What is the 101st digit after the decimal point

Unless I'm totally missing something, the solution requires us to perform a lot more mundane calculations than GMAT quant questions typically require.

First we must add 1/3 + 1/9 + 1/27 + 1/37 by finding the lowest common denominator (which is 999).
So, we get 333/999 + 111/999 + 37/999 + 27/999
Then add them to get: 508/999
Then we need to recognize that 508/999 = 0.508508508...

I don't think that the test-makers expect us to know how fractions in the form k/999 convert to decimals, almost all students would have to divide 999 into 508 to see that we get 0.50850850...

So, up to this point, we have a very rudimentary question that involves several tedious calculations. If this were a true (official) GMAT question, there would also be a simple (fast) approach that allows us to bypass these tedious calculations and get to the decimal 0.508508508... in a very short time. In fact, the great thing about almost all GMAT math questions is that they can be solved using at least 2 different approaches. Typically, one approach is much faster than the other(s).

Since there doesn't appear to be a second, faster approach, I'd have to say that this question is not GMAT worthy. That said, let's finish it.

We now have the decimal 0.508508508508...
Notice that the 8 is in the 3rd, 6th, 9th, 12th (etc) positions.
In other words, 8 is in the positions that are divisible by 3.
So, 8 will be in the 99th position.
Which means 5 will be in the 100th position.
Which means 0 will be in the 101st position.

Answer = A

Cheers,
Brent

J N wrote:Hi Brent

I did a problem where there is a fast way to calculate/ translate 9 or 99 or 999 in the denominator. If you know the rule/technique can you please pass along.

thanks

Sure, it goes like this.

k/9 (where k < 9) = 0.kkkkkkk...
For example, 4/9 = 0.444444444....

k/99 (where k < 99) = 0.kkkkkkk...
For example, 32/99 = 0.3232323232....
Or 7/99 = 07/99 = 07070707070707.....

k/999 (where k < 999) = 0.kkkkkkk...
For example, 473/999 = 0.473473473473473....
Or 13/999 = 013/999 = 013013013013013.....
Or 5/999 = 005/999 = 005005005005005....


Cheers,
Brent