guerrero wrote:What is the hundreds digit of the three-digit positive integer k if k<600

(1) The units digit of 2K/100 is 6

(2) The tens digit of 10k is 4

Target question: What is the hundreds digit of K?

Statement 1: The units digit of 2K/100 is 6
If the units digit of 2K/100 is 6, then the hundreds digit of 2K must be 6
If the hundreds digit of 2K is 6, then the hundreds digit of K must be 3
Since we can answer the target question with certainty, statement 1 is SUFFICIENT

Statement 2: The tens digit of 10K is 4
There are several values of K that meet this condition. Here are two:
Case a: K = 224, in which case the hundreds digit of K is 2
Case b: K = 324, in which case the hundreds digit of K is 3
Since we cannot answer the target question with certainty, statement 2 is NOT SUFFICIENT

Answer = C

Cheers,
Brent

rintoo22 wrote:Hi Brent,

Can you please elaborate on

Statement 1: The units digit of 2K/100 is 6
If the units digit of 2K/100 is 6, then the hundreds digit of 2K must be 6
If the hundreds digit of 2K is 6, then the hundreds digit of K must be 3
Since we can answer the target question with certainty, statement 1 is SUFFICIENT

Sure.
Let's look at some examples.

M = 123
This means that M/100 = 1.23
The units digit of M/100 is 1
The hundreds digit of M is 1

M = 619
This means that M/100 = 6.19
The units digit of M/100 is 6
The hundreds digit of M is 6

M = 5378
This means that M/100 = 53.78
The units digit of M/100 is 3
The hundreds digit of M is 3

Similarly, if the units digit of 2K/100 is 6, then the hundreds digit of 2K must be 6


Now, let's examine the 2nd part of my solution.

If the hundreds digit of 2K is 6, then 2K = 6 _ _ (with spaces representing the missing digits)
So, what does K look like?
Can K = 2 _ _ ?
No.
If we double 2 _ _, we cannot get a 6 as the hundreds digit.

So, if 2K = 6 _ _, it must be the case that K = 3 _ _
In other words, if the hundreds digit of 2K is 6, then the hundreds digit of K must be 3

Cheers,
Brent