Gmat_mission wrote:What is the tens digit of the number r?

1) The tens digit of r/10 is 3

2) The hundreds digit of 10r is 6

We need to determine the tens digit of the positive integer r.

Statement One Alone:

The tens digit of r/10 is 3.

Let's create an equation using this information, letting the right side of the equation be any 3-digit number that has a tens digit of 3. Note that A and B could be any of the digits 0 through 9, inclusive.

r/10 = A3B

Now multiply each side of the equation by 10.

r = A3B0

Thus we see that the hundreds digit of r must be 3. For example, r could be 1310 which has the required hundreds digit of 3; the tens digit is 1. Or r could be, say, 2360, which still has a hundreds digit of 3, but now the tens digit of r is 6. For r = 1310, the tens digit is 1, but for r = 2360, the tens digit is 6, so we don't have enough information to determine a single value for the tens digit of r. Statement one alone is not sufficient. Eliminate answer choices A and D.

Statement Two Alone:

The hundreds digit of 10r is 6.

Using logic similar to that used in statement one, we know that the tens digit of r must be 6. Let's do the math to show this. Again, we let A and B be any of the digits 0 through 9, inclusive. Using the information from statement two, we see that

10r = 6AB

Divide both sides of the equation by 10. Note that dividing any number by 10 is the same as moving the decimal point one place to the left. Thus, we have

r = 6A.B

We can now see that the tens digit of integer r must be 6. Statement two alone is sufficient.

Answer:B