value should not change drastically e.g. changing 4/23 to 4/24 would yield only a 4% change however changing 1/12 to 1/10 would yield a 20% change. Kindly provide your views on this and how can we decide to quickly manipulate one or both the fractions under time constraints?

[tim]

First, if you are not able to tell approximately how far your estimate will be from the real answer (and in what direction), DON'T use that estimation! There is nothing forcing you to use an estimation in the problem you describe, and if you have to calculate an exact answer and then find the closest answer choice to it, that's better than having too large an error and picking the wrong choice.

Second, if you can reasonably accurately ascertain the magnitude of your estimation error, DON'T use that estimation if the answer choices are close enough to be within the margin of error of each other. For instance, I wouldn't round 110 down to 100 (approximately a 10% error) if I saw answer choices of 9500, 9600, 9700, 9800, and 9900, but I would be okay with it if the answer choices were 1000, 2000, 3000, 4000, and 5000.

Third, remember that if you use multiple estimations in a problem, they can compound, so you have to take this into account in your overall margin of error.

[RAHULZ400]

Yes I can understand your point.. Thanks.

[RonPurewal]

excellent.

please let us know if there are any other questions about this problem. thanks.