Divisibility and Data Sufficiency

[QuinganZ341]

Hi,

Could you please offer some tips around DS questions involving divisibility? While I've memorized divisibility rules and understand how DS works, these problems are still taking me longer than 2 minutes/problem. My approach is to test numbers, which is generally the approach in the answer guides for both the OG problems and the CAT problems. Any tips/short cuts would be great!

Thanks,
Q

[RonPurewal]

what, exactly, is the actual issue here?

note: 'i'm taking more than 2 minutes' is NOT an issue.
'2 minutes' is an average—NOT a limit! most likely, you'll spend more than 2 minutes just as often as you spend less.

so, if the situation is 'i'm mostly nailing these problems but some of them take a long time', then, well, there's no issue in the first place—and trying to speed up the process could very well worsen the result (fast = sloppy).

[RonPurewal]

note—if, indeed, the only problem is timing (= if you're taking a long time but generally getting these problems correct), then think about efficiency improvements.

first, identify the efficiency 'bottlenecks'.
1/ when are you hesitating / staring at the problem?
2/ what are you doing inefficiently?

then, come up ith concrete plans to address these problems.

1/
if you're 'freezing' at the beginning of the problems, then invent an organizational framework that you can employ every time you see a particular type of problem. (e.g., if you watch the 'thursdays with ron' episodes from may/june 2015, titled "Setting Goals in Data Sufficiency", you'll see a reliable way of setting up 'yes/no' DS problems that can be used every time.)
if you're 'freezing' at some other point, then try to invent a similar organizational framework.
in any case, if you are 'freezing' or just staring at the problem, the solution is simply to have something to do. honestly, it doesn't even matter very much how good the plan is; what matters is that it's a plan, and that it's not ... not a plan. (the same goes for emergency preparedness: by far the most important part of, say, an earthquake plan is simply that a plan exists, giving you something to follow in moments of panic.)

2/
let's say you're testing WAY too many cases.
in this case, the problem is that you haven't defined your goal clearly enough.
in that case, you should try narrating your process aloud, as though you were doing the audio on a 'solution video'. (don't worry about timing here; obviously, if you're talking through the process, it will take longer.)
if you're narrating the process, then, suddenly, you'll have to be able to say WHY you're doing whatever you're doing. (e.g., "why are you testing THAT number?")
if you've never done this sort of thing before (or anything similar, e.g., trying to teach the problem to a study buddy), you may be surprised at how imprecise or directionless your thought process can be at certain times.

[QuinganZ341]

Ron - Thanks so much for guiding me to your study hall recordings on setting goals in DS - VERY helpful - esp. for DS problems on which I have no idea how to start. I watched all of them and have been practicing the set-up technique - I can't say I am getting all DSs correctly, but I can say that now I always have a way to start the problem. Thanks much again!

[RonPurewal]

sure.

by the way, you should be careful not to give me too much credit here... honestly, half the value of those set-up techniques is, simply, that they are things.
in other words, they are 'step one'. they are something you can do to overcome inertia—and that sort of inertia is a VERY big deal. it's the same inertia known as 'writer's block', etc. in fact, it's such a big deal that it begat a chinese proverb ('A journey of 1000 miles starts with a single step') that has lasted for more than two thousand years.

of course, the specific set-up has value, too. but, honestly, you could derive a significant fraction of the same value from doing absolutely anything as a ritual 'step one'.
this could even take the form of something that, in objective terms, adds absolutely zero value. for instance, if you're really really REALLY just stumped as to how to begin a problem, try just copying some stuff from the problem statement. you never know; you might kick-start a thought process that way.
actually, there's a pretty firm neurological basis for this. when you write stuff, you activate more neurons in your brain than you would if you just thought stuff. (note to people 10 or more years younger than me: that says 'write', not 'type'. typing does not activate the same neurons. nor does tapping on a smartphone.)

if you remain well and truly stuck, though, don't spend too much time. quit and move on. lose the battle, win the war.