Arithmetic strategy

[ds29]

Hi MGMAT team,

Quick question for you -- not related to a specific problem, more of a strategy question.

I was recently completing a question (OG question so I will not post it). I had memorized the approach and knew what to do, but when it came down to the arithmetic, I was very slow.

E.g. after quickly figuring out the technique, I needed to calculate:

q > 100,000/(0.95*5).

My goal was to determine if q > 21,000.

This is where I got hung up. I can do it, but I am quite slow. My approach:

• I first find 0.95 * 5 (which I do by calculating 5% of 5, then subtracting from 5). I end up with 4.75.


• Then I must divide 100,000/4.75. I can't do this in my head, so I must do long division. (I don't know a way to estimate if 100,000/4.75 > 21,000)


• This whole process can take over a minute, and suddenly I am at 2:30+ minutes for this question, despite knowing exactly how to crack this tricky problem. A bit disheartening because I feel like even if I learn the strategy for tons of questions, I will often get hung up on this arithmetic.

When Tim does this (in the video solution), he seems to do it instantaneously -- "so 0.95 of 5 is 4.75..."

When something takes me so long, I feel like I must be doing something wrong or missing a trick. For this reason, I would be interested to hear:

• a MGMAT Staff's approach to this arithmetic. Do you approach it as I did above? What mini-calculations do you do? Or can you just do it all in your head? Are there tricks I am missing/should know? How are you able to do this quickly enough? (I scanned the Foundation of Math book and couldn't find any techniques I didn't know)


• any suggestions for how to improve these skills.

Any guidance here would be much appreciated.

Thanks,

Dan

PS It is not all arithmetic that trips me up: these two issues (multiplying by a number between 0 and 1, and dividing by a decimal) are particularly slow for me.

PPS: the question is OG13 DS141 if that helps at all.

[jnelson0612]

Hi Dan,
I hope that others will be along to chime in on this so that you can get a variety of opinions. For me, one of the most important things that I've learned to do is NOT to do too much work. This sounds counterintuitive, right? Doesn't the GMAT want us to do a lot of work? Well, yes, they want to test that you know certain information and that you can think logically, quickly. But as far as grind-it-out math calculations, they generally don't make us do them. They give you a short cut.

Using your example, if I saw:
100,000
.95 * 5

The first thing I'm going to do is divide 5 out of the top and bottom. I'm then left with:

20,000
.95

Now I have two choices. I can go ahead and just divide 20,000 by .95, which doesn't take too long, or I can convert .95 to 19/20. If I flip and try to multiply that by 20,000 I can see that is going to get kind of gross, so I'd revert back to just dividing 20,000 by .95. Should only take about ten seconds to get three digits on the top and know if this result is larger than 21,000.

I think the biggest takeaway here is to develop an internal warning sign in your head of "STOP--math too time consuming". When you find yourself doing crazy calculations that no intelligent person can do in two minutes, you know there is a better way. You will NEVER have to actually calculate out a decimal to some high exponent--they're just not going to make you do that. There's always an easier way!

For example, my all-time favorite GMAT Prep problem is:
1001^2 - 999^2
101^2 - 99^2

Think of how ugly and long that would be to actually do the calculations. There must be a simpler way. Can you find it? :-)

[ds29]

This is a great answer.

I agree with your philosophy that too much math is a sign that you've gone wrong and i like the shortcut you use in this problem.

Thanks very much for taking the time to write such a thorough and helpful answer.

PS: I think I cracked your "all-time fav" problem -- I think the key is the fact that the expression contains two difference of squares!

[tim]

:)