Data Sufficiency

Questions about DIGITS are often related to powers of ten.

What is the tens digit of positive integer n ?

We don't necessarily need to know the value of n itself in order to know the tens digit. It is likely that the GMAT will give us information by multiplying or dividing by powers of 10. All of the following information would answer our question:
- the units digit of n/10
- the hundreds digit of 10n
- the remainder when n is divided by 100
etc.

Consider:

1) The hundreds digit of 10n is 2.

Strategy 1: Test Cases (keeping the statement information true).
10n = 240 --> n = 24
Can we get a tens digit of n that's not 2? Keep testing...
10n = 5,230 --> n = 523
10n = 89,270 --> n = 8,927

In all of these cases, the tens digit of n is 2. There is no example we could think of that would keep the statement true, but give us a different answer.

Strategy 2: Think conceptually.
By definition, the tens digit of any integer n must be the same as the hundreds digit (one digit to the left) of 10n (multiplying by 10 = shifting all digits to the left).

(2) The tens digit of n - 9 is 1.

Strategy 1: Test Cases (keeping the statement information true).
n - 9 = 19 --> n = 28
Can we get a tens digit of n that's not 2? Think about multiples of 10...
n - 9 = 10 --> n = 19

Since we got 2 different answers for 2 different cases (both of which complied with our statement), this is insufficient.

Strategy 2: Think conceptually.
When we subtract 9 from a given number, we usually end up with a different decade (meaning "unit of 10"). The only exception is when when go from a units digit of 9 to a units digit of 0. Insufficient.

The correct answer is A.

Here are some other questions with similarly coded language regarding DIGITS and POWERS OF 10:

https://www.beatthegmat.com/a-non-zero-h ... tml#766178
https://www.beatthegmat.com/remainder-t2 ... tml#767961
https://www.manhattanprep.com/gmat/foru ... it#p124826

Here's another related question (from the OG2016): https://www.beatthegmat.com/og2016-q171-t290508.html

Cheers,
Brent