# Odd ratios

ratios
Recent activity on Oct 09, 2018
1.5 k Views

Hello,

I've often found that when doing a case, if I am looking for a percentage of a whole or a percentage change, that if I get simple figures like 6/10, things go well (obviously).

But when I face ratios like today when I saw 8/13 for instance, I know it's roughly 60% but that doesn't come to me fast in interviews. I could always memorize 1/13 and mult that by 8 but I want to come up with a faster way to look at a figure like this and call out a percentage to the interviewer.

Thanks

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My preference for these cases was always to learn the table of fractions-decimals until 1/20. It takes a little while, but can come in handy in a ton of cases.

For example, I always remember that 1/14 = ~0.07, and this has come in handy multiple times (even on the actual job, when brainstorming and having to do a "rough order of magnitude" calculation).

As a final point - don't stress too much about appearing clever on percentages with interviewers. I've had candidates who clearly were strong at Math, but at every point there was a number in the interview they tried to somehow "impress" me by their arithmetic prowness. You should still practice this, of course, but there are more important aspcets of the case you should focus on.

In cases like this it's nice to get a feeling for using "tens" to your advantage. For instance, it might be easier to consider 80/13 for you, and since you can easily calculate that this is around 6 you know that 8/13 is around 0.6. The formula behind this is really simple:

8/13 = 80/13/10.

If you were interested in a more exact answer you could do this recursively ( 8/13 = 80/13 /10 = 78/13/10 + 2/13/10 = 0.6 + 20/13/100 = 0.6 + 0.01 + 70/13/1000 = 0.615...).

There's tons of such kinds of tricks, and one way will work better for you than another. The key is to just practice, but don't overdo it. Usually approximate numbers are good enough and the interviewers will give you time if they want you to do it exactly.

(edited)

You basically have 2 options: either learn the tables through 11, 12 or 15,

Or practice mental math assiduously. If you choose that route, leverage such sites as caseinterviewmath.com, which will rank you against other candidates by accuracy and speed.

There are also a ton of books on the subject, and PrepLounge has some solid material as well

Where can I find this table? Thank you!

The easiest way is to identify the closest regular fraction - i.e., 8/12, which obviously is 67%. So you know that 8/13 is just a little below that: around 60-65%. This thinking usually doesn't take more than a couple of seconds.

Cheers, Sidi

Hi,

Since this calculation is obviously not so direct, and if you just want to compare numbers, I would recommand to approximate in order to be faster.

- Identify quickly 50 % > 6.5 /13

- Then approximate the delta to add up to your number > 1.5/ 13 =Approx. 12%

So 8/13 would be approx. 62%

Hope this helps

Best

Benjamin