What is the tens digit of the number r?

[Gmat_mission]

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

[spoiler]OA=B[/spoiler].

I need some help here. Why is B the correct answer? Is not C?

[Vincen]

Hi Gmat_mission, welcome.

(1) The tens digit of r/10 is 3

When we divide a number by 10, then the hundreds digit is moved to the tens digit. Hence, this statement says that the hundreds digit of r is 3 and this is not sufficient.

(2) The hundreds digit of 10r is 6

When we multiply a number by 10, then the tens digit is moved to the hundreds digit. Hence, this statement says that the tens digit of r is 6. Therefore, this statement is sufficient.

Regards.

[Brent@GMATPrepNow]

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

Target question: What is the tens digit of the positive integer r?

Given: r is a positive integer

Statement 1: The tens digit of r/10 is 3
Since r is an INTEGER, 10/r will have 1 digit to the right of the decimal place.
So, r/10 = ????3?.? [each ? represents a digit. Notice that 3 is in the tens position of r/10]
Multiply both sides by 10 to get: r = ????3??
We can see that the HUNDREDS digit of r is 3, but we don't know the TENS digit of r
Since we cannot answer the target question with certainty, statement 1 is NOT SUFFICIENT

Statement 2: The hundreds digit of 10r is 6
Since r is an INTEGER, 10r will have a zero in the units position.
So, 10r = ????6?0 [Notice that 6 is in the hundreds position of 10r]
Divide both sides by 10 to get: r = ????6?
Perfect - the TENS digit of r is 6
Since we can answer the target question with certainty, statement 2 is SUFFICIENT

Answer = B

Cheers,
Brent

[Jeff@TargetTestPrep]

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